Full text of Improving the Monetary Aggregates : Staff Papers
The full text on this page is automatically extracted from the file linked above and may contain errors and inconsistencies.
Improving the Monetary Aggregates Staff Papers Board of Governors of the Federal Reserve System https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis Published in November 1978 Library of Congress Catalog Card Number 76--14548 Copies of this report may be obtained from Publications Services, Division of Administrative Services, Board of Governors of the Federal Reserve System, Washington, D.C. 20551. The price is $4.00 per copy; in quantities of 10 or more sent to one address $3.75 each. Remittances should be made payable to the Board of Governors of the Federal Reserve System in a form collectible at par in U.S. currency. (Stamps and coupons are not accepted.) https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis Improving the Monetary Aggregates Staff Papers Washington, D. C. https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis Preface In early 1974 the Board of Governors of the Federal Reserve System appointed the Advisory Committee on Monetary Statistics to provide a technical evaluation of, and a report on, the quality of the monetary aggregates used by the Federal Reserve in the formulat10n and implementation of monetary policy Improving the Monetary Aggregates Report of the Advisory Committee on Monetary Statistics was published by the Board in June 1976 The Advisory Committee on Monetary Statistics was chaired by Professor G L Bach (Stanford University), Professor Phillip D Cagan (Columbia University) served as Executive Secretary Other members of the Committee were Professor Milton Friedman (University of Chicago), Professor Clifford G Hildreth (University of Minnesota), Professor Franco Modigham (Massachusetts Institute of Technology), and Dr Arthur M Okun (the Brookings Institution) Professor Paul W McCracken (University of Michigan) was a member of the Committee originally, but withdrew because of the pressures of other duties At its final meeting, the Advisory Committee requested the publication of certain of the research papers that had been prepared by the Board staff for the Committee's use The Committee concurred with a recommendation of the Board staff that rev1S1ons of the studies be prepared for pubhcat10n, provided that the final versions would contain essentially the same information that had been made available to the Committee during the course of its dehberat10ns The Committee also requested further investigation of its tentative proposal for an alternative method of calculating M 1 , and a paper presenting this further work is included in this volume For three other papers, addit10nal staff research is also presented, this work serves to support the analysis onginally presented to the Committee "Transitory Variations in the Monetary Aggregates" expands upon the sources, estimat10n, and interpretat10n of transitory vanat10ns in the aggregates "Demand Deposit Ownership Survey" contains new staff research on the demand for demand deposits by var10us sectors Finally, m "Foreign Demand Deposits at Commercial Banks m the Umted States," addit10nal results are presented from attempts to model the demands for foreign deposits mcluded in M 1 Support of the work of the Advisory Committee on Monetary Statistics by the staff of the Board of Govei nors was supei vised throughout most of the penod by James L Pierce, who at the time was Associate Director of the Div1S1on of Research and Stausucs and 1s now Professor of Economics at the Umversity of Cahforma at Berkeley, subsequent staff work was overseen by Edwaid C Ettm, Associate Director of the D1v1Sion of Research and Statistics Board staff economists working closely with the Committee, aside from the authors of the papers m this volume, were Arthur B Hersey and Thomas Thomson J Charles Partee,Member of the Board Chairman, Board Committee on Research and Statistics https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis Contents Preface Transitory Variations in the Monetary Aggregates I Richard D Porter, Agustin Maravall, Darrel W Parke, and David A Pierce Foreign Demand Deposits at Commercial Banks in the United States 35 Helen T Farr, Lance Girton, Henry S Terrell, and Thomas H Turner Nonmember Banks and Estimation of the Monetary Aggregates 55 Darrel W. Parke Seasonal Adjustment of the Monetary Aggregates 71 David A Pierce, Neva Van Peskz, and Edward R Fry Demand Deposit Ownership Survey Helen T Farr, Richard D Porter, and Eleanor M Pruitt https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 91 Contents-continued Sources of Data and Methods of Construction of the Monetary Aggregates 117 Darwin L Beck An Alternative Method for Calculating M1 135 Anton S Nissen and Darwin L Beck Developing Money Substitutes· Current Trends and Their Implications for Redefining the Monetary Aggregates Steven M Roberts https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 147 I Transitory Variations in the Monetary Aggregates Richard D Porter, Agustin Maravall, Darrel W Parke, and David A Pierce Most of this work was completed in early 1977 Smee then updated estimates of transitory variations in the aggregates have been computed for the 1968-76 period These estimates are similar to the estimates reported here, though there appears to have been a small increase in the transitory variations in 1975 and 1976 Also, alternative methods of interpolating components that are not observed daily have been tried, and it seems that the choice of interpolation procedure has very little effect on the resulting estimates of transitory variation The views presented here are those of the authors and do not necessarily represent the views of the Board of Governors of the Federal Reserve System This paper contains materials presented to the Advisory Committee on Monetary Statistics as well as additional materials developed later We believe that the principal findings of this study are consistent with evidence that the Committee reviewed in making its recommendations It is hoped that additional results reported here improve the estimation of transitory variations tn the aggregates We wish to thank Greg Connor for very able assistance m all phases of this work We also wish to thank Darwin Beck, Edward Ettm, Donald Hester, John Kalchbrenner, David Lindsey, Juan Perea, and Steven Zeller for helpful comments Day-to-day movements m the not seasonally adjusted monetary aggregates display several systematic patterns Overall, there 1s a gradual upward trend m the senes with some cyclical vanat10ns Strong and fairly systematic shorter cycles for monthly, weekly, and NOTE -The authors are on the staff of the Divmon of Research and Statistics https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis even mtraweekly time spans are also evident For example, the demand deposit component of M 1 tends to fall on Fnday, while the currency component tends to nse Nevertheless, after accountmg for these systematic effects, unsystematic, or transitory, day-to-day variat10ns remam In this paper, the magmtudes of these unobserved transitory vanat10ns are mvest1gated m order to appraise the sigmficance of observed variat10ns m the monetary aggregates Day-to-day variat10ns m monetary aggregates sprmg from short-run payments flows between the nonbank pubhc and commercial banks, the Treasury, or the Federal Reserve Potential sources of day-to-day variation m private deposit balances mclude (I) compositional shifts m the allocation of private balances-dec1S1ons by the pubhc to shift from currency to demand deposits, from time deposits to demand deposits, and so forth, (2) shifts m balances held by the U S Government and commercial banks m relat10n to the public's holdmg of balances, (3) variations m the rate at which private deposits are created m the bankmg system, (4) fluctuations caused by Items delayed m transit or by reportmg errors To date, only hm1ted theoretical and empineal work has been done on deposit vanabihty at commercial banks 1 The report of 1 See, for example, Lyle E Gramley, "Deposit In stab1hty at Individual Banks," m Essays on Commercial Banking (Federal Reserve Bank of Kansas City, 1962), pp 41-53, C RangaraJan, "Deposit Vanabihty m Individual Banks," National Banking Review, vol 4 (September 1966), pp 61-71, and Fredenck M Struble and Carroll H Wilkerson, "Bank S1Ze and Deposit Vanab1hty," Monthly Review, Federal Reserve Bank of Kansas Ctty (November-December 1967), pp 3-9, and "Deposit Vanab1hty at Commercial Banks," Monthly Review, Federal Reserve Bank of Kansas Ctty (July-August 1967), pp 27-34 2 Improvmg the Monetary Aggregates Staff Papers the Advisory Committee on Monetary Stat1st1cs was, m fact, the first study of day-to-day transitory vanat1ons m monetary aggregates 2 Like the report of the Advisory Committee, this paper approaches the problem of measurement of transitory variauons empirically It neither attempts to explam m economic terms which part of observed vanauons is transitory and which is not, nor relates the systematic component to othei relevant senes m calculatmg the transitory component Rather, four different statisucal models are considered Each model contams a different spec1ficat10n and, therefore, a different measurement of transitory and systemauc vanat10ns Each of the models allows for two types of systematlc effects zntraweekly effects that account for systematlc differences between Mondays and Tuesdays, Mondays and Wednesdays, and so forth, and longer-run trends that mclude seasonal movement (other than mtraweekly effects) as well as trend and cychcal mov,ements m the usual sense Because there 1s no need to obtam separate esumates of seasonal and trend-cycle parts, both will be grouped mto one term, the "trend " In each model, the observauons are the logarithms of the measured aggregates, and trend 1s determmed locally m each model by smoothmg or averagmg the observed senes around each dally observat10n The four models differ essenually m the precise weights used m computmg the local trend The estimated transitory component (the part of the senes due to transitory variations) m each model 1s obtamed by subtractmg the estimated systematic part from the series Daily trend estimates for three of the four stat1st1cal models are based on an average of five weekday observauons 3 In the analys1sof-vanance (ANOVA) model, the esumated trend for each weekday m a given statement Summary of empirical results lmprovmg the Monetary Aggregates Report (Board of Governors of the Federal Reserve System, 1976) a The day-to-day vanauon m the aggregates 1s cons1derably less on weekends than on weekdays Thm, the analysis was limited to weekday observations, see the section "lntraweekly heteroskedastmty," p 19, for a further d1scuss1on of this pomt On balance, emp1ncal estimates for the 1968-74 sample penod md1cate that 95 per cent of the observed, annuahzecl, monthly growth rates of M 1 and M 2 he wlthm 4 and 2 per cent, respectively, of the unobserved systemJ.tlc growth rates Correspondmg values for 2 https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis week (Thursday to Wednesday) 1s the arithmetic mean of the five weekday observat10ns m that statement week In contrast, daily trend estimates m the symmetrical equal weights (SEW) model are based on an anthmeuc movmg average of five observat10ns centered on the current day Thus, esumated daily trend m the SEW model changes from one day to the next w1thm a statement week Fmally, m the symmetric quadratic weights (SQW) model, the estimated daily trend 1s a weighted movmg average (centered on the current day) with the largest weight attached to the current day In the fourth model, the trend for a given clay 1s also a symmetric weighted average of the observat10ns cente1ed around the current day However, the weights are not fixed a priori as m the three prev10us models but are estimated directly from the aggregate series Under certam assumpuons, aggregate data may be used directly to obtam the optimal statistical decompos1t10n (OSD) of the aggregate series mto Its transitory and trend components, each 1s a symmetric weighted average of the observations on the aggregate Because the ume-senes charactensucs of different senes are not 1clent1cal, the weights used m the OSD trend estimate will be specific to each senes The paper proceeds m the followmg way First, there 1s a sh01 t summary of the emp1ncal results A descnpuon of the four staUstlcal models 1s presented m the followmg sect10n Next aie sections clealmg with the est1mat1on of the models and related statistical tests, empn 1cal comparisons of the sources of transitory variat10ns, and exammat10n of confidencemterval estimates of the systematic component The conclus10ns are followed by two techmcal appendixes Transitory Variations the Monetary Aggregates in TABLE 1 95 Per Cent Confidence Intervals for Monthly Annuahzed Growth Rates, Alternative Methods Percentage pomts Monetary aggregate Method Currency I Demand deposits I M1 I ANOVA SEW SQW OSD 42 2 4 I 6 na 5 4 3 4 7 4 3 3 Other time and savmgs deposits 4 5 3 3 2 5 na I 0 9 7 na I M, 2 3 I 6 I 2 na n a Not available the four different statistical models are presented m Table I For example, the ANOVA estimate for M 1 of 4 5 per cent md1cates that about 95 per cent of all measured monthly growth rates of M 1 will he w1thm 4½ percentage pomts of the (unobserved) systematic growth rate of Mv and about 5 per cent of all measured monthly growth rates will depart from the systematic growth 1ate of M 1 by larger amounts These estimates apply only to not seasonally ad1usted data For data that are seasonally ad1usted usmg the Census X-11 program the values would be smaller, about nme-tenths of those m Table I Methodology Because monetary agg1egates tend to grow as the economy expands, transitory errors, measured m dollars, can be expected to have a long-run pos1t1ve trend m absolute terms Thus, lt 1s convement to put the stat1st1cal problem m 1elat1ve terms and work with the natural logarithm of the daily aggregate Tlus logarithmic transformat10n will tend to stabilize the transitory variance The equation of inte1 est is, therefore, (1) Yt = 'Y/t + f3t + Et where 3 The mdex t runs over successive 5-day penods excludmg weekends 4 The sum 7/t + f3t represents the systematic part of the model The parameter f3t allows for systematic differences between days w1thm a week The trend term 7/t represents long-run trends, mcludmg seasonal movement (other than the mtraweekly seasonal /3 1) as well as trend and cychc movemen ts m the usual sense If the systematic mtraweekly effects are constant across weeks, as we shall assume, then for all t The funct10n f3t 1s thus a periodic funct10n of time with period equal to 5 The day-of-week terms will be normalued to sum to zero ove1 a week, 3 that 15, for any t, We assume that the trend changes gradually and, therefore, 1t 1s esumated by averagmg observat10ns near t Given a particular spec1ficat1on of the trend, It may then be estimated along with the day-of-week effect The term E 1 m Equat10n 1 reflects the t1ans1tory vanat10ns m the observed series, y 1 It 1s generally assumed that Et has expected value zero [E( Et) = OJ and constant variance [EM) = o- 2], and 1s serially mdependent In other words, the effect of transitory components on Yt 1s, on average, zero with variance umform (homoskedasuc) across days, weeks, and months, and the current transitory error 1s mdependent of past or future transitory errors The assumpt10n of homoskedastiCity w1tlun a week will be relaxed m part of the analysis, and separate (heteroskedasuc) estimates of the transitory variance for each weekday will be computed y = the natural logarithm of the aggregate ri = the systematic trend (for y) /3 = the systematic day-of-week term E = the nonsystematic or transitory term t = a time subscript mdex (m days) https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 4 We have excluded weekend observations because they rcqmre a substanually different ueatment from weekday observat10ns, see the section "Transitory vanatlons m averages of daily data," pp 18-21 5 Although this simple spcc1ficat1on of the day of week terms will be adequate for most weeks, weeks contammg bank holidays may reqmre some special mod1ficat1ons, see the section "Emp1ncal results," pp 8-15 4 Improvmg the Monetary Aggregates Staff Papers The ANOVA, SEW, and SQW models for transitory variations The four models differ m their spec1ficat10n of trend The report of the Advisory Committee on Monetary Stat1st1cs .tssumes cl constant trend for all days withm a week but allows the trend to va1 y over d1ffe1 ent weeks 6 That model 1s a standard two-way analysis of vanance (ANOVA) model with five d.ty-ofweek column effects and as mclny row effects as there are weeks m the sample· To assume, alte1 ncltively, thclt the trend fo1 each day 1s app1 oprutely e5timated by ,t symmetn'c 5-day weighted clverclge of y 1 cente1ed cltound that day affords a mo1e symmetnc tieatment of days w1tlun weeks than 1s furmshed by the ANOVA model That 1s, each dcly 1s viewed as lymg m the center of 1ts own week (rather than cl fixed calendar or st.ttement week), and the trend fm th.tt day 1~ estimated hy 2 ~, = ~ (2) c,Yt+• = c_2Yt-2 B=-2 + Cl)'1+1 where for symmetry c, = oper,ttm defined by Biy 1 + c_1Yt-1 + coy1 + C2Y1+2 = c(B)y, c_,, B 1s the backsh1ft =y 2 _ 1 , 1 c(B) = ~c B 8 , 8 ,~2 .tncl 2 ~ c. = 1 (3) •=-2 or c(I) = 1 8 The estimate m Equation 2 1s cl (symmetnc) ,~e1ghted ave1 .tge of y1-the 1esult ot .tpplymg a linear filter to y 1 If the weights {e's} are equal, 1 (4) c, = 5' s = - 2, -1, 0, 1, 2 G [mprovmg the Monetary Agg1egatcs Report, pp 26-28 , It 1s pnmanly the contmual shift of the ttend between weeks that d1stmgmshc.s the trans1to1 y com ponent m Equation I from the "irregular" component of seasonal adJustmrnt model~ In the latter models the defimuon of the trend 1s generally mo1e restnc uve (see, for example, David A Pierce, Neva Van Pesk1, and Edward R Fry, "Seasonal Adjustment of the Moneta1y Aggregates," this volume), thm the. 11rcgula1 ,anance 1s higher than the transitory vanance m this paper s For a d1scuss10n of such approachc.s, ~cc Thcodo1e W Anderson, The Stat1st1cal Analysis of T1111e Series (Wiley, 1971) https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis such a trend filter will be called the symmetnc equal weights (SEW) filter The SEW model 1s qmte s1m1lar to the ANOVA model Assummg the sample consists of .tn mtegral number of weeks, the day-ofweek effects m both models can be estimated by takmg the differences between the averclge of all Mondays and the over-all average, the .tverage of all Tuesdays and the ove1 -all aver,1ge, .tnd so fo1 th In cldd1tion, for the m1ddleot-the-week or third observat10n, the estimated residual and trend will be the same m both the SEW and ANOV A models As stated ear her, the ANOVA model specifies trend a5 the arithmetic mean of the obse1 vauons m a fixed week Hut 101 the third or middle observ.ttion of a fixed week, the SEW estim.tte will ,tverage the s.tme 5 d.tys .ts the ANOV A, and hence both models '\\'Ill 1et111n the same 1emlu.tls and uend e5t1mate5 for th15 day Thus, if we define a week as the statement-week mterval from Thm sday to Wednesdcly, both models will show the same llend estimates ,md res1duah on l\Iondcly-m1dway th1ough the 5tatement week The SEW model 15 les5 ,trb1t1.try th.tn the ANOVA model, then, smce the 5EW t1eclt5 each clay as the center of a movmg 5-dcly week, wherea5 the ANOVA treats clclys as membe1 s of fixed, .i.rb1tranly defined weeks 9 Of course, the essential d1ffe1ence between the two models 1s the degree of smoothness m the t1 encl e5t1mate Trends ,tcross weeks change more smoothly m the SEW model than m the ANOV A model 10 Further general11at10ns of the ANOV A model are possible W1tlun the framework of Fquattons 2 and 3 the weights do not need "On the other hand, rcsene requnement~ for mcm hc1 hank~ arc ha~cd on avu age dcpo~1t~ O\el ,1 Thmsday th1ough \Vc.dnc~da} 11c.ck To the c.xtcnt that 1c~erve 1cqunc.mc.11ts affect depo\1t~, choosrng 'I hun day th1ough Wednesda} to compute. the t1c.nd 1s not entirely arbitrary 10 A related pomt 1~ that under ~mtablc assump t1orn, the estimated scne~ on •t 1s ~tauona1 y for the ~EW c~t1111atc. of the t1cnd but not fo1 the ANOVA c~t1m.itc I or Lxamplc, mmg the ~t.1tc.ment 11 c.c.k, the I.1st day (Wcclncscl,1}) estimate 1s complete!} clctcrmmed by the p1cv10m da} \ c~t1m,1tc.~, .1 property one 110111d not orchnanly want to asc11bc to the transitory com ponent of a senes 5 Transitory Variations in the Monetary Aggregates to be equal Suppose that the weekly trend were a polynomial of degree 2, (5) 71t+J = Wot + Wu) + W2tJ2 J = -2, -1, 0, 1, 2 where w01 , wit, and w2 t are parameters Then the appropriate symmetric filter m Equation 2 has weights given by11 (6) Co d1t10ns, the nature of such a process is determmed by its autocovariances, = 17/35, '-1 = C1 C-2 = 12/35, = C2 = -3/35 Because the weights displayed m Equation 6 are designed to ehmmate quadratic trends, we will refer to Equations 2 and 6 as the symmetric quadratic weights (SQW) model Given a 5-day smoothmg mterval, the SQW model is the highest-order detrendmg filter available, withm the class of lmear symmetric filters, for ehmmatmg polynomial time trends 'Ylk) = E(rJ17/t-k) which for lags k = l, 2, specify the way m which '1/t is related to its own past By the statlonarity assumption, the autocovariances do not change with the time t-that is, E(7Jt'1/t-k) = E(7Jt-s'1/t-s-k) for all s and k The lag 0 autocovariance, E( 711) = 11~, is the variance of 7/t, and y 71 (k) = y 71 (-k) As before, Et is assumed to be serially mdependent-that is, a white-noise process, y.(k) = 0, k ~ 0-and mdependent of 7/t Consequently, (8) }, the optimal Given {xt t = 0, ±1, ±2, (mm1mum mean square error) estimate of '1/e 1s of the form (9) Stochastic process rationalization of the transitory models: the OSD model The trend weights that have been considered so far are given a priori and, moreover, are chosen according to a "deterministlc" assumption about trend-that is, that locally it is well approximated by a polynomial m time Yet, the trend estimates (and hence the estimates of the transitory component), which are symmetric movmg averages or filters of the observed series, are appropriate for a model m which the data contam a "stochastic" component as well 1 2 Consider Equauon 1, rewritten as (7) Xi = y, - /31 = 7j1 + E1 - (over-all mean) but where the redefined trend '1/t is assumed to follow a stationary, nondetermmistic, zeromean stochastic process 13 Under smtable con11 For the derivation of these weights and further d1scuss1on of this approach, see Anderson, Statistical Analysts, pp 46--56 12 The remamder of this seclion 1s more techmcal than much of this paper and may be neglected with out losmg the essenlial ideas of the study 1a See, for example, George E P Box and Gw1Iyn M Jenkms, Time Series Analysis Forecasting and -control (Holden-Day, 1970), Wayne A Fuller, Intro duction to Statwnary Time Series (Wiley, 1976), and https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis where c(B) 1s a symmetric filter as m Equauon 2 but 1s now given by where 1s the autocovariance-generatmg funct10n of the series {7/t} 14 For example, suppose '1/t tollows a firstorder autoregressive process (11) 7/t = 'P'llt-i + Ef, I'Pl < 1 where {ED is a white-noise process with mean zero that 1s mdependent of Et Then the autocovariance-generatmg function of 7/t 1s Peter Whittle, Predictwn and Regulation by Linear Least Square Methods (Enghsh Umvers1ues Press, 1963) In the subsequent apphcal!ons to the aggregates, x 1 will not be stat1ona1y and fmther transformations will be required, see the d1scuss1on concernmg Equation 20 below 14 See Whittle, Prediction and Regulation, p 57 Improvmg the Monetary Aggregates Staff Papers 6 and c(B) is of the form ~ B•Rl•I (B) -- X.r,o(l (3- (32).~ ,., (13) C s=-co where15 f3 = 1 ~ + x.(1 ztr,o,,02) - ~, \f3\ <1 = v'l + 2X.(1 + r,o2) + x_2(1 _ r,o2)2 Thus, the span of the weights is infimte, but the weights approach zero since l,81 < I The vanances of both 1/t and Et can be estimated directly from observations on xt alone, provided the process generating x 1 obeys certain restnct10ns To illustrate this 1 esult, rewnte Equations 7 and 11 as (14) Xt = ,,OXt-1 + E~ + Et - ,,OEt-1 Then, mult1plymg successively by Xt-t and Xt_ 2 and takmg expectations, (15) -y.,(1) = r,o[-y.,(O) - u;] -y,,(2) = r,o-y,,(1) (16) ured with error at umform discrete time intervals accordmg to the equation Xt = '17t + Et, where Et 1s a wh1te-n01se random error that 1s independent of 1/t Then the stationary and mvertible autoregressive-moving average (ARMA) processes that approximate the contmuous process m discrete ume are identified (almost everywhere) from observations on x 1 Without gomg through the proof, the content of the result can be set out 17 Note first the assumption that the aggiegate exists in continuous time At every mstant there 1s a well-specified aggregate, but 1t 1s measured or sampled at d1sciete time pomts, say, at the close of each busmess day At each mstant, the aggiegate (actually the log of the aggregate) 1s equal to the sum of a systematic part, 1/t, and a transitory part, c;t, Xt (18) r,o u~ = 'Y z(Z) -yz(l) = 'Yz(O) - -yz(l) r,o Thus, 1f 1/t follows a first-ordei autoregiess1ve process, all the parameters m Equation 11 may be estimated directly from observations on the Xt process alone, that is, the model (for 1/t) 1s 1dent1fied 16 Moreover, this example is not an isolated special case but exemplifies a general result Theorem Let {'17e} be a stationary stochastic process m continuous time Let 1/t be measIbid, pp 35, 58-59 While Equations 17 and 18 mdicate that rp and u~ are identified, they do not necessarily provide the most efficient means for esumatmg these parameters 15 16 https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 'Y/t + Et where '17s and Et are mutually mdependent fo1 all s and t The process on Et 1s assumed to be independent between days but may be autocorrelated within a specified day Fm ther, '17t 1s assumed to follow a continuous-time stationary process, wluch can be wntten as Smee xt 1s observed, its variance y.,,(O) and lagged covanances y.,,(l) and y,,(2) may be estimated Then, from Equations 15 and 16, (17) = =[ 'Y/t c(t - u)df(u) 00 where {,J,(t)} 1s a continuous process with independent stationary mcrements and with differential d,J,(u). Given these assumpuons, the resultmg process for the trend, '17t, at the discrete sampled points (t = 0, ± I, ±2, ± ) 1s an autoregress1ve-movmg average model of ordei (n, n - l) 18 n (19) 1/t - ~ i=l n-1 ,,0,'Y/t-• = E~ - ~ 8,E~-, i=l 11 The proof 1s developed m Agustm Maravall, "Estl matlon of the Permanent and Transitory Component of an Economic Variable with an Application to M1," Special Studies Paper 85 (Board of Governors of the Federal Reserve System, 1976) 1s The approx1mat10n mentioned m the theorem 1s based on the followmg result Every lmearly regular, stationary, stochastic process m contmuous time 1s the hm1t m a Hilbert space of d1screte-t1me auto regressive-movmg average processes of order (n, n - l), as n approaches mfimty 7 Transitory Variations in the Monetary Aggregates where { Et } 1s a wh1te-n01se process that 1s mdependent of {Ee} 19 Fmally, whenever the autoregressive part of the model has a greater order than the movmg average part, all of the underlymg parameters are 1dent1fied m the econometric sense 2° Further, the 2n + I parameters, ip 1 , <p2, , 'Pn, 011 02, , 0,._1 , u;, u?,, can be estimated solely on the basis of observations on Xt Under the same cond1t10ns, the argument can be applied to d1screte-t1me stochastic processes m which the natural time umt of the process 1s small relative to the mterval m which observations are available Fmally, the systematic part, T/t, can have a nonzero and even nonconstant mean (for example, a determm1st1c day-of-week effect) and be generated by a homogeneously nonstationary process Homogeneously nonstat10nary processes mclude processes that may be transformed mto stationary processes by apphcat1on of one or more d1fferencmg operations Thus, the transformation from the homogeneously nonstat10nary process, T/t, to the stationary process, 81, 1s achieved by h (20) 51 = II (1 - B••)d•T/t = D(B)rii i=l wheres, and h are pos1t1ve mtegers and the d, are nonnegative mtegers Lettmg Zt = D(B)yi and Ct= D(B)Et m terms of the transformed senes we have (21) 10 The ,p's must satisfy appropriate statlonanty restrictions that imply that the roots of the polynom1al equation, q,(B) = 0, he outside of the umt cucle, where ,p(B) =1 - <p1B - <p2B 2 - - 'PnBn Smee 8t 1s stat10nary, 1t can be approximated to any desired degree of accuracy by an ARMA model of order (p, q) for some p and q The cond1t10n on p and q m Equat10n 22 that 1s necessary for 1dent1ficat10n of the paiameters on the nght-hand side of Equat10n 211s that p + d > q, where 21 d= h ~ i=l d,s, In the stat10nary case without d1fferencmg (Equat10n 19) p = n and q = n - l, so the parameters of the discrete-signal process are identified 22 But for situations m winch p + d .e::::. q, the parameters are not identified For example, consider a weekly stationary ume senes m which the weekly observation is an average of seven daily observations, endmg on Wednesday Thus, the weekly observat10n can be seen as systematic samplmg (every Wednesday) of an aggregate of daily observations Assume that the underlymg stochastic process for the daily time senes 1s contmuous and repre-, sentable by a differential equation Wlule the discrete-time ARMA eqmvalent would be of order (p, p - l ), the pnor operat10n of aggregat10n over a week would transform the model mto an ARMA (p,p) Fmally, systematic samplmg would produce an ARMA of order (p,p) 23 Hence, the correct weekly model 1s not identified However, It still may be possible to determme an upper bound for a; from the data (see the section on empirical results) Express10ns for the signal m terms of the parameters are also readily available Correspondmg to Equations 9 and IO we have 81 = d(B)zr where To 1dent1fy the movmg average palt of the model, 1t 1s also assumed that the roots of 9(B) 0 he on or outside the umt cucle, where d(B) = - - - - - - ' - - - - ' ' - - -1 - G.(B) + D(B)D(B- )u; See Marcello Pagano, "Estimation of Models of Autoregressive Signal Plus White Noise," Annals of Stat1st1cs, vol 2 Ganuary 1974), pp 99-108, and Agustm Maravall, Ident1ficat1on m the Shock Error Model (Sprmger-Verlag, forthcommg) For a proof, see Maravall, 'Estimation " See Pagano, "Estimation of Models " 23 See Kenneth R W Brewer, "Some Consequences of Temporal Aggregation and Systematic Samplmg for ARMA and ARMAX Models," Journal of Econometrics, vol l (June 1973), pp 133-54 G.(B) = 21 20 https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 22 Improvmg the Monetary Aggregates Staff Papers 8 and G6(B) = ~ 'Y6(k)Bk k=-oo Last, given d(B), the lmear filter for the signal = c(B)zi ~t can be constructed 24 Empirical results Standard error estimates for the ANOVA, SEW, and SQW models Estimated transitory standard errors are displayed m Table 2 for five aggregates and for three detrendIDg techmques, the ANOVA, SEW, and SQW Because the tl ansitory errors ID dollars turn out to be small relauve to the levels of the aggregates, the transitory standard errors of the logarithm of an aggregate can be IDterpreted (approximately) as a percentage of the aggregate's level (Appendix 1 shows that the error ID this approximauon 1s very small) These standard errors are estimated by usIDg 1,815 daily residuals for an IDtegral number of weeks from 1968 through 1974 The residuals from each model are grouped by day of week, by year, and collecuvely For each entry, the sum of squared residuals is divided by an appropriate constant to obtaID an estimate of the standard deviauon 25 The aggregate displayIDg the most transitory variation (expressed as a per cent of the level) is demand deposits, followed ID order by Mi, by currency, by M 2 , and by other time and 25 Let N, be the number of residuals associated with column I of Table 2 The d1v1sor, D,, 1s D, = N, N, See, for ex.imple, Whittle, Prediction and Regu lation, chap 8 21 - N. - ND where N, 1s a number associated with the detrendmg procedure (reflecting the fact that the residuals are estnnates of [l - c(B)]Et rather than •t themselves), and N n 1s the "prorated" share of the degrees of free dom lost by esumatmg the day of-week parameters For the ANOVA model, N, = the numbe1 of weeks m N, For the SEW or SQW = coN, \\here co= 1/3 for the SEW and 17 /33 for the SQW, ~ce Anderson, Statistical Analysis, p 53, Equation 28 TABLE 2 Estunates of the Standard Deviation of the Transitory Component, Alternative Methods Per cent Days Years Aggregate and method Mon Currency ANOVA SEW SQW I Tues I Wed I Thu Fn I 1968 I 1969 I 1970 I 1971 I 1972 I 1973 I 1974 1196874 (I) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) 4167 4165 2468 4121 2522 1816 5963 2664 1542 7331 3298 1776 3922 2275 2005 4988 2849 1642 5065 3243 2044 4847 2993 1776 5156 3019 2015 5475 3187 2112 5662 3143 2023 5666 2974 1964 5273 3062 1947 7164 7162 5278 5912 8436 4850 3311 8116 4404 5329 3571 5460 4307 3973 6517 4598 3285 7824 5540 4074 7428 5773 4356 6603 5636 3935 6516 5104 3506 7251 5360 4437 7601 6301 5272 7116 5485 4166 5159 5157 3804 4724 4207 3255 6750 3762 2560 6609 4017 2782 4405 3313 2967 5168 3534 2534 6206 4309 3099 5815 4454 3344 5219 4236 2945 5090 3764 2497 5749 3960 3261 5999 4649 3844 5614 4137 3104 1469 1468 1152 0919 0852 0639 1161 0743 0489 1193 0902 0612 1383 1361 1105 0972 0878 0601 1180 1060 0740 1044 0921 0821 1209 0920 0693 1010 0950 0679 1491 1405 1073 1658 1459 1164 1240 1104 0846 2491 2490 1779 2380 2110 1521 3366 1816 1278 3406 2009 1428 2279 1687 1510 2771 1850 1346 3312 2310 1603 3192 2399 1844 2648 2075 1467 2449 1805 1209 2724 1802 1385 2650 2011 1650 2828 2041 1512 Demand deposits ANOVA SEW SQW 5355 M1 ANOVA SEW SQW Other time and savings d~os1ts AN VA SEW SQW M, ANOVA SEW SQW NOTE -The estimates are expressed as a percentage of the level Thus, the entry m column I for the ANOV A model of the logarithm of currency md1cates that the estimated standard dev1at1on on Mon days was 4167 per cent of the level of currency The ANOV A estimates differ slightly from the estimates reported m /mprovmg the Monetary Aggregates Report of the Advisory Committee on Monetary Statistics (Board of Governors of the Federal Reserve System 1976), https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis table 5, p 27 The yearly estimates here are based on day of week effects estimated for the entire sample period, m table 5 of lmprov111g the Monetary Aggregates Report, the annual estimates are based on separate ANOV A's for each calendar year The t.~blc 1bove also corrects a mmor data error m the ANOV A calculauons m /mprovmg the Mo11etary Aggregates Report for both the other time and sav,ngs component of M, and M, Itself Transitory Variations in the Monetary Aggregates savmgs deposits The estimates provided by the ANOVA method are umformly higher than those from the other two methods Evidently, the more restrictive trend specification results m greater vanah1lity m the residual Except for other time and savmgs deposits, the ANOVA estimates are about 2 to 2 5 times as large as the SQW estimates and about 1 3 to 1 7 times as large as the SEW estimates For other time and savmgs deposits, the ANOVA estimates are about 1 5 times as large as the SQW estimates and about 10 per cent larger than the SEW estimates Assessment of intraweekly heteroskedasticity The over-all vahd1ty of the vanous models depends on, among other thmgs, the vahd1ty of the assumptions concernmg the residuals, namely, homoskedastic1ty and lack of senal correlation Senal correlat10n 1s treated later m the d1scuss1on of autocorrelation tests Concermng heteroskedast1c1ty, 1£ the transitory variance itself exh1b1ted a systematic patternfor example, an mtraweekly pattern-the foregomg efforts could not he aimed at a smgle measure of transitory vanab1lity hut only at a composite or average of such measures It 1s, therefore, important to ascertam 1f heteroskedast1c patterns exist The degree of heteroskedast1c1ty across weekdays 1s reported m columns 1 through 5 of Table 2 for different aggregates and methods For each of the methods, there are s1gmficant differences m the estimated mtraweekly standard deviations Observe that the ANOVA and SEW models are virtually equal on Mondays As noted earlier, this equality holds because a Thursday-to-Wednesday statement week was used to define a week m the ANOVA method It ts mterestmg, therefore, to compare Monday standard deviations with the other mtraweekly standard deviations for the three methods Table 3 presents the ratio of the standard deviation of each day of the week relative to the standard deviation for Monday, for each method On the basis of the SEW and SQW estimates, 1t appears that https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 9 TABLE 3, Relative lntraweekly Standard Deviations for M1 andM2 Method Tuesday Wednesday Thursday Fnday 92 82 86 1 31 73 67 1 28 78 73 85 64 78 96 85 85 1 35 73 72 1 37 81 80 91 68 85 M, ANOVA SEW SQW M2 ANOVA SEW SQW NOTE -Computed from columns 1 through 5 m Table 2 Monday has the highest transitory standard deviation With the ANOVA estimates, on the other hand, It appears that Wednesday and Thursday are the most n01sy days w1thm the week For the ANOVA method 1t appears, moreover, that the relative rankmg of the 4 days depends on how far the day of the week 1s from the center of the statement week (Monday) Assummg that the underlymg trend 1s centered on each day, the ANOVA method distorts what 1s occurrmg by est1matmg the trend usmg three-fifths of the appropnate days for Wednesday and Thursday and fourfifths for Tuesday and Fnday Thus, 1f 1t 1s true that Mondays have the highest transitory variance, the resultmg mtraweekly pattern m the ANOVA estimates 1s fully explicable Tuesday and Fnday trend estimates contam only one spurious day, so their standard dev1at1ons are smaller than the Wednesday and Thursday estimates, which contam two spurious days each The ANOVA heteroskedast1C1ty may, therefore, be regarded as evidence of the mappropnateness of the detrendmg procedure for this method In the other procedures (SEW and SQW), the observed differences between the estimated daily transitory variances appear to be smaller Nonetheless, there 1s evidence that Monday's transitory vanat1on 1s largest This add1t1onal random movement on Mondays may reflect desired adjustments of balances by the pubhc and banks that emerge after the close of business on Fnday but are not implemented until Monday transactions take place In what follows, It 1s important to recogmze also that Fnday tends to have less transitory variation than the over-all esttmate Improving the Monetary Aggregates· Staff Papers 10 Autocorrelation tests Recall that one of our assumptions 1s that the transitory component, Et, 1s senally uncorrelated Indeed, 1f 1t were autocorrelated (at least at lags other than a day or two), such a feature could scarcely be considered "transitory " 26 On the other hand, 1t 1s important to note that each of the detrendmg methods mduces mtraweekly senal correlation m the residuals In the ANOVA procedure, the residuals are con5tramed to sum to zero over a statement week, m the two movmg-average procedures, the residuals are estimates not of E1 but of [I - c(B)] Et The mduced autocorrelations, say, p11 p 2 , p 3 , and p4 can be calculated on the assumption that Et 1s itself senally uncorrelated (Table 4) Also affected are the standard errors of the sample autocorrelations of the residuals, as they depend on the population autocorrelations {p,J, 27 they are also shown m Table 4 Based on these results, statistics bearmg on the adequacy of the senal-mdependence assumption for the transitory component, Et, are displayed m Table 5 The actual sample autocorrelations of the residuals, rk, mmus the theoretical autocorrelations Pk, are presented for lags I to 4 Also, bened.th each autocorrelation 1s the statistic, zk = (rk -pk)/ vvar(r,3 A value of zk larger than 2 m absolute value 1s evidence of senal correlation Inspection reveals substantial low-order autocorrelation for all aggregates and methods The z statistics m column I for the lag I autocorrelation are all highly s1gmficant Columns 5, 6, and 7 present the autocorrelations for monthly, quarterly (r6 ;), and annual (r260 ) lags 28 For the AN OVA and SEW, the correlation at these lags 26 For example, 1f •t ,\ere seasonal, part of the com ponent could be predicted on the basis of \\hat occurred a month ago, a year ago, and so forth 27 var(rk) 1 "' = N ,.f"' (p, + = 2 P•-kP•+k - 4P,PkP,-k + 2p~pi] where N the sample sIZe, see Maunce S Bartlett, An Introduction to Stochastic Processes, 2nd ed (Cam bndge, England Cambndge Umvers1ty Press, 1966) 2s The monthly effect has a lag of about 20 or 21 days, the maximum of the two rm's 1s reported https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis TABLE 4. Expected Residual Autocorrelations and Their Standard Errors Under Alternative Detrendmg Methods Lag Method I 1 ANOVA SEW SQW - 160 ( 021) - 300 ( 016) - 800 ( 0091) I 2 - 120 ( 023) - 350 ( 014) 400 ( 030) I 3 - ( ( - ( 080 024) 100 027) 114 036) 4 - I 040 ( 025) 050 ( 028) 014 ( 038) >S . ( 024) * ( 028) ( *038) * Neghg1ble NoTE -The autocorrelations are denved under the null hypothesis that ., 1s not senally correlated Standard errors are shown m parentheses For a white noise process, the standard error 1s 1/(1815)'" = 0235 1s unquestionably s1gmficant and often important For example, consider the annual autocorrelation m the AN OVA model for currency, r 260 = 0 65 The autocorrelations at the next two multiples of 260 are r 520 = 0 34 and r 180 = 0 11 Ignormg all the other autocorrelations m the currency residuals, this would suggest that the residuals follow a process of the form 29 Et = 65Et-260 + Ut where u 1 1s the true transitory (white noise) process with vanance u! = (1 - 65 2 )u~ = 5775u~ That 1s, the 1mphed daily transitory standard deviation for currency would be about 0 76u, = 0 4007 per cent, and not 0 5273 per cent Only the residuals from the SQW model display some signs of senal mdependence at the monthly and quarterly lags Also, It 1s worth notmg that except for other time and savmgs deposits, the magmtude of the autocorrelation at the annual lag for the SQW model 1s markedly lower than that for the other two models However, the ANOVA and SEW methods have substantial monthly and quarterly effects that have not been ehmmated The monthly effect 1s qmte noticeable m the md1v1dual autocorrelations for M 1 that ate listed m Table 6 for the three methods Observe that for the ANOVA and SEW models, there are persistent autocorrelations at a monthly frequency (20 or 21 days and multiples thereof) ,o See Box and Jenkms, Tune Se11es Analysis Transitory Variations in the Monetary Aggregates 11 TABLES Residual Autocorrelations and Related Statistics, Selected Lags Method and aggregate r1 - Pl (I) ANOVA Currency Demand deposits M1 Other time and saV!ngs deposits M, SEW Currency Demand deposits M1 Other time and sa V!ngs deposits M, SQW Currency Demand deposits M1 Other time and sa V1ngs deposits M, I I r2 - p2 (2) I I ra - I I r, - P' (4) I I Tm (5) I I "' (6) I I r2ao (7) 51 (24 3) 33 (15 9) 34 (16 2) - 02 (- 9) - 08 (-3 6) - 09 (-3 9) - 20 (-8 3) - 14 (-5 7) - 16 (-6 9) - 25 (-9 9) - 16 (-6 4) - 16 (-6 2) 40 (16 7) 16 (6 7) 22 (9 2) 51 (21 3) 36 (15 0) 42 (17 5) 65 (27 1) 47 (19 6) 48 (20 0) 19 (8 9) 35 (16 8) - 21 (-9 0) - 09 (-4 0) - 22 -(9 0) - 17 (-7 1) - 06 (-2 5) - 16 (-6 5) 24 (10 0) 22 (9 2) 19 (7 9) 45 (18 8) 24 (10 0) 48 (20 0) 49 (30 3) 26 (16 5) 28 (17 3) 03 (2 I) - 06 (-4 3) 05 (3 8) - 31 (-11 6) -0 1 (-3 7) - 10 (-3 8) - 11 (-4 0) - 03 (-1 0) - 04 (-1 4) 18 (6 4) 10 (3 6) 10 (3 6) 21 (7 5) 11 (3 9) 14 (5 0) 48 (17 I) 24 (8 5) 22 (7 9) 25 (15 6) 30 (18 7) - 13 (-9 6) - 04 (-2 9) - 29 (-10 8) - 13 (-4 7) - 02 (- 9) - 06 (-2 I) 21 (7 5) II (3 9) 21 (7 5) 16 (5 7) 17 (6 I) 21 (7 5) 06 (7 0) 07 (7 5) 07 (7 8) - 11 (-3 6) - 15 (-5 1) - 16 (-5 4) 05 (I 4) 12 (3 3) 13 (3 6) - 02 (- 7) - 03 (- 8) - 02 (-1 I) 02 ( 5) - 02 (- 5) - 01 (- 3) 03 ( 8) - 01 (- 3) - 01 (- 3) 30 (7 9) 16 (4 2) 13 (3 4) 06 (7 0) 07 (7 6) - 15 (-5 I) - 15 (-5 2) 19 (5 5) 12 (3 5) - 25 (-6 8) - 03 (-1 0) 20 (5 3) - 02 (- 5) 13 (3 4) 01 ( 3) 16 (4 2) 08 (2 I) NOTE -Figures m parentheses are Zk values and that these autocorrelat10ns show no tendency to die out as the lag increases This pattern suggests that the underlying process for Et has a seasonal (monthly) nonstatlonanty Holiday effects Bank holidays likely represent an add1t1onal source of vanat10n m the time senes models under cons1derat1on Several attempts were made to mcorporate dummy variables for maJOr bank holidays mto the spec1ficat1ons of the ANOVA, SEW, and SQW models While these results most often yielded stat1st1cally s1gmficant regression coefficients for maJor bank holidays, on balance 1t appears that most of the effect 1s confined to Monday hank holidays The problem can readily he illustrated by cons1dermg the outliers for demand deposits from the ANOVA method In the sample, https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis pa (3) there were 29 Monday holidays on wluch all or a substantial port10n of commercial banks were closed, all of the residuals from these Monday holidays for the ANOVA model for demand deposits were negative, and all but one were greater m absolute value than one standard error The root mean square residual for the Monday holidays 1s I 35 per cent of the level of demand deposits, which is nearly twice as large as the over-all standard error for Mondays The source of the problem 1s an mteractton between the day-of-week effects and Monday holidays A holiday on which all or substanttally all of the banks are closed should properly receive the day-of-week effect on the nearest preceding day that banks were open Thus, Monday holidays should 1ece1ve the Fnday day-of-week effect rather than the Monday day-of-week effect The average residual on the Monday holidays was -1 30 per cent of the level of demand deposits This value 1s highly s1gmfi- 12 lmprovmg the Monetary Aggregates Staff Papers TABLE 6. Autocorrelations for M1 Lags Lags 2 3 5 4 7 8 05 05 16 03 04 19 09 03 07 07 - 01 04 - 10 03 03 02 - 06 22 13 11 - 03 15 - 09 01 03 10 11 08 05 01 01 02 03 02 - 13 - 13 - 01 13 12 13 - 01 11 07 11 12 08 05 10 30 - 01 - 10 04 02 07 11 18 08 00 10 - 9 10 11 12 - 04 09 14 21 - 02 14 - 11 - 02 - 03 03 01 07 - 09 04 - 09 - 07 00 - 00 - 16 - 02 04 02 - 04 - 15 04 - 04 - 10 - 10 - 12 04 04 01 01 - 03 - 05 - 09 06 - 01 - 10 - 04 - 05 - 06 10 14 - 02 00 - 15 - 06 - 04 - 02 - - - 08 - 05 - 08 06 09 01 04 - 13 - 06 - 09 - 12 00 43 09 04 - 07 - 02 - 06 - 03 02 05 18 - 01 - 00 02 04 04 21 04 04 - 00 - 04 - 01 08 04 01 05 03 11 02 - OS 02 03 03 03 - 08 - 02 14 06 6 ANOVA residuals 113253749617385- 12 24 36 48 60 72 84 96 97-108 109-120 121-132 133-144 145-156 157-168 169-180 181-192 193-204 205-216 217-228 229-240 241-252 253-264 265-276 277-288 289-300 18 07 - 01 - 02 - 12 - 13 - 03 19 - 15 16 06 13 11 02 02 03 08 - 21 02 - 00 05 - 13 - 14 - 03 10 - 10 28 01 11 09 01 07 05 12 - 09 03 02 09 04 01 - 05 - 06 - 00 03 - 17 - 06 02 05 - 02 - 13 - - - - 24 - 13 02 04 - 05 - 07 - 06 04 20 10 01 00 13 14 - 01 - 03 - - - - - 01 08 08 08 09 07 10 00 38 - - 16 04 04 02 02 17 07 03 17 06 08 06 08 02 42 05 - 03 - 05 04 08 09 04 06 03 - 01 11 07 02 - 10 - 13 - 06 05 11 40 01 05 05 00 05 01 09 - 00 - 03 - 03 - 03 - 01 - 00 03 13 01 06 01 02 01 05 06 04 - 09 - 02 03 - 10 01 14 03 - 02 03 05 - 01 - 01 - 01 - 01 - 03 - 03 01 02 04 02 - 10 - 07 00 - 04 - 02 15 - 00 02 01 07 04 03 01 03 16 - 02 - 06 - 10 04 - 02 - 02 08 07 03 03 02 03 01 03 02 00 - 07 - 02 - 04 01 - 07 - 06 - 03 - 05 01 - - - - - 11 00 02 04 - 11 - 08 03 - 00 10 03 39 07 04 06 10 08 04 05 02 18 11 05 - 01 - 11 - 14 03 02 07 03 02 02 - 06 - 07 - 13 05 - 02 - 15 - 06 - 01 20 08 09 01 02 02 00 - 03 - 05 00 01 10 08 15 16 02 '6 11 02 02 - 01 11 29 01 14 07 03 11 08 02 05 14 - 00 - 09 00 - 07 - 11 16 02 - 04 00 - 03 - 05 01 07 06 02 00 02 04 02 02 01 - 05 - 03 - 07 - 08 01 - 05 - 04 - 02 - 01 - 02 - 04 03 05 09 00 - 04 - 05 - 02 - 07 03 20 02 01 - 03 - OS - 05 01 05 01 10 - 04 - 01 02 - OS - 06 02 18 04 OS 01 06 03 01 - 01 05 12 04 - 03 03 - 10 - 12 - 02 12 08 00 03 03 06 00 04 02 - - 04 01 04 04 08 06 03 05 02 04 - 09 - - - 03 02 02 00 03 08 02 - 03 - - - - - - SEW residuals 113253749617385- 12 24 36 48 60 72 84 96 02 04 02 02 08 07 02 01 - - 97-108 109-120 121-132 133-144 145-156 157-168 169-180 181-192 193-204 06 17 - 04 - 02 - 01 - OS - 06 01 - 03 205-216 217-228 229-240 241-252 253-264 265-276 277-288 289-300 01 14 04 03 05 07 04 01 - 73 OS 04 03 04 05 06 03 24 04 - 01 - 02 05 - 04 03 - 03 - 02 00 01 02 04 03 01 03 - 03 - OS - 00 06 02 - 02 01 - 01 09 01 09 03 01 - 00 01 - 02 - 02 - 06 00 08 06 02 - 00 01 - 01 - 03 02 - 03 - 07 - 04 - 04 02 - 00 02 03 01 03 07 01 02 02 02 04 01 - - 02 - 03 - 02 02 - 02 - 05 - 07 02 01 02 04 01 - 02 - 07 - 03 02 - - 06 12 03 04 04 04 06 01 - - 01 04 04 06 09 02 02 08 - - - 03 02 01 03 06 04 12 - 00 - 04 22 09 02 - 05 - - 01 10 08 03 00 09 07 02 OS 05 05 04 22 01 03 01 - - - - 04 05 19 04 05 01 OS 09 - 02 07 09 04 - 06 - 00 - 08 - 09 SQW residuals 113253749617385- 12 24 36 48 60 72 84 96 97-108 109-120 121-132 133-144 145-156 157-168 169-180 181-192 193-204 205-216 217-228 229-240 241-252 253-264 265-276 277-288 289-300 https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis - - 03 05 04 01 03 - 03 04 01 - - 01 02 01 03 05 03 07 - 04 - - - 00 08 02 06 00 01 00 02 03 01 07 04 - 00 00 03 OS 01 - 02 02 02 04 - 04 - OS - 03 01 - - 02 - 08 - 01 01 - 01 03 00 02 06 03 - 01 02 02 - 02 - 02 - 00 - 06 01 01 00 - 03 02 05 - 02 01 - 01 01 - 02 03 - 04 - 05 02 - - 03 OS 02 01 02 01 03 06 02 01 08 03 - 04 - 06 - 01 04 07 02 - 01 09 06 06 07 02 03 06 00 02 08 04 - OS - 02 - 02 00 03 - 02 - 04 - 00 - 02 08 11 02 05 - 02 - 04 - 01 06 03 - 16 - 01 - 03 02 03 01 - 06 00 - 13 04 01 - 02 - 02 01 04 01 04 - 02 - 01 - 01 01 - 04 - 04 01 02 - 01 01 04 - - - - 01 06 01 02 04 00 04 03 03 04 01 02 02 04 - 09 02 05 05 05 03 00 05 08 - 04 - 08 - 00 07 00 03 01 03 06 08 02 01 00 01 02 04 03 - 07 - 07 - 02 - 01 05 05 04 - 02 02 01 - 02 - 04 - 05 - 03 05 01 - 02 - 03 - 04 Transitory Variations in the Monetary Aggregates TABLE 7 Differences JD Day-of-Week Effects JD the ANOVA Model for Demand Deposits Days Difference 95 -1 31 04 34 - 02 Thursday, Fnday Fnday, Monday Monday, Tuesday Tuesday, Wednesday Wednesday, Thursday cant 30 But 1f our assessment 1s correct, on average the Monday holiday residuals should be approximately equal to the difference between the Friday day-of-week effect and the Monday day-of-week effect, which 1s -1 31 per cent (Table 7) The data are thus remarkably consistent with our hypothesis 31 Table 7 also md1cates why the holiday problem 1s essentially a problem only for Monday hobdays Most of the other differences are small, and the only possible competitor, Friday, 1s a day with a relatively small number of holidays m most years This mterpretat10n 1s also supported by an outlier analysis of those holidays that were switched to Mondays by an act of the Congress George Washmgton's Birthday, for example, did not contam persistent residual outliers until 1971, when It became tied to Monday Fortunately, this m1sspec1ficat1on m the dayof-week effect 1s rather small For example, 1f the Monday-holiday residuals were dropped from the sample, the over-all AN OVA standard error would fall only from O7116 to O6966 Estimates based on the OSD model The model for optimal statistical decompos1t10n (OSD) discussed earher is apphed m this paper only to weekly (7-day average) data on the demand deposit component of M 1 over a 215-week sample period from November 24, 1971, to December 31, 1975 32 The logarithm 30 13 of the series, say z1, appears to be nonstat10nary and a stationary series has the form Zt = (1 - B52) (1 - B13)y, (23) = Yi S,(B) = 1 -1 30 = u,!v'n -1 30 = -9 84 111G/y29 31 S1m1lar results were obtamed for the SEW and SQW models 32 In subsequent work we shall apply this technique to all aggregates at a daily level For a fuller descn ptlon than that presented here, see Maravall "Estima- tion" https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis Y1-1a - Y1-02 + Y1-6s + B + B2 + +Erl= 1 - Bi 1 - B then z1 = (1 - B) 2Sia(B)Ssz(B)y, = D(B)y1 and 1t follows that z1 may be thought of as bemg generated m the followmg way First, pass the logarithm of the aggregate through two successive annual and qu<1rterly smoothmg filters, Sni(B) and S13 (B), and then take second differences of the smoothed series Consequently, the stat10nary quantity, z1, represents the acceleration (difference m the rate of growth) of a highly smoothed aggregate In Appendix 2, 1t 1s explamed how Equation 7, together with (24) 01 (25) Ot (26) Zt = = = D(B)r, 1 (/101-i Ot + E~ + Ct (where e 1 = D(B)e1), 1s a reasonable first approximation to the data Equation 25 md1cates that the systematic trend component 1s, after d1fferencmg and smoothmg, a first-order autoregressive process Usmg a quas1-max1mum-hkehhood techmque an iterative algorithm was devised to estimate Equations 24 to 26 33 The estimates obtamed by this procedure are fp = The appropriate test statistic 1s t = - that 1s, both quarterly and annual d1fferencmg of the data are req mred to achieve stationarity Lettmg 89, u?, = 226 X 10-4 u? = 561 X 10- 5 If the daily transitory errors are serially mdependent, the daily standard error associated with this weekly value of u; 1s v' 561 33 X 10-5 X v'7 = Ibid, pp 12-16, for further details 006267 Improving the Monetary Aggregates Staff Papers 14 This calculat10n assumes the errors have the same variance m each day Alternatively, one may wish to assume that the error on Saturday and Sunday 1s essentially that of Fnday, which implies that the dally standard deviation of demand deposits 1s V 561 X 10- 5 X y'49/13 = 004598 or 1t can be assumed that the error on Sundays is equal to that of Saturdays, which implies that the daily standard error 1s34 V 561 X 10- 5 X y49/9 = 005527 Thus, the implied standard deviation for daily demand deposits runs from about O 46 per cent to O 63 per cent dependmg on the treatment of weekend observat10ns This range of values 1s below the ANOVA estimate of 071 per cent but mcludes the SEW estimate of 0 55 per cent Stnctly speakmg, the use of weekly-average data to implement the OSD model is not appropnate That model applies only to data sampled once m some mterval, not to the average of successive sampled values, and 1t applies stnctly only to stattona1y senes It follows that we cannot mvoke the aggregat10n-contmmty mterpretation of that section to Justify the empmcal specification of Equation 7 and Equat10ns 24 to 26 However, there 1s an alternative way of completmg the model that has a legit! mate basis To brmg out the essential ideas m this alternative approach, let us temporanly s1m phfy the problem and suppose that et m Equation 26 1s a wh1te-no1se process To recap the model, then, we observe z 1 (27) and have decided on the basis of empmcal evidence that z 1 1s generated by an ARMA model of order (1,1) (28) Zt = <,?Zt-1 + a1 - Oa1-1 where at 1s a wlute-no1se process There are two possible models for the signal Bt that 34 The relationship between weekly and daily stand ard errors will be discussed m more detail later https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis are consistent with the over-all model for Zt m Equation 28 Either Bt 1s a pure autoregress1 ve process, (29a) or Bt 1s also an ARMA model of order (1,1), 35 (29b) If daily data were bemg used, we could adopt Equation 29a on the basis of the results above With weekly-average data, however, there 1s no reason to re1ect the less restnct1ve spec1ficat10n Equation 29b, which 1s still consistent with the over-all observed model for Zt But there 1s a catch m this alternative spec1ficat1on The model cons1stmg of Equations 27 and 29b 1s not identified m the econometnc sense To identify the model, add1t10nal restnct10ns on the parameters must be imposed One useful restncuon 1s to set 0 = -1 m Equat10n 29b Tlus choice 1s optimal 1f one does not wish to understate the impact of the transitory vanatlons, or, eqmvalently, 1f one wants to mm1m1ze the contnbuuon of the systematic vanat10n to the over-all observed vanat10n 36 35 Stnct notJ.tlon l\ould 1equne that \\e d1~tmgmsh bet\\een the white noise errors m Equations 29a and 29b Also, Equation 29a 1s a special c.a,e of Equation 29b ,\hen 8 0 Neverthdess, 1t 1s meful to cons1de1 these as d1~tmct model~ became they d1fft.r m the number of parameters 36 To ~ee this exphc1tly, observe that = (A) (B) u; 2 = -y,(O) = ( 1 +1 0_ - 2,pO) u~, -I u; <p 2 - (1 - ,pO)(,p - 0) ')', (1) 1 - <p2 2 "•' (See Box and Jenkms, Time ~eries Analysts, Equation 3 4 7) Thus, max1m1zmg u; given y,(O) and 'Y,(l) and <p (which 1s identified) 1s eqmvalent to mm1mmng (C) 1 + 02 - 2,pO ] [ (1 - ,pO) ( 'P - 0) -y,(l) \\Ith respect to 8 D1fferent1atmg Equation C with respect to 8 and setting the derivative equal to zero, 1t can be shown that 8 -1 gives the mm1mum value for ui, or maximum value for a;, given 'Y,(l) and q:, The idea of closmg the model m this \\ay was taken from t\\O papers, David A Pierce, "Seasonal Adjust mcnt When Both Determ1mst1c and Stocha~tlc Sea ,onahty Are Present," and George E P Box, Stephen Hilmer, and George C T1ao, "Analy~1s and Modehng of Seasonal Time Senes," prcscntul at the Nat10nal = Transitory Variations in the Monetary Aggregates Returmng to the more general specificatton m which e 1 = D(B)Et, a similar analysis shows that the maximum value for the transitory variance, ut consistent with the observattons on z1 is also achieved where 0 = - I m Equation 29b And 1t can also be shown that the maximum transitory variance, say, u; (max) and u; m the (1,0) ARMA specification (29:-), are related by the equation 2( (30) ) _ 2+ u. max - u, (l 25u;, + q, 2) 15 TABLE 8 Standard errors for OSD and Alternative Methods Per cent of the level of demand deposits Transitory standard Conversion factor error -v'7 u; (max) = 561 X 10- 5 6267 4598 5527 5485 SEW 4166 SQW 5485 SEW 7095 5206 6257 7116 ANOVA 5485 SEW 5485 SEW OSD estimate Nearest altemat1vc estimate Estimate Method u, (max) OSD estimate Nearest alternative Estimate Method 7192 X 10- 5 X y7 = 007095 transitory variances m currency and demand deposits, and the covariance between the transitory components of demand deposlts and currency The separate sources of tl J.nsitory VJ.nations m an aggregate are assigned m the followmg way Let Y 1 be an aggregate that is equal to the sum of m component aggregates Y ,t, 7192 X 10-5 X ~ (31) + 25 X 226 X 10- 4 (1 89) 2 = 7192 X 10_ 5 = (2 682 X 10-3) 2 The alternative daily standard deviations are then y y y V49/9 I u, estunate Substitutmg mto Equat10n 30 the estimated values for rp, u;,, and u;, we find that y49/13 I 7192 X 10- X 5 v49/9 = 005206 = 006257 Thus, dependmg on the assumptions made concernmg transitory errors on the weekends, values of the daily transitory standard error can be found that are very close to one of the three predetermmed trend weights Table 8 provides a summary of correspondmg values Sources of transitory variations in the aggregates Transitory variations for any aggregate that 1s the sum of various components may be expressed as a weighted average of the var1at10ns m the component parts and the covariance terms between the transitory parts of each of the components Thus, the transitory variance m M 1 1s equal to a weighted average of the Bureau of Economic Research-Census Conference on Seasonal Analysis of Economic Time Series, Washmgton, DC, September 9-10, 1976, m these papers s1m1lar restrictions were imposed on seasonal adjustment filters https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis Yi= ~Y,1 i=I Recalling that Yi = In (Yi) = '111 + f31 + Et = /1 + Et it follows that Yi = exp (/1) exp (Ei) Because Et 1s generally very small (for example, the standard error of Et for demand deposits is about 005), the first-order approximation (32) exp (1:1) = 1 + Ei is an identity for all practical purposes 37 Thus, from Equation 32 (33) Yi ::l:: exp (Ji)(1 + Ei) = Fi + Ei = exp (Ji), Ei = Yi - Fi ::l:: E,Fi Equation 34, 1f Et = 005, the error m (34) Fi In the approximation amounts to about 3¾ millions 37 This approximation 1s almost as accurate as that hsted m Table A-1 m Appendix I Improvmg the Monetary Aggregates Staff Papers 16 for an aggregate totalmg 300 billion Note also that (35) where the second approx1mat10n 1s also highly accurate (see Appendix I) Returnmg to Equation 31, 1t 1s desired to assess the contribution of the transitory variation m each component aggregate, Y,t, to that of Yt itself Note that the 1elat10ns analogous to Equations 32 to 35 hold for eacl1 component aggregate, for example, Y,1 E,t = = Y,t F,t - + f,t E,1 = Ey,t ,t Thus, we have (36) = In (1 + !:) (37 ) = Et = Et = ~ E,t = ~ Y,t Fe Ye ,=I Ye ,=I Ye E,t Y,e where the approximations m Equation 37 follow from Equations 32 and 35 Lettmg (38) W,t Y,t = Yi Equation 37 becomes (39) Assummg that the deposit shares are fixed, the relative transitory variance of Yt 1s approximated by m (40) m m o-; = ~ w!ut + ~ ~ w,w, cov(e,t, e,e) i=-1 1=1 1c::1l ,;,,, where cov(e,t, e1 t) denotes the covariance between the component transitory errors 38 This 38 The approximation error 1s potentially much larger over longer time mtervals, but the emp1ncal decompos1t1ons given later md1cate that 1t 1s generally qmte small https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis expression md1cates that the over-all transitory variance of an aggregate may be expressed approximately as a weighted average of the component variances and the covariance terms Table 9 lists three decomposit10ns-f01 gross deposits less cash Items at member banks, for Mi, and for Mi In each decompos1t1on, the terms on the right-hand side of Equat10n 40 are listed separately as a percentage of the over-all transitory variance All numbers are based on the ANOV A estimates, though we believe that the other methods would produce very similar results 39 The discrepancy term 1s mtroduced to account for the error m Equation 40 that arises because the deposit shares do not stay constant over the sample periods and because Equation 40 1s an approximate relation For M 1 and M~ Table 9 shows that almost all of the variat10n m both of these aggregates 1s due to the volatility m demand deposits The contribut10ns of the variat1ons m currency and other time and savmgs deposits are very small m relation to demand deposits, as are the contribut1ons of the covariance terms The other variance decomposition given 1s that of gross deposits less cash Items at membe1 banks This aggregate was chosen because a very high proportion of transactions mvolves offsettmg changes m gross deposits and cash Items For gross deposits less cash items, the relative contribut1ons are somewhat more equal, with demand deposits ad1usted and mterbank bank deposits accountmg for much of the variation The direct effect of government deposits declined s1gmficantly by the end of the sample period Though the share of government deposits 1s qmte small-averagmg around 3 3 per cent of the level of gross deposits less cash 1tems-1ts daily transitory standard deviat10n was far larger than any other aggregate, averagmg about 14 7 per cent 39 This belief follows from the empmcal result that alternative methods give approximately the same relative rankmg of transitory standard deviations for different aggregates For example, the ratio of the transitory standard deviation of M 1 to that of M 2 was about 2 for each method Transitory Variations in the Monetary Aggregates 17 TABLE 9 Relative Contnbution to the Over-All Transitory Vanance of Selected Aggregates, 1968-74 In per cent .Aggregate and source of vanauon Gross deposits less cash items at member banks Demand deposits ad1usted (DDA) Government (GOVn Interbank (IB) Covanance (DDA, GOVn Covanance (DDA, IB) Covanance (GOVT, IB) Discrepancy M1 Currency Demand deposits Covanance Discrepancy 1968 1969 1970 1971 1972 66 99 23 -60 -9 3 -21 5 3 5 9 7 2 8 4 98 -3 - 47 6 01 07 3 2 98 0 -1 I - 01 3 3 99 3 -2 S 4 8 96 6 -1 4 * * 4 99 2 -3 -2 * S 0 S 0 7 3 3 98 I -1 -2 * 3 92 2 -2 3 74 72 34 -46 -16 -3 -14 0 9 0 6 0 8 6 76 56 58 -35 -43 2 -15 7 5 8 6 7 2 0 101 33 118 -II -140 II -II 8 9 0 8 73 37 86 -23 -58 -5 -9 4 0 0 2 I 7 4 S 8 99 4 -SI . 1974 1968-74 -2 0 36 7 12 4 52 2 -69 -7 9 12 I I 4 58 32 47 -17 -21 4 -4 3 0 8 3 0 3 1 S I 95 I I - 2 4 8 94 7 7 - 3 4 97 -1 - 3 4 6 2 5 4 101 8 7 1 1 -16 7 2 5 - 2 107 1 9 5 8 -25 8 3 0 - I ss 4 98 4 -1 -7 3 I 7 6 0 7 8 1973 40 24 48 -13 2 * 7 3 I I 0 M, Currency (CUR) Demand deposits (DD) Other time and savmgs (OTS) Covanance (DD, CUR) Covanance (DD, OTS) Covariance (CUR, OTS) Discrepancy 2 7 S 1 9 5 1 5 3 3 S 8 2 4 95 4 -1 -4 7 6 6 4 7 7 s 6 103 4 -5 -9 0 9 S 4 7 5 1 *Negbg1ble Norn -For each aggregate decompos1t1on, the weighted vanance terms, w:u;,, are hsted as a per cent of the over.all transitory vanance for that aggregate, that 1s, as 100 w1u;.fu; Beneath the variance components are the relative covariance terms, 200 w,w; Cov(u,e,)/ul The discrepancy 1s also expressed as a per cent of u; of the level of government deposits over the 1968-74 sample period 40 From the M 1 and M 2 decompos1t1ons, it appears that demand deposits are the maJor source of transitory variation m these aggregates However, recent developments may alter this pattern In particular, passbook savmgs accounts at commercial banks probably now behave more hke demand deposit accounts m the short-run payments mechamsm 41 These developments appear to stem from several recent changes m bank regulations mcludmg passbook savmgs accounts for corporat10ns and State and local governments, telephomc transfers between passbook savmgs accounts and demand deposit accounts, and negotiable orders of withdrawal (NOW) accounts As a result of these changes, fluctuatmg payments between the pubhc and commercial banks or between the pubhc and the Treasury are more hkely to mclude some very short-run variatton m aggregate passbook savmgs deposits at commercial banks To mvestigate this possibility, we constructed ANOVA models of transitory variation for aggregate passbook savmgs accounts at member banks over two periods, before the mtroductlon of corporate passbook accounts and after the mtroductlon of such accounts 42 The estimated standard error before the change was O II I per cent of the level, tt Jumped to O 160 per cent afte1 the change m regulations regardmg corporate passbook accounts The appropriate F-stat1st1c to test the equality of the transitory variances m the two periods is F(l27,1423) = 2 03 Thus, the data mdicate a highly s1gmficant mcrease m the transitory variance of passbook savmgs accounts at member banks smce corporations have become ehg1ble to hold passbook savmgs accounts 43 40 Government deposits 1s the only aggregate we have considered for which the approximation represented by Equation 32 1s not highly accurate 41 See John D Paulus and Stephen H Axilrod, "Regulatory Changes and Fmanc1al Innovations Affect mg the Growth of the Monetary Aggregates," staff memorandum (Board of Governors of the Federal Reserve System, November 1976) https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 42 Corporations became eligible to hold such ac counts on November 10, 1975, about a year later than State and local governments The two penods used m this paper were from 1969 through the statement week endmg on November 5, 1975, and from the statement week begmnmg on November 13, 1975, to June 30, 1976 43 The data also md1cate that the change did not occur much earlier If the m1t1al ANOVA estimates are derived from the begmmng of 1974 to November 5, 1975, the resultmg standard error 1s only slightly larger, 112 mstead of 111 The associated F-statlstlcF(l27,379) 1 94-is also highly s1gmficant = 18 Improving the Monetary Aggregates Staff Papers Transitory variations in averages of daily data To examme transitory vanauons m mtervals longer than a day, one must mvest1gate transitory variances of sums or an thmeuc means of aggregates Let Y: be the anthmeuc mean of n successive daily observations for which u, 1s the daily transitory standard deviation of the natural log of Y t measured daily (The subscripts mdexes the n-day period contrasted with t, which denotes the daily mdex) As before, 1t 1s assumed that the trans1 tory errors m the daily aggregates are stat1st1cally mdependent of the systematic movements This mdependence 1mphes that the Federal Reserve does not mtervene and does not alter the systematic trend m the aggregates to offset 5ome or all of the accumulated transitory vanattons that occur Estimates of the impact of transitory variations on monthly and quarterly growth rates, which will be considered below, are sufficiently small so that this mdependence assumption 15 unlikely to be violated m most penods If the errors, Et, are serially mdependent, it 1s natural to assume that the relative transitory standard deviation for Y: 1s44 (41) .✓,i In fact, a more appropnate formula 1s (42) where Vn is the coefficient of vanauon fo1 the systematic part of Y: over the period s 45 If, mstead of the anthmeuc mean, the geometnc mean were used, then the simpler Expression 41 for the transitory standard devia44 Throughout this section, the standard deviation of a daily aggregate will be expressed relative to the level of that aggregate (expressed either as a pe1cent age or 1/100 of a per cent) <5 The matter 1s complicated owmg to the nonstatlonanty of the systematic part of Yi, generally, the current "level" of the series 1s substituted for the nonexistent population mean m V n https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis uon would be appropriate Because Expression 41 1s always smaller than Expression 42, the geometric mean will have a uniformly lower transitory standard deviation than the anthmetic mean It follows that the rate of growth of an aggregate formed by takmg the geometric mean of daily observations will have a lower observed transitory variance than will a daily-average aggregate Empmcal calculations confirm this result However, the differences between the estimated vanances are extraordmanly small and have no practical s1gmficance (They are nearly equal because rates of change m the aggregates-at least for daily, weekly, monthly, or quarterly dataare gene1ally so small that anthmetic and geometnc means will be very close to each other as will their trans1 tory variances ) A related empirical calculation mdicates that the term Vn m Expression 42 is very small so that Expressions 41 and 42 are practically equal Accordmgly, we will adopt the simpler expression, u,/Vn, to represent the relative standard deviation of a daily average of n observations Serial correlation in the residuals If the transitory errors are sen ally conelated, then the autocorrelations must be taken mto account when computmg the standard deviation of the daily averages Because the large autocorrelations m the estimated models tend to be positive, the imphed reduction m the standard deviation-from u, daily to u,/Vn for Y,:'-is probably too large 46 On the other hand, 1f one were to model the residuals from the ANOVA, SEW, or SQW model as a stationary stochastic process, the resultmg estimates of the transitory standard deviation would be lower This is true because there would be useful mformation m the model residuals about future "transitory" residuals and the fundamental uncertamty about the true transitory component would 1G The actual standard deviation 1s a, V k/n, where n-1 k = 1 +2 I: (1 -1/n)p, ,-1 and p1 1s the autocorrelation of lag J Transitory Variations in the Monetary Aggregates actually be less Models with a large degree of senal correlation m the transitory component (estimated residuals) seem to behe the notion of "transitormess" and redomg these models by mcorporatmg a time senes model to explam the senally correlated residuals would lower the standard error 47 Thus, it seems reasonable to regard the estimate u,/yn as an upper bound for the underlymg transitory standard deviation of Y: and to expect the bound to be closer to the correct standard deviation for models and aggregates havmg a smaller amount of autocorrelation m the residuals From daily to weekly estimates By excludmg weekends it is a straightforward matter to go from estimates of daily standard errors to monthly or quarterly estimates However, because alternative values for the weekend effects will be considered, it is convement to work with an aggregate Y: m mtervals of n/7 weeks Let u. be the daily standard deviation and assume that the transitory components are mdependent from day to day If the weekly average is an average of seven mdependent daily figures, the implied standard deviation m the weekly figures is, m accordance with Expression 41, (43) u,/v? = 378u, This estimate treats the transitory component on weekends as bemg fully eqmvalent to the component on weekdays But banks are closed on Sundays, makmg the Saturday observation 1dent1cal with Sunday's Thus, whatever transitory part exists m the Saturday observation 1s also present m the Sunday observation When 1t 1s assumed that the Saturday transitory component counts twice, the weekly transitory standard deviation becomes (44) ✓ (1 + 1 + 1 = ~2 1 + 1 I+ 22) ~= (Ti 3/7u. = 429u. That 1s, the residuals from the times senes model would have a lower standard deviation 47 https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 19 If the Fnday transitory component remams m both weekend observations and 1£ 1t 1s assumed that there 1s no mdependent source of transitory vanation on Saturday itself, then the Fnday transitory component counts three times m computmg the transitory standard deviation for the weekly observation 48 Under this assumption the 1mphed weekly trc1ns1tory standard deviation 1s (45) ✓ (1 + 1 + 1 + 1 + 3 )u; 2 72 /13 2 - '\J49 u, 515u, The correct weekly deflatmg factor 1s probably much closer to Equation 45 than to Equation 44 A convement compromise figure 1s to assume that (46) <Tw = u,/2 1s the weekly standard deviation for c1 dally aggregate I ntraweekly heteroskedasticity All of the foregomg blow-up factors fall to account for the mtraweekly vanation (heteroskedast1oty) m the estimated standard deviations As noted above, Fnday estimates are weighted more heavily than those of other weekdays m denvmg weekly standard deviations Because of the apparent difference between the standard deviation for Fndays and the over-all standard deviation, it 1s useful to consider the modifications that occur by takmg these differences mto account Instead of Equation 45, the appropnate substitute for the weekly standard deviation 1s (47) (ti <Ti, + 9<Ti5) 112 where J = 1 denotes Monday, J and so forth / = 7 2, Tuesday, From weekly to longer intervals To go from weekly standard deviations to monthly, quarterly, or other standard dt:v148 The Advisory Committee on Monetary Statistics adopted this assumption m Its report, Improving the Monetary Aggregates Report, p 28 20 Improvmg the Monetary Aggregates Staff Papers auons, one must, essentially, count the number of weeks m the ume mterval 49 Consider an "average" month m a 365-day year, which is viewed as havmg 28 cl.i.ys with prob.i.bihty l/12, 30 clays with probability 4/12, and 31 clays with probability 7/12 For tlus aver.i.ge month the transitory variance, CT~" is 2 (48) CT;, ;; [7/28 + + 4(7/30) (54) where CT~ 1s the weekly transitory standard deviation In view of Equ.i.uon 46, the monthly transitory standard deviauon is Um = (½) 35987' 156240 u, = 240 u, Similar expressions exist for 2-month averages (2m), qu.i.iterly averages (q), semiannual .i.ver,tges (sa), and annual averages (a) (SO) U2m uU(7/59) = + 2(7/62) 12 = + 9(7/61)1 1694CT, = = 1385u, = (52) Usa = uM(7 /181) + (7 /183) + (7 /184) + Um V2 Um 0 (7 /182)] 4 0979CT, = (53) Ua = ~= 0692u. == n· 7(7/31)] - 35987 2 - 156240 u,,, (49) an n-day average Notice that In (1 + g;') = In (Y!') - In (Y;'_ 1) = g~' Hence g!,' has approximately the same transitory variance as In (Y:') - In (Yf-i) But the relative transitory variance of is identical to that of In (n') Accordmgly, the variance of g!,' is CTm v6 02 assummg that the averages Y:,i and Y!,'_i are uncorrelated Given the special treatment of weekend observations this result can be expressed for the growth rates of designated averages v"M (55) Ug(m) (56) u g(q) (57) Ug(2ni) = ~ = 2396CT, (58) Ug(sa) = ~ = 1385u, (59) Ug(a) = = = 3394CT, ~ = 1959u, vrz;I = 0979u, where g( ) denotes the gi owth i .i.te ot the ,tver.i.ge withm the p.i.rentheses By convenuon monthly growth rates foi the monet.i.1y aggregates ,Lt the Federal Reserve Board are put .i.t .i.nnual percent.i.ge rates of change by multiplymg the simple monthly growth g(m) by 1,200, for quaiterly giowth rates the corresponding factor is 400, and so forth for other statistics Because the standard devi.i.uons for the transitory components are expressed as a pe1 cent of the level to obtam the standard deviation for the transitory component of an "annualized" growth rate, each of the expressions 55 through 59 should be multiplied by an annuahzmg factor 12 for monthly averages, 4 for quarterly averages, and so forth Growth rates Let g!' = (Y!' - Y!'-i)/Y!'-i be the growth rate at time s for an aggregate Y measured as Interval estimators for the systematic component of an aggregate 4 9 It also matters how many Fridays arc m, say, a month and the configuration of weekends wllhm the month However, these aspects will be ignored m the d1scuss1on that follows as they tend to average out over time Let Za; 2 be the pomt on a standardized (mean= 0, variance= 1) normal distribution such that the probability that a standardized normal random variable exceeds Za; 2 is a/2 https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis Transitory Variations in the Monetary Aggregates Then with confidence coefficient I - a, the interval 12g(m) ± 12Za/20"g(m) is a 100(1 - a) per cent confidence interval for the systematic part of an annualized monthly growth rate 50 If a = 0 05, z1112 = 1 96, the 95 per cent confidence interval is ± 12g(m) ± 12g(m) (60) 12(1 96u 0 cmJ) or 7 983u. in view of Expression 55 To illustrate these calculations let us take the SEW estimate of the daily transitory standard deviation for M 1 of 0 4137 per cent for the 1968-74 period (Table 2) The imphed confidence interval is 12g(m) ± (7 983)( 4137) = 12g(m) ± 3 3 per cent Table IO presents the relevant information for constructmg confidence-mterval estimates for two aggregates (M 1 and M 2 ), three methods (ANOVA, SEW, and SQW), and five confidence coefficients (50, 80, 90, 95, and 99 per cent) These estimates are based on the overall standard errors for each model for the 1968-74 sample period The table shows that if, for example, the measured monthly average growth rate were 8 per cent, the 95 per cent mterval estimate for the systematic growth rate m M 1 would range from 4 7 per cent to 11 3 per cent based on the SEW method The label "2-month-A" refers to growth rates computed by using Equatron 50 while the label "2-month-B" refers to the 2-month growth rates considered m certam short-run pohcy specifications of the aggregates 51 The growth rates for 2-month-B are computed by takmg 6(Ym - Y8 _ 1 )/Y8 _ 1 , wheres denotes the current month when the specrfications are chosen, for example, m September the growth 5o On average, 100(1 - a) per cent of the mtervals computed m this fashion will contam the underlymg systematic growth rate 51 See "Numerical Spec1ficat1ons of Fmanc1al Van ables and Their Role m Monetary Policy," Federal Reserve Bulletin, vol 60 (May 1974), pp 333-37 https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 21 rate for the September-October period is chosen based on the October average relative to the August average Panel B displays comparable mformation usmg the alternative heteroskedastic formula, Equatron 47 The entries m Panel B are generally slightly smaller than those m Panel A User-specified time intervals Consider Y: for various n The larger n rs, the smaller will be the transitory standard deviation of Y: How large must n be so that the (1 - a)IO0 per cent confidence mterval for an n-day growth rate will have a predetermmed length r~ For example, suppose we wish to determme for the ANOVA estimate of M 1 the appropriate n, such that 95 per cent of obse1 ved growth rates will be withm 1 per cent of the systematic growth rates In general, we have (61) 4 112 ) (~) Za/ 2 (3~ )(1n 5 = ; and wish to determine n, given rr., a, and r For the present example, r = 2, z111 ~ = I 96, rr. = 5614, so from Equation 61 ny'n = 365 V14 ( 5~14) 1 96 which yields n = 82 64 For this example, then, g10wth rates based on 83-day averages will have the desired property of bemg w1thm I per cent of the systematic growth rate m 19 out of 20 "tnals" Effects of seasonal ad1ustment on estimates of transitory variations A rather thorny problem m the assessment of transitory vanat10ns, which rs not considered either m the report of the Advisory Committee on Monetary Statistics or thus far m this paper, is the effect on transitory variations of seasonal adjustment of the data The seasonal adJustment process itself may change the extent of transitory vanations (and may change rt differently m prehmmary and m final Improvmg the Monetary Aggregates· Staff Papers 22 TABLE 10• lmphed Variation m Monetary Growth Rates Due to Transitory Fluctuations In percentage potnts Growth-rate Interval and method M1 Monthly ANOVA SEW SQW Quarterly ANOVA SEW SQW 2month-A ANOVA SEW SQW 2month-B ANOVA SEW SQW Semiannual ANOVA SEW SQW Annual ANOVA SEW SQW Confidence coefficient, per cent One standard devtatlon I M, so M1 I M, I I 80 M, I 90 I M, I M, I I l 95 I M, M, I M, I 99 M, I M, A Estimates based on alternative over-all standard deviations 2 29 I 69 I 27 I 15 83 62 44 32 24 22 16 12 30 22 16 81 60 45 41 29 22 I 14 84 I 5 I I 8 8 6 4 15 3 0 2 2 I 6 3 8 2 8 2 I I 9 I 4 I 0 4 S 3 3 2 5 2 3 I 6 I 2 5 9 4 4 3 3 3 0 2 I I 6 28 21 15 7 5 4 4 3 2 9 6 s 4 3 2 I I 8 6 6 4 3 s 7 I 6 I 2 9 8 6 4 2 I I 5 I 2 I 0 8 6 2 2 I I 8 6 3 0 2 2 I 6 I 5 Io 8 I S I I 8 08 II 6 4 3 4 3 27 20 IS I 0 8 6 4 3 I 3 I 0 7 4 58 42 31 8 6 4 38 28 21 I S I I 8 8 6 4 I 9 I 4 I 0 I o 7 6 II 10 08 06 05 04 03 20 15 09 08 06 04 II 10 07 05 26 19 14 II 08 30 22 17 II 08 40 30 22 20 15 II 055 040 030 028 020 01S 04 03 02 02 013 010 07 05 04 04 026 019 09 07 05 046 033 024 II 08 06 054 039 029 14 10 08 07 052 038 64 16 s s 13 I 6 I 2 15 B Est,mates based on heteroskedast,c model of mtraweeklv standard dev,atlons Monthly ANOVA SEW SQW Quarterly ANOVA SEW SQW 2-month-A ANOVA SEW SQW 2-month-B ANOVA SEW SQW Semiannual ANOVA SEW SQW Annual ANOVA SEW SQW 2 I I 5 I 3 I 0 8 6 I 4 I 0 8 7 s 4 2 6 2 0 I 6 I 3 I 0 8 3 4 2 S 2 I I 7 I 3 I 0 40 29 24 20 15 12 27 20 16 14 10 08 SI 38 31 26 19 16 6S 48 40 33 24 20 73 54 45 37 27 22 49 36 30 2S 18 IS 93 69 57 47 35 29 I 2 89 74 61 45 37 5 70 50 40 35 25 20 6S 50 40 I 7 I 2 I 0 85 6S 50 I 0 75 6S 4 3 I 3 I 0 8 4 0 3 0 2 5 2 0 I 5 I 2 5 3 4 0 3 3 2 7 2 0 I 6 40 29 24 I 0 76 63 52 38 31 I 4 I I 9 73 53 44 I 9 I 4 I 2 96 70 58 2 0 I 5 I 2 I 0 15 60 2 6 2 0 I 6 78 58 48 I 4 I 0 8 14 10 08 07 05 04 09 07 06 05 04 03 18 13 11 09 07 06 23 17 14 12 08 07 27 20 17 14 10 08 36 27 22 18 13 II 07 05 03 036 026 022 05 035 020 024 018 014 09 07 04 046 033 028 12 08 OS 06 04 04 14 10 06 07 OS 04 18 13 08 09 07 06 Non - Entries define the range, plus or mmus, around the systematic growth rate withm which the specified percentage (SO, 80, 90, 95, or 99) of observed growth rates will (on average) fall data) Seasonal adjustment rs basically an ave1agmg or smoothmg process, and smce necessarily both the transitory and the systematic components of the senes are smoothed, It rs generally true that seasonally adjusted data on the monetary aggregates exhibit fewer transitory vanations than do not seasonally adJusted data The magmtude of tlus effect depends heavily on the seasonal adjustment procedure employed In general, seasonal factors that are https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis relatively "fixed" are determmed from a relatively large amount of data, and the cur1ent observation carnes relatively less weight, thus, the variance (whether trans1to1 y, nontransrtory, or total) is reduced correspondmgly less by the adjustment process By contrast, seasonal adjustment procedures such as X-11 allow for a rapidly changmg seasonal that must be estimated from a smaller amount of data Thus, greater weight is given to the clllrent observat10n and mo1e of the variance Transitory Vanations in the Monetary Aggregates (mcludmg transitory variance) 1s removed from this observ<1t10n as a result of seasonal adjustment 52 To illustrate, cons1de1 a "fixed" seasondl est1m<1ted h om a movmg m-ye<1r regression on sedsonal dumnues If y 11 1s the observat10n from month J and yea1 t (assumed for s1mphc1ty to have a tero mean), the estimated seasonal component for month J is Y1 = 1 m - ,n ~Yt1 t=I and the seasonally adjusted v<1lue 1s m - 1 = -m--Y11 1 m ~ y,. ,,.,1 with t1<1ns1tory vauance (dssummg 5tausucal mdependence) (m - 1) 2 +m- m2 1 o-;= ( 1-1) m o-; where a~ zs the transitory variance of not seasonally ,tdJusted y Thus, 1f m = (<1llowmg tor a more rapidly chdngmg sedsondl), tr<1ns1to1 y Vdri<1ncc 1s 1educed through se<1son<1l <1d1ustment by 33 per cent, 11 m = !J, season,11 ad1ustment lowers the variance by 11 per cent The effect of the X-11 procedure on t1,ms1tory variance would be expected to fall between these two, as 1t 1s based on a 7-year dverage (though a weighted average, weightmg most heavily the current observauon), thus the ti ans1tory standard deviation 1s reduced by probably somethmg hke IO per cent 53 The fmegomg d1scuss10n concerm the effects of final seasonal factors applied to final datd 52 An opposite effect should also be nottd The pie, cnce of transitory error can increase the error 111 the t.sUmated sedsonal factors, tending to produce a 'no1s1er' scdsonally adjusted senes When the sea~onal pattern 1s relauvely fixed, this effect can offset much of the smoothing effect discussed here 5 J The daily procedure developed by Pierce and others m "Seasonal Adjustment of the Monetary Ag gregates," this volume, and recommended by the Adv1s ory Committee m Improving the Monetary Aggregates Report, however, would have very little effect on transitory variance because a given daily observat10n contributes almost nothmg to its own seasonal component https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 23 A separate effect stems from the 1ev1s10n of prehmmary seasonal factors ,ts ,tclcht10n<1l datd become available The first-published sedsonally adjusted 5eries 1s subject to two somces of 1ev1s10n e1101-th,1t discussed ed1he1 £01 not season,1lly adjusted datd <1ncl, ,1dd1t1on<1lly, th.tt due to 1ev1s10ns m 5e,1son,tl f.tcto1s Howe\-e1, even the fit st pubhshe<l 5e,tson.1lly <1dJ Usted d.tta will gene1,1lly h,t\-e sm.1llc1 t1<1ns1t01 y variance (,ts d15tmct horn the v.1u<1nce of these 1ev1s10n e1101s) than the fost published not 5eason<1lly ,tdJmted datd, ,15 the ,t\-eiagmg cffec.t chscussed ,tbove for fin,tl d,tt.t 1s p1esent wheneve1 ~e<1so1ul ,1d1ustment 15 unclertaken It will be a1gued m the followmg 5ect10n that the data rev1s1om that occm m not season,1lly ,tdJnsted d,1t,1 c,m 1e,150n,1bly be assumed to be st.1t1st1c<1lly mdependent of the tr<1ns1tory v,mauons Th15 mdependence assumption 1s equdlly vahd for the seasonal factm rev1s10ns 1f the 1ev1s10n method (conllasted with the adjusted data p1ocluced by the method) 1s determmed mdependently of the data bemg 1ev1sed-lor ex.tmple, a fixed f.tcto1 01 1egiess10n method or X-11 with unch,mgmg movmg ,1ve1 .tge weights Tlus assmnpuon could break down m situations whe1e, fo1 ex.tmple, d sequence of J,11ge t1dns1tory 01 not seasonally ,telJusted 1ev1s10n errm s produced seasonal-1rregul<1r 1.1t1os that would c<1use a chfferent ll end-cycle cm ve to be selected, or altern,1t1vely, whe1e Judgmental review 1s a part of the 1-e.1sonal adjustment procedure 54 Summary and conclus1ons We have ex<1mmecl four st<1t1st1cal models to isolate the part of the Vdriauons m M 1 and M 2 and their components that anse from very short-run transitory fluctuations On the basis of these results, lt appea1s that the standard deviation of the transitory component of daily not seasonally adJmted M 1 1s m the neighbor54 "Seasonal irregular rauos" are defined as the rauo of the not seasonally ad1usted series to the trend cycle component, which for the multrpltcatrve seasonal ad1ustment procedures, 1s equal to the product of the seasonal and trregular components Improvmg the Monetary Aggregates Staff Papers 24 hood of ½ of I per cent, for M 2 1t 1s about ¼ of a per cent The SEW and SQW models produced somewhat lower estimates, while the ANOVA estimates weie slightly higher 55 For annualized monthly rates of growth, the ½ of a per cent figure for M 1 1mphes that the 95 per cent confidence-mtei val estimate of the growth rate of the systematic component of M 1 1s equal to the measured growth rate plus or mmus 4 percentage pomts, wlule for Mi 1t 1s equal to the measured growth rate plus or mmus 2 peicentage pomts 56 Thus, on the average, about 95 per cent of all measured monthly growth iates of M 1 will he withm 4 percentdge pomts of the systematic component of M 1 , and about 5 per cent of all obse1 ved monthly growth rdtes of M 1 will deviate by more than 4 percentdge pomts from the systematic component of Mi, due to day-to-ddy transitory fluctuat10ns F01 quarterly 1ates of growth, the 95 per cent confidence mterval mcludes the measured growth rate plus or mmus ¾ of a percentdge pomt for M 1 and plus or mums 1/s of a percentage pomt for Mi Confidence-mterval estimates for other agg1egates or estimates can readily be determmed from Equat10ns 43 through 59 As md1cated m the precedmg section, the magmtude of the t1ans1tory vanat1ons m seasonally adjusted data depends on the method of seasonal ddjustment The daily procedure of 5easonal adjustment recommended by the Advisory Committee would leave essentially the same transitory effects m seasonally adjusted senes that existed m the not sedsondlly adjusted senes However, the effect of the X-11 seasonal adjustment proceclme would be to reduce the standard deviation of the transitory component by about IO per cent for seasonally adjusted data In all hkehhood, there are several sources of these transitory vanatlons, but we have not tned to explam the transitory vanat1ons 55 These estimates are based on the 1968-74 sample period and are hsted m Table I 56 For example, for M 1 the 4 per cent figure 1s ob tamed by substituting ½ for u, mto Equation 55 and then multlplymg by a factor of 12 to annualize and a factor of I 96 to make a 95 per cent confidence interval 3394 X ½ X 12 X I 96 3 99 https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis = m terms of an exphc1t economic model We did, however, work out an emp1ncal decompos1uon of the variation m Mv M 2 , and gross deposits less cash items For M 1 and M 2, the hon's share of the observed transitory vandt10n stems from transitory vanat1ons m the demand deposit component of M 1 There dre also some signs that vanat10ns m passbook savmgs accounts will account for more of the transitory vanat10ns m M 2 as these deposits become close1 substitutes for demand deposits Joint effects of data revisions and transitory variations in not seasonally ad1usted data This paper llds dealt ldl gel y with trans1 t01 y vanauons m the not sedsonally adjusted monetary aggiegates that are m final (revised) f01m For purposes of current andlys1s, there are add1t10nal sources of vanat10n owmg to rev1s10ns m the data fiom the time they dre first published to their appearance m final f01m We exdmme here the rev1S1on m ~easondlly unadjusted cldta, havmg cons1de1ed the effects of sedsonal ddjustment, mcludmg rev1s1ons m seasonal factors, m the precedmg section The "first-pubhshed" estimdte of the aggregates for each month 1s released about IO cidys after the end of the month More complete mcommg weekly data from member banks will often modify this first-published number durmg the next month Add1t1onal 1ev1s10ns are made periodically when call report data for nonmember banks become available Irregular rev1S1ons aie made either when 1eportmg errors are uncovered or when a review of the construction of the money stock leads to specific repairs m the senes-for example, the 1976 rev1s1on m the adjustment for cash-items bias 57 Given the nature of these rev1s10ns, It 1s plausible that the difference between the first-published not seasonally adjusted series and the final revised not seasonally adjusted senes 1s stat1st1cally mdependent of 57 See Edward R Fry, Darwm L Beck, and Mary F Weaver, "Rev1s10n of Money Stock Measures," Federal Reserve Bulletin, vol 62 (February 1976), pp 82-87 Transitory Variations in the Monetary Aggregates TABLE 11 Re,.Sion Errors m Monetary Aggregates, Jfot Seasonally AdJusted In annual percentage rates of growth Monthly Quarterly Aggregate Standard Mean / error RMSE error 5':~~'J 3 07 3 10 53 71 71 deposits Mi 2 98 2 26 85 3 03 2 33 86 63 60 21 1 19 91 42 l 66 1 25 51 M, / / / ~~~ rd S~~r: RMSE - 16 1 18 87 40 NoTE -Error equals difference between annual percentage rate of growth of first-published estimate and final revised estimate (as of December 1977) for 1968-74 penod RMSE denotes root mean square error the transitory vanat10ns If this 1s so, we can combme the two parts-the vanations caused by data rev1S1ons (other than seasonal-factor re'vlSlons) and the transitory vanat1ons m the revised senes-to obtam an over-all estimate of the noise m the current (first-pubhshed not seasonally adjusted) senes The mean error, standard deviation, and root mean square error of the rev1s10n errms for M 1 , M 2, and their components are shown m Table 11 58 Table 12 combmes the vanat1ons resultmg from the rev1S1on errors 1eported m Table 11 with the vanations resultmg from movements m the transitory component to give an estimate of the over-all nmse m the first-pubhshed senes For example, for monthly rates of growth of M 1 the over-all standard deviation of about 3 pe1 cent 1s determmed from the equation 3 04 = y2 26 2 + 2 03 2 , based on a rev1s10n standard error of 2 26 per cent and a transitory standard error of 2 03 per cent 59 The 1mphed 95 per cent confidence58 These eslimates are comparable to those m Im proving the Monetary Agg1egates Report, table 4, for seasonally adJusted data 59203 = 12 X ½ X 3344 TABLE 12. Over-All Estimate of Error m Rate of Growth Due to Both Rev1s1on and Transitory Errors Standard deY1at1ons of annual percentage rates of growth, m percentage pomts Aggregate Currency Demand deposits Mt M, https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis Monthly growth rate 3 3 3 1 36 60 04 33 Quarterly growth rate 1 06 1 25 99 46 25 mterval estimate of the systematic component for first-pubhshed monthly growth rates of M 1 would, thus, be dehmited by ±5 96 percentage pomts, the correspondmg figure for monthly rates of growth of M 2 1s 2 60 percentage pomts The comparable figures for the quarterly rates of growth are considerably reduced, the 95 per cent quarterly confidence mterval covers ± I 94 percentage pomts for M 1 and ±0 90 percentage pomt for M 2 Concluding observations Undoubtedly, users of monetary statistics should be aware of the transitory vanations m the senes, and the estimates thdt we have presented h1ghhght the range of magmtudes mvolved However, these estimates represent first eff01 ts, and there are several possible refinements I Day-of-week effects There 1s some evidence that the day-of-week effects are not mvanant over time In particular, the Fnday day-of-week effect for demand deposits generally fell over the sample penod And, when the Fnclay residuals from the ANOVA method were regressed on a short-term mterest rate (the Federal funds rate or commerodl paper rate), the regress10n coefficient was negative and s1gmficant A similar regression for the residuals from other clays md1cated no relat1onsh1p with mterest rates It 1s possible that when mterest rates are nsmg, the use of bankmanaged demand accounts mcreases, and the process has its largest daily impact on Fndays because Fnday deposit figures essentially count for 3 days m computmg reqmred reserves 60 The results were less clear-cut for the residuals horn other methods, but it would be useful to examme this phenomenon m more depth 2 Periodically correlated processes It has been observed that the transitory vanab1hty 1s not constant across days of the week Yet, for the most part, the detrended data have 60 See Stephen M Goldfeld, "The Case of the M1ssmg Money," Brookings Papers on Economic Activity, 3 1976, pp 683-730, and Raymond E Lomb1a and Herbe1t M Kaufman, "Commercial Banks and the Federal Funds Market Recent Development and Imphcatiom,' Eco nomic Inquiry, vol 16 (October 1978), pp 549-62 26 been modeled as stationary series A mo1e appropriate techmque may be to assume that the data are periodically correlated rather than stationary 61 3 Width of the detrending interval For the ANOVA, SEW, and SQW models 1t 1s apparent that we have not selected the appropriate smoothmg mterval to determme the trend The residuals from each of these models were correlated at several lags, mcludmg fairly long ones If the true trend at time t 1s a function not only of the observations m the "week" mcludmg t but also of more distant observations, such as those a year apart from t, 1t 1s not surprismg that a m1sspec1ficat1on 1s mtroduced m the ANOVA, SEW, and SQW models that produces the large autocorrelat10ns at annual lags, among others The results from the exphnt ume-series modelmg exercises md1cate that the appropriate smoothmg span to determme the trend 1s much longermore on the order of five quarters rather than a week Thus, fixed-weight detrendmg methods with a much wider smoothmg mtervaland with weights that largely follow an mverted V pattern-could be exammed 4 Correlated transitory components The transitory variations have been defined to be mdependent from day to day However, It r,1 See, for example, Wilham P Cleveland, "Analysis and Forecasting of Seasonal Time Senes" (PhD chsser tatlon, University of Wisconsin, 1972), Harry L Hurd, "Survey on Periodically Correlated Proces5es" (paper presented at the Multiple Time Senes and System Identification Confe1ence, Umve1s1ty of North Carolina at Chapel Hill, January 2-6, 1973), Richard D Porter and Paul N Rappaport, "Forecastmg Net Ba5in Sup plies on the G1eat Lakes" (paper presented at the TIMS Conferrnce, Houston, Texas, Apnl 1972), and Howard E Thomp5on and George C Tiao, "Analym of Telephone Data A Case Study of Forecasting Sea sonal Time Senes," Bell Journal of Economics and Management Science, vol 2 (Autumn 1971), pp 515-41 https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis Improving the Monetary Aggregates Staff Papers \ may not be desirable to 1mpose0trict serial mdependence for the first two or three lags A "bhp" m the daily data, which tak}l_a few days to d1ss1pate, might with JUst1ficat1on~t1II be regarded as "transitory " Hence, an exphc1t times series model, m which there 1s a low-order\ movmg average process for the transitory com- , ponent combmed with a mixed (ARMA) model \ \ for the trend component, may be a useful model to consider 62 5 Estimated data sources The daily series on the monetary aggregates are based m part on daily data reported by various financial mst1tut1ons and m part on estnnates of components that are not reported dally 63 For example, m December 1974 the estimated port10n of the daily series was nearly a third of the total for the demand deposit component ot M 1 Acrnrdmgly, changes m the reportmg frequency of data that are not available daily may hctve an impact on est1mcttes of transitory va11at10ns m the aggregates The sIZe of the impact would depend on the transitory variat10m of those data aml their wrrelat1on with data that are now available daily 64 Also, there <1.1e <1.lternat1ve ways of estlmatmg or mte1polatmg data that are 5ampled only l day per week or more mfrequently, and m further work It would be useful to examme the effects that alternative mterpolat10n procedures have on estimates of transitory variations 62 In general, the 1denuficauon of such models 1s more difficult than that of models in nh1ch the tlan s1tory component is independent See the references in footnote 20 1,1 for ,1 breakdown of M I data 5ources and then 1epo1 tmg frequencies, sec Improvmg the Mone/my Aggregates Report, table 3 G4 The new sample of nonmember bank data that 11as started in July 1977 may have a 51gmficant impact on c5Umatc.s of transitory vanatlom in the aggregate5 \ 27 Appendix 1: The Relationship between Et and the Relative Transitory Error Let so that (A-1) /1 = /31 + (A-6) 7/1 be the systematic part m logarithms) of Equat10n I (page 3) and (A-2) F1 = exp (/1) be the systematic part of the model m levels The 1mphed transitory error m dollars 1s E, = Ye - Fe (A-3) where (A-4) E Y, = Et upon droppmg second- and higher order terms m the Taylor-senes expansion of exp(-Ei) Table A-1 shows that the accuracy of the approximation m Equauon A 6 for values of Et less than or equal to 0 01 1s very good For example, for a 1 per cent value of Et, Et= 01, the approx1mauon mtroduces a discrepancy of only $15 mdhon when 1t 1s app1ed to a monetary aggregate of $300 bdhon TABLE A-1 Discrepancy between •1 and Ei/Y, Y1 = exp (y,) = exp (/, + Ee) . (1) 1s the level of the aggregate (m dollars) Also, m view of Equations A-4 and A-2 Y, (A-5) = F, exp (E1) The relative transitory error, E 1/Yt, 1s Ee= F1 exp (E1) - F1 Yt F, exp (E1) https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis = 1 _ exp (-E,) 001 002 003 004 005 006 007 008 009 010 Et/Yt D1screpancyt (2) 000999 001998 002995 003992 004987 005982 006976 007968 008960 009950 (3) I 45 X 10• 5 0 X 105 I 35 X 10• 240X10• 3 74 X 10• 539XIO• 7 33 X 106 9 37 X 10• I 21 X 107 1 50 X 10' t Column 1 mmus column 2 muluphed by $300 b1lhon 28 Appendix 2: Empirical Specification and Diagnosis of OSD Model -y.,(12) Model specification1 Consider first the plot of the autocorrelation function (ACF) for Zt, given m Chart I The first IO autocorrelations (AC) decrease exponentially followmg the pattern of an AR(l) model with ap proximately Ip = 0 85 (the m1t1al estimate of rp) Let p1 and r1 be the population and sample 7thlag autocorrelation Assummg that Zt follows an AR(l) process, the variance of r1 is approximated by 2 2 (A-6) v(r,) = __!_ [(l + 'P ) (l - 'P ') - 2J'P2,J N 1 - cp 2 = For J 13, the confidence reg10n for the sample esumate is given by (0 85) 13 ± 2[v(ri 3 )]1l 2 0 1209 ± 0 39 The sample estimate r 13 -0 35 falls outside this region, and the same is true for r 12 and r 14 Furthermore, the ACF displays high peaks at lags 39, 52, and 65 In particular, the large lag approximation = = with all other autocovariances equal to zero For J > 66, the variance of the estimated r1 1s approximately given by the express10n (A-8) p14 Pas 1mphes that, after lag 67, all r1 can be assumed to be approximately zero Now, consider the model consistmg of Equations 24 to 26 In terms of the observable variable, z1, It can be rewritten as = E~ + p39 P4o Po1 Po2 Poa Pe4 PB& Pse (1 - cpB) (1 - B 13) (1 - B•2)E 1 wluch mdicates that the variable x1 = (1 - cpB)z1 follows a movmg-average process Chart 2 repro duces the time series [x 1] for rp 85 The theo retlcal ACF for x 1 is given by = -y.,(0) -y.,(1) -y.,(13) = 4(1 + cp 2)u; + u:, = -4cpu;, = -y.,(52) = -2(1 + cp 2)u; = -2-y.,(39) = -2-y.,(65) 1 We shall use the followmg notat10n m this appendix for a variable x, {x,} will denote a stochastic process, [x,] will denote a time series reahzauon of the process, and x1 will denote the value of the variable at time t, AR(J) Will denote an autoregressive model of order /, MA(J) will de note a movmg average model of order 1 https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis - 18 085 - 18 085 - 042 085 - 042 085 - 18 085 - 042 085 - 042 Pl P12 Pia 2 (1 - cpB)z 1 v(r,) = ~{1 + 2~ p:} Chart 3 contams a plot of the ACF of Xt The dotted Imes represent the value ±2[v(r1)]1l 2 for J > 66 It is seen that all PJ for J > 66 can be assumed to be O Furthermore, comparing the theoretical (nonzero) autocorrelauons, co11espondmg to the mit1al values of the estimates with the sample autocorrelations, we have 2 cp ) hm v(r,) = - 1 (1-+ -J--+ 00 N 1 - cp 2 (A-7) = -y.,(14) = -y.,(51) = -y.,(53) = 2cpu: = -2-y.,(38) = -2-y.,(40) = -2-y.,(64) = -2-y.,(66) r1 r12 r1a r14 ras T39 r40 ro1 r52 roa T04 rs. ree = = = = = = = = = = = = = - 19 03 - 28 08 - 06 08 - 04 - 06 - 21 04 - 04 09 - 01 The two sequences present a fairly similar pattern We conclude that, as a first approximation, -c 1 can be assumed to follow the MA process Xt = E~ + (1 - cpB) (1 - B13) (1 - B62)E1 with rp, u!, and u, bemg approximately given by the mmal estimates Recalling that x 1 (I - rpB)zt, Equations 24 to 26 are JUStlfied as a first approximation to the process generatmg [z1] = 2 The m1t1al values-~= 85, a:, = ( 4)10-•, a; = ( 3)10_,,_ are derived m Agustm Maravall, "Est1mat10n of the Permanent and Transitory Component of an Economic Variable with an Apphcat1on to M1 " Special Studies Paper 85, Board of Gov ernors of the Federal Reserve System, 1976 Transitory Variations in the Monetary Aggregates Model diagnosis Chart 6 displays a plot of the partial ACF for Only the values correspondmg to lags 2 and 14 fall outside the approximate 95 per cent confidence region, given by ±2yN Thus, the estimated senes [tt] seems to be reasonably close to the theoretical model given by Equauon A-4 Fmally, Equation A-5 imphes that the theoretical ACF for et is given by A Once the model has been specified and the final esumauon has been perfon:ned, diagnosuc checks should be applied to the fitted model The Box Pierce test cannot be applied to our calculated residuals [et], and the fact that the esumator 81 does not converge m probability to the true /l 1 makes 1t difficult to denve appropriate tests Yet, a diagnosuc check can be earned out m the followmg way If our model is correct, the process {ll 1} is an AR(l) process, given by (A-9) lli Pia p39 Ct = Et - Et-13 - Et-62 + Et-66 We shall use the esumated senes [8 1] and [et] to check whether both assumptions seem reason able Chart 4 plots the ,tutocorrelauons of 81 Under the assumption that 81 follows the AR(!) process gnen m Equation A 4, express10ns A-1 and A-2 yie~d the variances of the sample autocorrelat10ns of 81 Base~ on these variances, the implied correlogram of [llt] seems to be m agreement with our model Chart 'i compares the autocorrelauons of the two senes [z 1] and [8 1] Although the two plots follow the same general pattern, the autocorrela t10ns for [z1] have bigger oscillations The pattern of the autocorrelations for (8 1] seems to follow an i\R(l) model more closely than those for [z,] The lugher order effects present m the ACF of (8 1] may ,tnse because we are dealmg with sample auto correlat10ns of an estimated time senes 1 -5 25 Pa2 P66 = - 5 = 25 and all other lagged correlauons equal zero Usmg the estimated senes [et], we obtam the values and the process [et] is an MA process given by (A-10) 29 713 - 55 752 739 27 766 = - 38 = 21 which are m close agreement with the theoretical dUtocorrelations Also, by usmg Equauon A-8, all correlauon for lags greater than 66 can be assumed to be zero Chart 7 presents a plot of the auto correlations for the senes [et] Agam, the estimated 5enes are m reasonable accordance with the theo retical model given by Equat10n A-8, and we con elude that our fitted model offer5 an acceptable ,tpprox1mat1on to the stochasuc process that gen crates the time senes [z,] 1 Recall that the covariance between t"o sample correla lions given approximately by 1 cov(rk,rk+,) = N .~.,P•P•+• can distort the plot of the ACF, \\h1ch may fat! to damp out 1ccordmg to expeclatlons see George E P Box and Gw1lyn l\l Jenkms 7 1111e ~enes A11al) us Forecasting n11(/ Control (Holden Day, 1970), p 35 CHART I Sample Autocorrelation Function for [ztl 8 4 0 -4 20 https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 40 60 80 100 120 140 Improvmg the Monetary Aggregates Staff Papers 30 CHART 2 Time Series Plot of [xtl 20 0 -20 20 40 60 80 100 120 140 CHART 3 Sample Autocorrelation Function of Xt 8 4 0 -4 100 140 CHART 4 Autocorrelation Function for [ot] https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 8 4 0 -4 Transitory Variations tn the Monetary Aggregates 31 CHART 5 Autocorrelation Function for [zt] and ['ot] 8 4 0 ACF for [ot] -4 20 40 60 80 100 120 140 CHART 6 Partial Autocorrelation Function for [ot] 8 4 0 -4 20 40 60 80 100 120 140 CHART 7 Autocorrelation Function for [e 1] 8 4 0 -4 20 https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 40 60 80 100 120 140 32 Improvmg the Monetary Aggregates Staff Papers Bibliography Anderson, Theodore W The Statistical Analym of Time Series New York Wiley, 1971 Bartlett, Maunce S An Introduction to Stochastic Processes 2nd ed Cam• bndge, England Cambndge Umvermy Press, 1966 Board of Governors of the Federal Reserve System Improving the Mon etary Aggregates Report of the Advisory Committee on Monetary Sta• tistics Waslungton Board of Governors, 1976 Box, George E P , Stephen Hilmer, and George C Tiao "Analysis and Modelmg of Seasonal Time Senes" Paper presented at the National Bureau of Economic Research-Census Conference on Seasonal Analysis of Economic Time Senes, Washmgton DC, September 9-10, 1976 - - - , and Gw1lyn M Jenkms Time Series Analysis Forecasting and Con trol San Francisco Holden-Day, 1970 Brewer, Kenneth R W "Some Consequences of Temporal Aggregation and Systematic Sampling for ARMA and ARMAX Models" Journal of Econometrics, vol 1 (June 1973), pp 133-54 C..leveland, Wilham P "Analysis and Forecastmg of Seasonal Time Senes" PhD dissertation, Umvers1ty of W1sconsm, 1972 Fry, Edward R, Darwm L Beck, and Mary F Weaver "Revmon of Money Stock Measures" Federal Reserve Bulletin, vol 62 (February 1976), pp 82-87 Fuller, Wayne A Introduction to Stationary T11ne Series New York Wiley, 1976 Goldfeld, Stephen M "The Case of the M1ssmg Money " Brookingl Papers on Economic Activity, 3 1976, pp 683-730 Gramley, Lyle E "Deposit Instab1hty at Ind1v1dual Banks," m Essays on Commercial Banking Federal Reserve Bank of Kansas City, 1962 Hurd, Harry L "Survey on Penod1cally Correlated Processes " Paper pre sented at the Muluple Time Senes and System Idenuficauon Conference, Umvers1ty of North Carolma at Chapel Hill, January 2-6, 1973 Jones, Richard H, and Wilham M Brelsford "Time Senes with Penod1c Structure" Biometrika, vol 54 (December 1967), pp 403-08 Lombra, Raymond E , and Herbert M Kaufman "Commercial Banks ,tn the Federal Funds Market Recent Development and Imphcauons Economic Inquiry, vol 16 (October 1978), pp 549-62 Maravall, Agustm "Esumauon ot the Permanent and Transitory Com• ponent of an Economic Vanable with an Apphcauon to M 1 " Special Studies Paper 85 Washmgton Board of Governo1s of the Federal Reserve System, 1976 - - - Identification in the Shock-Error Model New York Sprmger• Verlag, forthcommg "Numencal Specifications of Fmancial Vanables and Their Role m Mon• etary Policy" Federal Reserve Bulletin, vol 60 (May 1974), pp 333-37 https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis Transitory Variations in the Monetary Aggregates Pagano, Marcello "Estimation of Models of Autoregressive Signal Plus White Noise" Annals of Statistics, vol 2 (January 1974), pp 99-108 Paulus, John D, and Stephen H Axllrod "Regulatory Changes and Fmancial Innovations Affectmg the Growth of the Monetary Aggregates " Staff memorandum Washmgton Board of Governors of the Federal Reserve System, November 1976 Pierce, David A "Seasonal Adjustment When Both Determmisuc and Stochastic Seasonality Are Present" Paper present,ed at the National Bureau of Economic Research-Census Conference on Seasonal Analysis of Economic Time Senes, Washmgton, D C, September 9-10, 1976 Subsequently published as Speoal Studies Paper 107 Washmgton Board of Governors of the Federal Reserve System, 1977 Porter, Richard D , and Paul N Rappaport "Forecastmg Net Basm Supplies on the Great Lakes " Paper presented at the TIMS Conference, Houston, Texas, Apnl 1972 Rangarapn, C "Deposit Variability m Individual Banks" National Banking Review, vol 4 (September 1966), pp 61-71 Struble, Frederick M , and Carroll H WIikerson "Bank Sile and Deposit Variability" Monthly Review Federal Reserve Bank of Kansas City, November-December 1967, pp 3-9 - - - "Deposit Vanabihty at Commercial Banks" Monthly Review Federal Reserve Bank of Kansas City, July-August 1967, pp 27-34 Thompson, Howard E , and George C Tiao "Analysis of Telephone Data A Case Study of Forecastmg Seasonal Time Senes" Bell Journal of Economics and Management Science, vol 2 (Autumn 1971), pp 515-41 Whittle, Peter Prediction and Regulation by Linear Least Square Methods London English Umversities Press Ltd, 1963 https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 33 https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 35 Foreign Demand Deposits at Commercial Banks in the United States Helen T Farr, Lance Girton, Henry S Terrell, and Thomas H Turner This paper was completed in early 1976 Foreign depositors held about $13 brlhon m demand deposits at commercial b,mks m the Umted States at the end of 1975 Demand deposits that are held by foreign banks, nonbanks (m<lividuals, partnerslups, ,md corpm auons-IPC's), and official mstituuons are currently mcluded m tabulat10ns of the narrowly defined money supply (M 1 ) of the Umted States As of December 1975, foreign-owned demand deposits accounted for about 4 per cent of M 1 In this papei we discuss the genera] characteristics of these deposits dnd attempt to 1dent1fy empirically the factors th.1t <letermme the <lemdnd for them We also attempt to determme whether these deposits are closely related to U S macroeconomic variables and whether the relationship, if 1t exists, 1s suffinently similar to that of the other components of U S monetary aggregates so that foreign deposits should contmue to be mcluded m these aggregates The evidence p1esented, although not conclusive, md1cates that foreign demand deposlts at U S banks m general, and demand deposlts of foreign commercial banks dnd official mstitut10ns m particular, are not 1 elated to US activity variables m the same manner dS are other components of the nar1 owly defined money supply Charactenst1cs of foreign demand deposits at U S commercial banks The followmg sect10ns discuss m detail the charactensucs of the various kmds of foreign NoTE -Helen T Farr 1s on the ~t,1ff of the D1vmon of Research and Stat1st1cs, Lance Girton and Henry S Terrell are on the staff of the D1v1s10n of Internat10nal l mance, and Thomas H Turner was formerly on that staff https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis demand deposits held at US commercial banks those of foreign commercial banks, of foreign md1v1duals, p.1rtnersh1ps, and corporat10ns, and of foreign official msututrons Deposits of foreign commercial banks at U.S. banks Demand baldnces of lorergn commercial banks at U S banks are the largest and most volatile of foreign deposits, havmg grown from $3 4 brlhon m December 1971 to $7 5 b1lhon m Decembet 1975 1 At times, fluctuations m foreign bank demand deposits at U S commercial banks have had an apprenable impact on the growth of the narrowly defined money supply 2 The largest US banks currently mdmtam between 1,500 and 6,000 demand accounts for foreign commernal banks Of tlus total, 100 to 200 are usually characterued as active accounts belongmg to the largest foreign banks thdt are heavily mvolvecl m mternauonal finance The remammg, ~mailer, accounts tend to be relatively mactrve Most maJor foreign banks mamtam demand balances at several US money center banks The accounts of ma1or foreign banks dre extremely active Daily turnover m an account can be several hundred times the average endof-day balance A smgle transact10n through one of these accounts rs often several times as large as the average end-of-day balance, tins rs particularly true of Euro-dollar transact10ns, 1 Information m this section has been enhanced b} chscuss10ns with representative~ of US ,111d foreign tommercial banks 2 These deposits do not mcludc balances o\\ed hy US banks to the11 foreign branches or thosl. oned by U S agencies and branches of foreign banks to their head offices 36 lmprovmg the Monetary Aggregates Staff Papers m which often neither the dehvermg nor the receivmg bank is a US bank 3 Foreign banks use their accounts with domestic offices of U S banks to deliver and accept payment on their Euro-dollar transactions because US banks reqmre that the large credit Judgments associated with these transactions be made at their head offices • A related reason for clearmg dollar transactions m the Umted States is the prox1nnty of the Federal funds market, m which market participants can acqmre and place large sums of dollars on short notice The second-largest type of transaction m these accounts results from the settlement of foreign exchange contracts, an unknown portion of which is directly related to the financmg of exports or imports of the Umted States Some foreign exchange transactions reflect third-country trade and the special role of the dollar as a settlement currency m mternational t1 ade Also, a proportion of the transactions 1eflects the attempts of foreign banks to achieve a desired position m foreign exchange markets, either for their own account or for their customers Aside from the general purpose of clearmg Euro-dollar and foreign exchange transactions, Japanese banks, which are usually large net borrowers of funds from banks m the Umted States, utilize their demand balances at U S pattern of behavior appears to be limited to Japanese banks 5 As a general rule, a U S bank would not extend credit to a foreign bank that did not mamtam a demand balance at the U S bank An understandmg ot the mstitutional background is important m developmg a model to explam the behavior of foreign demand deposits over time and to compare this behavior with that of other components of the money supply From discussions with market participants, it appears that demand for such deposits by foreign banks is positively related to their needs for transactions balances m the Umted States and negatively 1elated to then costs of obtammg such funds m the market F01 US banks, the costs of supplymg these funds mclude the cost of servicmg transactions through the accounts Servicmg costs mclude the cost of U S banks' servmg as standby lenders m case a foreign bank's demand balance is m deficit durmg the day or after the close of busmess An important way that the U S banks are compensated is through the value of the mterest-free funds mamtamed on deposit by the foreign banks The value of these deposits to the US banks is determmed by an mternal mterest rate that reflects the cost savmgs from obtammg mterest-free demand balances compared with the costs of obtammg funds m the banks for an add1t10nal purpose To obtam market funds, Japanese banks have established numerous unsecured Imes of credit with U S banks and often agree to mamtam compensatmg demand balances of about 10 per cent of the Imes of credit The compensatmg balances play the role of commitment fees When the Imes of credit are drawn down, the Japanese banks often are reqmred to mamtam compensatmg balances of the same magnitude as those reqmred of domestic nonbank borrowers This a An account with an average end of-day balance of $1 mdhon may have transactions totahng several hundred million dollars on any busmess day • For example, durmg the course of a busmess day the payment orders from an account may exceed the funds received m that account and the U S banks must decide whether or not to honor the orders, thus extendmg credit (sometimes m large amounts) to the foreign commercial bank These mtrabusmess-day extensions of credit are often termed "daylight" overdrafts https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 6 Deposits of foreign individuals, partnerships, and corporations The second-largest category of foreigners holdmg demand balances at U S banks are 5 Canadian banks, which have important US operations, do not mamtam large demand balances at U S banks However, they do not borrow large amounts from U S banks because most of their Euro dollar and foreign exchange transactions are cleared through their New York agencies s US banks often mamtam complex relallonships with foreign commercial banks of which the demand deposit relationship is only one part Vanous mteracuons mclude, among other thmgs, parllcipation m iomt ventures, correspondent relationships, mtroductions to clients, and the provision of various mforma tion and trammg services In some cases, a U S bank might reduce its demand balance reqmrements to a foreign bank as a "loss leader" to develop a more profitable relationship m other busmess areas Foreign Demand Deposits at Commercial Banks in the United States foreign !PC's At the end of 1975, foreign !PC's held about $3 2 billion m demand balances m the Umted States, or about 1 pe1 cent of total M 1 Deposits of foreign !PC's do not show the same short-run volatility as deposits of foi eign commercial banks The nature of the transactions through the IPC accounts is harder to describe than are transactions mvolvmg deposits of foreign commercial bank& because of the larger number of depositors and the greater diversity among depositors 7 The factors determmmg the demand for IPC deposits are vaned, and it is difficult to assign a pnon weights to particular reasons for holdmg these deposits First, some deposits are held to finance exports from and imports to the Umted States, while others may be held to finance tlurd-country trade 8 Second, some deposits might be held to avoid confiscation of eai mngs of convertible currency by the governments of some developmg countries, although m this case lt 1s difficult to estabhsh a preference for a demand balance rather than an mterest-bearmg account Third, some deposits serve to mamtam Imes of credit at US banks for foreign commercial boirowers Deposits of foreign official institutions The term "foreign official mstitutions" covers a variety of mstitutions, mcludmg central banks, monetary authonues, governmentowned development banks, government-owned mstitutions that conduct commercial bankmg operations in their home country, some mternational orgamzauons, U S purchasmg missions, and embassies and consular offices At the end of 1975, foreign official mstitutions mamtamed about $2 6 billion m demand balances m the Umted States, mcludmg about $350 million of demand balances m Federal Reserve Banks 9 These deposits constitute 1 As noted earlier, most of the transactions in the demand deposit accounts of foreign commeraal banks are conducted by a small number of banks active m the Euro dollar market s For example, a Brazilian company may pay for its imports from Japan by drawing on its demand balance at a bankmg office m the Umted States 9 Foreign official demand deposits at Federal Reserve Banks are now included in the U S money supply https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 37 only a small fraction of the hqmd assets held m the Umted States by foreign official mstitutions As of December 31, 1975, foreign official msututions had $60 billion m U S Treasury securities and $17 billion m earmarked gold m custody at Federal Reserve Banks 10 As m the case of foreign nonbank depositors, the diversity of mstitutions and of nationalities m this category makes it qmte difficult to identify any general motives for mamtammg demand balances at bankmg mstitutions m the Umted States Empirical analysis In tlus section, we examme the issue of mclusion of foreign-owned demand deposits m the narrowly defined money supply 11 First, the degree of correlation between mcome and money, mclusive and exclusive of foreignowned demand deposits, is reviewed by regressmg changes m mcome on changes m alteinative measures of the money supply Second, demand functions for alternative defimuons of money are estimated, and the foreign deposit components are regressed separately on the same demand variables The estimated coefficients are then compared to see whether the factors that explam the demand for money also explam the demand for the foreign deposits Regressions are run from the middle of 1963, the first penod for wluch data on foreign demand deposits are available, through the end of 1974 Both monthly- and quarterly-average data are used, and all data are seasonally adJusted 12 10 Secuulles mclude marketable US Treasur} bills, certificates of indebtedness, notes, bonds, and nonmarketable Treasury securities payable m dollars and m foreign currencies The earmarked gold 1s valued at $42 22 per ounce, which understates its market value In add1t1on, it should be noted that foreign official mst1tut1ons hold about $20 b1lhon in dollardenommated assets at foreign branches of U S banks, an unknown portion of which 1s payable on short notice 11 The empirical analysis of the next two sections refers solely to the question of inclusion or exclusion of various foreign owned demand deposits m the narrowly defined money supply (M1) 12 The data on foreign commercial bank deposits are derived primarily from averages of smgle day (Wednesday) observations for any month, whereas the 38 lmprovmg the Monetary Aggregates Staff Papers TABLE 1 Quarterly Changes m GNP as a Function of Changes m Alternative Definitions of Money 1 Regression stat1sucs Independent variables Defimt1on of money Constant M MN MN+ FJPC MN + FfPC + FCB MN + FIPC + FOFF FIPC FCB FOFF 1 445 ( 5) 999 ( 3) 897 ( 3) 1 089 ( 4) I 074 ( 4) 18 351 2 (7 4) 15 952 2 (6 9) 19 358 2 (9 4) I AM, I 2 1 (3 1 (2 1 (2 I (2 I (3 46 (I 19 (I 12 (I 941 3) 731 3 6) 7732 7) 8262 9) 9202 1) 037 7) 023 7) 606 7) AM1-1 1 (6 1 (5 I (6 I (6 1 (6 19 (I 9 (2 7 (I 644• 8) 719' 9) 723 2 I) 659 2 5) 7252 5) 743 6) 613 3 6) 507 6) I I AM1-2 1 (4 1 (4 I (5 I (5 I (5 1 301' 9) 540 2 9) 520• 0) 3932 0) 4352 0) 992 3 ( 3 ( 005 6) 742 7) AM1-a (2 I (3 I (3 1 (3 1 (3 -7 ((1 ( ( I) 913 2 8) 194• 2) 1662 2) 027• 0) 052 2 1) 215 4) 800 1) 221 2) I I AM,_, (2 (2 (2 (2 (2 -7 (-1 ((- 479, O) 681• 4) 659 3 4) 563• 2) 573 3 2) 879 5) 801 4) 265 7) I Standard Sum R• 279 2 5) 864 2 2) 842 2 4) 6 468 2 (10 4) 6 704 2 (10 8) 52 678 (I 9) 29 0403 (2 6) 25 079 2 (3 4) 488 6 747 449 6 997 458 6 942 477 6 819 475 6 705 198 8 442 226 8 294 188 8 493 6 (IO 6 (10 6 (10 error 1 1-stat1st1cs appear m parentheses 2 S1gmficant at 99 per cent confidence level • S1gmficant at 95 per cent confidence level Income as a function of money Table l presents the results of regressions run with quartelly data In each equation, the change m gross national product (GNP) 1s the dependent variable Each of the defimt10ns of money used as the mdependent variable 1s one or a combmation of the followmg M = M 1 as currently defined, MN= M 1 mmus all foreign deposits, FfPC= foreign IPC deposits, FCB = foreign commercial bank deposits, and FOFF foreign official deposits A seconddegree polynomial d1stnbuted lag 1s estimated on the first differences of alternative defimt10ns of money and ts constramed to zero at t - 5 All equations have a first-order correction for serial correlation of the residuals Table 2 presents the results for the regressions run with monthly data In each equat10n, the change m personal mcome 1s the dependent variable and the defimuons of money = data for foreign official and foreign IPC deposits are denved from smgle day end of month observations In contrast, the data for demand deposits m M 1 are denved pnmanly from monthly averages of daily deposits Therefore, the three senes on foreign demand deposits may show greater month to month variation than the deposit senes m total M 1 For this reason, demand functions for the foreign components may have higher standard errors than those for monetary aggregates that mclude domestic deposits (Sec the appendix for a more complete treatment of the data sources used for foreign deposits) https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis are the same as those used m the quarterly regressions A second-degree polynomial distributed lag ts estimated on the change m the alternative defimuons of money and 1s constramed to zero at t - 16 For compactness, only the sum of the distributed-lag coefficients 1s presented, all distributed-lag coefficients are pos1t1ve The quarterly and monthly regressions yield consistent results Includmg each of the foreign deposit components m the defimtion of TABLE 2 Monthly Changes m Personal Income as a Function of Changes m Alternative Defimhons of Money 1 Independent variables Regression stat1st1cs Defimuon of money Sum of Constant coefficients on Amoney I 759 ( 8) 929 ( 9) 851 M MN MN+ FIPC ( 8) MN + F/PC + FCB MN+ FIPD F/PC FCB FOFF + FOFF 696 ( I) ( 4 (11 4 (8 5 (13 857 9) 9542 1) 028' 4) 465• 2) 5 1362 (22 6) 5 273 2 (21 4) 5 3162 (21 9) 5 2482 (22 6) 5 260• (22 1) 95 873 2 (13 9) 39 3262 (13 8) 29 0232 (14 5) • 1-stat1sucs appear m parentheses ' S1gmficant at 99 per cent confidence level R• Standard I error 180 4 093 148 4 171 154 4 158 174 4 107 162 4 137 068 4 363 148 4 171 027 4 458 Foreign Demand Deposits at Commercial Banks in the United States 39 TABLE 3 95 Per Cent Confidence Intervals for Regression Variances M MN MN+ FIPC MN + FIPC MN + FIPC I Quarterly regressions Definition of money Variance 45 48 48 46 46 + FCB + FOFF I 521 965 193 494 692 Confidence mterval 30 32 32 30 31 25~76 545-81 032-,80 902-77 034-78 money results m a shght mcrease (decrease) m R. 2 (standard error of estimate) relative to the regressions on money excludmg that component The improvements are small, however, and the question of their s1gmficance remams The 95 per cent confidence mtervals for the variances of each regress10n are compared with the pomt estimates of these variances m Table 3 13 (The degrees of freedom used m computmg the confidence mtervals are 37 and I 18, respectively) It 1s apparent that the confidence mterval for each equat10n's variance, monthly or quarterly, encompasses the variance of each of the other monthly or quarterly equations Although this 1s not a rigorous statistical test, the fact that the confidence mtervals overlap to such a large degree suggests that the variances may not differ s1gmficantly 14 191 955 663 819 151 I Monthly regressions Variance 16 751 17 17 16 17 396 289 868 116 I Confidence mterval 13 13 13 13 13 181-22 690-22 650-22 274-22 468-22 004 853 712 159 484 where Rep 1s the 30- to 59-day commercial paper rate, and Y 1s GNP m the quarterly regress10ns and personal mcome m the monthly regress10ns The second set of equations m the panels drop the lagged dependent variable and estimate distributed lags on Rep and Y The coefficients presented for Rep and GNP (Pl) are the sum of current and lagged coefficients on the respective variables The polynomials are second degree constramed to zero at t - 4 for the quarterly equations and at t - 10 for monthly equat10ns The results here are mixed In three of the four regress10ns for FfPC, the mterest rate enters negatively, though not sigmficantly In the fourth regress10n (monthly, distributed lag), the mterest rate enters positively and s1gmficantly In all FfPC regress10ns, mcome enters pos1t1vely but only m the quarterly distributed lag regress10n 1s it s1gmficant at the 95 per cent confidence level (At an 80 per cent confidence level, 1t is also sigmficant m the monthly d1stnbuted lag regress10n ) For FCB, the mterest rate enters negatively and not s1gmficantly m the demand equat10ns with a l.tgged dependent variable and positively and s1gmficantly m the distributed-lag regress10ns 15 In all but the monthly regress10n with a lagged dependent variable, FCB 1s pos1t1vely and s1gmficantly related to mcome at the 90 per cent confidence level or better Fmally, m all regressions, FOFF 1s pos1t1vely related to the mterest rate (sigmficantly m the distributedlag regressions) In no regress10n is FOFF s1gmficantly related to mcome, though the estimated relationship is positive Turnmg to the demand functions for the alternative defimt1ons of money, the mcome 13 See, for example, Henn Theil, Principles of Econo metrics (Wiley, 1971), pp 13~31 14 Rigorous statistical tests are not possible, given the way the alternative definitions of money are con structed If, mstead, the change m mcome 1s regressed on the changes m MN, FCB, FOFF, and FIPC as sepa rate mdependent variables, the standard types of tests on the coeffic1ents can be performed Smee the foreign components do not enter the regressmns separately but are summed with MN, such tests are not possible here 1 • An early memorandum presented to the Commit tee on Monetary Statistics did show FCB deposits negatively related to mterest rates, see Stephen Thur man, "Prehmmary Results of Tests on Inclus1on of Foreign Deposits m the Money Supply" (Board of Governors of the Federal Reserve System, October 1974) The coeffic1ents were significant at the 90 per cent confidence level The data ust.d m these earlier regressions have been substantially revised, which may explain the difference m results Demand functions Table 4 presents estimated demand functions for money and for the different foreign deposit components on a quarterly and on a monthly basis The first set of equations m panels A and B are all of the form ln M = ao https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis + a1 ln Rep + a2 ln Y + aa ln M_1 Improving the Monetary Aggregates Staff Papers 40 TABLE 4 Demand Funct10ns for Foreign Deposits and Alternative Defimbons of Money 1 Independent vanables and re11ress10n statlStlCS Dependent vanables lnFIPC I lnFCB I In FOFF I lnM I In MN I ln(MN + FIPC) + I ln(MN FIPC + FCB) I ln(MN + FIPC+ FOFF) A Quarterly demand functtons Equations with lagged dependent vanables Constant In RcP In GNP In M-1 .R• Standard error (-2 (- 848 5) 010 5) 018 ( 5) 1 0852 (12 9) 9695 0242 -2 331 (-1 8) - 003 (- I) 226 (I 7) 1 455 ( 8) 100 ( 9) 081 - 0132 (-3 2) 175 2 (2 9) 7762 (9 3) 9995 0040 ( 7) 906 2 631 2 (4 7) 8068 0910 -26 7532 (-7 3) 051 (I 9) 2 5022 (5 2) 9972 0241 4 289 ( 7) 4402 (4 2) 158 (12 I) 9977 0226 373 (I 7) 379 397 325 (I 8) (I 8) (I 7) - 0142 (-3 6) 163 2 (2 8) 788 2 (9 6) 9994 0042 - 0142 (-3 5) 1672 (2 9) 783 2 (9 6) 9994 0042 - 0132 (-3 4) 1662 (2 9) 7902 (10 0) 9995 0042 2 (6 (-9 I (5 (-9 450 (1 9) - 0132 (-3 3) 1762 (2 9) 7682 (9 O) 9995 0040 Equations with d1stnbuted lags Constant In Rep In GNP -17 (-1 (1 (3 .R2 Standard error 272 9) 002 7) 7262 3) 9623 0265 I (8 (-8 7632 5) 0432 6) 768• (8 4) 9993 0044 ( I) 8038 0921 2 0032 (6 7) - 0502 (-9 9) 750 2 (8 2) 9993 0044 7102 4) 0462 2 (6 (-9 0044 7722 (8 4) 9993 0045 0692 9) 0462 2) 7462 (8 3) 9993 0044 240 2 (2 9) - 007 2 (-5 3) 0662 (3 9) 9092 (35 8) 9997 0029 2003 (2 6) - 007 2 (-5 0) 0632 (3 7) 915• (37 I) 9997 0029 212• (2 5) - 007 2 (-5 I) 0592 (3 4) 919 2 (35 8) 9998 0027 012• 7) 0492 7) 750' (8 2) 9993 1) B Monthly demand Cuncttons Equations with lagged dependent vanables Constant In Rap lnP/ lnM-1 .R2 Standard error (-1 (- 206 7) 000 0) 010 ( 8) 1 0102 (34 7) 9631 0268 ((- 250 9) 005 8) 020 ( 6) 1 000 2 (52 4) 9978 0221 201 ( 5) 017 ( 6) 016 ( 6) 9412 (25 6) 8535 0812 1723 (2 2) - 006• (-4 8) 0562 (3 3) 926 2 (37 2) 9998 0028 240 2 (2 9) - 008 2 (-5 3) 067• (3 9) 9082 (35 6) 9997 0029 Equations with d1stnbuted lags Constant In Rep In PI .R• Standard error - 485 (- 2) 067• (2 9) 581 (I 3) 9511 0304 -21 369 2 (-7 2) 007 ( 4) 2 161 2 (6 5) 9976 0226 3 257 ( 8) 2412 (3 8) 289 ( 2) 8391 0850 2 (10 (-24 5812 9) 052 2 8) 7222 (17 9) 9998 0027 2 (16 (-25 831 2 I) 0552 8) 2 (16 (-25 702 2 (16 9) 9997 0028 851 2 I) 054 2 I) 7012 (16 7) 9997 0028 2 (12 (-23 588• 8) 052 2 9) 721 2 (17 0) 9997 0029 2 (14 (-25 8712 I) 053• 8) 700• (17 6) 9997 0027 1 1-stattstlcs are m parentheses 2 S1gruficant at 99 per cent confidence level 3 S1gmficant at 95 per cent confidence level and mterest rate coefficients are all significant and have the expected signs the R. 2 's and standard errors are approximately the same across regressions In three cases the standard error of the equation for MN is slightly higher than that for the equation for M, suggestmg that we may not wish to exclude all foreign components from the defimt10n of money In three of four cases m which FOFF is mcluded m the definition of money, the standard error is slightly lower than that for an equation excludmg this foreign component In two regressions mcludmg FCB m the defimuon of money, https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis the standard error is slightly higher than when The remammg standard errors are md1stmgmshable In summary, the differences among the standard errors for the demand functions for the alternative definitions of money are so small that little can be said, based on these regressions, about which foreign components should or should not be mcluded m the defimt10n of money More mformauon 1s gamed from the demand functions for the foreign components In no case does Rap enter significantly mto a demand function for a FCB 1s excluded Foreign Demand Deposits at Commercial Banks in the United States foreign component, except when the sign of the coefficient is positive 16 This result suggests that 1f the demand for any given foreign component 1s affected by movements m the commercial paper rate, 1t 1s affected m a manner that 1s very different from the way these movements affect the demand for the other components of the money supply There 1s some evidence of a relat10nship between FCB and mcome and less evidence of a relat1onslu p between FIPC and mcome Of course, the mcome variables may act as proxies for another transactions variable that 1s actually the determmant of the demand for these balances This conJecture will be mvestlgated further m the next section Fmally, while all the .R's are qmte lugh, the standard errors for the foreign components are very high relative to those for M, suggestmg that although domestic income and mterest rates do a good Job of explammg the demand for M, other variables may be relevant m determmmg the demands for the foreign deposits An alternative approach In this section we attempt to develop a more c.omplete model to explam the demand for demand deposits of foreign commercial banks (FCB) at U S banks For the demand deposits due to foreign official mst1tut1ons and to foreign md1v1duals, partnerships, and corporat10ns, further efforts are made to establish the existence of meanmgful correlations between the deposits and domestic macroeconomic variables Seasonally unad1usted quarterly and monthly data are used m these analyses, with quarterly and monthly dummy variables employed to remove the effects of any determm1st1c seasonal The hm1tat1ons imposed by the available data are discussed more fully m the appendix Demand deposits due to foreign commercial banks Foreign commercial banks hold demand deposit balances at US banks as part of broad 10 In the alternative model specified m the next section, the estimated coefficient on Rap 1s negative and https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 41 commercial relationships These balances facilitate the clearmg of their dollar transactions and serve to mamtam Imes of credit at U S banks U S bankers, as reported earlier, emphasized th<1t the returns and costs associated with these demand deposits are momtored closely both by the U S banks that accept the deposits and by the foreign banks that make the deposits In this sect10n a simple transact10ns model 1s set out to explam the level of foreign commercial bank deposits held m US banks Monthly d<1ta fiom 1971 through 1975 are used to test f01 the s1gmficance of the explanatory variables suggested by the transact10ns model A simple model of foreign commercial bank deposits Foreign banks are <1ssumed to attempt to mmtmlle costs associated with clearmg dollar tr<1nsact1ons m the Umted States For a typical foreign bank the total cost of clearmg transactions, per time period (TC), 1s given by17 (1) TC= A(T,D) + roD + S where A(T,D) = T = D ro = S = = the mternal accountmg and admm1strat1ve costs mcurred by the foreign bank m executmg its dollar transact10ns the dollar value of transact10ns through the account the level of demand deposits held the opportumty cost per dollar to the foreign bank of deposits held, m terms of mterest forgone the explicit service charges levied by the U S bank for clearmg transac- s1gmficant when another short term rate 1s entered m the regressions 11 In prmc1ple, Equation l and subsequent equations should be expressed m pnce deflated magmtudes This has not been done because of problems m choosmg the appropriate deflators for the different nommal magmtudes Also, costs should probably be related separately to the number of transactions and the average value of a transacuon Data hm1tat1ons prevent this refinement In the emp1ncal work we use a time trend m some of the regress10ns as a proxy for, among other thmgs, secular changes m the average value of a transaction 42 Improving the Monetary Aggregates· Staff Papers t10ns mmus charges for any nonclearmg services provided by the U S bank and not charged for explicitly Because data on the level of service charges (S) are not available, we need to denve an expression for S m terms of observable variables To do this, we look at the cost of servicmg the foreign demand deposits at the U S bank Service charges, m terms of dollars per time period, are equal to the difference between the costs of serv1cmg the foreign account, mcludmg profits, and the return the U S bank can earn on funds made available from the deposit 18 (2) S = C(T,D) + F(L) + 1r(D) - rLL = L = F(L) = 1r(D) = = rL the cost borne by the US bank m clearmg transactions through the foreign deposit account the volume of loans (or other asset purchases) that can be made with the funds held on deposit by the foreign bank the cost of serv1cmg the loans made with the deposit funds profits the loan rate at the U S bank We assume that the level of transactions costs-both for the foreign bank and the U S bank-mcreases with the volume of transact10ns, and that mcreases m deposit balances reduce clearmg costs mcurred by both the foreign bank and the U S bank Also, we assume that the costs of serv1cmg loans mcreases with volume That 1s, AT,CT (3) > 0, AD,CD < 0, and FL > 0 where subscripts denote partial derivauves of the functions L = (1 - p)D where pis the reserve ratio Usmg Equation 3 to ehmmate L from Equation 2 and subsututmg the resultmg express10n for S m Equation I, then (4) TC= C(T,D) + A(T,D) + 1r(D) + [r0 + F[(1 - - p)D] (1 - p)rL]D The foreign bank is assumed to hold the level of deposits that mmim1zes the costs of clearing its dollar transactions The costmm1mizmg condition obtamed by takmg the partial derivative of the cost function, Equation 4, with respect to D 1s 19 (5) where C(T,D) The US bank can use the deposited funds (D) to make loans of - (CD + AD) = To - (1 - p)(TL - FL) + 7rD The cost-mmimizmg level of deposits 1s given when the margmal cost savmgs per dollar of deposits [-(Cn + An)] is equal to the difference between r 0 , the opportumty cost of funds to the foreign bank, and rn, the margmal value of funds to the US bank, adjusted for the profits, where rn = (1 - p)(rL - FL) + 1rn Solvmg Equat10n 5 for D yields the mmimum-cost level of deposits r (6) D = H(T, To, TD) The demand for deposit balances (D) 1s a funct10n of the volume of transact10ns (T), the opportumty cost of holdmg the deposits (r0), and the rate of return on the deposits (rn) From the assumpt10ns made above, the partial derivatives of H with respect to the mterest rates have signs as follows Hr 0 < 0, Hrn > 0 Followmg standard transactions models, we would expect that for a given level of deposits, the value of margmal deposits m reducmg 10 We assume that T, p, To, and TL do not depend on D The second order cond1t1on 1s that 18 The level of service charges (S) may be positive or negative If the level of deposits 1s such as to pro vide abnormal profits with zero exphc1t charges, the U S bank 1s assumed to provide other bankmg services at less than full costs S 1s variable smce we assume that the US bank pays a competitive rate on the de posit even m the face of the prohibition on exphc1t mterest payments https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis Cnn + Ann + (1 - p) 2FLL + 1rnn > 0 where double subscripts denote second order partial denvauves If the US bank max1m1zes profits, then 'll'n 0 The rest of this section 1s consistent with profit maxi• m1zauon by the U S bank, but only the slightly weaker assumption that 'll'n 1s constant 1s needed = Foreign Demand Deposits at Commercial Banks in the United States transact10n costs mcreases with the level of transactions, that 1s, (CDT+ AvT) > 0 This assumption 1mphes that HT> 0 Empirical est1mat1on The exact form of the deposit demand function, H( ), will depend on the precise spec1ficat10n of the cost funct10n Here, we do not set out a fully developed model of transactions costs, but rather assume for estimation purposes that the H funct10n 1s log-hnear 20 All vanables--except the time trend-are m natural logarithms of levels Because data on md1v1dual deposit dccounts are not available, data on total demand deposits of foreign commeroal banks and total foreign dollar transact10ns cleared through U S banks are used to estimate the relat10nsh1p We contmue to assume that T, r 0 , and rv do not depend on the level of foreign deposits In the regress10ns reported below, the level of deposits (D) 1s pnmanly based on a monthly average of Wednesday figures The transact10ns vanable 1s represented by the monthly ,1verage of daily dollar figures for the Cleanng House Interbank Payments System (CHIPS) 21 Several mterest rates are used to represent r O the 90-day Euro-dollar rate (RE 90 ), the 30to 59-day commeroal paper rate (Rep), and the p11mary rate on 90-day U S certificates of deposit (Rev) 22 A maJor problem 1s the determmauon of a senes to represent the 1mphc1t rate of return on deposits (rn) As defined earher, rv = (1 - p)(rL - FL) + 1rv Fm the banks acceptmg these foreign deposits, margmal reserve reqmrements (p) were essentially unchanged over the sample penod Also, 20 The model md1cates that the algebraic difference m the interest rates should enter the H function We estimated the function m vanous form~ but the supenonty of any one form could not be established The 1egress1ons that are reported use the logarithm of the interest rates entered separately 21 CHIPS 1s an electronic system e~tabh~hed m 1971 by the large New York banks to clear their mternauonal dollar transactions 22 The market yield on 180-day Euro dollars and the 90 day US Treasury bill rate were also used The findings were entirely consistent with those to be re ported later https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 43 1f FL and 1rn are constant, then rv 1s a lmear funct10n of the loan rate (rL) 23 Several different rates could be used to represent rL For three reasons, m the regress10ns to be reported the pnme rate (RP) 1s the loan rate used First, the pnme lendmg market 1s a fairly competitive market with small <tdm1mstrat1ve costs, this rate then should move closely with the true cost of funds to the U S banks 21 Second, 1t was reported and venfied that overdrafts on the accounts of foreign commeroal banks are frequently charged at the pnme rate Assummg that U S banks perform then calculat10ns carefully, the rate such banks charge on overdrafts m these accounts should reflect the margmal mternal value of these deposits Third, although the Federal funds rate and the rate on repurchase agreements are also plausible candidates fo1 the loan rate, the performance of these rates was dommated m our empmcal work by the pnme rate Because deposits and transact10ns grew at a very rapid rate over most of the penod, the equations were estimated with and without a time trend The time trend was used as a rough proxy for omitted vanables to help explam tlus rapid growth 23 Several US banks md1cated that they use an average of several rate, to calculate a "treasurer's rate" for internal use m determmmg the profitab1hty of customer relat1onsh1ps See Beniamm Klem, "Com pet!Uve Interest Payments on Bank Depo~lts and the Long Run Demand fo1 Money," American Economic Review, vol 74 (December 1974), pp g3J-49, and Robert J Barro and Anthony M 5antom<-ro, Home hold Money Holchng~ and the Demand Dc.pcmt Rate," fournal of Money, Credit and Banking, vol 4 (May 1972), pp 397-413, for work that tnes to mea\ure rn c.hrectly 21 Borro,\lng at the pnme rate normally carnes a compensatmg balance reqmrement To the extent that the compensating balance reqmrement 1~ d result of the 1mpl1C1t payment of interest on deposits by lend mg at a favorable rate, the pnme rate will be less than the pure lcndmg rate and may be less thdn or greater than the 1mphc1t deposit iate A\summg 1ero mtc.rmc.chauon co~t~, the relationship bctwc1.n the pnme 1ate and the 1mphc1t deposit rate depends on the re \erve ratio and the compensating balance ratio For exdmple, 1f the margmal resc.rve 1c.qmrement 1s 17 pu cent with a 20 per c1.nt compensatmg balance 1eqmrement, the 1mphc1t deposit 1ate 1s 996 of the pnme lendmg rate 44 Improvmg the Monetary Aggregates· Staff Papers TABLE 5 Estimates of the Demand Function for Demand Deposits Due to Foreign Commercial Banks 1 In FCB, = a In RP, 0 + /3 In r, + ~ 'Y, In CHIPS,_, ,-o + at + t + (seasonal dummies) Independent vanables r, /3 a I 'Y• 'Y1 I 'Y2 I I -r, 'Ya I I 'Y• I I 'Yo I 0 t I A Regress10ns mcludmg a trend term RE,, Rep Ren 559• (5 74) 571• (5 16) 574• (4 99) (-2 (-2 (-2 209• 43) 237 6 19) 222• 14) 013 ( 25) 031 ( 55) 031 ( 55) (((- 043 76) 026 45) 034 59) - 580• (-5 12) - 689• (-8 90) - 647• (-9 07) 081 ( 96) 113 (I 58) 109 (1 55) (((- 053 62) 003 03) 025 34) (((- 040 70) 037 63) 036 61) 079 (1 37) 063 (I 05) 080 (I 36) ((- 004 07) 003 06) 002 ( 04) 068 (I 25) 060 (I 06) 052 ( 94) 007• (7 54) 007• (5 00) 007• (4 84) - 009 (- 18) 019 ( 34) 007 ( 14) 5 (42 5 (23 5 (23 640• 41) 604• 95) 450• 70) 3 (24 4 (34 4 (35 933• 28) 227• 65) 243• 36) B Regressmns without a trend term RE,, (6 Rep Ron (10 1 (10 928• 42) 998• 40) 010• 63) (-1 (-1 (-1 104 22) 089 19) 083 12) 021 ( 24) - 006 (- 08) 047 ( 61) (((- 012 15) 016 23) 001 01) 137 (I 70) 093 (I 28) 069 ( 97) 107 (I 45) 163 (2 65) 128• (2 09) 5 1 t-stat1sucs appear m parentheses All data are monthly, not seasonally adJusted, for the penod August 1971-November 1975 'F-stattsttc for test of ('Yo= = 'Yo= 0) F(7,30) for regressions mcludmg a trend term, F(7,31) for regresston without a trend term 3 F-stat1sttc for all variables except seasonals, trend, and constant F(9,30) for regressions with a trend term, F(9,31) for regresstons without a trend term • S1gmficant at 99 per cent confidence level 5 S1gmficant at 95 per cent confidence level In add1t1on, one set of regress10ns w<1s run with only a smgle mterest rate To the extent that funds are arbitraged between the U S bank loan market and the market that the foreign banks use for funds, rL and To are directly related If arb1 tr age were perfect, the two rates would be equal, and only a smgle rate would appear m the demand deposit equation The smgle mterest rate would enter with a negative sign m the deposit demand function with pos1uve reserve reqmrements If, however, the regress10n with a smgle rate were actually a m1sspec1ficat1on m the form of an omitted vanable-that 1s, the other rate-then the estimated coefficient on the entered rate would be biased 25 Estimated relat10nsh1ps, usmg Rp plus a second rate for TO and an unconstramed lag d1stnbut1on on current and six past values of CHIPS data, are summarized m Table 5 (with a time trend m panel A and without one m panel B) In all cases Rp has the expected positive sign and 1s s1gn1ficantly different from zero at least at the 99 per cent confidence level The F-stat1st1c for JOmt s1gn1ficance of all coefficients except those on the constant, trend, and seasonal dummies 1s s1gn1ficant at well <1bove the 99 per cent confidence level m all cases Takmg the regressions as a whole, there are several mterestmg results First, when RP 1s used m conJuncuon with a second rate, each of the rates used for To enters with the expected negative sign and each 1s s1gmficant at least at the 95 per cent level 26 Second, m all cases the F-test for JOmt s1gmficance of the coefficients on the lag d1stnbut1on for CHIPS 1nd1cates that these coefficients taken as a group are s1gmficantly different from zero at least at the 95 per cent confidence level Furthermore, m all cases the coefficient on current CHIPS has the expected pos1t1ve sign, although none of these 1s s1gn1ficantly different from zero Few of the md1v1dual coefficients m the lag d1stnbut1on are equal to or greater than their respective standard errors However, smce 1t 1s not difficult to conceive of models m which the transactions variable would enter with a d1stnbuted lag and smce collectively our estimated coefficients are s1gmficantly different from zero, reJecuon of the hypothesis that current and lagged values of the level of foreign transact10ns (as reflected by CHIPS) 25 See, for example, Theil, Principles, pp 548-56 https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 2s This result 1s also obtamed by usmg the rates mentioned m note 22 Foreign Demand Deposits at Commercial Banks in the United States TABLE 5-Contmued Regression staUstlcs F stattsucs R• (') (') Standard DW error p 2:'Y, 2 653• 23 644• 979 034 2 10 188 0064 2 812• 24 534• 980 035 I 94 143 1062 2 634• 23 419• 979 015 I 99 168 1028 6 956• 58 497• 911 055 1 58 356 1778 29 568• 130 144• 959 047 I 88 202 2544 28 571• 133 655• 960 046 I 89 204 2426 are a s1gmficant determmant of FCB 1s not possible 27 The exclusion of a time trend from the estimated relation alters the s1gmficance level, and on occasion the sign, of some of the estimated coefficients In all cases the coefficient on the rate used for r0 remams negative, but It becomes s1gmficant at well above the 99 per cent level when the trend 15 omitted Additionally, the test for JOmt s1gmficance of the coefficients on current and lagged CHIPS md1cates s1gmficance at well above the 99 per cent confidence level 28 The standard errors of the 21 It should be noted that our theory does not pro v1de a solid a pnor1 foundation for the expected form of the lag d1stnbution The regres~mns ID Table 5 also have been earned out by employ1Dg a quadratic lag chstnbuuon over six periods, the sixth be1Dg con stra1Ded to equal zero In each case the coefficients on the two mterest rates have the expected s1gns, and each of the rates used as r0 1s s1gmficant at approx1 mately the 90 per cent level The exact shape of the lag d1stnbut1on differs, of course, from the esllmated unconstralDed lag d1stnbulion (mdeed, the constramed form always yields a coefficient on current CHIPS with a negallve sign, although 1t 1s never s1gmficantly different from zero) But ID each case the sum of the coefficients 1s s1gmficant at least at the 95 per cent confidence level Thus, while the exact form of the lag d1stnbution may not be clear from the results, the CHIPS data do appear to be s1gmficant m expla1Dmg the level of these deposits 2s Alternative forms of the estimates ID Table 5 also https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 45 md1v1dual coefficients m the lag d1stribut1on are large, but m two cases coefficients on CHIPS 1_6 are s1gmficant at the 95 per cent level However, these 1esults could be spurious The sens1tiv1ty of macroeconometric results to the mclus1on or cxclus10n of a time trend 1s a well-known phenomenon, and 1t underscores some of the uncertamties and madequac1es mherent m cm rent econometric work A final note concei ns the signs and s1gmficance of the coefficients on the two mterest i <1tes The results m panel B of Table 5 could reflect a trend m the spread between the rates However, the ume series on Rl' and on the other rates md1cate that the spread between the iates narrows m the eatly part of the period considered <1nd widens agam over the final 15 to 16 months 29 Furthermore, ,1s Panel A shows, the mclusion of a trend does not alter the roles of the two iates m the equation Table 6 presents the results of regressions that parallel those reported m Table 5 but have only a smgle mterest rate The pos1uve sign on the rate-a negative sign 1s predicted by the model-and the rate's s1gmfiCdnce only m the presence of a trend constitute the most notable results of the regressions Use of a smgle mterest rate appears to be madequate and to result m specification error Given this hkely spec1ficat10n error, lt 1s not wrprismg that the coeffioents on the CHIPS lag distribution are s1gmficant only m the absence of a trend 30 have been obta1Ded by us1Dg shorter lag d1stnbut10ns on CHIPS data In all cases the results are highly sensitive to 1Dcius1on or exclusion of the trend ID terms of the s1gmficance of the coefficients on both CHIPS and 1Dterest rates 20 The 90 day and 180 day Euro dollar rates do not follow this pattern with respect to Rp, although the regression results with these rates are very similar to those reported with domesllc rates However, the prob !ems of senal correlation are more severe m tests with these rates 30 Regressions correspond1Dg to the results reported ID Table 6 for Rap and RE 90 also have been run by us1Dg a quadrallc lag d1stnbullon on the CHIPS data The coefficients on the rates are s1gmficant at the 95 per cent confidence level and pos1llve, but when the trend-s1gmficant at the 99 per cent level-1s mcluded, the sum of CHIPS coefficients 1s not s1gmficant 46 Improving the Monetary Aggregates Staff Papers TABLE 6 Estimates of the Demand Function for Demand Deposits Due to Foreign Commercial Banks 1 In FCB, = a In re + 6 ~ {J, In CHIPS,_, ·-• + -rt + Ii + (seasonals) Independent vanables r, a {J, {Ji {Jo I I I I fJa fJ, I fJ• I I fJ• Ii 'Y I I A Regressmns mcludmg a trend term REoo RoP Rev 189< (2 88) 247< (3 41) 232• (3 44) 019 ( 30) 003 ( 05) 007 ( 11) 114 (1 35) 127 (I 24) 123 (1 26) 055 ( 79) 053 ( 74) 055 ( 77) (((- 008 14) 084 63) 023 41) (((- 027 47) 030 54) 031 55) 021 ( 32) 005 ( 02) 012 ( 19) (((- 016 25) 024 37) 023 36) 065 (I 13) 070 (1 26) 052 ( 94) 004 ( 07) - 001 (- 02) - 007 (- 13) 030 ( 55) 040 ( 77) 045 ( 87) 009 ( 17) - 019 (- 36) - 009 (- 16) 0044 (5 67) 004< (6 20) 005• (6 34) 2 (16 2 (17 2 (17 310' 74) 472, 05) 555, 62) B Regressmns without a trend term RE,o RoP ROD 075 (I 27) 071 (I 20) 062 (I 05) 026 ( 44) 023 ( 38) 019 ( 32) 062 (I 05) 075 (I 31) 077 (I 34) 050 ( 87) 047 ( 79) 057 ( 98) 836• (7 31) 917 4 (7 75) 909• (7 77) i I-statistics appear m parentheses All data are monthly, not seasonally adiusted, for the period August 1971-November 1975 'F statistic for test of (/30 = = fJ• = 0) F(7,31) for regressions mcludmg a trend term, F(7,32) for regresstons without a trend term ' F-statlsllc for test of (a = {Jo = = {Jo = 0) F(8,31) for regressions mcludmg a trend term, F(8,32) for regressions wllhout , trend term • S1gmficant at 99 per cent confidence level ' S1gmficant at 95 per cent confidence level In order to obtain consistent estimates, as well as to provide a basis for mterpretmg the estimated relations as representative of behavioral relat10ns, T, r 0 , and rn must be statistically exogenous with respect to D 31 Utilizmg C W J Gr,mger's defimtton of causality and the eqmvalence of that defimtton with the econometrician's defimt10n of statistical exogeneity established by Christopher A Sims, one attempt is made-the direct empirical 1mplementat10n of Granger's defimt10nto determme if these conditions are met for the estimated relat10ns reported here 32 The iesults of these tests, which are summarized m Table 7, suggest that while we are not Justified m reJectmg the hypotheses that each of our right-hand variables is exogenous with respect to these deposits, neither are we JUStlfied m reJectmg the hypothesis of exogeneity of deposits with respect to each of the nghthand vanables considered 33 Thus, while CHIPS and each of the rates pass this test for exogeneity with respect to FCB, the results suggest that we should mterpret neither a regression of FCB on those vanables nor regress10ns m the reverse direct10n as representative of behav10ral relauonslups It should be noted that these tests are all bivariate tests To mamtam consistency with the model, the data penod should be extended and the tests reformulated m a four-variate representat10n reflectmg the relauonslups m Table 6 Because of the limited stze of the available d&ta set, further tests have not been earned out Thus, these results imply that caut10n must be exercised m mterpretmg these regress10ns as iepresentauve of actual demand or behav10ral relat10nships Some final caveats regardmg our results are m order The p mdicated m Table 6 represents <1n estimated first-order autoregressive parameter for the disturbance m the equation No attempt is made to correct for higher than first-order senal correlat10n m the residuals 31 In est1matmg the demand function for depostts, 1t 1s assumed that the value of transactions (T) 1s determmed by factors other than the rates mcluded m the demand 1elat10n To the extent that T 1s corre lated w!lh these rates, the estimators are meffic1ent a2 See Granger, "Invest1gatmg Causal Relat10ns by Econometnc Models and Cross Spectral Methods," Econ ometrzca, vol 37 (July 1969), pp 424-38, and Sims, "Money, Income, and Causality," American Economic Review, vol 62 (September 1972), pp 540-52 https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 33 The 180-day Euro-dollar rate 1s the one except10n to this, the 1ate appeanng to be exogenous with respect to FCB but not the reverse Foreign Demand Deposits at Commercial Banks in the United States TABLE 6-Contmued Regression stat1sucs F-stattsttcs (') (') R• Standard error ow p 2;(3, 940 3 604• 838 0402 2 27 665 0922 466 4 221• 849 0386 2 36 667 0282 358 4 380• 858 0388 2 31 654 0343 3 319• 3 807• 350 0451 2 14 850 2726 2 588' 4 ISO• 371 0456 2 03 842 2503 2 568 5 4 179• 371 0456 2 04 842 2541 In adcht10n, any seasonal biases that remam after the determmistic sedsonal effects repre5ented by the dummy Vdnables dre accounted for are not cons1deied H Many of these results are reported as F-tests on the JOmt s1gmficance of groups of coefficients Given the small number of observdt10ns, the relatively few degrees TABLE 7 Tests Employing Granger's Definition of Causahty 1 Y, = ,-1~' y In FCB In CHIPS In Rp In REoo In Rep In Ren a, y,_, + X In CHIPS In R" In Rcr In RE,o In Ren In FCB . ~ fJ,X,-, ,-1 + -rt + Ii + (seasonals) F(6,22) 2 I 380 I 300 I 098 I 962 I 469 828 819 I 305 764 982 F(9,22) 3 13 739• 4 930• 5 541• 10 299 6 5 312• 22 756• 30 126• 19 844• 22 638• 25 0664 1All data are monthly, not seasonally ad1usted, f01 the pc11od October 1971-November 1975 ' F-sta t1sttc for test of ((31 = = fJ• = 0) 3 F-stausuc for test of (ai = = a, = 0) 4 Stgmficant at 99 per cent confidence level • S1gmfican t at 95 per cent confidence level 34 For a ch~cuss1on of these t}pes of problem~. ~ec Christopher A Sims, "Seasonality m Regressmn," Journal of the American Statistical Association, vol 69 (Sep tembcr 1974), pp 618-26, and Kenneth F Wallis, "Seasonal Adjustment and Relations between Vanables," Journal of the American Statistical Association, vol 69 (March 1974), pp 18-31 https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 47 of freedom m many of our estimated relat10ns, and the mconclusiveness of the results, the F-tests could be considered weak tests of the ielevant hypotheses In summary, given the hm1tat10ns imposed by the data, mconclusiveness m certam results, and some mcompleteness m the theory, the evidence supports the content10n that demand deposits due to foreign commercial banks are determmed m large part by the level of foreign transact10ns cleared through CHIPS These transact10ns are generated primarily by financtdl transfers m the Euro-dollar market and foreign exchange markets Smee only a small proport10n of these foreign transactions are related to sales of goods and services produced m the Umted States, our results suggest that proximate determmants of these deposits may he better represented by foreign transactions than by U S macroeconomic variables Demand deposits due to foreign offecial institutions An eff01 t 1s made to supplement the 1esult5 tlldt employ sedsonally adjusted data to exdmme demand deposits due to foreign official mst1tut10ns (FOFF) Smee no monthly figures comparable to GNP (but not seasonally adJUSted) are avd1lable, the monthly mdex of mclustnal p1oduction (IPI), not seasonally adjusted, 1s used as a measure of U S economic dct1v1ty to capture dny relat10nsh1p that may exist between these deposits and their use for purchase of U S goods and services These deposits a1e pos1uvely correlated wtth some sh01 t-term mterest rates (Table 8), but they do not exl11b1t any s1gmficant correlat10ns with US economic act1v1ty as measured by the IP[ Removal of the trend does not s1gmficantly altei the results, m most cases, the correlat10ns are reduced to even lower levels Table 9 shows the results of regress10ns of quarterly GNP on current and lagged Vdlues ot various components of M wtth seasonally und<lJusted data The coefficients on FOFF, whethei taken dS a group or smgly, are not s1gmficantly chfferent from zero regardless of 48 Improvmg the Monetary Aggregates Staff Papers TABLE 8 Correlations of Demand Deposits Due to Foreign Official Institutions with Short-term Rates and Index of Industrial Produchon 1 In FOFF, = a In r, + 6 I: ,-o /3, In /Pli-, + "It + li + (seasonals) Independent variables " a /3o I 522• (2 17) 526• (3 23) 575• (2 73) 282 (I 73) 582 6 (2 98) RP RFF RcP REoo RcD /3, /31 I -I (-1 (-1 (-1 (-1 (- 513 ( 25) - 413 (- 22) - 028 (- 01) 148 ( 07) - 343 (- 18) 609 54) 668 57) 841 65) 316 45) 515 54) {J, {Ja I I 1 ( 1 ( I ( 1 ( 770 58) 012 34) 709 59) 583 52) 954 ( 33) -1 088 (- 36) 348 ( 12) -1 059 (- 37) - 740 (- 25) - 406 (- 14) 1 t-stat1st1cs appear 1n parentheses All data are monthly, not seasonally adJusted, for the period August 1971-November 1975 'F stattStlc for test of ({Jo= = {J, = 0) {J, {Jo I I 2 ( 2 ( 2 ( 2 ( 3 711 88) 151 72) 806 95) 538 83) 124 (I 07) I -3 (-1 -4 (-1 -3 (-1 -3 (-1 -4 (-1 662 21) 220 42) 862 34) 425 15) 529 58) li "I I 1 ( 1 ( ( 1 ( 1 ( 107 50) 220 59) 977 47) 570 72) 232 61) I 007 6 (4 72) 009' (7 91) 007° (6 50) 008 6 (6 48) 008 6 (6 74) 4 423 (I 88) 8 (3 7 (2 2 844 6 01) 103• 52) 726 (I 37) 7 7266 (2 75) 'F-stat1st1c for test of (a = {Jo = = {J, = 0) • S1gmficant at 95 per cent confidence level • S1gmficant at 99 per cent confidence level foreign items due to mdividuals, partnerships, and corporations (MN + FIPC), the mtroducuon of current and lagged values of FOFF results m coefficients on FOFF that, taken as a group, are not sigmficantly different from zero m explammg GNP the presence or absence of a trend (However, considerable first-order autocorrelat10n obviously remams m the estimated relations ) Table IO further mdicates that whether GNP is regressed on current and lagged M net of all foreign-owned items (MN) or MN plus TABLE 9 Regressions (Quarterly) of GNP on Vanous Money Measures 1 6 ~ a, In M,_, In GNP, = ,-o + {Jt + "I + (seasonals) Independent variables M a, ao I a, I ao a, aa I I I a, I {J I "I I A Regressions mcludmg a trend term M MN FCB FOFF FIPC 1 0498 (2 79) 973 3 (2 70) 2048 (2 17) 021 ( 94) 152 (I 79) ((- 8943 74) 8243 67) 214 94) 017 52) 385 94) ((- 169 34) 121 28) 023 ( 20) 026 (I 04) 088 ( 95) ( ( ((( 243 42) 290 60) 062 54) 010 38) 053 58) 729 (I 30) (I ( ( ( 720 53) 050 42) 004 15) 004 04) 201 39) 146 32) 012 ( 11) 009 ( 36) 037 ( 35) ((- 381 ( 87) 381 ( 95) - 056 (- 46) - 033 (-1 27) - 096 (- 90) (((((-1 225 66) 214 64) 014 12) 021 87) 168 60) ((- 002 84) 002 83) 005• (3 90) 007• (34 96) 007• (13 16) - 790 (-1 24) - 794 (-1 18) 2 168• (176 04) I 918 4 (198 35) 1 925• (59 30) B Regress10ns wtlhout a trend term M MN FCB FOFF FIPC (2 (2 (I ( (I 152 31) 138 32) 036 ( 27) 023 ( 68) 386 (I 87) ( ( ( ((2 115 21) 173 37) 028 22) 009 27) 417 05) 727 (I 31) 677 (I 47) 123 ( 93) 002 ( 05) 465• (2 14) 1 l•sta t1st1cs appear m parentheses All data are quarterly, not seasonally adJusted, for the period 1965 Q2-1973 Q4 2 F-stallsllc for test of (ao = = a, = 0) F(7,23) for regressions mcludmg a trend term, F(7,24) for regressions without a trend term https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis (((- 332 67) 268 63) 009 07) 005 ( 13) 338 (I 42) 394 ( 91) 372 ( 94) 002 ( 01) - 037 (-1 06) 245 (I 02) (-1 (-1 346 13) 327 08) 171 (I 49) - 018 (- 53) 274 (I 15) S1gmficant at 95 per cent confidence level • S1gmficant at 99 per cent confidence level 3 (-4 (-3 1 (204 243• 17) 215• 65) 656• 64) 359• (52 78) 1 111 • (28 73) Foreign Demand Deposits at Commercial Banks in the United States 49 s1gmficantly different from zero m explammg TABLE 8-Conhnued FOFF Regression stausucs F(7,31) 2 F(8,31)' 528 R' Standard error DW :E/3, p 2 502• 734 099 1 90 412 - 2583 890 3 688' 790 094 1 93 355 -1 5696 779 2 954, 746 095 1 98 428 -1 2980 458 2 079 695 099 1 93 460 3583 896 3 240• 760 093 1 94 417 -1 4831 It might also be hypothesized that deposits hke FOFF could be held for purchases such as m1htary items As the last hne of Table 10 shows, neither the coefficients on current and lagged GNP nor those on current and lagged US m1htary export sales are, taken as a group, TABLE 9-Contmued Regression statistics R• Standard 2 687 3 982 009 2 17 793 1 8077 2 234 979 009 1 96 808 1 8843 F-stausuc• error DW Xa, p 2 065 987 011 I 76 582 994 983 012 I 47 636 I 507 984 Oil I 84 632 0069 97 231• 981 009 2 03 801 1 3003 73 381• 979 009 1 85 822 1 3122 120 112• 975 013 1 42 677 5653 376 910 017 86 948 14 560• 864 026 54 749 https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 1579 - - The evidence, m shoi t, does httle to suggest that demand deposits due to foie1gn offiCial mst1tut10ns ale ielated m any sigmficant way to US output or mcome 0003 0019 2 5120 Demand deposits due to foreign individuals, partnerships, and corporations Results of the efforts to supplement the earher analysis of demand deposits due to foreign mdividuals, partnerships, and corporat10ns (FIPC) are presented m Table 11 Coefficients on current and lagged IP/ are, as a group, sigmficantly different from zero at the 95 per cent level or above only when Rp or RE. 111 1s mcluded m the estimated relat10n Furthermoie, when the trend 1s removed, even these results d1sappea1 As Table 9 shows, however, when the trend 1s removed from the quarterly regress10ns, the coefficients on FIPC are s1gmficant at well above the 99 per cent confidence level Unfortunately, the poss1b1hty of senous first-order autoconelauon m this estimated relat10n also exists Table 12 md1cates that coefficients on FIPC a1e not, as a group, s1gmficant m explammg GNP when mcluded ma regress10n of GNP on M net of all foreign Items (MN) The same type of relat10nslup, estimated monthly by usmg IP/ for output, shows these coefficients to be s1gmficant at the 99 per cent level both when a trend is mcluded and when It 1s excluded Agam, however, m these cases there 1s strong evidence of senal correlation m the estimated relation (Indeed, tests usmg an estimated first-order autoregressive parameter resulted m no improvement, as mdicated by the Durbm-Watson statistic) In summary, these results do little to resolve the question of meanmgful relationships between demand deposits due to foreign IPC's and U S macroeconomic variables 50 Improvmg the Monetary Aggregates Staff Papers TABLE 10 Further Evidence on the Correlation of FOFF with GNP 1 Independent vanables a, ao a, (Jo (J, /j1 -y (Ja 3 !: a, In MN,_, + I:' /Ji In FOFF,_, + -rt + ll + (seasonals) A In GNP,= 883' (2 07) 068 (- 11) 070 ( 12) 3 3 ,-o 595 ~ 0002 ( 001) (I 12) 3 a ,-o ,-o 005 ( 24) - 909 (-1 21) 0009 (- 41) + -YI + ll + (seasonals) fJ, In FOFF,-i 010 ( 45) 021 (I 47) 745 (- 36) 3 061 (I 45) 010 ( 46) !: a, In (MN + FIPC),_, + 0002 005 ( 22) ( 01) 0009 (- 40) - 919 (-1 23) - 031 (-1 56) -7 320 (-1 37) !: a, In GNP,_, + !: /J, In MIL,_, + -rt + ll + (seasonals) C lnFOFF,= 766 ( 38) 022 (I 15) ,-o 088 ( 15) 083 (- 14) ,-o 607 (I 51) B In GNP,= 895• (2 10) ,-o 1 126 ( 54) 022 ( 20) 108 097 ( 96) (I 03) 1 1-stattst1cs appear m parentheses MIL = VS military export sales All data are quarterly, not seasonally adJusted, for the per10d 1965Q2-1973Q4 2 F-stat1st1c for test of (ao = = (Jo = 0) 016 (- 14) ' F-stat1sttc for test of (ao = = aa = 0) • F stat1st1c for test of (/Jo = = (Ja = 0) • S1gmficant at 95 per cent confidence !eve I TABLE 11 Correlations of Demand Deposits Due to Foreign lndmduals, Partnerships, and Corporations with Short-term Rates and Index of Industrial Produchon 1 In FIPC, = a In r, + ,-o !:' /J, In JpJ,_, + -YI + ll + (seasonals) Independent variables " a (Jo 167• (2 09) 043 ( 61) 039 ( 45) 035 ( 58) 058 ( 73) RP Rrr Rep R&o RcD (J, (J1 I I -1 (-1 -1 (-1 -1 (-1 -1 (-1 -1 (-1 538 75) 752 94) 680 86) 715 89) 736 93) 1 ( 1 ( I ( 1 ( I ( (J, (Ja I I - 296 92) 360 96) 325 95) 399 99) 361 97) - 661 (- 47) - 392 (- 27) - 498 (- 35) - 478 (- 33) - 452 (- 32) 616 (- 43) - 531 (- 37) - 483 (- 34) - 521 (- 36) - 571 (- 40) 1 t-stat1st1cs appear m parentheses All data are monthly, not seasonally adiusted for the period August 1971-November 1975 ' F-stat1st1c for test of ((Jo = = fJ• = 0) I I 2 736 (I 90) 2 503 (I 72) 2 548 (I 77) 2 563 (I 75) 2 607 (I 79) I -2 784 (-1 94) -2 859 (-1 98) -2811 (-1 98) -2811 (-1 93) -2 897 (-2 02) ll -y (J, (Jo I I 009 5 639 ( 66) I 049 (I 07) I 043 (I 06) I 049 (I 06) I 023 (I 05) (14 96) 009• (15 75) 008• (15 17) 009• (15 88) 009 5 (15 61) 9 (8 7 (5 6 (4 7 (7 7 (5 087• 69) 262 5 13) 785• 97) 021 5 35) 342 5 34) - 155' F-stat1st1c for test of (a = (Jo = = fJ• = 0) S1gmficant at 95 per cent confidence level • S1gmficant at 99 per cent confidence level 3 4 TABLE 12, Further Evidence of Correlations between FIPC and US Economic Actmty 1 Independent vanables a, ao aa ... A Quarterly estimate In GNP, 1 026' (2 53) 363 (- 71) 194 ( 40) = 3 3 ,-o 1-0 I 338 391 ( 37) (I 05) 310 ( 24) 055 ( 72) 370 (- 37) I 056 ( 62) 525 ( 28) 318 ( 15) 576 ( 43) = 6 6 ,-o ,-o 031 ( 36) 385 ( 30) I 441 ( 72) 1 l-stat1st1cs appear m parentheses Quarterly data are for the period 1965 Q2-1973 Q4 monthly data are for the penod August 1971December 1975 All data are not seasonally adiusted 2 F stat1st1c for test of all a, = all (J, = 0 https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 009 ( 09) 117 (I 23) !: a, In MN,_, + !: /J, In FIPC,_, + -YI + ll + (seasonals) 232 ( 31) 129 6 (2 10) 073 (I 16) C Monthly estimate, without trend Same as B, ncept -Y - 110 (- 05) (Ja !: a, In MN,_, + !: /Ji In FIPC,_, + -YI + ll + (seasonals) 579 (I 96) (J, (Jo a, (I 71) B Monthly estimate, with trend In /Pl, 1 262 a, -1 105 (- 98) 112 (I 14) s 056 ( 56) 044 ( 67) 049 (- 73) (-2 43) - 006 (- 06) - 029 (- 27) - 230' (-2 32) 0 ' F stat1sttc for test of all a, = 0 ' F-stat1st1c for test of all (J, = 0 • S1gmficant at 95 per cent confidence level • F(8,22) Foreign Demand Deposits at Commercial Banks in the United States 51 TABLE 10-Contmued Regression stat1st1cs F(8,22) 2 F(4,22)' F(4,22)' 2 643 5 4 139 5 0 741 2 652 5 4 156• 0 687 0 895 0 850 0 551 Standard - error DW 988 00983 1 82 988 00982 l 83 608 092 11019 I 39 638 p TABLE 11-Contmued Regress10n sta Ust1cs F(7,31) 2 F(8,31) 3 R• Standard error DW 3 720 5 3 256• 930 042 2 02 208 9291 2 150 2 094 905 044 2 01 292 6211 p J;{J, 2 044 I 956 897 044 2 03 319 5558 2 368• 2 135 907 044 2 00 281 5144 2 175 2 107 904 044 2 02 297 66S0 TABLE 12-Contmued Regresston sta usucs {J, {J, I - 151' (-2 45) -1 55• (-2 56) - 258 6 (-2 72) - 273• (-2 96) I 'Y I (') I (') I I (•) I R• I Standard error - 0009 (- 45) - 606 (- 85) 2 473 5 ,, 3 220•, 7 638 7 985 00939 - 016' (-6 51) -48 676' (-8 60) 69 539,,, 17 855•,10 6 664', 10 961 0131 -12 2458 (-9 04) 29 611•, 11 25 794,,12 45 856',12 901 0208 'F(4,22) 8 S1gmficant at 99 per cent confidence level • F(l4,26) https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis a F-stat1sucs 10 11 12 F(7,26) F(l4,27) F(7 27) jow I 2 00 69 49 p 707 ' 52 Appendix: Discussion of Data Used In order to perform the emp1ncal work requested by the Committee on Monetary Statistics, as well as to construct the body of supportmg evidence presented m this study, It 1s important that each of the series used be constructed m a consistent manner over the entire period used m the study Unfortunately, this consistency 1s not easily obtamed for the series on foreign demand deposits m the money stock, and some compromises have been necessary The particulars regardmg the series on foreign-owned demand deposits m U S commercial banks are discussed here Demand deposits due to foreign commercial banks The prmc1pal sources of data on these deposits are the Treasury-Foreign Exchange Reports B-1 (TFEX) data and the deposits reported by weekly reportmg banks that are members of the Federal Reserve System The TFEX data do not yield a consistent series because, prior to December 1971, hab1hties of U S banks to their foreign branches were included as demand deposits due to foreign banks Smee no separate senes exists for these latter deposits pnor to that date, It 1s 1mposs1ble to remove them from the compiled senes The figures compiled from the reports of weekly reportmg member banks do not yield a complete measure of the desired senes In particular, data are not mcluded for demand deposits due to foreign banks at (I) US agencies and branches of foreign banks, (2) Edge Act corporations, (3) member banks not reportmg weekly to the Federal Reserve, and (4) nonmember banks Accordmgly, an estimated senes has been constructed m an effort to overcome these om1ss1ons wlule mamtammg as much consistency as possible m the resultant senes Estimates for nonweekly reportmg member banks and nonmember banks have been obtamed by mterpolat1on from call report data 1 Added to these figures are last Wednesday-of-the-month figures for (I) agencies of foreign banks m the Umted States and mvestment compames m the Umted States that are ma1onty owned by one or more foreign banks, and (2) Edge Act corporations, complied from Federal Reserve Reports 886a and 886b, respectively (For the penod pnor to November 1972 these figures are estimates based on a monthly compounded growth rate for the penod over which data are available, November 1972 through November 1975) Finally, data have been obtamed for branches of foreign banks m the Umted States from Federal Reserve Report 886a (For the penod pnor to January 1973 these figures are mcluded m the estimates for nonweekly-reportmg member banks and nonmember banks ) These senes are added then to the averages of Wednesday figures for weekly reportmg member banks, and this resultant senes 1s used m the empmcal work Although this senes does not measure the desired senes exactly, It 1s as consistent as available data will permit and mvolves mm1mal extrapolations when data are not available Demand deposits due to foreign official institutions and to foreign individuals, partnerships, and corporations Smgle observation, end-of-month data for these senes are taken from the Federal Reserve Bulletin, "Short-Term Liab1hties to Foreigners Reported by Banks m the Umted States, by Type " These data were chosen m order to provide the longest consistent senes possible and, m the case of foreign official mstltutions, to avoid the om1ss1ons mherent m the average data available for weekly reportmg member banks The data used are revised as of January 1976 Other data series employed 1 Estimates were provided by the Board of Governors of the Federal Reserve System, D1v1s1on of Research and Stat1st1cs https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis The CHIPS data used are monthly averages of daily close of-busmess figures for the Clearmg Foreign Demand Deposits at Commercial Banks in the United States House Interbank Payment System These averages are based upon the number of busmess days m a month, the daily figures bemg provided by the Federal Reserve Bank of New York The penod for the monthly regressions employmg the CHIPS data 1s determmed by the penod of available CHIPS data, that 1s, the daily data are not available pnor to January 1971 AU other monthly and quarterly data, with the exception of GNP and personal mcome figures, seasonally adjusted and not seasonally adjusted, are taken from vanous issues of the Federal Reserve Bulletin or provided by the D1v1S1on of Research and Statistics, Board of Governors of the Federal Reserve System The seasonally adJUSted data were prepared by usmg the version of the X-ll seasonal adjustment program available at the Board of Governors The quarterly unadjusted GNP figures are taken from pubhcat1ons of the https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 53 Department of Commerce 2 (At the ume tlus study was bemg conducted, these figures were bemg substantially revised, and consequently, data were available only through the fourth quarter of 1973) In addition, not seasonally adjusted GNP 1s not recorded m exactly the same way as are other not seasonally ad1usted data, and the results obtamed with those data should be mterpreted with this m mmd The supplemental work was done m response to a subsequent request by the Committee The miual penod for the quarterly regressions with unadJUSted data 1s determmed by the earliest penod for wluch the FOFF and FIPC senes were available, that 1s, begmnmg m July 1963 2 National Income and Product Accounts of the United States, 1929-1965, Statistical Tables, Supplement to the Sur vey of Current Business (August 1966), US National Income and Product Accounts, 1961-69 (July 1973), and Survey of Current Business, vol 54 (July 1974) 54 Bibliography Barro, Robert J , and Anthony M Santomero "Household Money Holdmgs and the Demand Deposit Rate" Journal of Money, Credit and Banking, vol 4 (May 1972), pp 397-413 Granger, C W J "Invesugatmg Causal Relations by Econometric Models and Cross-Spectral Methods" Econometrica, vol 37 (July 1969), pp 424-38 Klem, Benpmm "Compeuuve Interest Payments on Bank Deposits and the Long-Run Demand for Money" American Economic Review, vol 74 (December 1974), pp 931-49 Sims, Christopher A "Money, Income, and Causality" American Economic Review, vol 62 (September 1972), pp 540-52 - - - "Seasonality m Regress10n" Journal of the Ame11wn Statisttwl Association, vol 69 (September 1974), pp 618-26 Theil, Henn Principles of Econometrics New York Wiley, 1971 Thurman, Stephen "Prelimmary Results of Tests on Inclusion of Foreign Deposits m the Money Supply" Memorandum Washmgton Board of Governors of the Federal Reserve System, October 1974 US Department of Commerce The National Income and Product Accounts of the United States, 1929-1965, Statistical Tables Supplement to the Survey of Current Business, August 1966 US National Income and Product Accounts, 1964-69, July 1973 - - - Survey of Current Business, vol 54 (July 1974) Wallis, Kenneth F "Seasonal Adjustment and Relations Between Vanables" Journal of the American Statistical Association, vol 69 (March 1974), pp 18-31 https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 55 Nonmember Banks and Estimation of the Monetary Aggregates Darrel W Parke This paper, written in early 1976, presents a case for expanded collection of deposit data from banks that are not members of the Federal Reserve System In June 1977 the Federal Deposit Insurance Corporation began collecting daily deposit data from a sample of about 600 nonmember banks This survey will continue for the next 2 years, after which the mues discussed in this paper will be reassessed In June 1976 the Federal Reserve estimated the narrowly defined money stock (M 1) f01 January 1976 to be $301 3 b1lhon Of this dmotmt, $161 9 billion was m demand deposits ,tt commernal banks that are members of the Federal Reserve System-demand deposits adJUsted (DDA) at member banks, $73 7 billion was m cun ency, and $62 5 bilhon was m DDA at nonmember banks 1 The Federal Reserve constructs M 1 by adclmg these estimates to estimates of other components 2 Thus, to obtam accurate current estimates of total M 1 , 1t 1s imperative to have accurate current estimates of nonmember bank DDA because 1t constitutes more than 20 per cent of M 1 Unf01 tunately, estimates of nonmember bank DDA have often been maccurate Deposit d.tta are available from nonmember banks for only 4 days each year-the call report dates The estlmatmg procedure, which will be descnbed m detail m the next sect10n, 1s based on an extrapolation of the nonmember DDA se11es from prev10us call report dates to obtam a current or "m1t1al" estimate This estimate 1s successively revised as add1t10nal call reports are processed until the call reports for elates surrounclmg the penod m quest10n are dvailable, at which time a "final" estimate 1s made A list of m1t1al and final estimates for the weeks of the call dates smce 1970 1s given m Table I Exammat1on of Table I reveals that the rev1S1ons have been a5 large a5 $2 billion, or .tbout 4 per cent of aggregate nonmember bank DDA The average of the absolute values of the rev1S1ons 1s $9~2 million, and the root mean 5quare of the rev1s10ns 1s $1,116 million To gam some perspective on these numbers, consider the computation of a quarter-toquarter growth rate m M 1 Suppose the value of M 1 for the base quarter 1s known, but the TABLE 1 Weekly-Average Estimates of Nonmember Bank DDA for Selected Weeks around Call Dates In milhons of dollars NoTF-The author 1s on the staff of the Div1S1on of Research and Statistics He wishes to thank Stephen Taubman and Lucy McCurdy for their programmmg assistance, staff members of the Federal Deposit In ~urancc Corporation for helpful comments on earlier d1afts, Gerald Nickelsburg for assistance m the early 5tagcs of this study, and Richard Porter for many valuable d1scuss10ns 1 Federal Reserve Bulletin, vol 62 (May 1976), p Al2 All figures used m this report arc not seasonally ad Justed 2 See Darwm L Beck, "Sources of Data and Methods of Construction of the Monetary Aggregates," this volume https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis Total Imual estimate Fmal estimate 1970-June Dec 1971-June Dec 1972-June Dec 1973-Mar June Oct Dec 36,388 40,406 39,251 44,133 43,874 51,761 47,496 50,228 52,011 57,100 35,475 40,476 39,368 45,104 45,490 52,489 48,831 52,220 53,821 57,475 -913 70 117 971 1,616 728 I, 335 1,992 I 810 375 1974-Apr June Oct Dec 1975-Apr June Sept Dec 56,491 56,996 57,460 59,554 59,970 59,109 58,560 63,111 55,349 55,755 57,236 58,830 58,136 58,638 58,272 62,729 -1,142 -1,241 -224 -724 -1,834 -471 -288 -382 Call date rev1s1on 56 estimate for the current quarter is understated by $2 billion At the current level of M 1 -about $300 billion-the annualized rate of growth would be understated by 2 7 percentage pomts To aid the Federal Reserve m developmg improved estimates of nonmember bank deposits, the Federal Deposit Insurance Corporation (FDIC) conducted an experimental survey m late 1974 and early 1975 The FDIC asked all of the I 78 nonmember banks with more than $100 milhon m deposits and a sample of 395 smaller nonmember banks stratified by size to report their deposit balances on a weekly (daily-average) basis The FDIC then supplied the Federal Reserve with deposit data aggregated m various ways, although it retamed the mdividual bank data m order to mamtam confidentiality This study aims to determme (1) whether mformation extracted from the FDIC survey can be used to modify and improve the present estimation procedure, and (2) whether estimates based on the sample data from the survey are substantially more accurate than the present estimates This paper presents a descnpt10n of the present method of estlmatmg nonmember bank DDA by the Federal Reserve and some of the hmitatlons of this method, a comparison of the present method with estimates based on the sample data, an assessment of the accuracy of the sample estimates, a discuss10n of alternative estimation procedures, and some concludmg remarks Present-method estimates All member banks report their deposit balances for each day of the year Most of these banks report withm a week after the close of the statement week, and the remamder report withm 2 or 3 weeks All msured banks report deposit data as of the last day of each quarter on the call reports 3 These data gena Durmg the period under study, the sprmg and fall call dates vaned from year to year Data for nonmsured banks are available only for the June and December call dates No s1gmficant problems appear to have been encountered m esumatmg the deposits of these banks https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis Improvmg the Monetary Aggregates· Staff Papers TABLE 2 Ratios of Nonmember DDA to Country Bank Data Call date 1967-June Dec 1968-June Dec 1969-June Dec. 1970-June Dec 1971-June Dec 1972-June Dec Rt 5471 5562 5614 5730 5969 6136 6178 6307 6365 6585 6808 6953 Call date 1973-Mar June Oct Dec 1974-Apr June Oct Dec 1975-Apr June Sept Dec R, 7230 7357 7361 7553 7587 7709 7796 7889 7849 8029 8057 8174 erally become available 4 or 5 months after the call date To estimate nonmember DDA for a given statement week by the present method, the Federal Reserve staff first tletermmes the ratios of nonmember DDA to the DDA of a subset of member banks, the "country banks," 4 on the call dates that precede and follow the statement week A series of these ratios 1s displayed m Table 2 A lmear mterpolation of the call-date ratios with smtable adjustment for changes m bank structure yields the estimated ratio for the statement week The estimate of nonmember DDA 1s obtamed by muluplymg the estimated ratio by the reported country bank DDA for that week Before the rat10s of nonmember DDA to country bank DDA become available for the call dates, they are estimated by extrapolatmg the senes of ratios obtamed from the call reports that are available Suppose, for example, that the statement week is the first week m January The "1mual estimate" of nonmember DDA is made durmg the fourth week m January even though the series of known ratios from the call reports extends only to June of the precedmg year 5 Extrapolations are 4 "Country banks" 1s the class1ficat10n of a group of member banks pnor to November 9, 1972 Although the term 1s no longer officially used to descnbe these banks, the group still exists and will be referred to as country banks m this report s In this report, we will be d1scussmg revmons and errors m the esl!mates of nonmember DDA Smee the d1scuss1on begms with the estimate made 3 weeks after the statement week, rev1s10ns and errors will be due solely to uncertamty about nonmember DDA and not to uncertamty about country bank DDA, which 1s known by this lime Our "m1tial esl!mate" corresponds to the first rev1S1on discussed m Improving the Monetary Aggregates Report of the Advisory Com mzttee on Monetary Statistics (Board of Governors of the Federal Reserve System, 1976), p 25 57 Nonmember Banks and Estimation of the Monetary Aggregates made f10m this known senes to obtam 1at10s for December and March, which are mterpolated to obtam the estimated rat10 for the January statement week Mult1plymg tlus estimated rat10 by reported country bank DDA for the statement week yields the m1tial estimate In February, the September rat10 1s calculated by usmg the September call report data, which have JUst become available New extrapolations are made to rat10s for December and March, the mterpolation procedure 1s repeated, and a revised estimate 1s obtamed for the January statement week In May, when the Decembc1 call report data are available, a new extrc1polat1on 1s made to March, and the known December and extrapolated March 1at10s are mterpolated as before to obtam a third estimate for the January st,ttement week The March call report data then become available m July Interpolatmg the known December and March rat10s yields the fourth and final estimate of nonmember DDA for the statement week Each of the estimates was made by usmg the same value for country bank DDA, only the estimate of the ratio of nonmember bank ODA to country bank ODA 1s revised In the hypothetical example, four estimates were made, and the final one was made 6 months ,tfter the statement week In practice, three or four estimates (or, rarely, two) are made with the final estimate made 3 to 8 months after the statement week The number of estimates and the lag depend on the position of the statement week with respect to the call dates, the time between the call dates, and the time 1 eqmred to process the call report data Throughout the procedure, the estimates ,md proJecuons are modified to account for structural changes (banks droppmg their membership, nonmember banks mergmg with member banks, and so on) For example, 1£ a country bank resigns from the System, the estimated rat10 for that week 1s revised upward, and rat10s for succeedmg weeks are obtamed by mterpolatmg between the revised rat10 and a revised extrapolated rat10 for the next call date The process of extrapolatmg the series of ratios was exclusively a Judgmental one prior https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis to 1974 In early 1974 a regress10n model was developed that appeared to explam, m large part, the variation m the series 6 Tlus model 1s now used to provide pred1ct10ns, which a1e Judgmentally mochfied, of the nonmembe1 DOA and count1 y bank DOA ratios The regress10n model 1s of the fo1m (1) Rt = bo + bit + b2ti + b3 RTBi whe1e R 1 1s the estimated rat10 of nonmember bank DDA to country bank DDA at time t and RTB 1 1s the average 91-day T1easury hill rate fo1 the half year precedmg t The Treasm y bill rate 1s a proxy for the constellation ot sh01t-tc1m money market mte1est rates beheved to mfiuence the demand f01 demand deposits It enters the equation with a s1gmficantly positive coefficient presumably beCc1use the elasticity of the demand funct10n for demand deposits at nonmember banks 1s Iowe1 than that at counu y banks The present procedme 1s to refit Equation I to the ratios each time a new ratio becomes available and then to extrapolate the resultmg equat10n The extrapolations then undergo some Judgmental adjustments, and the estimat10n proceeds as described earher Equat10n 2 1s an example of how the regress10n model provides a good fit This equation was estimated on May 13, 1974, when the December 1973 call report data first became available The estimated equation and standard errors of the coefficients (m parentheses) are (2) R., = 52496 + 00559t ( 00817) ( 00163) + 00064t 2 ( 00010) + 00359RTB 1 ( 00121) whe1e t = I for June 1967 and mcreases one umt each 6 months The equation explams 99 4 pet cent of the vanat10n m Rt The standard enor of the estimate 1s O0034 Country bank DDA was about $78 3 b1lhon at the time, so the O 0034 standard error for the a See Darwm L Beck and Joseph Sedransk, "Rev1S1ons of the Money Stock Measures and Member Bank Reserves and Deposits," Federal Reserve Bulletin, vol 60 (February 1974), pp 81-95 58 Improvmg the Monetary Aggregates Staff Papers rat10s translates mto a standard error of about $266 million for nonmember bank DDA estimates Unfortunately, Equat10n 1 does not fit as well outside the sample penod as it does mside the period For example, when Equation I was extrapolated after receipt of the December 1974 call report data, the estimated ratios for Apnl and June 1975 were 0 7697 and 0 7845, respectively As can be seen from Table 2, these estimates are m error by O 0110 and 0 0136 or, m dollar terms, about $860 million and $1,060 milhon-far m excess of the standard error withm the sample penod Why the equat10n breaks down outside the sample penod is not known The present-method estimates over the penod studied, from the week endmg August 28, 1974, to Apnl 16, 1975, are shown m Table 3 The first entry m each line of the table is the mitial estimate for that statement week (made about 3 weeks later), followed by succeedmg estimates as additional call reports aie processed The last entry m each lme is the final estimate, and the differences between the final estimates and the early estimates are given m the columns labeled "Revision" For example, the June 1974 call report was not available until October 30 The imtial estimate for September 18 of $57,251 million was based on an extrapolation from the Apnl 1974 call report The senes was revised on October 30, takmg mto account the June call 1eport data This revis10n yielded an mtenm estimate fo1 September 18 of $56,774 milhon This estimate was further revised on January 31, 1975, when the October 1974 call report data were processed By this time, direct observat10ns of the ratio of nonmember to country bank DDA were available for dates before and TABLE 3 Estunates of Nonmember DDA Usmg the Present Method, 1974-75 In m11hons of dollars Last call report avadable at time of estimate End of week Apr 1974 Estimate 1974-Aug 28 Sept 4 11 18 25 Oct 2 9 16 23 30 I Rev1s1on I I June 1974 Estima\e I Revtston I I Oct 1974 Estimate I I Revts1on I I Apr 1975 I RevtSton I Estimate Dec 1974 Estimate 55,204 56,006 57,390 57,251 55,620 -534 -571 -614 -641 -652 54,785 55,566 56,926 56,774 55,142 -115 -131 -150 -164 -174 54,670 55,435 56,776 56,610 54,968 55,064 -679 55,113 56,228 57,460 56,852 55,983 -188 -205 -224 -257 -290 54,925 56,023 57,236 56,616 55,749 -21 -56 56,595 55,693 Nov 6 13 20 27 56,859 57,846 57,514 56,620 -334 -406 -412 -442 56,634 57,627 57,292 56,392 -109 -187 -190 -214 56,525 57,440 57,102 56,178 Dec 4 11 18 25 57,711 58,354 58,685 58,451 -560 -602 -640 -674 57,487 58,134 58,465 58,229 -336 -382 -420 -452 57,151 57,752 58,045 57,777 1975-Jan 1 8 15 22 29 59,554 60,389 -724 -775 59,338 60,221 59,464 58,057 56,054 -508 -607 -682 -732 -772 58,830 59,676 58,912 57,510 55,525 -62 -130 -185 -243 59,614 58,782 57,325 55,282 Feb 5 12 19 26 56,322 56,586 56,412 55,620 -857 -940 -1,020 -1,074 55,767 56,006 55,816 55,020 -302 -360 -424 -474 55,465 55,646 55,392 54,546 Mar 5 12 19 26 56,539 57,437 56,959 56,239 -1,185 -1,290 -1,351 -1,410 SS,900 56,759 56,271 55,547 -546 -612 -663 -718 55,354 56,147 55,608 54,829 Apr 2 9 16 57,077 58,979 59,970 -1,500 -1,687 -1,834 56,364 58,169 59,087 -787 -877 -951 55,577 57,292 58,136 https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis Nonmember Banks and Estimation of the Monetary Aggregates after September 18, and an mterpolation yielded the final estimate of $56,610 million 7 Thus, the Federal Reserve's estimate of nonmember DDA for the week of September 18, 1974, was $57,251 million until October 30, from October 30 to January 31, 1t was $56,774 million, and after January 31, It was $56,610 million The total rev1s10n was $641 million, and the rev1s1on of the mte11m estimate was $164 million During the study pe11od, each successive estimate was closer to the final estimate than was Its predecessor Typically, one would expect the revised estimate to be better than the m1trnl one, but there 1s no guarantee of this A rev1s10n of an m1trnl estimate 1s simply a new estimate that uses the add1t10nal mformatlon provided by new call report data There 1s no guarantee of the accuracy of the final series, which 1s JUSt a set of estimates made after all data believed to be relevant are available Only nonmember deposits as of the smgle day call report dates are known with certamty Insofar as rev1s10ns are concerned, the study pe110d 1s typical of the general experience 5mce 1970 The root mean square of the total rev1s10ns for the weeks of the three call dates (October 15, December 31, and April 16) covered by the study period 1s $1,146 million The 1oot mean square of all such revISlons from 1970 to September 30, 1975, 1s $1,116 million A few of the weekly-average estimates could be improved 1f the call report data had been processed more qmckly If, for example, the June 1974 call report data had been processed w1thm ~ rather than 4 months-that Is, by September 30-the 1mt1al estimate of $57,251 million for the week of September 18 would not have been made Instead, the m1t1al estl7 A m1S1nterpretat1on of the October 1974 call report resulted m an overstatement of nonmember DDA fo1 October 16 of $574 mllhon The error wa~ dis covered and corrected m May 1975 dunng the Decem ber benchmarkmg In an effort to ehmmate the effects of the mmnterpretauon, which 1s totally unrelated to the matters at hand, $574 m1lhon was subtracted from all estimates based on the October call data Thus, for example, the total rev1S1on for Apnl 16, 1975, was actually $2,408 m1lhon but 1s given m Tables I and 3 as $1,834 m1lhon https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 59 mate would have been the one m the June column of Table 3-$56,774 million-and the total benchmark revIS1on for that week would have been $164 milhon, not $641 mzlhon On the othe1 hand, the 1mtial estimate for the week of September 4 would still have been based on call data only through April, so the total rev1s10n of $571 m1ll10n for that week would be unaffected by the I-month reduction m processmg time In general, 1f processmg time were reduced to 3 months, 11 of the 34 total revIS1ons considered here would have been reduced FDIC-sample estimates The FDIC experimental sample was d1v1<led accordmg to the banks' total deposits mto 5even strata, 1angmg from less than $5 million to more than $100 million Average nonmember bank DDA for week t, for example, was estimated by usmg the separate ratio estimator (3) Y(t) where y11 (t) 1s the average aggregate DDA of the stratum h sample banks durmg week t, y11 (c) 1s the aggregate DDA m the sample banks as reported on the most recent available call report, and Y11 (c) 1s the aggregate DDA m all stratum h nonmembe1 banks as repo1 ted on the most recent call report The first formula-the one most often found m textbooks-expresses the notion that the aggregate of all stratum h banks 1s estimated to have grown at the same rate as the aggregate of sample stratum h banks The second formulation of the estimator m Equat10n 3 1s p1esented m order to emphasize the similarity between the sample estimator and the present-method estimator In the present method, a projection of the ratio of nonmember bank DDA to country bank DDA 1s made and, m turn, 1s mult1phed by the known weekly-average country bank DDA The sam- Improvmg the Monetary Aggregates Staff Papers 60 DDA are presented m Table 4 The difference m total rev1S1ons between the sample and the present-method estimates 1s stnkmg While total rev1S1ons of the present-method estimates ranged from $205 million to 11,1,834 million over the study penod, those of the sample estimates were much smaller, rangmg from $20 million to $410 million 8 Of the 65 m1t1al and mtenm sample estimates m Table 4, only 2 reqmred larger rev1S1ons than did the correspondmg present-method estimates ple estimate for stratum h banks 1s constructed by estimatmg the ratio of nonmember bank DDA to sample bank DDA and then mult1plymg by the known weekly-average sample bank DDA Summmg all strata gives the estimated aggregate The accuracy of either method depends on the accuracy of the estimates of the respective rat10s The mtenm and final sample estimates are also analogous to those of the present method When a new call report becomes available, an updated ratio of nonmember bank DDA to sample bank DDA 1s obtamed and applied to the known sample bank DDA for week t When call reports for dates before and after week t are available, a lmear mterpolation of the two ratios 1s applied to the sample bank DDA fo1 week t m order to obtam the final estimates .,, The sample estimates of nonmember bank s The revmons m Table 3 for the present-method c~Umates are "smooth" funct10ns of time This 1s due solely to the mterpolat10n procedure In prmc1ple, the revmons of the sample estimates should also be smooth They were not because (1) structural changes occurred mvolvmg the sample banks, (2) data from as many as 15 banks per week were screened out as "outliers," and (3) ddfermg numbers of banks reported each week Of the 573 banks asked to report, the number actually reportmg ranged from 439 to 550 TABLE 4 Sample Estimates of Nonmember DDA, 1974-75 In m11lmns of dollars Last call report available at time of estimate End of week 1974-Aug 28 Sept 4 11 18 25 Oct 2 9 16 23 30 Apr 1974 I June 1974 I Oct 1974 I Revts1on 53,618 54,881 56,064 56,094 54,078 410 389 287 204 363 53,778 55,109 56,408 56,374 54,392 290 161 -57 -76 -49 54,028 55,270 56,351 56,298 54,441 54,250 408 54,676 55 958 56,959 56,324 54,924 -20 28 47 191 -18 54,658 55,938 56,987 56,364 55,124 7 -9 56,371 55,115 Estunate I Revision I Esttmate I I Apr 1975 I Rev1s1on T Esttmate Dec 1974 Estimate I I Revts1on I Estimate Nov 6 13 20 27 56,603 57,445 56,992 55,842 284 129 34 23 56,867 57,513 57,041 55,941 20 61 -15 -76 56,887 57,574 57,026 55,865 Dec 4 11 18 25 56,817 57,331 57,862 57,106 162 51 71 261 57,049 57,422 57,870 57,418 -70 -40 63 -51 56,979 57,382 57,933 57,367 1975-Jan 1 8 15 22 29 58,081 59,820 133 296 58,430 59,963 58,429 58,046 54,858 -216 153 259 -59 145 58,214 60,135 58,666 57,953 54,906 -19 22 34 97 60,116 58,688 57,987 55,003 Feb 5 12 19 26 na 55,995 55,935 54,709 -67 -69 53 na 55,905 55,898 54,693 23 -32 69 na 55,928 55,866 54,762 Mar 5 12 19 26 56,396 57,001 56,765 54,793 -290 -235 -91 30 56,147 56,801 56,498 54,582 -41 -35 176 241 56,106 56,766 56,674 54,823 2 55,643 57,911 58,564 -133 -213 -179 55,619 57,888 58,531 -109 -190 -146 55,510 57,698 58,385 Apr 9 16 n a Not available https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 61 Nonmember Banks and Estimation of the Monetary Aggregates In add1t10n to requmng smaller benchmark rev1s10ns, the sample provides a somewhat different vers10n of the h1stoncal senes from that of the p1esent method These estimates-the last columns of Tables 3 and 4aie repeated in Table 5 The sample estimates tended to be lower than the presentmethod estimates in 1974 and higher in 1975 In part, these differences may be clue to the single-day call reports The accuracy of either method depends upon its ratio (nonmember to country bank or nonmember to sample bank) as determined from the call report data and how rep1esentat1ve 1t 1s of the days and weeks surrounding the call report date To the extent that the rat10s of weekly (or monthly) averages are subject to less random vanat10n than smgle-day rat10s, the accuracy of the e~t1mates would be improved 1f all nonmem- ber banks reported deposit data for a week (month) along with their call rep01 ts 9 On the other hand, there 1s cons1de1 able week-to-week vanab1hty in the differences between the two senes For example, the sample estimate was $1 bilhon lugher than the cor1esponding present-method estunate for March 19, but a week later 1t was $6 million lower Tlus vanat10n in the differences would still 1emain 1f add1uonal data were available on the call 1ep01 ts That 1s, even 1f, for example, deposit data for a week had been provided on the call 1eports, there would still have been large d1ffe1ences between the sample and the present-method estimates because of the chffe1ent week-to-week movements in the deposits of the sample banks and the deposits of the country membe1 banks Accuracy of the sample estimates TABLES Fmal Nonmember DDA Series Generated by Two Methods, 1974-75 In mdbons of dollars End of week 1974--Aug 28 Sept 4 11 18 25 Present method Sample 54,670 55,435 56,776 56,610 54,967 54,028 55,270 56,351 56,298 54,441 642 165 425 312 527 Difference Oct 2 9 16 23 30 54,925 56,023 57,236 56,595 55,693 54,658 55,938 56,987 56,371 55,115 267 85 249 224 578 Nov 6 13 20 27 56,525 57,440 57,102 56,178 56,887 57,574 57,026 55,865 -362 -134 76 311 4 11 18 25 57,151 57,752 58,045 57,777 56,979 57,382 57,933 57,367 172 370 112 410 1975-Jan 1 8 15 22 29 58,830 59,614 58,782 57,325 55,282 58,214 60,116 58,688 57,987 55,003 616 -502 94 -662 279 Feb 5 12 19 26 55,465 55,646 55,392 54,546 na 55,928 55,866 54,762 -282 -474 -216 Mar 5 12 19 26 55,454 56,147 55,608 54,829 56,106 56,766 56,674 54,823 -752 -619 -1,066 6 Apr 2 9 16 55,577 57,292 58,136 55,510 57,698 58,385 67 -406 -249 Dec na Not available https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis The usual formula for estimating the samphng vanance of the separate ratio estimator (the estimator used to construct the sample estimates) 1s10 (4) s2 = L ~ Nh(Nh - nh)sh2/nh h=l whe1e N,. 1s the numbe1 of banks in stratum h, n,. 1s the number of sample banks in stratum h, L 1s the number of strata, and sh 2 1s the sample vanance around the stratum h regress10n line nh (5) Sh2 = ~ [yh,(t) - ThYh,(c)]2/(nh - 1) ,~1 where Yh,(t) 1s the DDA of the tth bank in stratum h at time t, y11 ,(c) 1s the corresponding value on a call report, and 9 Smee March 1976 the FDIC has been collecting 7 days of deposit data from nonmember banks along with each call report 10 See, for example, Wilham G Cochian, Sampling Techniques (Wiley, 1963), p 158 The sampling variance refers to the variation among estimates based on the potential samples that could be selected, not to the vanat1on of weekly estimates based on a given sample 62 Improvmg the Monetary Aggregates Staff Papers is the estimated ratio of stratum h DDA for the statement week to its DDA given on the call report Equation 4 is appropnate when the samplmg withm a stratum is done on a purely random basis In the application discussed here, the samplmg was not done on a purely random basis, rather, the sample was constramed so that its distribution (geographic, urban-rural, and so on) would reasonably reflect that of the populat10n of nonmember banks Thus, Equat10n 4 would not seem to be an appropriate estimator of the variance of the sample estimates However, 1t can be plausibly argued that Equation 4 should give an upper bound (possibly a crude one) for the variance of the sample estimates Let u::ii represent the variance of estimates based on any conceivable sample, mcludmg the ones that would have been reJected as unrepresentative Roughly half of the samples will yield s 2 's smaller than u~ii and half will yield s2's larger than u;11 Among the samples yieldmg smaller s2 's will be the geographically homogeneous ones, precisely the ones that would have been reJected as unrepresentative The samples yieldmg the larger s2 's are the ones that mcorporate the geographic variat10n-the "representative" samples Thus, smce representativeness is reqmred, the value of s2 yielded by the sample 1s likely to overestimate uJii Furthermore, u~ 11 Itself is likely to overstate the actual samplmg variance smce 1t is the variance of a set of estimates that should have a larger dispersion than has the set of estimates based on representative samples Equat10n 4 was applied to the sample data for the week of October 16, 1974, and the June 1974 call report data to obtam an estimated upper bound for the sampling standard error of the mitial estimate of about $300 million Calculat10ns for other weeks gave similar results Usmg the normal approximation, we may say that we are at least 68 per cent confident that a sample imtial estimate is withm $300 million of actual nonmember bank DDA, or at least 95 per cent confident that a sample 1mtial estimate is w1tlun $588 million of actual nonmember bank DDA The sample https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis final estimates, bemg eqmvalent to weighted averages of imtial estimates, will have somewhat smaller sampling standard errors 11 From Table 5, we note that the presentmethod final estimates differ from the correspondmg sample final estimates by as much as 3 5s ($1,066 million for the week of March 19, 1975) We mfer that the present-method final estimates depart substantially from "truth" as well as that movements of nonmember DDA between call dates differ from those of country banks A more direct way of mvestigatmg the accuracy of these particular sample (and presentmethod) estimates is to consider estimates made for the call dates Aside from reportmg errors-and the deposits of nomnsured banks on the sprmg and autumn call dates-we know aggregate nonmember bank DDA on these dates We can construct estimates for these dates m exactly the same way as we constructed weekly-average estimates JUSt substitute the call date DDA for the weeklyaverage DDA for the sample banks or for the country banks m the present-method estimates Then by comparmg the mitial estimate with the aggregate determmed from the call report, we obtam the erro1 resultmg from the method for that smgle day In the case of the sample estimates, these smgle-day errors are likely to be larger than those for weeklyaverage estimates because of the additional day-to-day vanat10n 12 The results of these calculations are given m Table 6 The Imes labeled "Estimate" give the actual estimates that were made, while the Imes labeled "Estimate with call data" gwe the estimates that would have been made had the sample banks (or the country member banks for the present method) reported the same deposits m the survey as they did m the call report The differences between these two Imes mdicate the effects of reportmg errors 11 As shown m Appendix 1, the samplmg standard error of a final esumate for a week about halfway betneen two call dates 1s at most about i240 m1lhon 12 This pomt 1s elaborated m Appendix 2, where 1t 1s also shown that errors committed by the sample estimates of weekly averages are hkely to be smaller than the rev1s1ons of those estimates Nonmember Banks and Estimation of the Monetary Aggregates 63 TABLE 6 Estimates of Nonmember DDA on Call Dates, Selected Methods, 1974-75 In mtlhons of dollars Last call report avatlable at time of estimate Method and data used I I June 1974 Estimate I Error Oct 1974 Estimate I Error I I Dec 1974 Estimate I Error Estimate for October 15, 1974 (actual = 58 228) Present method Estimate Estimate with Oct call data Sample method Estimate Estimate with Oct call data 58,452 58,583 224 355 58,124 58,192 -104 -36 Estunate for December 31, 1974 (actual = 60,333) Present method Estimate Estimate with Dec call data Sample method Estimate Estimate with Dec call data 60,858 61,041 525 708 60,659 60,474 326 141 59,917 60,198 -416 -135 60,290 60,579 -43 246 Estimate for Apnl 16, 1975 (actual = 58,658) Present method Estimate with Apr call data Sample method Estimate Estimate with Apr call data The actual present-method mitictl estimates chffered from the three call report aggregates by $224 million, $525 million, ctnd $1,755 milhon The sctmple mitial estimates differed from the call report aggregates by $104 million, $416 million, and $141 milhon-a 74 per cent improvement on average If the sample banks and the country membe1 bctnks had reported in the1r respective surveys the data they lctte1 reported in the call reports, the peicentage improvement would have been even greater The root mean square error of the five sample smgle-day miual and mtenm estimates was $210 million As shown m Appendix 3, tlus amount translates mto a root mean square error for the final sample weekly-average estii ates of, at most, $130 million to $167 million, with the size of the bound dependmg on the closeness of the statement week to the call date Thus, the final sample senes appears to be considerably more accurate than the present h1stoncal senes 60,413 60,499 1,755 1,925 59,558 59,642 900 984 58,799 58,809 141 151 58,776 58,787 ll8 129 raises two questions Would estimates of nonmember bank DDA based on data from a group of member banks similar to the FDIC sample banks perform equally well? Can satisfactory estlmcttes be obtamed by using data from a subset of the sctmple-for example, the 178 large nonmembe1 bctnks? The following d1scuss10n addresses these issues The matched-banks method For each of the 573 sample nonmember banks, the staff of the FDIC found ct membei bank that was similar with respect to size and location Dally deposit data are available for these matched banks as they are for all member banks Estimates of nonmember bank DDA were then constructed by using the matched banks as 1f they constituted the sample of nonmember banks, that 1s, Equation 2 was applied with the matched-banks DDA substituted for the sample-banks DDA The results can be summauzed in two ways First, the rev1s10ns of the matched-banks estimates are presented in Table 7 13 The re- Alternative est1mat10n procedures The increased accuracy of the FDIC sample esumates over the present-method estimates https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 13 At the time this portion of the expenment wa~ conducted, sufficient data for makmg estimates were available only through January I, 1975 64 Improvmg the Monetary Aggregates Staff Papers TABLE 7. Estimates of Nonmember DDA Usmg Matched Member Banks, 1974-7S In mtlhons of dollars Last call report available at time of estimate End of week Apr 1974 Estimate 1974-Aug 28 Sept 4 11 18 25 Oct 2 9 16 23 30 I June 1974 I Revmon I Estimate I I l Oct 1974 I Rev1s1on Estimate I Revmon I Dec 1974 Estimate 53,248 53,969 55,171 55,037 53,452 1,309 1,342 1,527 1,534 1,503 54,488 55,237 56,470 56,332 54,705 69 74 228 239 250 54,557 55,311 56,698 56,571 54,955 53,514 1,567 54,770 56,164 57,263 56,864 55,982 311 291 338 348 372 55,081 56,455 57,601 57,201 56,338 11 16 57,212 56,354 Nov 6 13 20 27 56,814 57,611 57,064 56,158 483 505 515 523 57,252 58,056 57,504 56,595 45 60 75 86 57,297 58,116 57,579 56,681 Dec 4 11 18 25 57,257 57,993 58,203 57,656 491 500 335 310 57,714 58,456 58,666 58,117 34 37 -128 -151 57,748 58,493 58,538 57,966 1975-Jan I 58,912 290 59,377 -175 59,202 v1s1ons, rangmg up to $1 5 b1lhon, are considerably larger than the rev1S1ons of the sample estimates (Table 4) and are of the same order of magmtude as those of the present method (Table 3) Second, a comparison of final estimates for the matched-bank and sample methods 1s given m Table 8 Smee these estimates differ by as much as $1 2 billion, It appears that the matched banks do not track nonmember deposits very well between call dates TABLE 8 Nonmember DDA Senes Generated by Two Methods, 1974-75 In mtlhons of dollars End of week 1974-Aug 28 Sept 4 11 18 25 Sample method Matched-banks method 54,028 55,270 56,351 56,298 54,441 54,557 55,311 56,698 56,571 54,955 -529 -41 -347 -273 -514 Difference Oct 2 9 16 23 30 54,658 55,938 56,987 56,371 55,115 55,081 56,455 57,601 57,212 56,354 -423 -517 -614 -841 -1,239 Nov 6 13 20 27 56,887 57,574 57,026 55,865 57,297 58,116 57,579 56,681 -410 -542 -553 -816 Dec 4 11 18 25 56,979 57,382 57,933 57,367 57,748 58,493 58,538 57,966 -769 -1,111 -605 -599 58,214 59,202 -988 1975-Jan https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis Large-banks method To evaluate the usefulness ol depos1 t data obtamed only from the 178 large nonmember banks, an estimator was constructed that 1s essentially a mix of the present-method and sample estimators The data for the 178 large nonmember banks were used to estimate the DDA of those nonmember banks reportmg more than $100 million (the lughest stratum) m total deposits m the call report, JUSt as they were m the sample method The DDA of the smaller nonmember banks was estimated by formmg the rat10 (small nonmember bank DDA)/(country member bank DDA), for each call date smce 1967, fittmg a regressionquadratic m time and lmear m mterest rates-to these ratios, and proceedmg exactly as m the present method We call this the largebanks method The estimates and their rev1s1ons are given m Table 9 These estimates reqmred larger rev1S1ons than did those of the sample but represented a considerable improvement over the present method Experience with the present method md1cates that care should be taken m extendmg the results of the large-banks method beyond the mitlal study period The regressions for estimatmg small nonmember bank DDA may easily deteriorate as did the present-method regress10ns The final estimates for large banks dif- Nonmember Banks and Estimation of the Monetary Aggregates 65 TABLE 9, Estunates of Nonmember DDA Usmg the Large-Banks Method, 1974-75 In m1lhons of dollars Last call report available at time of estimate Apr 1974 End of week Estimate 1974-Aug 28 Sept 4 11 18 25 Oct 2 9 16 23 30 I Rev1S1on June 1974 I I Estimate I Rev1S1on Oct 1974 I I Esllmate I Rev1S1on I I Dec 1974 Esllmate 54,912 55,994 57,107 57,185 55,119 -475 -489 -373 -372 -483 54,589 55,682 56,952 57,060 54,896 -152 -177 -218 -247 -260 54,437 55,505 56,734 56,813 54,636 55,163 -326 55,112 56,144 57,275 56,669 55,667 -275 -301 -328 -347 -368 54,837 55,843 56,947 56,359 55,313 -37 -14 56,322 55,299 I Revmon l I Apr 1975 Esllmate Nov 6 13 20 27 57,033 57,814 57,610 56,506 -336 -380 -368 -311 56,734 57,488 57,302 56,269 -37 -54 -60 -74 56,697 57,434 57,242 56,195 Dec 4 11 18 25 57,295 57,785 58,183 57,833 -339 -533 -503 -423 57,083 57,509 57,936 57,703 -127 -257 -256 -293 56,956 57,252 57,680 57,410 1975-Jan I 8 15 22 29 59,151 59,927 -412 -307 59,059 59,609 58,479 57,117 55, IOI -320 11 -222 -344 -333 58,739 59,681 58,348 56,888 54,919 -61 -91 -115 -151 59,620 58,257 56,773 54,768 Feb 5 12 19 26 na 55,574 55,538 54,562 -416 -433 -382 na 55,349 55,338 54,467 -191 -233 -287 na 55,158 55,105 54,180 Mar 5 12 19 26 55,827 56,551 56,270 55,432 -525 -528 -603 -592 55,559 56,320 55,927 55,133 -257 -297 -260 -293 55,302 56,023 55,667 54,840 Apr 2 9 16 56,244 57,961 58,820 -534 -539 -589 56,117 57,857 58,701 -407 -435 -470 55,710 57,422 58,231 n a Not available fered from the correspondmg sample final estimates by dS much as 1H billion, mdicatmg that the movements of nonmember deposits between call dates have still not been captured TABLE 10 Series for the Estunahon of Small Nonmember Bank DDA 1 Call report date 1967 Dec 1967 June 1968 Dec 1968 June 1969 Dec 1969 June 1970 Dec 1970 June 1971 Dec 1971 June 1972 Dec 1972 Spnng 1973 June 1973 1973 Fall Dec 1973 Spnng 1974 June 1974 Fall 1974 June SNM/LNM 3 3 3 3 3 3 3 3 3 3 2 2 3 2 3 2 3 3 3 5612 4898 4701 4701 2417 1893 1286 1529 0354 0886 9816 9519 0428 9462 0733 9805 0861 0253 1380 SNM/CB 4403 4499 4465 4570 4620 4715 4709 4811 4818 4973 5041 5123 5284 5354 5413 5521 5575 5582 5687 Treasury bill rate 4 085 4 185 5 275 5 39 6 14 7 18 6 89 5 84 4 04 4 615 3 595 4 535 5 28 6 15 7 46 7 91 7 56 7 885 8 17 1 SNM = small nonmember banks, LNM = large nonmember banks, CB = commercial banks https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis Anothet suggested approach is to use the large nonmember banks to estimate the DDA of the small banks duectly We have been unable to find any relationship between the large and small banks that works as well as the method Just outlmed Call report data used to pursue this alterndtive are presented m Table 10 Conclusions This study was mitiated m response to mcreasmg concern about the large revisions of the money stock brought about by the extensive revis10ns of the estimates of nonmember bank DDA These revis10ns, m turn, are caused by a lack of understandmg of the forces that cause movements of nonmember bank deposits to differ from those of member bank deposits One approach to reducmg the s12e of the revisions is to gam a better under- 66 Improvmg the Monetary Aggregates Staff Papers standmg of the forces governmg nonmember bank deposits, but given the paucity of data on nonmember deposits-which are available for only 4 days per year-the p1ospects for this approach appear hm1ted A second app1oach 1s to estimate nonmember DDA directly by collectmg daily deposit data from a subset of nonmember banks s1m1lar to the sample selected by the FDIC The estimates based on the sample reqmred much smaller rev1S1ons than did the present-method estimates-the accuracy, as measured by the errors made on call dates, was improved by nearly 75 per cent While the study period was admittedly short, covermg only three call dates, 1t 1s difficult to conceive of any results that could have been obtamed from the FDIC experiment that would have more strongly Justified the use of a sample 14 14 The FDIC plans to remstitute the sample program begmnmg m late 1976 or early 1977 https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis Another problem 1dent1fied m this study 1s that even after all rev1s10ns have been made, the historical estimates of nonmember DDA may be wide of the mark except on call dates The sources of these errors are the different movements of member and nonmember deposits between call dates-for example, different seasonal patterns and the poss1b1ht) that the ratio of nonmember DDA to country bank DDA on the call date may not be representative even of the penod immediately surroundmg the call date Reasonable measures of the relative contributions of these sources of error are not available because of the shortness of the study period Nevertheless, 1t 1s clear that some improvement m the presentmethod final estimates could be obtamed 1f deposit data for more than 1 day were supplied by all nonmember banks m conJuncuon with the call reports Sample estimates would also benefit from the avallab1hty of such data 67 Appendix 1: Sampling Standard Error of a Final Estimate The final esumate 1s a weighted average of two rauo esumates, one based on the call report 1ust precedmg, and the other based on the ca11 report JUSt followmg the statement week The weights reflect the relative lengths of the time mtervals between the statement week and the two caB dates For convemence, assume that the statement week 1s halfway between the two ca]] dates, and suppose that the vanances of the two estimates are equal (to a- 2) Then the samplmg vanance of the final estimate 1s V(f) = u 2 (1 = $232 million We may tlunk of aggregate nonmember DDA, say Y(t), as havmg a trend component, TR(t), and an error component, e 1, which 1s senally mdependent Y(t) = TR(t) + ee Inchv1du,tl nonmember banks behave s1mdarly J (t) = tr(t) + Ut To show that p can be equal to -1, we assume that et= Uc= 0, for all t Thus, when we draw a sample of banks to follow over time, we are really drawmg ,t sample of trend5 Further assume that the trends are sud1 that for any s R.(t) = Y(t)/y.(t) = a, + b.t where y.(t) 1s the aggregate DDA of the banks https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis and The final esumate 1s Y(t) = + p)/2 where p 1s the correlauon coefficient between the two estimates A bound on u ($300 million) was ob tamed m the text We now show that, under reasonable assumpt10ns, p 1s no more than 0 2 ,md may be near -1, winch implies that the standard error of the final estimate hes between zero and (300) (1 2/2) 1 12 m sample s at time t Let t1 and t2 be two consecutive call dates, t 1 < t < t 2 The estimates of Y(t) based on the call reports are [(t2 - t)R.(t1)y.(t) + (t - t1)R.(t2)y.(t)]/(t2 - t1) [(12 - t)R. (ti) + (t - t1)R.(t2)]y.(t)/(t2 - t1) = R,(t)y.(t) = Y(t) l hus, the final estimate 1s Y(t) regardless of which ~ample 1s drawn, the vanance of the final estimate 1s Lero, and the correlauon coefficient p I As the error v<1.nances become large relative to tl1e trend m R,(t), the correlation moves away from -I Io obum an upper bound for p, we take the extreme case that R.(t) 1s a constant-that 1s, all banks follow the same trend and the only source of vanauon m the estimates 1s the random component Specifically, we assume that the variance of an aggregate 1s proportional to Its s12e, that Y(t 1) and Y(t 2) are known, and that the mean of a sample of banks vanes mdependently over time A straightforward extension of the proof of Theorem 2 5 m Cochran's Sampling Techniques shows that the correlat10n between Y 1 (t) and Y2 (t) 1s approximately the same as the correlation between =- and y, (t) - G2y, (t2) = = where G1 Y(t)/Y(t 1), G 2 Y(t)/Y(t 2), and y,(t) represents tl1e mean of the sampled banks at ume Improving the Monetary Aggregates Staff Papers 68 t G1 and G 2 are the unknown trends that all nonmember banks are assumed to follow Now the covariance matrix of y,(t 1 ), y,(t 2 ), and y,(t) IS 0 1/G2 0 (The G's reflect proporuonabty to size and the 13/49 1s the variance of a 7-day average) Hence the covariance matnx between y,(t) - G1 y,(t 1) and https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis y,(t) - G2 y,(t2) IS v 2 (13/49 + G1 <r 13/49 13/49 ) 13/49 + G2 So the upper bound on the correlation between Y 1 (t) and Y 2 (t) 1s approximately p = !! [G! + G1)G! + G2) Jl/2 = 02 when the trend 1s fairly umform over (t 1, t 2) and G1 and G 2 are close to 1 69 Appendix 2: On the Relationship between Errors and Revisions Consider the sample estimates of nonmember DDA for some week t fallmg between the October and December 1974 call dates For convemence, we neglect &trauficauon, nonreporters, structural changes, and so on The esumates are Initial (Xi/x1)Y1 = r1Yt Interim (X./x.)y, = r.y, Final a,(X./x.)y, + (1 - a1)(Xd/xd)y1 = [a,ro + (1 - a1)rd]Y1 where X 1, X,,, Xd are the population aggregates and x1' x 0 , xd are the sample aggregates on the June, October, and December call reports, Yt 1s the average aggregate of the sample banks for week t, and a 1 1s the proporuon of days between the October and December call dates that remam after ume t The 1ev1swn of the m1trnl estimate (Table 4) can be written (A-1) r1y1 - [a1ro + (1 - a1)rd]Y1 = y,{ri - [a1ro + (1 - a,)rdl) ,md the rev1S1011 of the mterim esumate can be written (A-2) roJt - [a1ro + (1 - a1)rd]Y1 = y 1(1 - a,)(r. - Td) From Equation A-1, we see that the revmon of the mmal estimate will be small 1f and only 1f the difference between the rauo r1, determmed from the June call report, and the weighted average 0£ r 0 and rd, determmed from the October and De cember call reports, 1s small From Equation A-2 we see that the revmon of the mterim esumate will be small 1f and only 1f the difference between r0 and ra 1s small or at 1s large (at 1s large when week t 1s close to the October call date) The error made by the m1t1al estimate 1s (Xi/x 1)y, - Y, = y,(Xi/x1 - Y,/y,) = y,(r1 - r,) where Yt 1s the actual population aggregate for week t Similarly, the error made by the mterim esumate 1s v,(r. - r,) https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis and the error made by the final estimate 1s y,[a,r. + (1 - a,)rd - r,] I hese errors will be small 1f rt 1s close to r1, 1 0 , and ra Is Tt close to r1, 1 0 , and 1,1? We cannot directly compare rt wuh the other r factors because us numerator, Y 1, 1s unknown But cons1dcr the sequence r 1 , 1 2 , of daily rauos of the population aggregate to the sample aggregate We have observed a sample of five of these ratios m tlus study r1, r"' rd, and the April 1974 and April 1975 call report rauos 'I he unobserved rauo 1 1 for week t can be regarded as an average of five of these daily rauos 1 Now the r's are sub1ect to two sources of variauon a trend, and random day-to day fluctuation If the trend effect 1s large, then the revmons will be large and perhaps only the final esumate will be reasonably accurate (smcc only the final estimate exphc1tly mcorporates a trend effect) If the random fluctuations are large, the rev1s1ons will be large and none of the estimates 1s hkely to be very accurate (although the final estimate 1s hkely to be more accurate than the others) But we have evidence that neither the trend effect nor the random fluctuations are large That evidence 1s the sample of five ratios we obtamed from the call reports That there was not much variab1hty m these ratios 1s evidenced by the smallness of the benchmark revmons We therefore mfer that smce the sample of 1 's showed little variability, the population of r's also would show little variability Thus we can say that rt 1s likely to be close to r1, r0 , and rd, and that the errors mcurred by usmg r1, r0 , or r,1 m the estimate are small We have shown that small rev!Slons of the simple rauo estimate are associated with small errors of the estimate To see that the same conclusion applies to the separate ratio estimate, the argument 1s applied to the md1v1dual strata 1 Actually, r 1s a ratio of weekly averages, not an average 1 of daily rat10s This d1stmct10n 1s not crucial to the argu ment, however 70 Appendix 3: Root Mean Square Error of the Final Estimates It was shown m the text that the root mean square error (RMSE) of the five sample m1t1al and mtenm estimates of nonmember DDA on call dates was $210 million Here we formulate a simple model m order to translate that RMSE mto a bound on the RMSE of final weekly-average estimates As before, we neglect stratification, nonreporters, structural changes, and so forth Let t 1 and t 2 be two call dates The ratio estimate of nonmember DDA for day t 2 based on the t 1 call report data 1s that an estimated upper bound for 2u 2y2 can be obtamed by settmg f3 = 0 But then, Ee;2 = 2u2), 2 1s not a function of ume and can be estimated by the mean square error of the five call date estimates ($210 million) 2 Let w be the average value of t for the state ment week and rw be the average of the rt's for that week We regard rw as approximately equal to the ratio of the weekly averages of Yt and y 1 The final estimate for the statement week 1s [(1 - a)r11 where rt= Yt/Yt, Yt 1s nonmember DDA, and Yt 1s the sample-banks DDA on day t The estimate 1s m error by where t 1 and t 2 are the call dates preceding and following the statement week The error committed by the final estimate 1s ew The use of the ratio estimate amounts to guessmg that rt 2 = r 11 and the error, of course, 1s a function of the difference between the r's Suppose that, m fact, rt 1s given by rt = a + {3t + Et where et 1s serially mdependent with mean zero and variance o- 2 Approx1matmg Yt by a constant y (m fact, Yt vanes over short mtervals of time by only a few percentage pomts), the expected squared error may be calculated https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis + ar12]y,., - r,.y,. a)r11 + ar,2 - rw] = [(1 - a)r11 = y[(1 - where agam we have approximated Yw by y After some algebraic mampulauon, we have e,. = y[(1 - a)E11 + aE12 - e,.] where Ew 1s the average of the E t's for the state ment week and thus has variance 13 o- 2 /49 The mean square error of the final estimates 1s Ee! = y 2u 2[(1 - a) 2 + a + 13/49] 2 Settmg 2u 2y2 to our empmcal bound ($210 million) 2 , we obtam the estimated bound on the mean square eror of the final estimate -call It M 2 (a) M 2 (a) By msertmg the appropriate values for ti and t 2 m Equation A-3, we can calculate the expected squared error for any call date estimate For our ultimate purpose of obtammg an upper bound for the root mean square error of a final weekly-average estimate, we will see that we need an upper bound for 2u 2y2 Now, given an empirical estimate of Ee~2 , 1t 1s clear from Equation A-3 + ar12]Yw = 210 2[(1 - a) 2 + a 2 + 13/491/2 M(a) reaches its maxunum value when a= 0 or I, when the statement week 1s the week of a call date M(O) = M(1) = $167 million M(a) reaches its mm1mum value when a= 1/2, halfway between two call dates M(l/2) = $130 million 71 Seasonal Adjustment of the Monetary Aggregates David A. Pierce, Neva Van Peski, and Edward R. Fry Research for this paper was completed in 1975 and early 1976 Consequently, the applzcatwns of seasonal ad7ustment procedures and statistical tests discussed in the paper do not take account of data after 1974 or 1975 Seasonal ad7ustments f 01 the published monetary aggregates series were 1evzsed in February 1977 and March 1978 in accordance with procedures described in the discusszon of "Seasonal ad7ustment of published M 1 series" There was some evidence in monthly data fo1 1976 and 1977 that a new qua1 terly 5easonal pattern wa5 developing in the demand deposit component of M, Based on Census X-11 seasonal ad7ustments, the quarterly pattern of fiuctuation wa5 partially eliminated in the 1978 1evt5ton The Boa1 d's staff has continued to develop and experiment with the daily seasonal facto1 method, as described later The baste program ha1 been improved by including an optwnal log t1ansformatzon and by improving the rnPthod of selectmg harmonic terms to include m the regression In addztzon, work is in progress to take account of changes m the seasonal pattern, by using a iatzo-to-momng-average technique to 1emove seasonality remaining in the irregular component from the series ad7usted by the method desc1 ibed here Thzs is analogous to X-11 except that the weights of the moving aveiage a1e designed to match the 1tatzstzcal characteristics of the particular 1eries Seasonah ty 1s a widespread phenomenon m economic time se11es, and much has been and contmues to be written regardmg Its nature NoTL -The .iuthon .ire on the of Research and Statistics https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis \t.iff of the D1v1s1011 and its treatment The monetary aggregates <1re no exception Particularly with the mcreasmg attention duected toward the monetary aggregates as an mdicator and a target of monetary pohcy, it 1s important to have ,1vailable reluble means for se<1sonally adJustmg the monetary aggregates m order to disentangle purely penodic, calendar-lmked movements m the narrow measure of the money supply (M 1) and related sene5 from others, perhaps economically more meanmgful Procedures for <1ccomph~hmg d reh,1ble 5eason,1l adjustment, mcludmg particularly the development and apphcat10n of a new method, <1re reviewed and compared m this p<1per The adjustment of a senes for "se<1sonal v,m<1t10n" presupposes a not10n or concept of what the term means For the monetary aggreg,1te~ there are at lea 5t three meanmgs The 5ea5onal (facto1 01 component) m the money ,;tock that actually occurs m the data is referred to as the dcsn iptive seasonal In general, It 1s the combmed result of two conceptually distmct clements, referred to as the natural seasonal and the policy seasonal The former anses not only from natur,11 phenomena such as the weather but also from mcial phenomena such as holidays or taxpayment dates The latter 1s the iesult exphotly or implicitly of pohcy decJS1ons of the Federal Reserve-for example, whether to accommodate an mcrease m the natural seasonal m money at Chnstmas 01 to allow mterest rates to nse These chstmct10ns <1re descnbed m more detail m another Board pubhcation, 1 they are 1 Improving the Monetary Aggregates Report of the Advisory Committee on Monetary Statistics (Board of Governors of the Fuleral Reserve System, 1976) 72 Improvmg the Monetary Aggregates Staff Papers made here pnmarily to focus this paper Except for the section on the published seasonally adJusted series, which discusses how the policy seasonal is now estimated, this paper is concerned largely with the descriptive seasonal and with alternative ways to estimate it The first sect10n discusses briefly the nature of seasonality and seasonal adJustment procedures, mcludmg regression and movmgaverage approaches This is followed by a descript10n of the Board's current seasonal adJustment procedure Another section presents an alternative procedure to the Census Bureau X-11 method, suggested by Friedman and developed by one of the authors (Van Peski), for adJustmg any monetary aggregate or other time series for which dally data are available This procedure has the feature that, once daily seasonally adJusted data are determmed, then weekly, monthly, or quarterly seasonal adJustments can immediately be calculated and will be consistent with each other Included also m this section are several tests for stable versus movmg seasonality, concentratmg on the period from 1968-74 (prior to which seasonal shifts such as tax-date changes were known to have occurred) The last section compares three seasonal adJUStment procedures, the ordmary and "fixedfactor" X-11 procedures and the daily procedure developed earlier It is found that, for demand deposits and currency durmg the time period studied, the daily seasonal method gives results qmte close to both the ordmary and the fixed-factor X-11 seasonal adJustment (which are fairly close to each other) This paper is confined largely to an analysis of currency and demand deposits-the two components of M 1-although the procedures developed or described are equally applicable to M 2 as well as to reserve aggregates, mcludmg, with mmor modifications, those series for which weekly but not daily data are available 2 2 See David A Pierce, "Relationships-and the Lack Thereof-Between Economic Time Senes, with Special Reference to Money and Interest Rates," Journal of the American Statistical Association, vol 72 (March 1972), pp 11-26 https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis Nature of seasonality and seasonal adjustment The primary problem m seasonally adJUStmg a monetary aggregate or other time series is the determmation of the part of the series that is purely "seasonal" This determmation is often facilitated by simultaneously determmmg a "trend cycle" as well, with the remamder of the series then referred to as "iri egular " There are two basic schemes for representmg this decompos1t1on The multiplicative seasonal model for a time series {Yt} IS (1) where Pt, St, and E 1 aie, respectively, the trendcycle, seasonal, and irregular factors of Y 1, all at time t Ordmanly the trend factor is the dommant part of the series and retams the umts (dollars, m the case of monetary aggregates) associated with the senes The seasonal and irregular factors, expressed as ratios to trend cycle, are umty when there are no seasonal or irregular effects, and are above or below l, respectively, when the effect of seasonal or irregular mfluences is to mcrease or decrease the level of the series Many economic series exlubit exponential growth and for these the muluphcatlve model is most appropriate For other series, however, an additive model may be more smtable In fact, the additive model may be derived from the multiplicative model by takmg logarithms I£ Yt = log Yt, Pt= log Pt, and so forth, then Equation l becomes (2) Yt = Pt + St + et which is the additive seasonal model The term St is the seasonal component of Yt Of course, m many cases {yt} will be actual series rather than the logarithm of a multiplicatively generated series The seasonally ad7usted series Yf and yf are then (3) Seasonal Ad1ustment of the Monetary Aggregates and (4) yf = Yt - St where the circumflex denotes that the "true" seasonal 1s never known but mstead must be estimated ma smtable manner The problem of (descriptive) seasonal ad1ustment 1s thus the problem of obtammg estimates of the seasonal components or factors To accomplish this, some restrictive assumpt10ns regardmg the nature of the senes must be made, particularly concernmg the nature of the seasonal component St (or factor S1) The remamder of this section bncfly descnbes the assumptions underlymg the X-11 and regress10n procedures for seasonal adJustment Methods now m use for seasonal adjustment generally fall mto one of two broad categories, dependmg on whether the senes' seasonality 1s assumed to be "determm1st1c" (capable of representation by such determm1stic funct10ns of time as smes and cosmes, dummy variables, and mteraction of these with powers of time), or "stochastic" (representable by a seasonal autoregressive movmg-average-ARMA -model, or as a component of such a model) A determ1mst1c seasonal has the feature that it can be predicted without error from seasonals of previous years For example, 1f m Equation 2 the data are monthly and the seasonal component 1s (5) where d 11 , , d 121 are seasonal dummy vanables and }:8 J = 0, then year after year the January seasonal 1s 81 , February's 1s 82 , and so forth In general, regression methods for seasonal adJustment are appropriate for determm1st1c seasonality, and the simplest of these would be a regression on the seasonal dummies m Equation 5 A flexible regression method, which allows for changmg trend and seasonality, 1s that of Stephenson and Farr 3 a "Seasonal Adjustment of Economic Data by Apphcatton of the General Linear Stat1st1cal Model," Journal of the American Statistical Association, vol 67 (March 1972), pp 37-45 https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 73 For stochastic seasonality 1t 1s known that the optimal (mm1mum mean square error) procedure consists of the application of a symmetric movmg average to estimate the seasonal, 4 that 1s, (6) where 8_, = 8, Insofar as Yt is stochastic and only partially predictable from its past, St will also exh1b1t these features Moreover, s 1 and s t+ 12 (for monthly senes) will r,u ely be identical, a pomt to wluch we return shortly The Census X-11 program 1s essentially of this form,5 and m fact Cleveland and Tiao have found a particular ARMA model for which X-11 is nearly optimal 6 The d1stmct1on between determm1stic and stochastic seasonality 1s conceptually a fundamental one, however, m practice it is not always obv10us whether the seasonality ma senes is determm1st1c, stochastic, or both The money supply 1s a pnme example lt i& generally adJUSted by usmg the X-l l program, yet ma subsequent subsect10n 1t will be seen that its seasonality can sometimes be adequately captured with monthly dummy variables And the daily method to be presented uses features of both the regression and the movmg-average approaches A related distmct10n m seasonal adJustment concerns the issue of fixed versus movmg seasonality A senes displays fixed or stable 4 Wilham P Cleveland and George C T1ao, "A Model for the Census X II Seasonal Adjustment Pro gram," Techmcal Report 312 (Umvers1ty of W1sconsm, 1974), and Peter Whittle, P1ed1ction and Regulation by Linear Least Square Methods (English Umvers1lles Press, 1963) s See "The X-11 Variant of the Census Method II Seasonal Adjustment Program," Bureau of the Census Techmcal Paper 15, revised (Government Prmtmg Office, 1967) Add1t1onal features of X II that are outside the symmetric filter framework mclude provmons for outliers and tradmg day variation See Kenneth F Wallis, "Seasonal Ad1ustment and Relat10ns Between Variables," Journal of the American Statistical Assoc1at1on, vol 69 (March 1974), pp 18-31, as well as "X-II Variant" s See Cleveland and T1ao, "Model for the Census X-II" 74 seasonality 1f its seasonal factor for each month remams unchanged from year to year, otherwise, 1t possesses movmg seasonality A fixed seasonal 1s necessarily a determ1mst1c seasonal, as, given knowledge of the true model, 1t can be predicted from year to year without error However, methods such as X-11 can produce estimates of a fixed seasonal 1f constramed to do so, and regressron methods can mcorporate a movmg determrmstic seasonal In mvestrgatmg alternative ways to seasonally adJust the monetary aggregates, It rs important to ascertam whether the evidence 1s m favor of a fixed or a movmg seasonal pattern This quest10n rs addressed m several ways m the third section, as the method presented there assumes a constant monthly seasonal pattern (apart from tradmg-day effects) Improvmg the Monetary Aggregates Staff Papers CHART I M 1 Total and MaJor Components Billions of dollars 300 260 -+Not seasonally adjusted 220 Seasonal adjustment of published M1 series On a contmumg basis the Federal Reserve publishes a seasonally adJusted monthly money supply (M1), and revises the monthly seasonal factors periodically (m general every year) 7 The procedure employed consists essentially of (1) applymg the X-11 program and then (2) Judgmentally mod1fymg the X-11 seasonal factors to take account of elements of both natural and policy seasonals felt to be madequately captured by X-l l (a descnptive method) In this section both aspects of this procedure are discussed The pubhshed seasonally adJusted M 1 series rs derived by summmg separately adJusted currency and demand deposit components This procedure has been followed over the years smce m1t1al publication of the money supply data because of analytical mterest m the two component series 8 Chart 1 shows total 1 The data and seasonal factors are published m the Federal Reserve Bulletin For example, the rev1S1on published m Apnl 1978 reflected both revmons m seasonal factors and other techmcal adjustments See "Money Stock Revmons," Federal Reserve Bulletin, vol 64 (Apnl 1978), pp 338-39 a Compansons of direct adjustment of total M 1 with sums of separately adjusted components md1cate that the resultmg differences m movement are relatively minor https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 180 80 60 1971 1973 1975 M 1 and the cm rency and demand deposit components, both seasonally adjusted and unadJusted, as pubhshed m January 1976 It rs evident from the chart that most of the fluctuation m total M 1 , not seasonally adJusted, reflects seasonal changes m deposit balances The seasonal pattern of currency rs well defined but relatively small m dollar terms Currency growth makes a substantial contributron to the longer-run trend of M 1 , while demand deposits not only contribute to growth but also account 75 Seasonal Ad1ustment of the Monetary Aggregates for most of the irregular fluctuat10ns and longer-run slufts m growth rates The X-11 computation As ment10ned earlier the X-11 program is a ratio-to-movmg-average procedure that m some respects provides considerable flexibility for identifymg seasonal characteristics and for tailoring seasonal adjustment to mdividual series u The X-11 opt10ns employed m adjustmg M 1 mclude computat10n of multiplicative seasonal factors and use of moderately flexible movmg averages to take account of movmg seasonality For M 1 , a mult1plicat1ve relationship of the seasonal component to trend appears to be appropriate for most months smce, under the assumpt10n of an additive relationslup, the seasonal and trend-cycle components appear often to be strongly related, by contrast, the facto1s or components m Equations 1 or 2 are generally assumed to be mdependent This i elat10nship of seasonal to trend-cycle components is seen m Ch,trt 2 (pages 76-77), which chsplays relat10nships of seasonal-irregular differences to trend cycle as computed by an X-11 adcht1ve adjustment for the period 1965-75 As may be noted, the correlauon coefficients mserted on the scatter diagrams are relatively high for 9 of the 12 months Similar correlat10ns for the currency and demand deposit components (not shown m the chart) also are relatively high for 8 of the 12 months, suggestmg that strong relat10nships exist between the dollar amounts of the seasonal component and the level of M 1 Proport10nal changes m the dollar amount of the seasonal and the trend cycle represent multiphcat1ve relat10nships While a multiplicative relationship 1s not perfect, it appears more representative of the seasonal characteristics of M 1 than is the addiuve seasonal alternative, and multiplicative adjustments are used for the published M 1 senes 10 See "X-11 Vanant" Correlat10ns for January, Apnl, and August are relat1vely weak for total M 1 , reflectmg either greater relative fluctuations m the irregular component or 9 10 https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis Another X-11 opt10n employed m M 1 seasonal adjustments is the use of moderately flexible movmg averages to allow for movmg seasonality The X-11 program provides tests for movmg seasonality for mdividual months,offermg the possibility of controllmg the flexibility of the process by which average seasonal factors are derived for each month from the seasonalirregular (SI) rauos 11 These tests suggest that movmg seasonality was a sigmficant characteristic of both the currency and the demand deposit components durmg the 1965-75 period 12 Fmal X-11 seasonal factors were derived by smoothmg the SI rat10s by a 3-term average of a 5-term average of the rat10s Judgmental modifications Fm several reasons the seasonal factors produced by X-11 may not adequately mcorporate httle relat10nsh1p ben1een the size of the seasonal component and the level of M 1 m the5e 3 months It 1s likely that the M 1 5ea5onal 1eflects a wmbmatlon of muluphcame and acl<htnt. 1clat10mh1p5 fhe mulu phcat1ve opt10n 1, used becamt. 1t appear5 to be most wns1stent nllh the obsuved 1dauonsh1p of !vf1 sea 5onaJ5 to trend qcle It m,ty he noted th,ll an adchuve adJmtment of a sencs that d1spl,1y5 muluphcauve relauomh1ps ,1 ill also give reason,1hle rc5ults 1f the add1t1vc dolla1 seasonal factor5 shift horn }l.Jr to yea1 by amounts com1stent with the muluphcauve 5ea5011al 1at105 for 5cncs m which the ,ea5onal component 1s changmg m p10poruon to an expandmg trend cycle, this relat10mh1p can be expres5ed c1thc1 as a stable 1at10 (muluphcat1ve) 01 as a ch.ingmg dolla1 ,,mount (adtht1ve) It 5cems prefeiable to apply ,L muluphca t1vc procedme 111 this case, especially 1f Judgmental mod1ficat10ns are to be made h15toncally and 111 pro iectccl factors for a year ,thead To the c.xtent that mult1phcat1ve relat10ml11ps can be 1ep1e5entcd m stable 1at10 factors, 1t may be ca51er to 1clent1fy ch.tngmg 5c.asonahty resultmg from other mfluence5 11 SI ratios represc.nt the 5<-a5onal 11 regular com ponent of the senes-that 1,, th<- rat10 of the not sea sonally adiusted data to the trend cycle component as computed by X 11 12 Movmg 5ca~onahty rat10s (MSR'5) computed by X 11 1clate average year to year changes of the megu Jar and sea~onal components, 111d1catmg the 1mpo1 tance of average year to year changes 111 the seasonal for a given month relative to changes 111 the nregula1 I his rat10 can be used as a gmdc fo1 controllrng the flex1b1hty allowed m X I I computauom of 5easonal factor5 for any month MSR's computed for M 1 5ugge,t that moderately flex1blc movmg average5 are appropnate for I l of the 12 calendar months 111 the case of currency and for IO months 111 the case of demand deposits 76 Improvmg the Monetary Aggregates Staff Papers the seasonality present m the money supply First, while the smoothed movmg averages are moderately flexible m allowmg for movmg seasonality, Judgmental modificat10n of the X11 results has been desirable to stabilize the computed seasonal factors m some penods and to make them somewhat more flexible m others Such modifications are based on analysis of the computed SI ratios for each month at vanous stages of the X-11 computat10nal process Factors causmg a change m seasonal patterns are taken mto account when known, and impacts of nonseasonal mfluences on the SI ratios also are weighed m modifymg the computed factors If an abrupt shift occurs m SI ratios for a given month, the X-11 averagmg process would take account of this shift only gradually m the seasonal factors for surroundmg years, but the timmg of the change can be sharpened by Judgmental modification when appropriate, as for example m the case of a modification m tax remittance schedules that results m a change m seasonal needs for money In addition, the computed seasonal factors are sometimes changed Judginentally to reduce the weight of SI rat10s that are thought to reflect nonseasonal mfluences m particular years Seasonal factors computed for the latest years get special scrutmy, because X-11 movmg seasonals sometimes are more responsive to fluctuations m SI ratios m termmal years of a senes than seems Justified by contemporary mformat10n on seasonal mfluences In such cases, Judgmental modificat10ns often are made to stabilize the seasonal factors for the last few years of the senes, unless a trend m SI rat10s has been well established or unless there is a known mfluence causmg a shift m the seasonal pattern Judgmental modificat10ns of the computed seasonal factors are constramed by the reqmrement that monthly factors must average approximately 100 per cent over the year (or total 1,200) while hmitmg tendencies CHART2 Relat1onsh1p Between Seasonal Component and Trend-Cycle Component, 1965-75 Seasonal January r= 395 66 • • •• • •• • •• • • • • 50 •• • • August • -14 •• • • •• •• r= 192 280 * Scales dtffer for February and December 200 240 Trend-cycle • 280 • r=- 777 September -18 • -3 0 • -0 4 • • •• • • • -2 2 -3 8 -1 0 • https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis -2 2 • r=- 822 • 04 -12 240 March • •• 200 • • • • • er= 945 • ·- • r=- 937 -0 6 58 July • February* • -0 4 • • ••• -1 2 •• • -2 6 • • 200 240 280 -2 0 Seasonal Adjustment of the Monetary Aggregates toward repetitive movements m the seasonally adjusted data m successive years On balance, these modified X-11 (3 X 5) seasonal adjustments have produced movements m M 1 that tend to be between X-11 (3 X 5) and X-11 (3 x 9) adjustments, movements that have tended more toward a stable seasonal than the X-11 (3 x 5) seasonal adjustments In recent years, a major concern m reviewmg the X-11 M 1 seasonal adjustments has been the tendency toward rapid expansion of this senes m the first half of the year, followed by slower growth m the second half This pattern 1s evident m the half-year growth rates for the most recent years, as shown m Table I In fact, the ummg of all six of the major shifts m expans10n rates m the 11 years was such that first-half growth rates exceeded secondhalf rates substanually However, m each instance these major shifts m growth rates appeared to be trend-cycle m nature rather than seasonal From a techmcal v1ewpomt, some of r= 207 Apnl 77 TABLE 1 Half-Year Changes m M 1 Seasonally adiusted annual rates m per cent • • • 4 0 5 7 5 5 0 6 7 I 8 1 5 9 9 1970 1971 1972 1973 1974 1975 4 9 8 6 5 5 6 3 1 9 3 6 5 3 9 4 3 2 6 5 9 8 9 7 NOTE -Data are derived from seasonally ad1usted levels for June and December Growth rates based on half-year or quarterly averages show similar patterns, except m 1975, m which second-half expansion exceeded that m the first half by these alternattve computations the shifts did not occur m successive years and the t1mmg of turnmg pomts m monthly growth rates vaned from February to August l\Ioreover, the durat10n of fast and slow growth differed somewhat m these periods Most important, the second-half slowmg and the rapid expans10ns that followed m each of r=- 866 •• • • ••• •• r= 523 • November • -0 4 •• • -0 4 • 240 • • • December* r= 920 24 • 08 • 280 • • • •• • •• • 200 NOTE -Amounts are m b1lhons of dollars Variables denved from X-11 additive seasonal adJustment of Mt https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis • • • 200 240 Trend-cycle -0 2 -1 0 •• • • • 16 -1 2 • 280 •• • •• 06 • -44 • r=-944 October 200 •• -3 6 • • • • -2 8 08 • •• • Seasonal r= 853 June • • • • • Hi! 3 5 6 7 4 May 16 I HI 1965 1966 1967 1968 1969 24 • Change Year 240 9I • 75 59 280 Improvmg the Monetary Aggregates Staff Papers 78 the six periods were associated with monetary or other national economic policy act10ns that are considered nonseasonal mfluences As a further check on the nature of these movements, several alternative seasonal adjustment procedures were compared m conjunct10n with the M 1 rev1S1on published m January 1976 13 In general, the alternative procedures also reflected these shifts m M 1 growth as trend cycle, rather than seasonal, m nature Behavior of M 1 adjusted series and seasonal factors The extent of change m the published M 1 seasonal factors over the past two decades 1s shown m Table 2 The largest net changes m M 1 seasonal factors over the past 20 years have been m February, Apnl, and July, with shifts m demand deposit seasonals most important Smee 1965 the largest changes m M 1 seasonal factors have mcluded reduct10ns of nearly I percentage pomt m the January and February factors and mcreases exceedmg I percentage pomt m the June and July factors S1gmficant port10ns of the latter shifts were recogmzed m the rev1S1on published m January 1976, 13 See Edward R Fry, "Seasonal Adjustment of M 1 Currently Published and Alternattve Methods," Staff Economic Studies 87 (Board of Governors of the Federal Reserve System, 1976) based on trends m SI rat10s that appeared to be developmg m the last several years However, add1t10nal data will be needed to determme whether or not these slufts are still m process As has been noted, the seasonal adjustments computed for M 1 components are based on monthly levels However, observers of current monetary cond1t1ons tend to focus on monthly changes m the seasonally adjusted levels expressed at annual rates Chart 3 shows monthly changes m dollars m the upper panels and percentage changes at the bottom It may be seen that much of the monthly fluctuat10n m the not seasonally adjusted M 1 levels (top curve) 1s removed as seasonal change (second curve), leavmg relatively small and usually positive residual changes m the seasonally adjusted senes (third curve) The tendency for monthly seasonally adjusted changes to be pos1t1ve, of course, reflects underlymg growth m the money stock However, monthly fluctuat10ns 1n the Irregular component, pos1t1ve and negative, are large enough relative to short-run growth to obscure shifts m underlymg rates of growth This is especially evident m the bottom panel of Chart 3, which shows the seasonally adJusted monthly changes m per cent and also m per cent at annual rates While It 1s common to express monthly seasonally ad1usted money stock changes at annual rates, this practice unavoidably gives equal weight to the irregular and trend-cycle TABLE 2 Changes m Seasonal Factors for Money Stock, 1955-75 In percentage pomts Total Mi 1 Month Level of seasonal factor 1975 Demand deposits Level of seasonal factor Change 1965-75 Jan Feb Mar Apr May June 102 98 99 100 98 99 04 78 05 55 35 76 - 91 - 92 - 05 02 40 I 14 July Aug Sept Oct Nov Dec 100 98 99 99 100 102 07 92 36 65 62 86 - 1 08 53 08 61 32 17 I 1955-65 35 - 78 - 58 I 35 - 70 - - 72 08 33 03 32 26 55 1975 102 98 99 100 97 99 9 8 0 9 9 6 99 98 99 99 100 102 2 6 6 3 Currency Level of seasonal factor Change 1965-75 - 9 -11 - I 3 1 3 1 1955-65 s 9 - 7 I 7 9 -1 0 1 25 9 5 - - 55 1 7 3 I - 5 1 5 3 7 1975 Change 196s-1s l 1955-65 99 98 99 99 99 100 35 70 20 45 75 25 - 42 - 23 08 31 48 45 - IS - 29 - 12 04 03 30 100 100 99 99 100 JOI 75 35 85 80 70 85 32 12 - 13 - 33 - 39 - 18 30 29 - 22 - 36 09 03 1 Total Mi IS derived by summmg separately adJusted demand deposits and currency Implied seasonal factors shown were derived by d1v1dmg the not seasonally adJusted total Mi by the seasonally adJusted total https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis Seasonal Ad1ustment of the Monetary Aggregates CHART 3 1M1 ,Total, Month-to-Month Change Btlhons of dollars IO + 0 I . ! . . - - - ' - - - - ' - - - - ' - - - - ' - - - ~ - ~ 10 79 data are available, was suggested to the Federal Reserve staff by Professor Milton Fnedman As thus far developed, It computes stable daily seasonal factors, makmg no allowance for movmg seasonality However, monthly factors calculated from the daily factors vary from year to year because the daily factors mclude .in ad1ustment for mtraweekly movements and the weekdays mcluded m a given month vary from year to year In add1t10n, the mtroduct10n of dummy vanables to adjust for hobdays and other special events also provides flex1b1hty Description of the method Seasonally adjusted, per cent Annual rate L---L----l-----'---......__ _........-:--=-__,10 1973 1975 1971 components However, irregular fluctuations seldom cumulate m one direction over a span .is long as a year, m contrast to the trend-cycle component Consequently, m assessmg the underlymg growth rate, 1t 1s necessary to view average fluctuations m the money stock over a long enough span to reduce the importance In the daily seasonal method, the first step 1s to compute day of-the-week factors and use them to remove mttaweekly movements, then ttend 1s removed from this adjusted senes to arnve at seasonal-irregular ratios A Founer transfo1m of the5e rat10s 1s made and the sme and cosme terms havmg the largest amplitudes are selected to form an estimate of the seasonal In order to mcorporate dummy vanables, the coeffioents of the terms selected are determmed not from the Founer transform, hut fl om .i 1egress10n usmg the seasonalirreguidI ratios as the dependent vanable and both the sme and cosme terms and the dummy vanables as mclependent vanable5 Daily sea5onal facton computed from the regression coefficients are combmed with mtl aweekly factors to seasonally adjust daily observat10ns of irregular changes or to consider the season- A detailed cle5ci 1pt10n of the method fol- ally adjusted level of the money stock m relation to a longer-run trend level 14 lows I Removal of mtraweekly movements a The rat10 of each clay's observat10ns to a 7-day centered movmg average 1s computed b The rat10s for each day are ave1 aged by quarters, and analyses of vanance tests are made for changes m the rat10s between years and between the quartet 5 w1thm a year c If the tests m (b) show no s1gmficant change, seven day-of-the-week factors are computed by .iveragmg rat10s for all Mondays, all Tuesdays, and so forth If there 1s s1gmficant between- or w1thm-year change, day-of-the- A daily seasonal adjustment procedure A seasonal adjustment method for senes such as the money supply, fo1 which daily 14 Alternative methods for measuring the contnbu uon of the irregular component, or at least that part of the 1rregular component that arises f1om ve1y short run day to day variations m M 1 , are proposed m Richard D Porter, Agustm Maravall, Darrel Parke, and David A Pierce, "Transitory Variat10ns m the Mon etary Aggregates," this volume https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis lmprovmg the Monetary Aggregates Staff Papers 80 week factors must be computed that allow for the change (So far, this has not been done ) d Observations m the origmal series are divided by appropriate day-of-the-week factors to get an adjusted series used m subsequent calculations 2 Calculation of seasonal factors a A trend-cycle component is estimated by calculatmg for each observat10n a 365-day centered movmg average of the adjusted series b The trend-cycle curve is d1v1ded mto the series derived m l(d) to obtam seasonalirregular rat10s In leap years, the February 28 rat10 1s calculated by averagmg the February 28 and 29 rat10s, and February 29 1s omitted c A Fourier transform is made of the seasonal-irregular ratios, calculatmg the A and B coefficients m the equation (7) Yt = ½Ao+ ~ AK cos(~!~) 1s2 + fj Bk sm (2k1rt) 365 d A regress10n 1s run with the seasonalirregular rat10s as the dependent variable and the N largest sme or cosme terms, plus dummy variables for holidays, tax dates, and other such effects as mdependent variables 15 Dummy variables are used for holidays or other events that fall on a different date each year or that cause the series to "spike" too sharply to be represented adequately by sme and cosme terms The coefficients estimated by the regress10n are used to construct a final dally seasonal factor series 3 Fmal adjustment and calculat10n of weekly and monthly averages a An adjustment factor for each day 1s constructed as the product of the daily seasonal factor and the appropriate day-of-the-week factor (For February 29, the February 28 dally seasonal factor 1s used) Future daily adjustment factors may be projected usmg the regression coefficients and day-of-the-week factors The origmal series 1s d1v1ded by the dally 15 Thus far, no smgle cntenon has been selected for determmmg N For the money supply components, 30 terms were used, see note 16 https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis adjustment factor to get a final seasonally adjusted series b Weekly and monthly seasonally adjusted series are calculated as the appropriate averages of the dally seasonally adjusted data c Implied monthly (and weekly) seasonal factors may be calculated for periods for which origmal data are available by d1vidmg the monthly average of the origmal data by the monthly average of the seasonally adjusted data For projectmg future monthly seasonal factors, the projected dally adjustment factors may be averaged, these factors (for most series) will differ only slightly from the imphed monthly factors, which can be calculated only after origmal data become available Application of the daily seasonal method to M 1 This sect10n presents the results of applymg the daily seasonal adjustment to the demand deposit and currency components of M 1 for the years 1969-74, and compares them with an X-11 adjustment The computation of day-of-the-week factors (see item l above) yielded the factors shown m Table 3 The origmal series was adjusted for the mtraweekly pattern, the estimated trend was divided mto this adjusted senes to yield seasonal irregular rat10s, and a Fourier transform of this ratio series was made The 30 sme or cosme terms havmg the largest amplitude were selected as mdependent variables m the regress10n used to compute the seasonal factors 16 The mdependent variables m the regres16 The number of terms used was determmed experimentally by computmg three seasonal factor senes havmg, respectively, 18, 30, and 50 sme-cosme terms and TABLE 3 Day-of-the-week Factors for Money Supply Components Day Monday Tuesday Wednesday Thursday Fnday Saturday Sunday Demand deposits 1 i 1 1 00614 00578 00227 00322 99326 99472 99458 Currency 99625 98959 98936 99405 I 00995 I 01050 1 01031 Seasonal Ad1ustment of the Monetary Aggregates TABLE 4 Summary Measures, Demand Deposit and Currency Regressions, 1969-74 Measure R' Standard error of estimate Fstat1st1c Demand deposits Currency 886 0068 420 8 421 887 0039 81 made by d1v1dmg the ongmal daily observat10ns by a factor cons1stmg of the product of the day-of-the-week factor and the daily seasonal factor 5 Tests for changing seasonal pattern s1on mcluded, m adcht10n to the sme and cosme terms, 11 dummy variables These dummy variables were for Washmgton's Birthday, the April 15 tax date, Easter Monday, Memorial Day, July 4, Labor Day, Columbus Day, Veterans Day, and the days before Thanksg1vmg, Christmas, and New Year's The treatment vaned when hohdays fell on Saturday and Sunday, some hohdays are commonly observed by makmg an ad301mng weekday a nonworkmg day when the hohday falls on a weekend In such cases the postt1on of the dummy variable was slufted accordmgly, otherwise, the dummy was omitted for the year m which the holiday fell on a weekend Some results of the two regress10ns are given m Table 4 The coeffioents of the 41 variables were used to compute 365 daily seasonal factors 11 Seasonal ad3ustment of the daily series was then , companng the vanance of the differences between the actual seasonal uregular rat10s and the computed sea~onal factors For the demand deposit component, the vanance was s1gmficantly smaller when 30 rather than 18 ,.inables were used, but usmg 50 rather than 30 van.ibles did not make a further ~1gmficant reducuon For currency, there was a statistically s1gmficant ~mailer ~tandard deviation when 50 variables were used, how ever, as the dollar magnitude of the cu11ency senes (and thu~ of the reduction m standard dev1at10n) is much smaller than that of the demand deposit senes, 1t was clec1ded to use 30 terms here also 11 Actually 40 vanables plus the constant term The latter is eqmvalent to the expression (½)Ao m Equat10n 7 Several tests were performed m an attempt to determme whether, at least over the 196974 period, the evidence 1s m favor of fixed or changmg seasonal factors We present here the results of tests for stab1hty m the day-of-theweek effect and several tests for stab1hty of the monthly factors The tests do not always yield 1denttcal conclus10ns, however, they are all consistent wtth the assertton that any changes occurrmg m the descripttve seasonal ovet this period have been mild We consider fitst a test of stab1hty m the mtraweekly patterns, that 1s, m the day-of-theweek factors Analysis of variance was used m order to test for slufts both between years and between quarters w1thm a year The data used were the rat10 of each daily observation to a centered 7-day average of daily observations Seven tests were made, one for each day of the week In e,tch test, all the data for 1 day (say, Monday) were d1v1ded mto 24 cells-6 years and 4 quarters-and the variances of the quarterly means and the yearly means were compared wtth the wlthm-cell variance Table 5 shows, m the columns headed "Quarters," the rat10 of the variance of quarterly means to the w1thm-cell variance, and m the columns headed "Years," the ratio of the variance of yearly means to w1thm-cell variance Under the hypothesis of unchangmg mtraweekly factors these rattos possess F-d1stnbut10ns with degrees of freedom as md1cated m Table 5 TABLE S F-tests for Change m lntraweekly Factors Demand deposits Day Monday Tuesday Wednesday Thursday Fnday Saturday Sunday t Significant at 5 per cent level https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis Quarters F(3,289) I 0993 5304 2 76291 2158 I 8424 6069 3 06611 I Years F(5,289) 1 0585 3080 1 0163 I 8763 3893 5 02061 3 47131 Currency Quarters F(3,289) 4244 I 6845 I 6868 1281 I 9050 I 4876 6442 I Years F(5,289) I 8134 2 74091 3181 2 1411 3704 6185 5025 82 Improving the Monetary Aggregates Staff Papers Those ratios that md1cate stat1st1cally s1gmficant between-quarter or between-year differences are md1cated m a footnote Wlule there are s1gmficant differences for some days, either m years or m quarters, most days show no s1gmficant differences, and hence stable rather than movmg mtraweekly factors were used m the daily seasonal adjustment of the M 1 components Three tests were conducted to examme the poss1b1hty of a change m the monthly seasonal factors The first test 1s based on the monthly averages of the residuals from the regression Each monthly average 1s assumed to be an estimate of the residual mean, and a test 1s made (assummg a normal d1stribut10n for the residuals) of whether this estimate of the mean differs s1gmficantly from the "true" mean 18 In fact, the test was made by usmg two different estimates of the "true" mean residual In one test the true mean residual was assumed to be the average residual for that month, m the other, the true mean residual was assumed to be zero The variance of the mean was estimated for each month separately, usmg data for that month for all 6 years m the series If average residuals are s1gmficant m a given month, a shift m seasonal patterns could be md1cated Table A-1 m the appendix shows the results of this test It contams two groups of five columns, one group for demand deposits and the other for currency The first two columns 18 The variance of the mean was computed as k) ] Sm2 =s2 - [n-1 :E ( 1 - -n k p nk=O where Pk = N :E (xD2 1-1 S2 = variance of observat10ns for the given month over the whole series S! = variance of mean for the given month n = sample size (number of days m the given month) pk = correlat10n coefficient for observations k days apart calculated from the set of N = 2190 m each group show the deviat10n of the mean residuals from the true mean, adjusted for the estimated variance of the mean, m the first column, the "true" mean 1s assumed zero, while m the second column, the true mean was estimated for each month as the average of the residuals m that month over the entire series On the assumption that these stat1st1cs are normally distributed, those that exceed 90 per cent confidence hm1ts (5 per cent m each tail) are marked with an asterisk, those that exceed 95 per cent limits, with a dagger The table shows a susp1c1ously large number of months with high residuals However, the fact that they generally cluster together suggests a defect m the esumation of trend rather than a s1gmficant change m seasonal The second test for movmg seasonahty 1s based on the idea that 1f seasonality remams m the residuals from the regression (thus md1catmg movmg seasonality), 1t will be reflected m the autocorrelat10ns of the residuals at the "seasonal" lags-that is, m the correlations of observat10ns in successive years or quarters Thus, with daily data, large residual autocorrelat10n at or neat lag 365 would md1cate an annual seasonal pattern unaccounted for by the daily seasonal adjustment method, and sigmficant autocorrelat10n at or near lags 91, 182, or 273 would pomt to a remammg quarterly pattern However, when the autoc01relat10ns of the daily residuals are exammed, any possible existence of seasonality 1s masked by the dominant first-order autocorrelation Tables A-2 and A-3 show these autocorrelat10ns, from the demand and currency regress10ns, respectively, for the first 370 lags These autocorrelation coefficients are m both cases largest at the lowest lags In fact, this low-order autocorrelation remforces the conclus10n that it 1s trend more than seasonality that is madequately treated A common approach m the presence of such serial correlat10n patterns is to compute first differences (daily changes) of the series 19 In regression residuals x' N = deV1at1on of observations (that 1s, the residuals) = from their mean number of observations 1n entire series https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 19 See George E P Box and Gw1lyn M Jenkms, T11ne Series Analysis Forecasting and Control (HoldenDay, 1970) Seasonal Ad1ustment of the Monetary Aggregates TABLE6 Quarterly and Annual Autocorrelatmn m F1rst-D1fferenced Residual Senes Interval Lag m days 3 months 91 92 182 183 273 274 364 365 366 28 35 63 6 months 9 months I year 4 weeks 5 weeks 9 weeks Value for demand deposits 153 039 149 025 133 038 155 125 - 064 * * * Value for currency - - 208 003 195 044 148 023 269 154 129 157 122 139 * Neghgtble the present context we would expect at least that the presence or absence of seasonality would be more clearly revealed after detrendmg the residuals m this way This was found to be true, and m fact the lughest autocorrelation coefficients m the senes of daily residual changes occur at the quarterly and annual lags Table 6 shows these coefficients While they are never h1ghei than O 27 and are usually below O 20, they are m several mstances very lughly s1gmficant statistically owmg to the large sample site, the standard error of a sample autocorrelation coefficient 1s about O03 To examme the possible impact of this, consider a simple case m wluch the annual autocoirelation coefficient has a value of O 155 (the sample value for demand deposits) and other coefficients are essentially zero This would imply that the residuals (first-differenced), say c 1, had an annual autoregressive model of the form (8) Ct = 155 Ct-365 + Ut For the demand deposit component the standard deviation of Ct was O0052, thus the standard deviation of (0 l55ct_ 365), whICh 1s the change m the ratio at time t resultmg from takmg this autocorrelation mto account, is 0 0008 This could affect the seasonally adJUSted (dally) demand component figures (if their level 1s $200 billion) by ±$160 million Wah currency the comparable effect would be about ±'$50 milhon While occasionally a cumulative effect of several such occurrences https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 83 could be substantial, this effect on the whole would appear to be rather mild The third test of stable seasonality 1s similar to the one Just described except that It is based entirely on monthly data As md1cated earlier, the log of the seasonal factor 1s the seasonal component of the log of the senes We therefore estimated the regression equation 12 (9) A log Mu = ~ a 3d 3 t J=I + Ct First differences of the loganthms are used m order to obtam senally uncorrelated regression residuals, however, 1t can be shown that seasonal components for levels are all unchangmg 1f and only 1f this 1s true for the differences As m Equation 5, dit, , d 12 t are seasonal dummy vanables 20 Smee the seasonal dummies m Equat10n 9 capture all the fixed seasonality, any seasonality m the regress10n residuals ci mdicates movmg seasonality m A log Mu (hence m M 1 i) To test for seasonality m Ct the autocorrelations of tlus senes were computed, they are chsplayed m Table 7, for lags 1-30 (an autocorrelation of lag k 1s the sample correlation coeffioent between residuals k months apart) Sea5onahty m tlus senes would ordmanly mcluce 5enal correlation at the annual lags of 12, 24, , ,md perhaps also at the quarterly lags 3, 6, The standard errors of these autocorrelation coefficients, under the null hypothesis that there 1s httle actual senal correlation m the residual senes, are about O 12, so that sample values above O 24 could be regarded as statistically s1gmficant (at the 5 per cent level) In Table 7 1t 1s seen that no autocorrelation coefficients are 51gmficantly nonzero, m particular, those at the seasonal lags give no evidence whatever of any seasonality remammg m tlus senes We conclude from this test that the fixed seasonal model (Equa20 The term ~a,d,t m Equat10n 9 also mcorporates a constant term (which 1s the average rate of growth of M 1 over this period), so that ~a, ~ 0, contrasted with the case m Equation 5 If a = ~a,/12 denotes this constant, then the a's m Equation 9 and the o's m Equat10n 5 are related by a, = a + o, The seasonal component for the Jth month 1s o, = a, - a ImprovIDg the Monetary Aggregates Staff Papers 84 TABLE 7. Autocorrelations of Residuals from Fixed Seasonal M1 Regress10n Lags 1-10 11-20 21-30 - 13 03 04 2 3 4 - 08 - 07 - 03 - 14 - 20 03 05 01 - 06 t10n 9) adequately captures seasonality ID the money supply over this period (1969-74) However, the fact that a fixed-seasonal model appears adequately to capture seasonality m a series does not necessarily imply that the series does not contam movmg seasonality There 1s rather limited mformauon m only a few years' data-six ID this mvest1gat1on of M 1-concernmg various seasonal patterns possible, and so the tests employed are likely to have low power Indeed, the prev10us two tests do find evidence for changes ID the seasonal factors over this penod, with no more-though also no less--ev1dence than m Table 7 that any seasonality remams after applymg these procedures Even the regress10n on seasonal dummies, however, revealed movmg seasonality m prior sample penods A very different seasonal structure was found for M 1 for the penods 1959-68 and 1965-75 21 Also for the former sample penod, application of the Stephenson and Farr method found s1gmficant seasonal-trend mteract1ons, a clear md1cat1on of movmg seasonality 22 On the other hand, for the 1969-74 penod, the techmque descnbed and applied to M 1 above has also failed to find movmg seasonality for M 2 as well as for the currency, demand, and time deposit components of these aggregates separately One possible conclus1on is that over shorter penods seasonality 1s generally best described by fixed-factor procedures An alternative detrending method Both the tests on monthly residual means and the daily autocorrelation analysis JUSt described have IDd1cated an madequate trend 21 David A Pierce and Richard D Porter, "Lmear Models and Lmear Filters m the Analysis of Seasonal Time Senes," American Statistical Association, 197J Proceedings of the Business and Economic Statistics Section, pp 537---42 22 "Seasonal AdJustment of Economic Data" https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 6 16 - 04 - 03 09 08 - 05 7 - 02 01 06 8 - 07 - 01 11 9 - 00 06 08 10 08 - 02 - 05 removal m the daily procedure In order to get a more flexible trend lme than 1s provided by a 365-day movmg average, the basic daily seasonal adjustment method was altered by makmg a prelimmary seasonal adjustment of the origmal senes by usmg daily seasonal factors constructed from the 30 sme and cosme terms havmg the largest coefficients as well as the day-of-the-week factors A quadratic was then fitted to N days centered on each date m this seasonally adjusted series (Values of N of 181 and 365 were tned) For each day the rat10 of the origmal data (adjusted for day of the week) to the middle term of the quadratic centered on that day was computed, and these ratios were then used m exactly the same way as the rat10s of daily data to 365-day averages were used m the baste adjustment methoda Founer transform was made and the 30 sme and cosme terms havmg the largest amplitudes were used with 11 holiday dummies m a regress10n There are a variety of comparisons that can be made between the baste method and the quadratic-trend vanant Comparmg the residuals from the regression shows that a quadratic fitted to 365 terms reduces the mean square deviat10n s1gmficantly, and that usmg a 181-term quadratic reduces 1t even further It 1s necessary to be cautious m mterpretmg this result, however A quadratic does not eliminate seasonal movements, hence, a seasonal remammg m the seasonally adjusted series from which the trend was computed with the quadratic could be mcorporated mto the trend component In addition, a sufficiently flexible trend could mcorporate some of the irregular movement m the senes For both of these reasons the over-all variance of the seasonal-irregular ratios would be reduced, and the smaller sIZe of the deviations from the regress10n would not necessarily mdicate a superior trend computation Seasonal Adjustment of the Monetary Aggregates Runmng the residual-means test for a changing seasonal for the two van an ts also shows mterestmg comparisons Estimatmg trend with a 365-term quadratic yielded results qmte similar to the basic method m that there were nearly as many "s1gmficant" deviations of monthly-average residuals from the "actual" mean deviat10n However, usmg a 181-term quadratic reduced the number of months m which a changmg seasonal was triggered for demand deposits to ll, it was 19 under the basic method In addit10n, the pattern of seasonal-change signals with the 181-term quadratic trend 1s quite different from that with the basic method With the basic method, spurious signals come m clusters, all bearing the same sign and thus seemmg to come from defects m the estimate of trend, but with the 181-term quadratic, signals, when they occur close together, have opposite signs These results mchcate that further work 1s needed to improve the detrendmg procedure m the daily seasonal method Comparison of daily and X-ll seasonal adjustment procedures Table A-4 m the appendix shows the money supply, Mv adjusted by three different methods -a stable-seasonal variant of X-1 I, the standard (movmg-seasonal) X-11 adjustment, and the daily seasonal adjustment 23 In all cases the demand deposit and currency components were adjusted separately, and the results summed Table A-4 also shows the differences between the daily seasonal method and these two vers10ns of the X-11 method Table 8 5hows summary measures of the differences The results of the X-11 movmg adjustment 5hown here are not those that would be obtamed were the same method used on a longer time span A 6-year penod may contam too few observations to identify meanmgful 23 The senes shown here does not mcludc the latest revmons and hence differs from current published figures In addition, m a few months there are small d1ffcrences between these figures (which come from the daily file) and published figures (which come from the monthly file) that result from differences m the averaging methods used for Edge Act deposits https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 85 TABLE 8 Alternative AdJustments of M,, 1969-74 Data In mdhons of dollars ---------...- - -.......- - - - Absolute Comparison Dally seasonal versus X-11 movmg seasonal Dally seasonal versus X-11 stable seasonal average difference Range of difference 218 - I, 151 to 414 153 -652 to 256 moving-seasonal factors, given the problem of separatmg seasonal from irregular and the fact that a large proport10n of the factors m a 6year senes are estimated by special procedures for termmal years at both ends of the senes Given a longer time span, the X-11 movingseasonal method could give results either closer to or further from those shown m Table 8 One would expect that the daily seasonal method, which computes stable seasonal factors, would give results closer to the X-11 stable-seasonal adjustment than to the X-1 I moving-seasonal adjustment, and Table 8 shows this to be true However, when the seasonally adjusted components of the money supply are exammed separately, 1t 1s seen that the daily seasonal adjustment of the demand deposit component 1s closer to an X-11 stableseasonal adjustment, wlule the daily seasonal adjustment of the currency component 1s (shghtly) closer to an X-11 movmg-seasonal adjustment (see Table 9) Evidently, the mtraweekly pattern m the currency component (the "tradmg-day" vanat10n) 1s strong enough to account for a substantial part of the year-toyear movement 1n the seasonal factors generated by the X-11 movmg-seasonal program The stable-seasonal X-11 1s constramed to compute a constant seasonal factor for each month and thus cannot allow for the effect of mtraweekly movements To summarize, a daily seasonal adjustment method has been presented that, at least for the money supply components, produces seasonally adjusted senes not greatly different from those produced by X-11 over the past several years The method produces stable daily seasonal factors and thus monthly factors that are stable except for "tradmg-day" vanat1on 86 Improving the Monetary Aggregates. Staff Papers TABLE 9 Alternative AdJustments of M1 Components, 1959-74 Data In millions of dollars Demand deposits Companson Daily seasonal versus X 11 movmg seasonal Dally seasonal versus X-11 stable seasonal Average absolute difference Range of difference Average absolute difference 206 -1, 111 to 400 52 -93 to 155 128 -645 to 196 53 -132 to 162 I Several refinements and further work with this method are still needed The effects of usmg logarithms have not yet been mvest1gated, no method has yet been developed for dealmg with a changmg mtraweekly pattern, and further work 1s needed concernmg the number of sme-cosme terms to mclude as mdependent variables m the regress10n But perhaps the most basic issue 1s the question of whether to adJust the money supply with stable or movmg seasonals If It 1s decided to use stable seasonals, the daily method has the advantage of allowmg for the mtroduct10n of dummy variables to adJust for holidays and other special events It also gives consistent weekly and monthly seasonal adJustments, which present a problem when X-l l 1s used On the other hand, apphcat10n of the dally method to M 1 adJustment would reqmre determmat10n of which segments of the series can https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis Currency I Range of difference be appropriately adjusted by a constant seasonal procedure and how such segments can be lmked together durmg periods when seasonal factors are known to be changmg If 1t is decided to use a movmg-seasonal method, X-1 l 1s an obv10us choice, though there 1s still the question, m estimatmg the descriptive seasonal, of whether to use the results "raw" or to adJust for known special events and pohcy changes Judgmental review ts used, at present, to ehmmate effects on the X-l l factors considered to be mduced by nonseasonal movements Wlule this adJustment is based largely on Judgment, such effects can be quantified by usmg artificial series constructed with a known seasonal pattern 24 21 Results of a pn.hm1na1y study of this nature a1guc agamst mmg an X 11 adiustmcnt without iudgmcntal review 87 Appendix Tables TABLE A-1 Test for Change m Seasonal Monthly averages of residuals from the regressmn, baste daily seasonal ad1ustment Demand deposits Month X/SD 1969-Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec 1970-Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec 1971-Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec 1972-Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec 1973-Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec 1974-Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec 2 2 I 1 450527t 34961lt 961078t 148012 531941 - 206847 - 948509 -I 849700* - 974997 0 - 387205 -1 580070 I 420191 - l 846124* - 690009 0 - 780180 -2 068474t -3 035229t - 756696 1 665619* I 289507 172091 -I 061610 - I 448038 - I 208371 435795 - 337651 I 914988* 1 802527* I 517614 I 975815t 934372 564159 -2 022070t -1 802268* -2 366986t -1 077699 544744 303886 -1 205733 -1 950275* -1 169827 - 882811 243749 886536 0 2 049155t I 531579 939845 -1 380017 -2 464849t 0 I 713878* I 612464 798734 -2 153116t -2 619309t - 043023 I 061610 - 863254 167829 907907 337651 0 I 241083 1 391147 966889 0 523862 I 548820 962856 - Jex M)/SD J 144221t 517440t 961078t 418132 461016 - 088649 - 569106 - I 723583* - 934372 0 043023 -1 333185 I 113875 - I 678293* - 690009 270121 - 851106 -1 950275* -2 655825t - 630579 1 706243* 1 289507 602319 - 814725 -I 754354* -1 040542 - 435795 - 067530 I 844062* 1 920726* 1 897017* 2 101932t 974997 564159 -1 591843 -l 555383 -2 673302t - 909308 544744 574006 -1 276658 -1 832076* - 790424 - 756696 284374 886536 430228 2 29604lt I 225264 1 107674 -I 380017 -2 194730t - 070925 I 832076* 1 991869t 924850 -2 I 12493t -2 619309t 387205 1 308496 -1 169569 335659 907907 607771 - 070925 1 359282 1 770550* 1 093004 040625 523862 1 979048t I 209742 X 2 2 1 1 -- --- - - - - - - - 0088 0070 0054 0034 0015 0007 0030 0044 0024 0 0009 0064 0051 0055 0019 0 0022 0070 0096 0018 0041 0032 0006 0043 0052 0036 0012 OOIO 0054 0061 0048 0047 0023 0014 0047 0073 0085 0032 0015 0009 0034 0066 0037 0021 0006 0022 0 0083 0055 0028 0038 0073 0 0058 0051 0019 0053 0065 0001 0043 0031 0005 0025 0010 0 0042 0044 0023 0 0013 0036 0039 I M 0011 - 0005 0 0008 0002 0004 0012 - 0003 0001 0 - 0010 - 0010 0011 - 0005 0 - 0008 0002 - 0004 - 0012 0003 0001 0 - 0010 - 0010 0011 - 0005 0 - 0008 0002 0004 - 0012 0003 - 0001 0 0010 - 0010 0011 - 0005 0 - 0008 0002 - 0004 - 0012 - 0003 - 0001 0 - 0010 - 0010 0011 - 0005 0 - 0008 0002 0004 0012 - 0003 - 0001 0 - 0010 - 0010 0011 - 0005 0 - 0008 0002 - 0004 0012 - 0003 - 0001 0 - 0010 - 0010 -- -- - -- - Nom -The symbols have the followmg defimllons X M = average of residuals for that month = average of residuals for the given month over the enttre series, that 1s, all January's have the same value SD = estimated standard dev1at1on of the mean for the given month, estimated over the entire series, that 1s, all January's have the same value https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis I SD 0036 0030 0028 0030 0028 0034 0032 0024 0025 0025 0023 0041 0036 0030 0028 0030 0028 0034 0032 0024 0025 0025 0023 0041 0036 0030 0028 0030 0028 0034 0032 0024 0025 0025 0023 0041 0036 0030 0028 0030 0028 0034 0032 0024 0025 0025 0023 0041 0036 0030 0028 0030 0028 0034 0032 0024 0025 0025 0023 0041 0036 0030 0028 0030 0028 0034 0032 0024 0025 0025 0023 0041 I I Currency X/SD 2 1 1 -1 -2 -1 - 391307t 993044t 026415 769279* 583534t 364684 228294 843187 769371 2 174907t I 570616 050072 - 341615 - I 845411 * -I 710692* -1 873355* 1 022649 1 213053 1 712202* I 037767 839314 - 679659 -I 094671 - 951367 -I 229815 - 442899 -I 026415 - 312226 - 538236 227447 3 19611lt 2 91872lt 3 077483t I 631180 - 380755 -1 552230 -I 844723* - 222082 1 283019 - 468339 - 322942 - I 516315 -I 198542 -2 010675t -1 538741 543727 285566 650935 068323 811981 - 342138 I 873355* I 560885 2 426105t 570734 - 518884 -I 049142 -2 310839t -2 094154t - I 852662* - I 708076* - 147633 1 881763* 2 603882t 1 991474t 227447 -1 598056 - I 491791 - I 328913 0 1 285048 1 151654 - I (X M)/SD I 527953+ 214493 111950 300941 422062t 516315 027322 389163 349714 2 174907t 1 903775* 751079 - 204969 -1 623961 - I 625158 -l 405016 1 184119 l 061420 913175 582745 419657 - 679659 - 761511 - 250360 -1 093168 - 221449 - 940881 156113 - 376765 075816 2 397082t 2 464699t 2 657826t 1 631180 - 047594 - 851223 -1 708076* 0 I 368554 0 - 161471 -1 667948* -1 997570t -2 464699t -1 958398* - 543727 618727 1 351942 204969 - 590532 - 256604 2 341693t 1 722356* 2 274474t - 228294 - 972908 -1 468779 -2 310839t -1 760993* -I 151654 -1 571430 073816 1 967297f 3 070221 2 152944t 075816 -2 397082t -I 945815* -1 748569* 0 1 618210 I 852662* 2 2 1 - I -2 -1 -1 X - - - - - - -- - - - 0035 0027 0012 0034 0048 0018 0004 0013 0011 0032 0033 0001 0005 0025 0020 0036 0019 0016 0030 0016 0012 0010 0023 0019 0018 0006 0012 0006 0010 0003 0056 0045 0044 0024 0008 0031 0027 0002 0015 0009 0006 0020 0021 0031 0022 0008 0006 0013 0001 0011 0004 0036 0029 0032 0010 0008 0015 0034 0044 0037 0025 0002 0022 0050 0037 0003 0028 0023 0019 0 0027 0023 I M - - - - - - - - -- - -- - - - - 0002 0003 0001 0009 0003 0002 0014 0007 0006 0 0007 0014 0002 0003 0001 0009 0003 0002 0014 0007 0006 0 0007 0014 0002 0003 0001 0009 0003 0002 0014 0007 0006 0 0007 0014 0002 0003 0001 0009 0003 0002 0014 0007 0006 0 0007 0014 0002 0003 0001 0009 0003 0002 0014 0007 0006 0 0007 0014 0002 0003 0001 0009 0003 0002 0014 0007 0006 0 0007 0014 I SD 0015 0014 0012 0019 0019 0013 0018 0015 0014 0015 0021 0020 0015 0014 0012 0019 0019 0013 0018 0015 0014 0015 0021 0020 0015 0014 0012 0019 0019 0013 0018 0015 0014 0015 0021 0020 0015 0014 0012 0019 0019 0013 0018 0015 0014 0015 0021 0020 0015 0014 0012 0019 0019 0013 0018 0015 0014 0015 0021 0020 0015 0014 0012 0019 0019 0013 0018 0015 0014 0015 0021 0020 XI SD= monthly average of daily residuals, ad1usted for standard dev1at1on of the mean (X - M) / SD monthly average of difference between daily residuals and monthly average of residuals for that month, ad1usted for standard dev1atton of the mean • S1gmficant at 90 per cent confidence level t S1gmficant at 95 per cent confidence level = 88 lmprovmg the Monetary Aggregates Staff Papers TABLE A-2 Autocorrelations of Residuals from Demand Deposit Regression Lags 1- 10 11- 20 21- 30 31- 40 41- 50 51- 60 61- 70 71- 80 81- 90 91-100 101-110 111-120 121-130 131-140 141-150 151-160 161-170 171-180 181-190 191-200 201-210 211-220 221-230 231-240 241-250 251-260 261-270 271-280 281-290 291-300 301-310 311-320 321-330 331-340 341-350 351-360 361-370 - 704 347 289 226 217 145 084 031 034 061 076 109 093 056 039 057 017 033 032 016 036 033 005 071 081 086 040 080 081 087 076 015 063 080 097 072 136 - 2 3 4 534 343 291 217 190 162 081 030 050 024 072 086 123 069 021 033 035 032 078 011 025 038 020 055 096 075 053 040 069 081 061 022 060 084 105 076 117 457 366 300 216 173 165 058 037 068 037 083 087 123 067 012 000 029 022 037 007 016 072 042 056 089 076 048 012 063 073 064 007 086 089 118 092 065 436 394 298 215 138 150 026 015 094 071 081 069 112 066 002 009 027 000 021 001 015 073 058 047 061 091 057 014 056 067 094 012 049 075 112 111 028 - - - 410 372 311 226 II I 129 024 002 096 076 070 060 104 067 007 014 011 026 052 002 006 065 065 041 035 092 067 063 076 052 097 030 034 035 123 119 029 - 6 7 8 9 0 381 327 278 226 Ill 109 036 008 074 092 086 062 092 078 038 037 003 032 047 007 002 059 061 065 056 072 086 092 059 032 075 037 029 031 122 127 044 375 299 274 243 116 078 034 014 064 110 093 082 083 069 050 020 031 023 042 008 024 055 071 083 068 052 108 083 043 026 057 039 034 073 106 132 079 367 293 295 260 117 062 032 000 074 116 108 090 068 062 053 018 045 033 049 022 046 053 075 095 047 042 101 081 036 038 051 055 062 098 096 149 101 362 276 297 262 126 047 011 010 049 096 125 062 044 044 051 020 033 026 061 036 052 028 080 097 045 016 097 095 060 075 031 064 074 082 066 146 109 347 286 263 241 125 056 009 021 007 082 123 057 042 039 057 030 029 015 047 043 037 001 071 088 058 029 092 087 077 091 000 064 083 084 055 136 132 - - - - TABLE A-3 Autocorrelations of Residuals from Currency Regression Lags 1- 10 11- 20 21- 30 31- 40 41- 50 51- 60 61- 70 71- 80 81- 90 91-100 101-110 111-120 121-130 131-140 141-150 151-160 161-170 171-180 181-190 191-200 201-210 211-220 221-230 231-240 241-250 251-260 261-270 271-280 281-290 291-300 301-310 311-320 321-330 331-340 341-350 351-360 361-370 https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 2 - 683 317 283 272 207 155 108 097 Oil 085 055 097 084 191 175 158 201 182 091 129 130 023 067 090 022 000 067 025 032 020 026 014 016 023 016 015 018 - 534 311 285 283 210 152 134 102 014 022 076 098 114 203 161 147 196 164 019 098 134 057 060 093 027 020 037 015 010 038 022 003 005 011 014 028 003 - 3 4 5 6 7 8 9 0 464 305 299 287 216 151 147 089 034 037 Ill IOI 129 204 154 098 183 153 068 113 147 075 068 083 009 017 017 077 003 041 035 004 014 007 034 026 094 414 329 300 284 190 143 072 056 042 038 131 099 132 198 160 059 182 174 144 141 128 083 074 063 034 009 017 046 007 025 035 019 010 004 025 021 239 375 327 294 294 184 135 044 030 005 033 123 102 134 194 171 116 184 148 164 160 IOI 072 090 062 045 016 020 002 038 021 018 020 009 049 008 020 215 327 313 268 225 180 147 080 Oil 013 030 121 102 158 186 168 162 203 150 157 159 097 061 090 070 015 024 013 000 056 018 005 006 012 068 010 044 092 293 307 290 206 180 155 IOI 001 006 043 117 118 197 197 160 138 199 141 136 149 080 067 084 076 045 055 011 018 058 007 016 004 023 002 017 066 048 277 309 359 222 176 146 112 022 015 055 109 111 204 203 131 150 193 147 142 148 070 094 075 066 023 059 006 030 046 010 010 008 025 036 024 058 019 308 306 332 226 164 123 103 033 028 068 108 066 187 197 136 149 204 155 138 136 063 102 076 038 011 055 004 019 016 042 014 014 014 019 014 031 008 318 290 287 223 155 105 093 023 019 065 099 058 179 191 156 173 198 155 137 129 008 079 081 022 013 073 004 007 001 055 025 024 016 008 002 025 027 - - - - - - - - - - - - - 89 Seasonal Adjustment of the Monetary Aggregates TABLE A-4 Alternative Seasonal AdJustments of M1 In m1lbons of dollars Month Stable X-11 I Col 3 Moving I Dally I less X 11 seasonal col 1 I Col 3 less col 2 Month Stable X-11 I Col 3 Moving I Daily \ Col 3 I less X 11 seasonal c~"\ col 2 (5) -652 -314 -3 11 208 2 -42 112 241 348 -44 -658 1972-Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec 236850 238678 240724 241663 242333 243034 245383 247564 249722 25151 l 252776 256366 (2) 237131 238654 240769 241763 242334 242957 245410 247504 249605 251426 252670 255905 (3) 236336 238482 240701 241765 242334 243229 245639 247602 249756 251578 252758 256078 (4) -514 -196 -23 102 l 195 256 38 34 67 -18 -288 (5) -795 -172 -68 2 0 272 229 98 151 152 88 173 1969-Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec 204138 204603 204930 205125 205527 205861 206129 206616 207616 208667 209132 209183 (2) 204340 204657 204893 205158 205384 205988 206362 206602 207325 208363 209256 209531 1970-Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec 211835 210472 211902 212915 213851 213992 214522 217001 219280 220148 220880 221822 211952 210415 211819 212899 213695 214067 214725 216992 219027 219912 221000 222059 211375 210285 211803 213018 213877 214098 214761 217050 219257 220202 220916 221516 -460 -187 -99 103 26 106 239 49 -23 54 36 -306 -577 -130 -16 119 182 31 36 58 230 290 -84 -543 1973-Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec 257897 258465 258268 259058 261877 264295 265303 265869 265669 266741 269388 271977 258351 258527 258384 259236 262013 264157 265235 265817 265692 266808 269239 271251 257245 258228 258264 259128 261892 264515 265523 265946 265701 266813 269400 271604 -652 -237 -4 70 15 220 220 77 32 72 12 -373 -1106 -299 -120 -108 -121 358 288 129 9 5 161 353 1971-Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec 223279 224732 226258 227384 229854 231115 232237 233566 234313 235082 235084 235766 223419 224652 226197 227375 229749 231138 232375 233531 234105 234912 235096 235680 222838 224538 226187 227471 229887 231254 232491 233571 234299 235237 235028 235488 -441 -194 -71 87 33 139 254 5 -14 155 -56 -278 -581 -114 -10 96 138 116 116 40 194 325 -68 -192 1974-Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec 272019 273681 275189 276279 277151 278904 279724 280287 280724 281863 283410 284935 272525 273734 275304 276486 277372 278712 279608 280297 280905 282116 283349 284181 271374 273443 275200 276300 277216 279126 279951 280379 280702 281957 283436 284496 -645 -238 11 21 -1151 -291 -104 -186 -156 414 343 82 -203 -159 87 315 (!) https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis (3) 203688 204343 204890 205169 205592 205990 206320 206714 207566 208711 209212 208873 (4) -450 -260 -40 44 65 129 191 98 -50 44 80 -310 (I) 65 222 227 92 -22 94 26 -439 90 Bibliography Board of Governors of the Federal Reserve System Improving the Monetary Aggregates Report of the Advisory Committee on Monetary Statistics Washmgton Board of Governors, 1976 Box, George E P, and Gw1lyn M Jenkms Time Se1tes Analysts Forecasting and Control San Francisco Holden-Day, 1970 Cleveland, Wilham P, and George C Tiao "A Model for the Census X-11 Seasonal Adjustment Program" Techmcal Report 312 Madison Umvers1ty of W1sconsm, 1974 Fry, Edward R "Seasonal Adjustment of M 1-Currently Published and Alternauve Methods" Staff Economic Studies 87 Washmgton Board of Governors of the Federal Reserve System, 1976 "Money Stock Rev1S1ons" Federal Reserve Bulletin, vol 64 (Apnl 1978), pp 338-39 Pierce, David A "Relauonsh1ps-and the Lack Thereof-Between Economic Time Senes, with SpeCial Reference to Money and Interest Rates " journal of the American Statistical Association, vol 72 (March 1972), pp 11-26 - - - , and Richard D Porter "Lmear Models and Lmear Filters m the Analysis of Seasonal Time Senes," m American Statistical Association, 1973 Proceedings of the Business and Economic Statistics Section (Washmgton), pp 537-42 Stephenson, James A, and Helen T Farr "Seasonal Adjustment of Eco nom1c Data by Apphcauon of the General Lmear Stausucal Model" Journal of the American Statistical Association, vol 67 (March 1972), pp 37-45 US Department of Commerce "The X-11 Variant of the Census Method II Seasonal Adjustment Program" Bureau of the Census Techmcal Paper 15, revised Washmgton Government Prmtmg Office, 1967 Walhs, Kenneth F "Seasonal Adjustment and Relations Between Vanables" Journal of the American Statistical Association, vol 69 (March 1974), pp 18-31 Whittle, Peter Prediction and Regulation by Linear Least-Square Methods London English Umvers1ues Press, 1963 https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 91 Demand Deposit Ownership Survey Helen T Farr, Richard D Porter, and Eleanor M Pruitt This paper was initially completed in the summer of 1976 It has been updated (Jee particularly pages 103-()6) to make 1 eference to additional wo1 k that has made uJe of the Demand Deposit Ownership Swvey Theoretically, the determm,mts ol: the dem,md fo1 money differ among VJ.nous classes of holders ol: demJ.nd deposits Howeve1, until 1970, when the Federal Reserve began to collect sample data on demand deposit holdmgs by ownership category, there were no 1egularly available monthly data that could be used to test hypotheses about sectoral money demands About 5½ years of dat,t now exist thJ.t appear to be reliable m the sense that they accurately 1eport ownenh1p ol deposits by md1viduals, pa1tne1 sl11 ps, J.nd cm pm a t10ns (IPC' s) Even with severe data hmitations, reasonable sectm J.! demand functions have been successfully estimated The results suggest quite 1>t1ongly that estimates of aggiegate money demand cJ.n be imp1oved by usmg the mformat10n m chsagg1egated, sectoral demand funcuons 'I he sectoral demand funct10ns can be used du ectly, and the mf01 mat10n on elasticities and speeds of adjustment that are dellved from the estimated sectoral demand equat10ns can also be used m constrammg estimated coefficients m aggregate demand funct10ns The first two 5ect10ns desc11be the natme of the demand depo5lt ownership survey (DDOS) and the test5 of the 1ehab1hty of the reported NOTE -Helen T Farr and Richard D Porter an. members of the staff of the D1v1s10n of Research ,md Statistics Eleanor M Prmtt, ,~ho has since died, was liso a member of that staff https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis data 1 1 he next sect10ns detail the results oi esumatmg secto1al demand funct10m and examme seve1 J.l othe1 cuuent uses of the DDOS data evaluat1on1, ol 5hort-run movements m the agg1egates, J.nalysis of the short-run impact oi tc1x rebates ,mcl refunds on deposit holdmgs, e,umat10n of the Boa1d's monthly money mai ket model, 1,tud1e, of 5ectorc1l veloot1es c1nd deposit turnover rates, and the usefulness of the DDOS data as a data somce for other ,e11e, A b11cl 5111 vey of potentIJ.l longer-term 5tud1e1, 15 followed by two c1ppemhxe5 H1sto1 y and outlme of the survey ~mce June 1970 c1 Fede1 ,tl Reset ve ~ystcm survey h,ts p1ov1dcd dc1tJ. on the ownership ol dem,md depo1,1t bc1Lmcc, of !PC's 2 1 he DDOS c!J.ss1fie1> totJ.l IPC halc1nce1> mto fi'vL mutuc1lly exclu~1vc cate,~011e5 financial bu1,1 ne,s, nonhnc1noc1l bmme'>'>, homehold, foreign, c1nd J. 1c,1duJ.! (<1tcgory tc>uned ,ti! othe1 IPC deposits, wluch mdude5 depo51t'> ol nonp1 oht msu tu uons c1ml ti us t depc11 tmen t 5 of I epo1 t1 ng banks Monthly s,1mple dat,1 J.l e med to p1 epc11 e esumates on c1 d,uly-ave1 c1ge bas1, £01 e<1ch cc1tegory at weekly 1epo1 tmg bc1nk 5, c1ml ,m expc1nded s<1mple pi ov1des e1>t1mc1te~ 1:oi ,ti! commeic1,1! bank5 l:or the Lt,t month ol: ec1cl1 quc1rte1 In the ongmal survey, 413 banks weie <hosen to supply repo1 ts for the end-monthof-qu,n te1 e5t1mate, am! 225 of these were J.lso 10 ,upply monthly 1cpo1 t5 Became of me1gen 1 These ~ccliom .i.nd Appemhx I J.tc based 011 ca1 hu unpublished I cdcral Re~e1ve staff \\ork ot James L Pierce and Martha S 'ic.i.nlon 2 For a more deta1led descnpt1on of the survey, see Sm vey of Dc.mand Deposit 0\\ nushtp," Federnl Re ,ewe nullctw, 10! r,7 (June. l!J71), pp 4'16-67 92 lmprovmg the Monetary Aggregates Staff Papers and other problems, the numbe1 of reportmg banks has declmed and it actually fluctuates somewhat from month to month At present, about 380 banks report m the quarterly sample and about 215 report monthly The sample 1s divided mto strata based on s1Ze classification All banks with IPC deposits of more than $1 b1ll1on were mcluded m the first stratum, and a stratified random-samplmg techmque was used to select banks m the other five size classes Durmg the m1t1al 6 months of operat10n of the survey-m the latter half of 1970-there were a number of problems associated with procedures for reportmg and ed1tmg the data Staff at the reportmg banks, the Reserve Banks, and the Board attempted to solve these d1fficult1es, and except for occas10nal problems, they have made substantial progress m estabhshmg procedures that produce timely and accurate reportmg of data Results are tabulated w1thm 5 to 6 weeks of the close of the survey month and are published m the Federal Reserve Bulletin with a 2-month lag Reliability of the DDOS data No benchmark data on ownership of demand deposits by category are available to edit sample data or to test the validity of the published estimates directly An mdirect test of data quality, which mvolves comparmg the DDOS total for IPC demand deposits with a measure of gross IPC demand deposits denved from money stock data, suggests that the total IPC estimates from the DDOS are reliable Table 1 shows the dollar amount of the difference between the quarterly estimates from the DDOS and from the money supply senes Appendix 1 provides an explanation of the relationship between the two The DDOS figures have differed from the denved money stock balances by amounts rangmg from less than $50 million to as much as $3 5 billion, with the average absolute difference over the survey penod amountmg to approximately $600 million, about O4 per cent of gross demand deposits In most penods the absolute difference was less than 1 per https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis TABLE 1 Comparison of the Estimate of Gross IPC Demand Deposits Derived from M1 with the Estwate from DDOS In billions of dollars, not seasonally ad1usted Quarter 1970-Q3 Q4 1971-Ql Q2 Q3 Q4 1972-Ql Q2 Q3 Q4 1973-Ql Q2 Q3 Q4 1974-Ql Q2 Q3 Q4 1975-Ql Q2 Q3 Q4 1976-Ql Mi estimate 167 174 169 175 178 186 182 188 195 207 200 206 209 220 211 218 218 226 215 223 227 236 228 2 6 8 8 1 0 6 0 6 9 4 7 2 l 4 5 6 7 4 8 5 9 4 DDOS estimate 167 175 170 175 177 187 181 188 195 208 200 206 210 220 211 215 216 225 216 222 227 236 227 9 1 9 8 9 5 2 4 4 0 0 3 3 1 2 0 8 4 3 2 0 9 9 Difference 1n estimates Difference as percentage of M1 estimate 4 3 6 - 7 - 5 -1 I 2 -1 6 I 4 - 4 2 - 1 4 4 -I I - 1 8 8 2 1 0 2 2 5 2 3 5 1 8 1 3 9 I 6 5 0 I 6 8 6 4 7 2 5 2 cent of gross IPC demand deposits In 1974 the DDOS estimates of gross IPC deposits began to diverge s1gmficantly from the prelimmary estimate denved from M 1 However, subsequent rev1S1ons m the M 1 data brought the money stock-denved estimates back m lme with the DDOS figures, suggestmg that the survey does provide a reasonably reliable mdependent estimate of gross IPC deposits The DDOS was cles1gned pnmanly not to estimate total IPC demand deposits but rather to estimate the distribution of deposits among the var10us ownerslup categories The appropriate test of the quality of the data would be a companson between movements m the DDOS estimates of the various ownership categones and the true values Unfortunately, no such benchmark data exist DDOS estimates are sub1ect to both reportmg and samplmg errors Some concern has been expressed from time to time about the quality of the reported data However, a recent analysis of the variance of percentage shares reported quarterly by each of the md1vidual banks on the panel md1cated that senously maccurate data appeared to be a problem at only about 2 per cent of the banks As for sampling error, the standard errors of Demand Deposit Ownership Survey 93 TABLE 2 IPC Demand Deposit Ownership, by Type of Holder, All Commercial Banks1 In bllbons of dollars, not seasonally ad1usted Type of holder Month Financial Foreign I 3 ( 2) 5 2) 4 3) 1 ( 1 ( 4 1) 5 2) 11 0 (I 7) 12 3 (1 5) 188 (1 208 (2 4 6) 0 2) 67 (3 70 (2 2 0) 2 8) 2 ( 2 ( 0 2) 4 2) 11 7 (I 6) 11 7 ( 8) 206 (2 219 (I 1 3) 8 4) 9 0) 2 0) 71 (2 73 (2 2 2) I 0) 2 ( 2 ( I 2) 3 2) 11 1 (I 2) 11 7 (I 1) 214 6 (2 0) 224 1 (I 4) 1 2) I 0) 74 8 (I 2) 78 0 (2 4) 2 ( 2 ( 3 2) 4 2) 10 6 ( 8) 11 3 222 2 (2 4) 236 9 (I 6) 60 (2 65 (2 l06 (3 116 (3 6 5) 4 2) 18 2 ( 8) 18 9 (I O) 111 (3 118 (4 19 ( 20 (1 115 (3 125 (3 1973-June December 17 (1 17 ( 1 1) 3 9) 85 (1 92 (I 18 ( 18 ( 1 9) 5 8) 89 6 (2 0) 98 4 (I 2) 17 ( 18 ( 9 9) 9 7) 97 (2 l09 (3 18 5 ( 7) 19 0 ( 7) 1974-June December 4 8) 1 0) Total 175 8 (I 2) 187 5 (2 0) 6 4) 9 5) December I 10 (1 IO (1 1 3 1972-June All other 162 5 (I 9) 175 1 (I 3) 2 7) 6 3) December I 9 6 (I 3) 10 3 (I 0) 56 (1 58 (2 1971-June 1 I 1 ( I ( December December I Household 49 0 (I 7) 53 6 (1 9) 1970-June 1975-June I Nonfinanc1al 3 4) 7 8) 6 1) 3 1) ( I) 5 4) 7 2) ( 6) Figures m parentheses are two standard errors of the est1111ate Figures may not sum to total because of rounding estimate have been small relative to the estimated deposit levels for all ownerslup categories throughout the survey penod, especially for the largest ownership categones-nonfinancial businesses and households (See Table 2) Money demand studies Motivation for disaggregated studies Several considerations suggest that disaggregating the demand for demand deposit balances by sector will improve our knowledge of the aggregate demand for such deposits First, each of the elasticities in the aggregate demand function 1s a weighted average of the corresponding disaggregated sectoral elasticities with the weights equal to the share of deposits held by each sector 3 For example, the a To demonstrate this pomt, first let the deposit demand function for the 1th sector be written as D, = D,(x) where x 1s a vector of explanatory variables If elements of x do not belong m a particular sector, the associated coefficients m the function D,(x) will be zero Hence, It can be assumed that x 1s common to all https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis aggregate interest rate elast1c1ty is a weighted average of the rate elasticities for households, nonfinancial businesses, financial businesses, and so forth This averaging implies that were the shares held by each sector to change, the aggregate rate elasticity would change even 1f the chsaggregated elastic1t1es were unchanged Though the sectoral shares appear to have been relatively constant to date, they are hkely to change in response to particular changes in the payments mechamsm that are currently developing But more important, given disaggregated estimates, It 1s possible to test &ectors Aggregate deposits, D, are the sum of deposits m the md1v1dual sectors D = ,-1 fn, where p 1s the number of sectors It follows that the aggregate elast1c1ty of D with respect to the rth component of x, x,. ts aD)(x') ( ax, /) _= f ,-1 f ,-1 (aD aD, )(aD,)(x') ax, D (aD•)(::.1:)(D•) ax, D D, = f ,-1 (aD,)(:."....) ax, D, (/,) where f, ts the share of aggregate deposits held by 1th sector 94 Improving the Monetary Aggregates Staff Papers whether the elast1c1ties that are estimated by usmg aggregate data alone are "correct" or are statistical artifacts In addition, the disaggregated coefficients suggest plausible values for the aggregate coefficients that can, 1£ It 1s warranted, be imposed (with any level of prec1S1on desired) on the aggregate estimates themselves usmg Bayesian or mixed estimation techmques For example, lt 1s worthwhile to consider a s1gmficant puzzle m the standard aggregate equation for demand for demand deposits Estimates of the long-run elastiot1es for the shortterm rate, the commercial paper rate or the Treasury bill rate, generally range from about -0 04 to -0 25, while the elast1C1ty for the savmgs deposlt rate-however measured-is generally two to three times larger m absolute value Smee over sample periods before November 1974 only consumers would be affected by the savmgs deposit rate and smce consumers hold only about a third of deposits, lt 1s unclear why the savmgs deposit elasticity should be so large relative to that of the commercial paper rate (or the Treasury bill rate) The disaggregated equations shed some hght on this puzzle Next, the basic dete1mmants of money demand presumably differ somewhat across sectors Until recently, corporat10ns could not hold savmgs accounts at commercial banks, and so the savings rate was an alternative yield for consumers but not for firms S1m1laily, smce consumers hold less than 1 per cent of commercial paper outstandmg, the commercial paper rate 1s presumably not a particularly relevant alternative rate for most consumers Also, the relevant scale (transact10ns) variable will also differ across sectors For example, consumei dem,md for money probably depends on a consumer transact10ns measure (personal mcome or consumption), and nonfinanoal busmess demand may depend on busmess sales 4 At the aggregate level, such 4 Intmt1vely, busmess sales appear to be a reasonable measure of tran~att1ons volume for nonfinancial firms Goldfeld used this variable m his work, see Stephen M Goldfeld, "The Demand for Money Revmted," Brookings Pape1s on Economic Activity, 3 1973, pp 577-643 Miller and Orr have developed a model of https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis transact10ns variables are qmte collmear, and it is difficult to obtam reliable estimates of their separate impacts Fmally, sectors are also d1stmgmshed by how qmckly the money holders m each ad1ust to changes m transactions measures and mterest rates-the relative speeds of adjustment Fmancial firms appear to adJUSt very qmckly, much more qmckly than nonfinancial firms, which, m turn, appear to ad1ust more qmckly than households Because none of the md1vidual sectors represents more than about half of the total demand for demand deposits, the demand equations for mdividual sectors may each exlubit less simultaneous-equations bias than the equation for aggregate demand for demand deposits Besides the primary cletermmants of the demand for demand depo~its (mterest rates ,md transact10ns), there a1e secondary vanables that affect only particular sectors Undoubteclly, one of the most important of these 1s the compensatmg-balance reqmrement that banks impose on commercial and mdustnal loans Deposit holdmgs of nonfinancial businesses may well depend on the level of commeroal and mclustrial loans m add1t1on to the transact10ns and mte1est rate variables' th<. demand for money m which the "~cale" variable 1~ th<. "arian(e of the change m th<. daily deposits of a fnm havmg stochastic mflows and outflows Although the1e u, a positive relat10mh1p bet\\ccn this variance and sales, Miller and Orr md1cate that the relation ship 1s loose, see Merton H M1llcr and Dame! Orr, 'A Model of the Demand for Money by Firms," Quarte1 ly Journal of Econo1111cs, vol 80 (August 1966), e:.pec1ally pp 425-26 See also Dame! Orr, Cash Man agement and the Demand for Money (Praeger, 1971) ,, To be sure, the relat1onsh1p bet\\een the demand fo1 demand deposits and compensatmg balances 1s complex The rationale for a loan variable (or compcnsatmg balances) m the demand funct10n 1s not well established Desired transactions balances for some firms may match, on average, their compensatmg balance~, and, accordmgly, the loan coefficient for those hrms 1s zero See Jared Enzler, Lewis Johnson, and John Paulus, "Some Problems of Money Demand," B1ookzngs Papers on Economic Actnnt)', I 1976, p 274, and Orr, Cash Management, pp 98-100, for further d1scuss1ons of this pomt Moreover, there are other 1casons for holdmg compensatmg balances, such as payment for Imes of credit and payment fo1 other ~erv1ces that cannot be econom1cally pnced directly, ~<.c, for mstance, Richard Homonoff and David Wiley Mullms, Jr, Cash Management (Lexington Books, 1975) Demand Deposit Ownership Survey In an aggregate demand deposit regression, the effect of compensatmg balances as represented by commercial and mdustrial loans can be lost m the welter of other variables and mfluences, but lt shows up sigmficantly m the disaggregated regression explammg deposits of nonfinancial busmesses Another secondary variable is the change m government deposits Tlus variable probably has a transitory impact on all of the sectors, but the impact disappears m a matter of days or weeks for most The only sector m which the impact of the monthly change m government deposits could be measured is the household sector Fmally, speculative motives for holdmg deposits appear largely m the financial sector, accordmgly, "speculative" variables, such as the expected change m short-term mterest I ates, appear to have a decisive mfluence there but not elsewhere In summary, one advantage of d1saggregatmg deposit demand 1s that tlus procedure permits us to obtam reliable estimates of the elasticities of some ~econdary variables that are qmte difficult, 1£ not 1mposs1ble, to estimate directly at the ,iggiegate level 95 the penod of fit permitted us to simulate over this period and test the gam from usmg disaggregated demand functions All equations were estimated m natural logarithms, only the equat10n for financial busmesses 1s not m real terms The variables (h5ted below) are not seasonally adjusted except personal mcome, which 1s available only on an adjusted basis Data are monthly and thus deposit data are for the weekly reportmg banks only All equations were estnnated by usmg a two-stage least-squares techmque 7 with a "rho" term Polynomial distributed lags were second degree constramed to zero at the nghthand tail The follow mg hst pi ovides the symbols and abbrev1at10m used m the equations and tables below HO USR GOVR PIR RPQ R90 Sectoral money demands In Appendix 2, we analyze a standard money demand funct10n and show that sigmfican t differences exist among sectors m their responses to changes m mterest rates and mcome Given this evidence that the ma1or holders of deposits react differently to some "standard" set of determmants of deposit holdmgs, demand equat10ns were estimated for each sector with explanatory variables that differed ao oss sectors The series contammg "reliable" DDOS data begm m December 1970, thus, the periods of fit of most of the equations begm m January 1971 The second half of I 97 4 and all of I 97 5 were excluded from the penod of fit because a number of 5tud1es have md1cated that standard aggregate money demand functions do very poorly m explammg tlus penod 6 Such exclus10n from 6 Sec, for example, Enzler and others, "Some P1ob !ems," pp 261-80, and Charles Lieberman, "The https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis = balances of households deflated by U1-1 R. 2 SE DW DF = P the consumer pnce mdex (CPI), not seasonally adjusted government deposits deflated by the CPI, not seasonally adjusted personal mcome, deflated by the CPI Regulation Q ce1lmg on savmgs 90-day Treasury 6111 rate lagged error term squared coefficient of correlation, adjusted for degrees of freedom standard error of estimate, adJusted for degrees of freedom Durbm-Watson statistic degrees of freedom superscript denotmg that a polynomial d1stnbuted lag was estimated T1 ansact10ns Demand fo1 Money and Technological Change, ' Review of Economics and Statistics, vol 59 (August 1977), pp 301-17 7 The reduced fo1m was Ci In R, = ao + a1Ci. In Pl{' + a2 Ci In Mf,_ + 1 In RFFf'--i here R 1s the commercial pape1 rate (RCP) or the 'JO da} I 1easmy bill rate (R90), Pl 1~ penonal rncome, and RFF t~ the I ulcul funds tale Ih1, 1uluced fo1m 1s consistent with the money ckm1.nd funct10ns m the monthly money market model and an ,1ssumed "1eact1on funct10n" that relate\ change~ m the Federal funds r,lte to deviations of the la~ged rate of g1011 th of money f1om mme de,11ul 1,1te 11 a 3 Ci 96 Improving the Monetary Aggregates Staff Papers s, NFBR = seasonal dummy variables = balances of nonfinancial CILR BSR = RCP FIN = DEBF = NYSE TOTR SUM businesses deflated by wholesale pnce mdex net of farm products (WPIN), not seasonally adjusted commercial and mdustnal loans deflated by WPIN, not seasonally adjusted manufacturmg and trade sales deflated by WP[ N, not seasonally adjusted rate on 30- to 59-day pnme commercial paper balances of financial busmesses, not seasonally adjusted debits at seven financial centers, not seasonally adjusted New York Stock Exchange mdex sum of HOUSR and NFBR projection of TOT R from disaggregated equat10ns Demand of households. The explanatory variables chosen for the household equation are the change m government deposits, the level of personal mcome, the Regulation Q ceilmg on the savmgs rate, 8 and the 90-day Treasury bill rate The pnce mdex used to deflate household demand deposits, personal mcome, and government deposits was the consumer price mdex, not seasonally adJusted Among households, nonfinancial busmesses, and financial busmesses, the change m government deposits -at least over a period as long as a monthseems to be related only to household holdmgs of money, when tned in the other two equations, it did not enter sigmficantly Personal mcome is obviously a transact10ns proxy that is relevant only to households Until recently, savings accounts were an alternative asset holdmg only for mdividuals, and thus the savmgs deposit rate belongs m the household equation but not m the equat10ns for nonfinancial and financial busmesses 9 Finally, the 90-day Treasury bill rate was also mcluded s Savings rates offered were essentially at the ce1lmg rate m the penod under study 9 State and local governments and corporations became eligible to hold such accounts m the fall of 1974 and 1975, respecuvely, after our esumauon penod ended https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis Goldfeld used the commercial paper rate m his household demand equation, he also used flow of funds data on holdings of M 1 10 However, mdividuals have greater access to the bill market than to the commercial paper market, and so we prefer the specification that uses the bill rate The results of estimatmg the equation and mformation on the lag characteristics are given in Table 3 11 Note first that all variables have the correct sign and only the savmgs rate is not statistically sigmficant at the 90 per cent confidence level The lack of significance for the savmgs rate is not surpnsmg given the very short sample period and the smgle change m the rate durmg the relevant time span Also, the elastIC1ty for the savmgs rate (-0 152) 1s only slightly larger than that for the Treasury bill rate ( -0 110) This result suggests that estimates of the elasticity for the savmgs deposit rate two to three times larger than that for the Treasury bill rate (or the commercial paper rate) m aggregate equations are statistical artifacts and do not possess an empirical basis m the microeconomic relations that underpin the aggregate equation Demand of nonfinancial businesses Commercial and mdustnal loans, busmess sales, and the commercial paper rate appear as explanatory variables m this equation, shown in Table 4 The loan variable, as expected, appears to affect only the demand of nonfinancial busmesses, 12 when tried m the other Goldfeld, "Demand for Money " In all tables presentmg estimated equations, the numbers m parentheses are t-staUst1cs The long run coefficients of the d1stnbuted-lag variables are presented m the exposition of the equation, and md1v1dual monthly coefficients are presented below Mean lag 1s the average length of lag (m months), length of lag 1s the total number of lagged months m the d1stnbut10n 12 The magmtude of the loan coefficient may provide a rough estimate of the fract10n of firms that, on average, hold more m compensatmg balances than 1s required to carry out transactions Alternatively, a pure transactions model may be appropnate, but our scale vanable (busmess sales) 1s the wrong measure If both the level of loans and the level of sales are functionally related to the true scale vanable, say, the aggre gate vanance of daily cash flows, the sum of the coefficients on loans and sales may represent a mixture of the underlymg Miller and Orr transaction elast1c1ty and the coefficients relatmg loans and sales to the true scale vanable 10 11 Demand Deposit Ownership' Survey 97 TABLE 3 Balances of Households, Equation with R90 In HOUSR, = - 021 A In GOVRf + 602 In Pl Rf - 152 In RPQf - 110 In R90f (-1 75) (4 62) (-0 91) (-4 30) Per10d of fit July 1971-June 1974 R2 = 9671,SE = 0060,DW =217,DF = 16 Item A In GOVR, lnPIR, I I + 12 ~ /3,S,, ·-• lnRPQ, + 589 U,_, (4 38) I In R901 Polynom1al d1str1buted lag weights Lag t - I t - 2 I - 3 1-4 t - 5 t- 010 012 239 168 109 061 025 550 I 117 4 - 033 037 036 029 017 I - 6 t - 1 t - 8 DMtnbuted lag character,stlcs Mean lag Length of lag I two equations, it was not s1gmficant and often entered the equation with the wrong sign 11 The deflator used 1s the wholesale pnce mdex net of farm products A certificate of deposit rate was mcluded along with the commercial pape1 rate, but these rates did not enter simultaneously and RCP performed better Our results for nonfinanoal busmesses are m sharp contrJ.st to those of Goldfeld 14 His transact10ns variable did not enter s1gmficantly, his long-run mterest rate elasticity was only -0 018, and his speed of adjustment only 0 I per quarter, wlule our longest lag 1s only 6 I 741 4 p 274 14 Goldfeld, m "Demand for Money," p 629, con \1dered the results for this sector to be unsatisfactory TABLE 4 Balances of Nonfinanc1al Busmesses 12 = 583 In CILR, + 731 In BSRf - 241 In RCPf + ~ (3,S,, + 915 U1-1 (2 98) (2 17) (-6 98) ·-• (14 74) Period of fit January 1971-June 1974 R2 = 9796, S E = 0086, D W = I 94, D F = 26 Item In BSR, I lnRCP, Polynomial d1str1buted l~g weights Lag I 1-1 I- 2 I - 3 I- 4 I - 5 I - 6 Dlslr,buled lag charac1er1s11cs Mean lag Length of lag https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 074 110 131 136 125 099 057 2 895 6 004 010 014 016 017 017 015 Oil 006 4 171 8 months Given these 1esults, the DDOS data appear to yield more reasonable results than the flow of funds data Demand of financial busmesses. Fmanc1al busmesses represent a hodgepodge of deposits held by (I) trust departments of other banks, (2) sales, commercial, and pe1sonal finance compames, (3) security brokers, dealers, and exchanges, (4) commodity contracts brokers, dealers, and exchanges, (5) other nonbank finanoal 111st1tut10ns (mcludmg holdmg and other mvestment compames, clearing house associations, 1nsm ance earners, mortgage compames, savmgs and loan assocrnt10ns, agricultural credit assoc1at10ns, and so forth), and (6) mutual savmgs banks Goldfeld treated this sector as 1f it represented exclusively money holdmgs by savmgs and loan assoc1a- 11 Unconstramed estimation l\1th aggregate data has failed to produce a s1gmficant positive loan vauable, ~cc, for mstance, Enzler and others, "Some P10blems," In NFBR, - - 064 056 046 036 025 013 I 756 5 Improvmg the Monetary Aggregates Staff Papers 98 t10ns and mutual savmgs banks 15 Though money holdmgs of these thrift mstitutions are sizable, they represent slightly less than a quarter of money held by financial businesses 16 Thus, it is not too surprismg that the scale variable of total deposits at savmgs and loans and mutual savmgs banks did not perform satisfactorily the sum of deposits at these mstitutions had a negative coefficient When these variables were entered separately, deposits at savmgs and loans had a negative sign, while deposits at mutual savmgs banks had the antiCipated sign and were sigmficant It appears that the motives of other financial busmess deposit holders are not well represented by these transactions proxies Instead of trymg to develop separate proxies for each holder, one composite variable was constructed-a proxy for financial debits, defined as total demand deposit debits at New York City and six other large financial centers 17 This transaction measure enters sigmficantly m the estimated equation for balances of financial busmesses In FINi = 086 In DEBFi + 075 A In RCPi (5 86) (3 12) + 142 Aln NYSEi (2 64) + 12 ~ (3,S, 1 i=l + 436 (3 14) Ui-1 Period of fit January 1971-June 1974 R. 2 = 8731,SE = 0109,DW =150,DF =27 The equation also contams the change m the commercial paper rate-a speculative money demand variable mdicatmg extrapolative expectat10ns-and the change m the New York Stock Exchange mdex (NYSE) NYSE may be viewed as a close proxy for changes m wealth Alternatively, because changes m stock market mdexes and stock market volume are posltlvely correlated, the stock market variable 15 Recall that Goldfeld, m "Demand for Money," used flow of funds data for M1 16 See Flow of Funds, Assets and L1ab1lities Out standing, 1974 (Board of Governors of the Federal Reserve System, 1975), pp I, 2 11 The six other centers are Boston, Ph1iadelphia, Chicago, Detroit, San Franc1sco-Oakland, and Los Angeles-Long Beach https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis may be viewed as an additional transactions proxy Other than the speculative mterest rate variable, no mterest rate was sigmficant 18 Furthermore, as expected, all explanatory vanables entered without lags, reflectmg the very high speed of adjustment m this sector A pnon, one might expect that demand by financial busmesses for money balances would be m real terms, as are the demands of households and nonfinancial busmesses Efforts to estimate a real demand equat10n for financial busmesses were not too successful The best equation was In FINR 1 = 063 In DEBFR 1 + 065 A In RCPi (1 58) (1 96) + 171 A In NYSERi ~1~ + 12 ~ (3,S, 1 - 1 + 84 Ui-1 000~ Period of fit Januaiy 1971-June 1974 R. 2 = 8573, SE = 0189, D W = 90, D F = 33 where R appended to the mnemomc mdicates that real values were used In terms of R 2 and standard error, this equat10n is similar to the one 1n nommal terms However, when the equation 1s simulated over the last half of 1974 and all of 1975, 1t exh1b1ts severe detenorat1on In dynamic simulation, the root mean square error 1s nearly 12½ times the standard error On the other hand, when the equation for financial busmesses in nommal terms 1s simulated, the root mean square error m dynamic s1mulat10n over the same penod 1s only a little more than twice the standard error (See the next subsection for further details ) Implicit m estimatmg a money demand equat10n m real terms 1s the assumpt10n that the coefficient on pnces 1s I We tested this homogeneity restnct10n m the case of the equation for financial busmesses by regressmg nommal deposits on pnces, on the other real variables, and on mterest rate terms (all m natural logarithms) In fact, the estimated coefficient on prices 1s s1gmficantly different from 1 ~ This mcludes Goldfeld 's proxy vanable for the outflow of deposits at thrift mst1tut10ns (the Treasury bill rate divided by the savmg deposit rate) See Goldfeld, "Demand for Money " 99 Demand Deposit Ownership Survey TABLE 5 Total Balances of Households and Nonfinancml Busmesses In TOTR, = 516 In CILR, - 012 (3 15) (-2 38) ll. In GOVR, R2 = Item + 369 In P/Rf - 179 In RCPf - 303 In RPQf (-7 39) (-2 68) Period of fit January 1971-June 1974 9838, SE = 0062 D W = 1 49, D F = 22 (I 62) In PIR, I 12 + ~ {J,S,, ,-1 lnRCP, + 880 (12 01) u,_, In RPQ, I Polynomral d1stnbuted lag weights Lag I ,_ 1 t - 2 I - 3 t-4 I - 159 210 - 042 - 040 - 035 - 029 - 022 - 012 569 1 918 5 5 Distributed lag characteristics Mean lag Length of Jag I I, suggestmg that a real demand equation may not be <tppropnate for financial busmesses 19 Nevertheless, much more work on the specification of this sector is undoubtedly necessary before one can accept the test result at face value and drop the reqmrement of homogeneity with respect to pnces A comparison with an "aggregate" equation for households and nonfinancial busmesses To illustrate what 1s lost or ludden by aggregat10n, ,i simple ,iggregate equation for the total of deposits of households and nonfinanci,il businesses, TOTR, was also considered A limitation m the distributed lag estimation program prevented mclusion of all of the v,iriables appearmg m the sectoral equat10ns, therefore, the Treasury bill rate was dropped smce 1t 1s, m general, highly correlated with the commercial paper rate However, even without this rate, the aggregate equation was not sensible In particular, sigmcant coefficient estimates for both transactions variables, real personal mcome and real busmess sales, could not be obtamed Smee mcome worked better m terms of the R. 2 and standard error of the equation, It was used alone with the results reported m Table 5 Except for mcome, all the variables are sigmficant at least at the 98 per cent sigmficance level The equation displays the curiosity, noted earlier, that the long-run savmgs deposit elasticity 1s more than l ½ times the comGoldfeld, m "Demand for Money," also estimated his financial busmess equation m nominal terms 19 https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis - 213 - 081 - 010 2 329 merc1al paper rate elasuc1ty This result contradicts our disaggregated estimates Table 6 compares the direct ,iggieg,ite estimates with two sets of aggregate estimates made by usmg the disaggregated coefficients and weightmg them by the average share of deposits held by consumers (0 308) and nonfinancial busmesses (0 692) The first estimate 1s based on the assumption that the Treasury bill rate elasticity is the same as the commercial paper rate elast1c1ty for households, while the second estimate uses an alternative equation for households, which contams the commercul paper rate explicitly (see Table 7) The two sets of derived estimates are very similar but differ s1gmficantly from the direct aggregate estimates Thus, the disaggregated equations do not support the aggregate findmg Because consumers hold an average of only 30 8 per cent of the total deposits held by nonfinannal busmesses and households, a <.hsaggiegated elast1C1ty for household demand with respect to the savmgs deposit rate of -0 984 would be reqmred to yield this aggregate elasticity This implausibly large value (m absolute terms) is nearly 6½ times the disaggregated elasticity e~t1mated directly, TABLE 6 Alternative Elasticity Estimates Type of estimate Direct aggregate estimate Denved aggregate estimates D1saggrega ted model I Disaggregated model 2 Savings depos1 t rate Commercial paper rate - 303 - 179 - 047 053 - 201 200 100 Improvmg the Monetary Aggregates Staff Papers TABLE 7 Balances of Households, Equation with RCP In HOUSR, = - 019 A In GOVRf + 680 In PIRf - 112 In RPQf - 107 In RCPf (-1 76) (4 80) (-0 99) (-4 35) Period of fit July 1971-June 1974 R• = 9693, SE = 0058, D W = 2 34, D F = 16 Item In GOVR, I In PIR, I 12 + l: {J,S,. ,-1 In RPQ, + 634 (4 92) I u,_, lnRCP, Polynom1al d1stnbuted lag weights Lag I t-1 1-2 I- 3 I - 4 I - I I I - - 008 - 011 5 6 7 8 Distributed lag characteristics Mean lag Length of lag I 561 -0 152 It appears, then, that the disaggregated equations provide more reasonable estimates of the aggregate elasticities This result exemplifies the sigmficant payoff to disaggregatmg the money demand function or, at least, mcorporatmg mformation derived from the disaggregated esumates mto aggregate estimates 20 Simulations It 1s mstructive to examme the post-sample predictions from each of the equations These simulat10ns are reported m Table 8, for the period from July 1974 through December 1975, for consumers (HOUSR), nonfinancial busmesses with the loan variable (NFBR) and without the loan variable (NFBR -no CILR), 21 financial busmess (FIN), and the sum of HOUSR and NFBR (TOTR) with and without loans and government deposits 22 It was pomted out earlier that ma true aggregate equation the impact of loans or govern20 The aggregate equation presented here probably understates the gams from disaggregation because only household and nonfinancial busmess deposits are aggregated When a s1m1lar equation is estimated with the demand deposit component of the money supply as the dependent vanable, the results pomt up even more strongly the mformat10n lost m aggregation In the demand deposit equat10n, neither loans nor government deposits enter s1gmficantly Thus, the disaggregated equations yield mformat1on about the impact of these vanables that we would not have otherwise An even more stnkmg result 1s that the estimated savmgs rate elast1c1ty m this aggregate equation 1s eight times the estimated commernal paper rate elastmty 21 See Table 9 for the specification of this equation 22 See Table 10 for the spenficauon of this last equation https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 123 161 166 142 086 - 048 - 044 - 037 - 028 - 015 I 862 I 534 4 4 - 014 015 015 015 014 012 010 007 004 3 311 8 ment deposits could not be identified Smee TOTR mcludes the deposits of only the ownership classes that these variables affect, the equation ism some sense biased toward bemg able to identify these impacts Thus, the TOTR equation mcludmg these variables provides more mformation than an equation for a broader aggregate probably would Therefore, a more accurate illustration of what can be lost m aggregation may be provided by simulatmg an aggregate equation without these variables Fmally, an alternative estimate of TOTR, denoted SUM, was also constructed by addmg predictions of the separate equations for consumers and nonfinancial businesses Overall, most of the equations tended to overpredict money demand startmg m the second half of 1974 This period comcides with a similar breakdown m the aggregate equation for demand deposits of both of the Board's econometric models-the monthly money market model and the quarterly Massachusetts Institute of Technology-Umversity of Pennsylvama-Social Science Research Council (MPS) model Only the financial busmess equation does not eventually overpredict by a sizable percentage Though the percentage errors and the root mean square errors are large for consumers and nonfinancial businesses, the disaggregated equations, when summed (SUM), do better m simulation than either equation for the aggregate (TOTR) Demand Deposit Ownership Survey 101 TABLE 8 Post-Sample Sunulahons, July 1974--December 197S Not seasonally adiusted Standard error ofesttmated equation (per cent) Root mean square error Correlatton squared of actual and predicted Bdhons of dollars HOUSR NFBR NFBR (no CILR) FIN TOTR TOTR (no CILR, GOVR) SUM 0072 4977 2994 4698 0035 0004 1863 1 452 3 452 4 447 346 6 797 8 228 4 870 HOUSR NFBR NFBR (no CILR) FIN TOTR TOTR (no CILR, GOVR) SUM 5302 8304 6893 5056 8088 7619 8155 672 802 125 341 409 855 315 Equation I Per cent Mean absolute error (b1lhons of dollars) Mean error (b1lhons of dollars) Dynamic s1mulat1on 7 8 10 2 11 13 8 65 17 97 35 35 53 24 60 86 98 I 09 62 76 na I 304 3 257 4 123 289 6 390 7 659 4 561 -I -3 -4 -6 -7 -4 304 257 123 043 390 659 561 598 655 928 277 1 203 1 717 1 159 -1 -1 -1 598 544 840 018 203 717 143 Nondynam1c s1mulauon I 1 l 1 3 2 2 2 2 3 2 63 06 88 33 44 22 29 60 86 98 1 09 62 76 na n a Not available rhe aggregate equation mcludmg the loan ,md government deposit variables has approximately a 40 per cent higher root mean square error and mean absolute error m dynamic s1mulat1on than does the total based on the d1s,1ggregated equat10ns (SUM) When loans and government deposits are excluded from the equation, these errors are almost 70 per cent higher than the errors for SUM S1m1larly, error statistics mcrease when compensatmg balances are excluded from the equation for nonfinancial busmesses (NFBR-no CILR) as wmpared with the equation mcludmg these balances (NFBR) Smee It 1s difficult to measure the effects of compensatmg-balance reqmrements at the aggregate level, the ab1hty to do so by usmg d1sagg1egated data ,1gmficant Conclusions regarding money demand functions The DDOS d<1ta <1ppear to yield reasonable d1saggreg<1ted equations for the demand for money The results of the estimated demand equat10ns suggest that different factors mfluence the demands of different sectors Although many mterest rates-and transactions vanables-are collmear and could probably be substituted for one another m regression analysis, theoretically the rates and transactions vanables mcluded m the demand equa- TABLE 9 Balances of Nonfinanc1al Busmesses, Equation Excludmg CILR 12 871 In BSRf - 204 In RCPf + ~ {J,S,, + 873 (2 90) (-6 35) •·1 (11 58) Period of fit January 1971-June 1974 R•= 9732,SE = 0098,DW = 223 DF = 26 In NFBR, = Item lnBSR, I u,_, lnRCP, Distributed lag weights l.Ag I 1- 1 1-2 t-3 I - 4 I - 5 I - 6 Distributed lag characteristics Mean lag Length of lag https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 185 173 155 134 107 076 040 2 225 6 1s - 050 046 040 032 023 013 1 860 5 Improving the Monetary Aggregates Staff Papers 102 tions for each sector are the most appropriate for that sector Further, such variables as the change m government deposits (m the household equation) and the level of commercial and mdustrial loans (m the equat10n for nonfinancial busmesses), when tested m other demand equations, proved to be ms1gmficant and often of the wrong sign ----The large variety of determmants of money demand disclosed by the sectoral demand equat10ns provides a great deal of mformat1on about what may be happemng to the aggregate demand for deposits Much of this mformation could be lost when analysis 1s confined to an aggregate demand function First, to the extent that common variables affect different sectoral demands, an aggregate equation will estimate only an average impact, 1f the sectoral impacts differ and the sectoral shares change, mformation will be lost even if the sectoral demand functions are lmear Second, as seen from our "aggregate" equation, which attempted to combme only two sectors, all relevant variables cannot be mcluded m the aggregated equauon Mult1colhneanty, among other problems, produces msigmficant coefficients and often wrong signs-the equat10n presented was the best m terms of tstatistics, expected signs, and standard error If all mterest rates and all transactions vanables were perfectly correlated, the loss of variables m the aggregate equat10n would be ummportant, no mformation would have been lost However, such perfect correlation 1s not the case, and divergent movements could give" us considerable mformation, assummg we were dealmg with sectoral demand equations rather than an aggregate one The DDOS also permitted us to check whether the elasticity of the aggregate demand for demand deposits with respect to the rate paid on short-term mterest-bearmg accounts at commercial banks23 was too large The estimated aggregate elasticity does appear to be larger than the disaggregated data would warrant This result casts some doubt on the large, expans10nary GNP multiplier ,associated with changes m Regulat10n Q ceilmgs that has been adduced by some economists, who rely on more traditional estimates of aggregate demand deposit elast1c1t1es 24 Our simulation results confirm the loss of mformation m aggregation Summary statistics are presented for TOTR (the aggregate equation for the sum of deposits of households and nonfinancial busmesses) and for SUM, the sum of the simulation solutions for the sectoral demand equations for households and nonfinancial busmesses In dynamic s1mulat10n, all err01 statistics are higher when the aggregate equat10n is simulated than when the two sectoral equations are simulated and the errors summed, the mcrease m the root mean square error is better than 15 per cent Furthermore, when loans and government deposits are excluded from the TOTR equation, 2a Spec1fically, the passbook rate ce1lmg, or an average of the passbook rate and the rate paid on conmmer type certificates of deposit, weighted by quan t1ty 24 See Myron B Slovm and Mane E Sushka, Inter est Rates on Savings Deposits (Lexmgton Books, 1975), e~pecially chap 10 TABLE 10 Total Balances of Households and Nonfinanc1al Busmesses, Equation Excludmg CILR and GOVR In TOTR, Item 12 = 615 In P/Rf - 138 In RCPf - 324 In RPQf + I; {3,S,, + 837 (2 96) (-5 47) (-2 37) ••I (9 90) Period of fit January 1971-Junc 1974 R•= 9752, SE= 0076, DW = 185, DF = 24 lnPIR, I U1-1 In RCP, I lnRPQ, D1strtbuted lag weights Lag t t - I t - 2 t - 3 t - 4 t - 5 439 177 024 028 028 026 020 012 - 080 - 135 - 108 2 197 5 I 087 2 - Distributed lag characterrstrcs Mean lag Length of lag https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis I 287 103 Demand Deposit Ownership Survey as would be likely m a more aggregated equation, the mcrease m the root mean square error 1s 40 per cent While even sectoral demand equations did poorly m terms of the standard errors of the estimated equations, they still suggest that better results would have been obtamed by usmg all the mformatlon available from sectoral equations than by usmg the more hm1ted mformauon mcluded m an aggregate demand equation Fmally, recent pred1ct10ns of the aggregate demand for demand deposits relative to GNP and short-term mterest rates have been cons1clerably off the mark, actual deposit growth (at least through the first quarter of 1976) m the current recovery has been unusually slow compared with the predictions of many standard money demand equat10ns Apart from financial busmesses, the disaggregated equations have also tended to overpred1ct deposit growth The detenorat10n appears to be worse for nonfinancial busmesses (see Table 8) Smee dis- aggregated ownership data help to identify the sectors performmg least well, they may also be useful m 1solatmg the factors causmg the detenorat10n-factors that 1t may not be possible to isolate at the aggregate level Preliminary results for an aggregate demand equation using constraints derived from the DDOS equations After most of the work reported so far m this paper was completed, a program became <1.vailable that enabled us to estimate a dem<1.nd equat10n for the demand deposit component of M 1 <1.nd to make use of the mformauon gamed from our disaggregated equat10ns to constram sums of current and lagged coeffioents Table 11 prc5ents the 1 esults We estimated chstubuted lags usmg the Sluller techmque w1th soft (mexact) constramts apphed JUSt to the sums of d1stnbuted lag TABLE 11 Demand Deposit Component of Mi. Constramed Estimation 1 In DDR = 223 In P/Rf + 269 In BSRl - 012 a In GOVRf - 128 In 015 In DEBFR, + 014 (2 32) (I 31) + R• = Item lnPIR, I In BSR, RCPl - 055 In RPQl a In NYSER, + 008 a In RCP, + 0 0 In WPINl + 998 (I 32) Period of fit January 1968-June 1974 9676 S E = 0067, D W = 5225, D F I a In GOVR, I + 310 In CILR, (24 04) U1-1 = 73 In RCP, I In RPQ, I In WPIN1 Shiller distributed lag weights lag I r- I I - 2 I - 3 I- 4 093 (4 43) 070 (7 61) 047 (5 06) 024 (2 09) 001 ( 05) t-5 I - 6 073 (6 26) 062 (10 05) 051 (12 60) 040 (7 79) 028 (4 76) 014 (2 85) 001 ( 17) - 004 (-1 16) - 005 (-1 38) ((- 002 58) 000 05) I - 7 I - 8 (-3 (-4 (-4 (-4 (-4 (-4 (-3 (-2 (-1 021 27) 018 68) 016 47) 015 13) 015 31) 015 37) 103 85) 010 99) 004 12) -(I (-1 (-1 ((- 019 01) 015 70) Oil 23) 007 71) 003 27) Sum constramts2 1 2 - Ill 034 142 212 238 191 105 - 021 - 186 - 177 I 012 4 22 I 291 6 26 3 - 846 01 3 230 8 - 15 DDR 1s demand deposits deflated by WPJN superscnpt S denotes a Shiller d1stnbuted lag ln CILR = 030, In DEBFR = 001, .J. In NYSER = 002, a In RCP= 001 https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 670 244 I - 9 I - 10 t - 11 Distributed lag characterrst1cs Mean lag Length of lag - I 293 4 - 06 0 0 Improvmg the Monetary Aggregates Staff Papers 104 coefficients, 25 mdividual lag coefficients were free to assume any value withm the constramts on the degree of the estimated polynomial The values of the sum constramts were derived by multiplymg sums estimated with the disaggregated DDOS data by the average share of the relevant component of total gross IPC deposits, and addmg We did not estimate demand equations for the "foreign" and "other" components m the DDOS, and variables affectmg the components for which we did estimate equations could affect these other components While the "foreign" and "other" shares of the total DDOS deposits are small, which would lead to a mimmal impact on coefficient sums, tightness priors on sums were such that the sums could deviate somewhat from those implied by the estimated component equations Thus, the estimates may allow for the effects of the other sectors as well as for the fact that 2s See Robert J Shiller, "A D1stnbuted Lag Estimator Derived from Smoothness Priors," Econometrica, vol 41 (July 1973), pp 775-88 the demand deposits used here are "net" and DDOS deposits are "gross" (see Appendix 1 for the differences between the two concepts) Program size constramts were such that we could not mclude all relevant variables and seasonal dummy variables as well, therefore, the equat10n w<1s estimated m seasonally adJusted terms We also deviated somewhat from the disaggregated DDOS equations by puttmg financial busmess demands m real terms usmg WPIN as the cleflator Fmally, an 11-period distributed lag m WPIN with weights summmg to zeio was mcluded Without this distributed lag m prices, money holders are assumed to aclJust immediately to the current price level Includmg the distributed lag m prices permits lagged adJustment to price changes, with the sum of the lag coefficients constramecl to zero, however, long-run homogeneity with respect to prices 1s preserved The distributed lag on prices affected the estimated coefficients on the other mdependent variables very httle, but 1t did result m a TABLE 12 Demand Deposit Component of Mi, Unconstramed Estimation 1 In DDR = 851 In PIRf - 093 In BSRf - 019 <I. In GOVRf - 057 In RCPf - 134 In RPQf + 010 In DEBFR, + 006 <I. In N YSER, + 005 <I. In RCP, + 0 0 In WPINf (070) (0 52) (0 49) Penod of fit January 1968-June 1974 R• = 9876, SE = 0041, D W = 1 3031, D F = 64 Item lnPIR, I lnBSR, I A In GOVR, I lnRCP, I + + 072 In CILR, (0 66) 998 Ut-1 lnRPQ, I In WPIN, Shiller distnbuted lag weights Lag I- 1 1-2 I - 3 I- 4 338 (5 51) 254 (5 57) 170 (5 50) 086 (5 09) 001 ( 16) I- 5 t-6 ((((((- 28 54) 023 53) 018 51) 013 48) 008 44) 004 38) 000 ( 12) (-1 (-1 (-1 (- 005 42) 007 93) 004 24) 003 86) t- 7 t - 8 - 004 (-' 77) - 004 (-1 30) - 005 (-1 69) - 006 (-2 17) - 008 (-3 01) - 010 (-3 68) - 009 (-3 62) - 007 (-3 00) - 003 (-1 14) (-1 (-1 (-1 (-1 (- 046 68) 038 84) 029 85) 018 65) 004 56) 119 - 042 023 075 143 157 158 145 120 159 1 009 4 I 559 6 1 270 3 4 261 8 • DDR 1s demand deposits deflated by WPIN, superscnpt S denotes a Shiller d1stnbuted lag https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis - 115 I- 9 I - 10 I - 11 Distributed lag characteristics Mean lag Length oflag - 934 1 236 4 Demand Deposit Ownership Survey 105 somewhat more satisfactory lag pattern m the estimated coefficients on the commercial paper rate Table 12 presents the results of est1matmg the same equation without constramts except that on the distributed lag m prices Only the estimated elast1c1ty with respect to the change m government deposits, debits, and the change m the paper rate approximate those 1mphed by the disaggregated equations Among other thmgs, the estimated elast1c1ty with respect to the commercial paper rate 1s less than half what 1s 1mphed by the disaggregated equations, and we ag,un observe the phenomenon of the estimated savmgs rate elasticity bemg almost 2½ times the estimated paper rate elasticity Further, without constramts, the busmess sales variable has the wrong sign and 1s not s1gmficant Fmally, It 1s no longer possible to 1dent1fy the mfluence of such variables as loans and debits smce their estimated coefficients are not significantly different from zero Table 13 p1csents the results of s1mulatmg the constramed and unconstramed equations Although the standard error of estimate of the unconstramed equation 1s almost 40 per cent less than the constramed equation, the results of the dynamic simulations pomt up dramatically the gams from makmg use of the disaggregated elast1c1ty estimates to place con~tramts on the estimated aggregate elast1c1t1es For example, the root mean square error of the unconstramed equation 1s almost 2½ times as large as that of the constrained equation Further, m percentage terms, the constramed equation does better than our simple aggregate equation (TOTR) m which we attempted to estimate determmants for only two classes of money holders The potential for makmg use of mformat10n derived from disaggregated equat10ns 1s obviously sizable Other current uses of the DDOS Current analysis The DDOS data are used m current analysis to evaluate unusual movements m the aggregate demand deposit component of M 1 If, for example, a strong surge m M 1 growth m a a particular month or quarter 1s accompamed by an unusual change m the deposit shares, the source of the mcreased demand for balances can be more accurately pmpomted The DDOS data have been particularly helpful m evaluatmg the impact of tax rebates and tax refunds on short-term movements m demand deposits The results from this analysis md1cate that, under current operatmg procedures of the Desk, about a quarter of rebates distributed umformly over a given month will be held m demand deposits m that month ,md about half of that (or about one-eighth of the origmal dollar flow) will be present m the followmg month Direct estimates of such impacts usmg only aggregate deposit data tend to produce much more 1mplaus1ble short-term impacts of rebates on aggregate demand deposits As a source of data, the DDOS survey 1s bemg used regularly by the Flow of Funds Section of the Board's Division of Research and Statistics to separate demand deposits from cash holdmgs and to estimate deposit TABLE 13 Summary Statistics of Post-Sample S1mulatlons, July 1974-December 1975 Equation Correlation squared of actual and predicted Root mean square errors Billions of dollars I Per cent Standard error of estimated equation (per cent) Mean absolute Mean error error (billions of dollars) (billions of dollars) 6 056 14 94 -6 056 -14 94 1 332 1 451 - 370 -I 397 Dynamic s1mulauon Constramed Unconstramed 1540 0917 6 860 17 09 Constramed Unconstramed 6503 9052 1 644 1 619 5 29 12 64 67 41 Nondynam1c s1mulat1on https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 1 30 1 28 67 41 Improvmg the Monetary Aggregates Staff Papers 106 holdmgs by sector, and also by the Department of Commerce for use m the national mcome and product accounts to estimate services rendered without fee by financial mtermedianes other than hfe msurance earners Several large commercial banks m New York City are known to use DDOS data m analysis of money stock movements, and it 1s believed that these and other banks make use of the data m their marketmg research Monthly model The elasticity estimates derived from the DDOS demand equations have been used m constrammg estimated coefficients m a simplified aggregate demand deposit equat10n (versus the equation presented m the last part of the previous section) In parucular, we constramed the commercial paper rate elasucity to be m the neighborhood of the disaggregated elasuciues (weighted by deposit shares) In an unconstramed estimation, the elasticity of the rate on other time and savmgs deposits ends up bemg over five times that of the commercial paper rate When the paper rate elasticity is constramed, the rat10 is less than two to one While our experience is limited, the constramed equat10n appears to produce more reasonable responses of money growth to changes m the paper rate It has also been very helpful m evaluatmg the impacts of alternative monetary policies Studies of velocity by ownership class The DDOS-will also help m velocity studies and, thus, m the pred1ct10n of mcome Table 14 presents the end-of-quarter-transaction velocities (computed with the quarterly DDOS data) consistent with the different sectoral money demand funcuons presented m the second section, VFIN is financial debits divided by deposits of financial busmesses, VNF is business sales divided by deposits of nonfinancial busmesses, and VCON is personal mcome (not at an annual rate) divided by deposits of households Chart 1 plots these numbers It can be seen that the sectoral velocities move qmte differently from one another For example, from the cyclical trough m the fourth quarter of 1970 to the peak m the fourth quarter of 1973, the velocity associated with financial busmesses mcreased about 43 per cent, or about 3½ per cent per quarter, while those associated with nonfinancial busmesses and households rose IO per cent and 3 per cent, respectively, for average quarterly mcreases of about O8 per cent and O 3 per cent For the pe110d from the cyclical peak m the fourth quarter of 1973 to the trough m the second quarter of 1975, the average quarterly mcreases m velocity were 2 7 per cent, 2 per cent, and 0 9 per cent, respectively Such d1ffermg behav10r 1s not likely to be captured m an aggregate relationship, thus, the use of disaggregated mformat1on may eventually lead to better predictions of aggregate mcome TABLE 14 Quarterly Transactions Veloc1ties Quarter VFIN I VNF I VCON 1970-Q4 40 931 1 1977 1 2761 1971-Ql Q2 Q3 Q4 39 38 38 43 060 425 520 314 I 1 1 1 2953 3268 2678 2346 I 1 I I 2878 2887 2588 2675 1972-Ql Q2 Q3 Q4 38 44 41 47 446 117 272 190 1 1 1 1 3309 3223 2790 2378 1 1 1 1 4017 2713 2599 2640 1973-Ql Q2 50 344 52 435 1 3942 1 3997 I 3088 I 2977 Quarter VFIN VNF I I VCON 1973-Q3 Q4 49 314 58 429 1 3421 1 3197 1 3019 I 3161 1974-Ql Q2 Q3 Q4 60 62 66 72 085 275 894 721 1 1 1 I 4917 5091 5000 3886 1 1 I 1 3240 3357 3675 3647 1975-Ql Q2 Q3 Q4 68 67 67 75 763 964 653 239 1 I 1 1 4479 4858 4844 4485 I 1 1 1 3718 3873 3929 3891 1976-Ql 91 413 1 6206 1 4421 NorE -Veloc11les are not at an annual rate None of the data are seasonally adjusted except for personal mcome, which 1s available only m seasonally adjusted form Sufficient quarterly DDOS data do not yet exist to seasonally adjust these senes https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis Demand Deposit Ownership Survey 107 CHART I Veloc1t1es 90 60 30 - VNF I 50 - VCON I 20 90 1971 1973 Owneiship data have also been used by J &mes Pugash m esumatmg sectoral turnover 26 1 cttes Pugash reported the followmg results I Estimated demand deposit turnover rates differed s1gmficantly across ownership categones 2 Estimated turnover rates by ownership categones also differed across three bank sizes 3 The estimated sectoral turnover rates, comparing the two cross-sectional estimates made for June 1970 and June 1972, were sigmficantly different m most cases, suggesting that, especially for consumers, the use of demand deposits changes over time Most of Pugash's results are qmte plausible 26 S~e James Z Pugash, ' The Demand for Money m Six Sectors," Unpublished m.inuscnpt (Board of Gov ernors of the Federal Reserve System, January 1974) https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 1975 It is important, however, to try to go further and explam the movements of turnover rates ovei time as mclexecl by ownership category and bank size Advances m cash management techmques that lower the average level of money balances 1elat1ve to some transact10ns measure are difficult to measure at the aggregate level These disaggregated turnover measures should provide mdependent evidence of such shifts For example, consider those banks that offe1 large corporate custome1 s a bankmanaged account from which the banks automaucally mvest man ove1mght money market mstrument all funds m excess of an agree<lupon balance If managed accounts become s1gmficant, there should be a once-and-for-all spurt m estimated corporate turnover at these banks 108 Improvmg the Monetary Aggregates Staff Papers Potential studies Bank portfolio models Innovations in the payments mechanism The DDOS data may also be used to study bank portfolio behavior It has been shown that asset preferences of banks are related to the compos1t10n of their liabilities This result 1eflects the different probabilities of withdrawal associated with each type of deposit The probability of withdrawal will likely differ not only between time and demand deposits but also among different classes of demand deposit holders The differences m turnover rates across sectors, noted earlier, are undoubtedly related to these probabilities Thus, the disaggregated data from the DDOS can aid m analysis of bank portfolio decmons A variety of financial and techmcal mnovauons have mcreased the turnover rate of demand deposits m the Umted States bankmanaged demand accounts, payable through drafts, money market mutual funds with check features, Imes of credit, telephomc transfers between savmgs and demand accounts, and other cash management techmques The DDOS data may help to predict the aggregate impact of such mnovat10ns m the payments mechamsm If the mnovat10ns result m shifts m deposit shares, we may, without bemg able to predict the shifts, recogmze earlier what 1s occurring Several mnovat10ns that appear to have qmte specific sectoral impacts are developing The followmg illustrate these developments l The spread of automatic clea1 mghouses (ACH) The mcrease m ACH's will tend to reduce bank float Smee ACH's facilitate almost mstantaneous transfers of funds, corporations may well reduce their balances to some mm1mum except for times when payments are to be made Smee the funds for payments would be deposited and almost immediately withdrawn, lower average balances would be observed 2 Use of ACH's to facilitate the direct deposit of payrolls through preauthonzed payments, agam reducmg float 3 Pomt-of-sale termmals If these permit retail customers to make direct transfers from mterest-bearmg accounts, they may dramatically reduce the levels of demand deposits that consumers will wish to hold for transaction purposes 4 Contmuous real-time momtormg of mdividual bank accounts (mcludmg credits and debits) Time-sharmg computer systems that permit direct, contmuous readout of individual account mformat10n are likely to be offered to and to be used by corporations Such systems clearly offer timely mformat1on about current cash flows, thus reducmg uncertainty and therefore probably lowermg average cash balances https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis Expanding the linkages between real and financial markets Recent study has provided some empirical evidence that the state of balance sheets 1s important m determmmg expenditures 21 The usefulness of this idea has been limited by an mab1lity to explam the state of the balance sheets However, 1t appears that we will now be able to model the flow of funds accounts because of a nearly completed project funded by the N atlonal Science Foundation 28 The project has already developed spec1ficat1ons and estimates to explam the portfolio holdmgs of almost all of the maJor sectors m the accounts The plan 1s to mcorporate this flow of funds model mto the Board's quarterly MPS model Several new lmkages between financial markets and real activity (such as 21 See, for example, James R Kearl and Frederic S M1shkm, "Ilhqmd1ty, the Demand for Res1dent1al Housmg and Monetary Pohcy," forthcoming m Journal of Finance, Frederic S M1shkm, "Ill1qmd1ty, Con sumer Durable Expenditure, and Monetary Pohcy," American Economic Review, vol 66 (September 1976), pp 642-54, and Edward Yardem, "A Portfolio Balance Approach to Corporate Fmance" (Ph D d1ssertauon, Yale Umvers1ty, 1976) 2s The work has been earned out largely at Yale Umvers1ty (by James Tobm, Wilham M Brainard, Gary Smith, and Gary Fromm) and at the Umvers1ty of Pennsylvama (by Lawrence R Klem and Albert Ando) Demand Deposit Ownership Survey housmg, mventory mvestment, plant and eqmpment expenditures, and consumpt10n) can then be entertamed Thus, the DDOS will be used mdirectly because 1t provides a basis for constructmg more accurate estimates of the M 1 balances m the flow of funds accounts In addition, some recent work by Tmsley 20 and by Kalchbrenner and Tmsley30 suggests that quarterly real forecasts can be substantially improved by takmg mto account the correlat10ns between the mnovat1ons m quarterly 1eal variables and those m monthly financial variables The DDOS data can be of help m mch filtermg exercises by expandmg the set 20 Peter A Tmsley, "On Proximate Explmtatlon of Intermediate Information m Macroeconomic Forecast mg," Special Studies Paper 59 (Board of Governors of the Federal Reserve System, 1975) ao John H Kalchbrenner and Peter A Tmsley, "On the Use of Feedback Control m the Design of Aggregate Monetary Polley," American Economic Review, vol 66 (May 1976), pp 349-55 https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 109 of monthly financial data mcluded m the analysis Summary The precedmg d1scuss10ns of potential uses of the DDOS data suggest the sizable .tmount of research that this body of data may facilitate or enhance To date, many of these proJects have not been undertaken because of the ielauvely small number of observations available m the DDOS data base, the number of monthly observations may now be sufficient for some 1elatively hm1ted studies, but the quarterly base is still very small-about 22 observations The potential return from monthly and quarterly ownership data appears la1ge The ab1hty to be able to identify special factors accountmg fo1 shifts m sectoral money demands, and hence m aggregate money demand, alone has great potential for 1mprovmg pred1ct10ns of money demand and mcome llO Appendix 1: Relationship of Gross IPC Demand Deposits to the Money Supply Gross !PC demand deposits differ from the demand deposit component of the money supply m that the money supply deposit figure is net of cash Items m process of collection (CIPC) and Federal Reserve float and mcludes several types of deposits besides !PC deposits (for example, de posits of State and local governments, foreign governments, foreign official mstitutions and foreign commercial banks,1 and certified and officers' checks) These differences are expressed m Table A-1 m terms of ad1ustments necessary to go from the demand deposit component of the money supply to gross IPC demand deposits by usmg data for the fourth quarter of 1975 The figures for Federal Reserve float are, of course, supplied by Federal Reserve Banks and are the true daily-average values for this item for each month All other data are partly estimated Currency figures are as reported m money supply data for these months They were denved by first obtammg from the Federal Reserve Banks data reflectmg the total volume of currency outstand1 lncludmg deposit balances mamtamed by foreign official mst1tut10ns and mternat1onal ms11tut1ons at Federal Reserve Banks mg m each month The volume of currency held by banks m their vaults was then deducted from tlus total, data on the actual volume of currency held by Federal Reserve member banks were combmed with an estimate of currency holdmgs at nonmember banks The figures for CIPC are also based on data reflectmg the actual volume of these Items at Federal Reserve member banks and estimates for tlus item at nonmember banks The values for all of the vanous deposit categones were estimated by usmg data from weekly reportmg banks and call reports Estimates of daily-average balances m these deposit categones mamtamed at weekly reportmg banks were obtamed by averagmg balances repo1 ted on each Wednesday of the reference month, straight-lme mterpolations were used m those mstances m winch the week precedmg a Wednesday report date spanned the end of a calendar month Estimates for nonweekly reportmg banks were obtamed by usmg a ratio esumatmg techmque Ratios reflectmg the relationship between the vanous deposit categones at nonweekly reportmg banks and at weekly reportmg banks outside New York on call report dates were first calculated These ratios were then used, together with data reflectmg esu- TABLE A-1 Reconc1hation of the Money Stock with the DDOS, Fourth Quarter, 1975 In mtlhons of dollars, not seasonally adiusted Demand deposit component of Mi Plus CIPC all commercial banks Federal Reserve Hoat Less Edge Act and Agency adJustment CIPC plus Federal Reserve Hoa t, adJusted Gross deposits m Mi Less Mi-type balances at agencies and branches Foreign official deposits with the Federal Reserve Foreign commercial bank deposits, all commercial banks Foreign government deposits, all commercial banks Foreign adiustment-Total All other deposits-Total Less Cerufied and officers' checks, all commercial banks Stale and local deposits, all commercial banks Total cerufied and officers' checks plus State and local deposits Derived estimate of IPC demand deposits DDOS esllmate of !PC demand deposits Difference https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 228,095 42,849 270,944 9,213 261,731 24,855 236,876 236,910 -34 Demand Deposit Ownership Survey mates of daily-average balances m the vanous de posit categories at weekly reportmg banks outside of New York-calculated m the same way as were the estimates for all weekly reportmg banks-to obtam estimates for nonweekly reportmg banks An estimate of gross IPC demand deposits based on d,lta received on reports from DDOS sample banks is presented m Table A-1 for comparison with the gross IPC figures denved by makmg the vanous adjustments to the money supply The estimates are reasonably similar to each other https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis Ill It is not clear which of the two approaches yields estimates that most closely approximate the true daily-average values for gross IPC deposits Both are subject to error-the DDOS estimate because of samplmg vanation and the estimate denved from the money supply because proxy estimates were utihLed at vanous stages of the calculation I he weakest estimates m the adjustment of the money supply figure are the figures for "certified and officers' checks" and for "State and local demand deposits " 112 Appendix 2: Tests of the Equality of Coefficients across Ownership Classes Using "Standard" Money Demand Equations One assumption underlymg the discussion of potenual uses of the DDOS is that different ownership categories have different demand functions for money, to assess the vahdity of this assumption, sets of tests were undertaken Both deal wtth the three mam ownership categories m the DDOS financial busmesses, nonfinancial busmesses, and households These categories accounted for 92 8 per cent of total IPC deposits as of December 1975 Demand functions were also estimated for total DDOS deposits Monthly, not seasonally adjusted data for the sample subset of weekly reporting banks were used m estimaung the equauons Data for the first 6 months of the survey were excluded because sur' ey start-up problems made those data less rehable Data for the second half of 1974 and for all of 1975 were also excluded A number of staff studies mdicate that standard money demand equations, for some reason as yet not fully explamed, do very poorly m explammg tlus penod Including these data m the demand equauons discussed below led to severe deteriorauon m the estimated relat10nships NoTE -Helen T Farr and Arthur M Havenner prepared this appendix TABLE A-2 Demand Function Interest Rate Coefficients and Summary Statistics Fmancial busmesses Households Interest rate R30 Coefficient (1-statisuc) (-1 (-1 - R90 RCP (-2 CD, (30-59 day) CD, (60-89 day) CDa (90-119 day) RCDS RFF (-2 (-2 (-2 (-2 ( (-2 ROTS 0122 682) 0143 839) 0157 242) 0163 374) 0159 229) 0176 310) 0162 146) 0005 414) 1317 039) I R• Coefficient (l-stat1suc) SB I 0257 9833 0073 9836 0075 9844 0073 9847 0072 9844 0073 9846 0072 9842 0073 9817 0079 9841 0074 Nonfinanc1al busmesses R• Coefficient (I stat1st1c) SE 7965 0138 7934 0139 7960 0138 7975 0138 7980 0138 8011 0137 7976 0138 8067 0135 7831 0143 (I 473) 0254 (I 324) 0278 (I 451) 0286 (I 527) 0302 (1 550) 0346 (I 686) 0305 (1 530) 0049 (1 913) 0752 ( 656) (-2 (-2 - (-3 (-3 (-2 (-2 (-2 ( (-1 I R• SB Total Coefficient (-1 (-1 - 9874 0070 9876 0069 9892 0065 9891 0065 9889 0066 9887 0066 9885 0067 9860 0074 9870 0071 (-1 - 018 (-6 75) 001 ( 85) - 024 (-6 94) - 021 (-8 53) (-6 ((-6 (-7 0193 192) 0220 384) 0262 188) 0258 070) 0258 983) 0268 913) 0255 791) 0015 658) 1463 658) I (1 Sla!ISIIC) (-2 (-2 (-2 (-2 (-1 (2 - 0120 454) 0149 723) 0178 294) 0168 237) 0164 089) 0178 104) 0162 948) 0039 013) 1239 929) R• SE 9884 0061 9887 0061 9895 0058 9894 0059 9892 0059 9892 0059 9890 0060 9896 0058 9893 0059 TABLE A-3 Coefficients and t-Stat1stics for BIii Rate and Income R90 coefficients Deposit category a Sum of all DDOS deposits 2 Fmanctal bustness (2 ( 3 N onfinanc1al bustness (I 4 Households https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis (3 012 24) 008 58) 012 61) 018 41) I a, - 001 (- 30) 006 ( 82) - 004 (-1 24) 001 ( 40) I a, - 010 (-7 48) 003 ( 98) - 016 (-8 71) - 011 (-8 62) I a, - 016 (-7 75) 002 ( 34) - 022 (-8 24) - 019 (-9 57) I a, 016 22) 000 02) 021 29) 019 97) I a, (-5 (- 010 92) 000 07) 013 (-5 93) - 012 (-7 00) Demand Deposit Ownership Survey 113 First tests In the first tests, all demand functions estimated were of the form In D= a. + a1 In R + a2 In Pl 11 + aa In D_1 + ~ {3,S, ,~i where D is the deposit category, R is an mterest rate, PI is personal mcome, and S, are seasonal dummies For each demand equation, nme different mterest rates were tned separately the 30-day Treasury bill rate, the 90 day Treasury bill rate, the 30- to 59-day commercial paper rate, the 30- to 59-pnmary CD rate, the 60- to 89 day primary CD rate, the 90- to 119-day primary CD rate, the 90-day secondary CD rate, the Federal funds rate, and a composlle time and savmgs deposit rate The mterest rate that gave the "best" equation m terms of R. 2 and standard error vaned accordmg to ownerslup category For total DDOS depos!ls and for nonfinancial busmesses, it was the commercial paper rate, for households, It was the 30- to 59 day primary CD rate 1 For financial businesses, nellher personal mcome nor any mterest rate was s1gmficant Table A 2 gives the estimated mterest rate coefficients and their t statistics (m parentheses), the R. 2, and the standard error for the estimated equations The results provide evidence that different mterest rates are relevant for different holders of money Second tests In the second tests, demand functions were estimated for the three mam ownership categories 1 As noted m the paper, most aggregate money demand equatlons show a large and s1gmficant impact of the time deposit rate Theory suggests that such an impact would arise predommantly m the consumer sector (only smce November 10, 1975, have corporations been permitted to hold savmgs deposits) These results md1cate that the house hold category 1s the only ownership category m which the time deposit rate has a s1gmficant impact and for aggregate deposits All equations were of the form 6 In Di = ~ a, In R901-, 1,-=-() ,~ 11 +~ -y,S,1 + 'Y• ,=i where D 1s the deposit category, R90 1s the 90 day Treasury bill rate, Pl 1s personal mcome, and the S, are seasonal dummies The coefficients and t statistics for the two mam mdependent variables of the total and component equations are presented m Table A-3 The equations were estimated by a stacked regress10n techmque that took account of the fact that the contemporaneous errors m -e,1ch regress10n are probably correlated but that all errors are uncorrelated over time The coefficients of the polynomial d1stnbuted lags were assumed to he along a second degree polynomial constramed to zero at the tail, with a total length of 7 months Tests were made of the s1gmficance of the differences between the a,'s, f1.'s, and y,'s of the compo nent equations 'I he e, 1dence mchcates that the coefficients of the component equations differ s1gmf1cantly from each other In evahutmg these results, 1t should be noted that only 37 observations were used, that 1s, each equation had only 21 degrees of freedom, which may be too few observat10ns to estimate adequately all of the differences among the var10us ownership categories However, even with the limited degrees of freedom, the tests strongly md1cated differences If the ob1ect of the tests had been simply to estimate the best equation for each ownerslup category, different variables would have been used for each category 2 By usmg separate polynomial d1stnbuted lags on mcome and the mterest rate, however, It was possible to allow different time response patterns between the two variables, unlike models that constram the re- 'See the section of this paper on TABLE A-3-Contmued Pl coeffic1ents /Jo 364 (4 15) 578 (2 55) 120 (I 04) 264 (3 16) https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis (6 (2 (2 (5 /31 /32 227 13) 263 75) 133 74) 185 25) 119 9) 257 26) 136 6) 120 6) (26 (2 (23 (28 /3, 038 (I 43) - 134 (-1 94) 129 (3 68) 068 (2 68) /3• ((-2 (2 ( 014 35) 217 14) 112 18) 031 82) 6 + ~ (3, In P/1_, /3, ((-2 037 96) 222 21) 085 (I 66) 007 ( 18) /3, (-1 (-2 033 27) 150 25) 047 (I 40) - 004 (- 14) Money demand studies" 114 Improvmg the Monetary Aggregates Staff Papers TABLE A-4 Test Results Stat1st1c1 Type I error Fa,"= 8766 24Xl0-" 2 Equabty of nonseasonal coefficients m all equations a1, - a2, = 0 and a2, - aa, 0 and fJh - fJ2, = 0 and {J,, - /Ja, = 0, 1 = 0,6 Fa"= 17 869 7 I X 10-10 3 Equabty of seasonal coefficients m all equations "Yb - 'Y2, 0 and 'Y2, - 'Ya.= 0, i = 0,11 F,. = 1 3 X 10-" 4 F, '" = 5 987 F, = 18 045 2 6 X 10-11 = 34 538 1 4 X 10-" Test Equabty of coefficients m all equations ab - a2,= 0 and a2, - aai,= 0 and /Jl, - /3h= 0 and {J,, - {!,, = 0 and '>'1, - 'Yo,= 0 and 'Y2J - 'Ya,= 0, I= 0,6,J=< 0,11 = = Equably of rate coefficients m all equations a11 - a2,= 76 13 381 0002 Oanda21- - aai= 0, i= 0,6 5 Equality of mcome coefficients m all equations 13,. - /3,, = 0 and /3,, - {J,, ""' 0, 1 = 0,6 10, 6 Equality of nonseasonal coefficients, financial and nonfinanc1al equations ai. - a,,= 0 and {J1, - {J,, = 0, I= 0,6 F. "' 7 Equably of nonseasonal coefficients, nonfinanc1al and household equations a2, - aa. = 0 and /32, - fJh = 0, 1 = 0,6 F, ,oa= 8 Equality of nonseasonal coefficients, financial and household equations ah - aa, = 0 and /j11 - {Ja, = 0, i = 0,6 F, 10, 1 At the 99 per cent confidence level, Fao so = 2 03, Fa 100 ""' 2 69, Fu sponse pattern by spec1fymg a lagged dependent vanable The statistic used to test equality of the coefficients 1s attnbutable to Zellner and 1s best descnbed m his paper, "An Efficient Method of Estlmatmg Seemmgly Unrelated Regress10ns and Tests for Aggregation Bias " 3 Table A-4 presents the values of the test statistics for the different compansons made when, for example, the a 1 , are the coefficients on the bill rate m the financial business equat10n, the {3 2 , are the coefficients on personal mcome m the nonfinancial busmess equation, and the y 3 , are the seasonal coefficients and mtercept m the household equation In order to argue that no additional mformat1on 1s gamed by d1saggregatmg mto ownership classes, all respective coeffioents m all equations must be equal (test 1) One can be 99 99999999999998 per cent certam that this 1s not the case (1 mmus the type I error times 100) Test 2 md1cates that 3 Arnold Zellner, Journal of the American Statistical Association, vol 57 CT une 1962), especially pp 354-56 https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis = I 326 32 507 10 = 2 07, F. 265 I 4 X 10-10 100 = 3 51 this result 1s not due to the (nmsance) seasonal coefficients, because the nonseasonal coefficients are also s1gmficantly different The seasonal coeffi oents are s1g111ficantly different also, however, as test 3 demonstrates Breakmg the coefficients mto subcategones, 1t can be seen that wlule the responses to mterest rate changes are s1gmficantly different (test 4), the differences are not nearly so great as m the case of mcome responses (test 5) D1saggregatmg over ownership categories, tests 6 through 8 show that whereas financial and nonfinancial holders respond to mterest and mcome changes m a substantially different manner (test 6), households are not s1gmficantly different from nonfinancial mst1tut1ons (test 7) Smee households are not s1gmficantly different from nonfinancial busmesses, 1t 1s not surpnsmg that they are s1gmficantly different from financial busmesses (test 8) Tests run with the 30- to 59 day commercial paper rate mstead of the 90 day bill rate gave essentially the s<1me results 115 Bibliography Board of Governors of the Federal Reserve System Flow of Funds, Assets and Liabilities Outstanding, 1974 Washmgton Board of Governors, 1975 Emler, Jared, Lewis Johnson, and John Paulus "Some Problems of Money Demand" Brookings Papers on Economic Activity, l 1976, pp 261-80 Goldfeld, Stephen M "The Demand for Money Rev1S1ted " Brookings Papers on Economic Activity, 3 1973, pp 577-643 Homonoff, Richard, and David Wiley Mullms, Jr Cash Management Lexmgton, Mass Lexmgton Books, 1975 Kalchbrenner, John H, and Peter A Tmsley "On the Use of Feedback Control m the Design of Aggregate Monetary Policy" American Eco nomic Review, vol 66 (May 1976), pp 349-55 Kearl, James R, and Frederic S J'vhshkm "Ilhqmd1ty, the Demand for Res1dent1al Housmg and Monetary Pohcy" Journal of Finance, forthcommg Lieberman, Charles "The Transactions Demand for Money and Technological Change" Review of Economics ancl ',tatisticv, vol 59 (August 1977), pp 307-17 Miller, Merton H, and Damel Orr "A Model ol the Demand for Money by Firm~" Q11arte1 ly Journal of Economics, vol 80 (August 1966), pp 413-35 l\hshkm, Frederic S "Ilhqmd1ty, Consumer Durable Expenditure, and Monetary Policy" Ame11cnn Economic Review, vol 66 (September 1976), pp 642-54 Orr, Dame! Cash Managemrnt and the Demand for Money New York Praeger, 1971 Porter, Richard D "Debits, Turnover, and Money Demand " Memo randum Washmgton Board of Governors of the Federal Reserve System, January 1976 Pugash, James Z "The Demand for Money m Six Sectors" Unpublished manuscript, Washmgton Board of Governors of the Federal Reserve System, January 1974 Sluller, Robert J "A Distributed Lag Estimator Derived from Smoothness Priors" Econometrica, vol 41 (July 1973), p 775-88 Slovm, Myron B, and Mane E Sushka Interest Rates on Savings Deposits Lexmgton, Mass Lexmgton Books, 1975 "Survey of Demand Deposit Ownerslup " Federal Reserve Bulletin, vol 57 (June 1971), pp 456-67 Swamy, P A V B Statistical Inference in Random Coefficient Models Berlm Sprmger-Verlag, 1971 Tmsley, Peter A "On Proximate Explo1tat10n of Intermediate Informat10n m Macroeconomic Forecastmg" Special Studies Paper 59 Washmgton Board of Governors of the Federal Reserve System, 1975 https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 116 Improving the Monetary Aggregates· Staff Papers Yardem, Edward "A Portfolio Balance Approach to Corporate Fmance" PhD d1ssertauon, Yale Umversity, December 1976 Zellner, Arnold "An Efficient Method of Est1matmg Seemmgly Unrelated Regressions and Tests for Aggregauon Bias" Journal of the American Statistical Assoc1at1on, vol 57 (June 1962), pp 348-68 https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 117 Sources of Data and Methods of Construction of the Monetary Aggregates Darwin L Beck This paper is a somewhat more detailed version of the study originally prepared for the Advisory Committee on Monetmy Statistics zn 1976 The first senes on the money stock published by the Federal Reserve was based on data for dem,mtl and time deposits of banks and currency m circulation for June call dates £01 the penod 1892 to 1922, and for June and December call dates for 1923 to 1941 1 In February 1944, the Board first began to publish smgle-day monthly data (for the last Wednesday of the month) similar to that based on call report data In October 1960 a revised and improved measure became available for the penod begmnmg with 1947, 2 it was a daily-average, rather than a smgle-day, series and was available twice each month Wlule the money stock senes has been revised many times smce 1960, the narrow measure, Mi, cmrently published by the Board 1s consistent with that first published, on a semimonthly basis, m 1960 In August 1962, m d. mmor rev1s10n, foreign demand balances with Federal Reserve Banks and demand deposits of banks m US terntones and possess10ns held at U S commercial banks were added to the demand deposit component of the money supply At the same time weekly estimates of the money stock back to 1959 were published for the first time 3 From 1963 to 1968 the money stock was Norn -Danvm L Beck 1s a member of the staff of the Board's D1vmon of Research and Statistics 1 Banking and Monetary Stat1st1cs (Board of Governors of the Federal Reserve System, 1943) 2 "A New Measure of the Money Supply," Federal Reserve Bulletin, vol 46 (October 1960), pp 1102-23 a "Revmon of Money Supply Senes," Federal Reserve Bulletin, vol 48 (August 1962), pp 941---51 https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis d.dJUSted five times to mc01 pm ate new benchmark dd.ta for nonmember b,mks and revised seasonal factors based on add1t10nal data Furthermore, m 1969 and ag,1_m m 1970, the money stock was adjusted to conect fo1 downward bias m the level and uend of the seues that had developed m assoc1at10n with expans10n of check-clearmg ope1at1ons of f01e1gnielated mst1tut10ns m New York C1ty 4 In early 1973, anothei statistical iev1sion a1ose from changes m Federal Reserve iegulations that c,tused a chscontmmty m the rep01 ted data fiom winch money stock measures are constructed" In the early years, the narrow money stock measure, Mi, was given the greatest emphasis Time deposits adjusted were also published, but no effort was made to construct broade1 monetary measures by addmg such deposits, and deposits of nonbank mst1tut10ns, to M 1 6 However, m Apnl 1971, the Board also began regularly to publish broader monetary aggregate measures, M 2 and M 3 More recently, begmnmg m Apul 1975, the Board added M 4 and M 5 to the published data The tabulat10n below describes the public's financial assets mcluded m each of the measures of monetary aggregates regularly published by the Board of Governors of the Federal Reserve System In general, the pubhc 1s defined as all mdiv1duals and mst1tut1ons, do4 See "Revmon of Money Supply Senes," Federal Re serve Bulletin, vol 55 (October 1969), pp 787-803, and "Rev1S1on of the Money Stock," Federal Reserve Bulletin, vol 56 (December 1970), pp 887-909 s "Revmon of the Money Stock Measures and Member Bank Reserves and Deposits," Federal Reserve Bulletin, vol 59 (February 1973), pp 61-79 a Time deposits adjusted are defined as total lime and savmgs deposits at commercial banks less US Government and mterbank time deposits us Improvmg the Monetary Aggregates. Staff Papers mest1c and foreign, other than the U S Goverment and domestic commercial banks Money stock measure Assets included Currency m crrculation All currency and com outside the U S Treasury and Federal Reserve Banks less currency and com held m the vaults of U S commercial banks or m transit to or from Federal Reserve Banks Currency m circulation plus demand deposits ad3usted at all U S commercial banks (gross demand deposits less de mand deposits due to the US Government, demand deposits due to domestic commercial banks, cash items m the process of collection, and Federal Reserve Reserve float), M 1 type deposits at Edge Act corporations, branches and agencies of foreign banks, and foreign investment corporations, and foreign official deposits at Federal Reserve Banks M 1 plus total time and savings deposits at all commercial banks less (a) negotiable time ceruficates of deposit issued m denominations of $100,000 or more by large weekly reporting banks, (b) time deposlls due to domestic commer c1al banks, and (c) time deposits due to the U S Government M 2 plus deposits at mutual savmgs banks, savings and loan shares, and credit umon shares M 2 plus negotiable Ume certificates of deposit issued m denommauons of $100,000 or more by large weekly reportmg banks Ms Ma plus negotiable time certificates of deposit issued m denommauons of $100,000 or more by large weekly reportmg banks Economists and financial analysts generally agree that money stock series should be constructed by measurmg the various financial assets that have been categorized as moneycurrency, demand deposits, savmgs deposits, time deposits, and so on-from the records https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis of the actual money holders This ts the "holder record" concept of the money stock However, umverse reportmg of actual money stock on such a basts ts not possible, and a sample survey also appears to be impractical Even 1f an adequate sample could be drawn or reportmg arranged for the umverse of domestic holders of money stock assets, a large segment-foreign holders-could not be readily accounted for A rough equivalent of the holder-record measure of the money stock can be derived from the records of the Treasury, Federal Reserve Banks, and other financial mstitut10ns if proper adjustment 1s made for the recordmg of some items on the books of two banks at the same time With that adjustment, such a measure would differ from one based on holder records only because of "mail float"checks issued and deducted from holders' records but not yet received and deposited m payees' accounts The mail-float discrepancy between holder records and bank records may be offset, so far as economic motivation 1s concerned, by the expectation of an mflow of funds by the drawer of the check before the check is presented for payment To the extent that such an offset exists, measures based on unduphcated bank records and holder records are very similar All of the measures of the money stock published by the Board are derived from the records of the Treasury, Federal Reserve Banks, domestic commercial banks, and other financial mstitut10ns The basic adjustments that must be made to these data mclude adJUstments for double countmg and est1mat1on of weekly- and monthly-average levels of deposits at bankmg mstitut10ns that do not report on so frequent a basis In addition, deposits of some holders, such as foreign commercial banks, must be esumated usmg supplementary data because the basic data do not provide a sufficient breakdown to permit direct measurement Inasmuch as currency m c1rculat10n 1s a bmldmg block common to all of the broader money stock measures, the description of the Sources of Data and Methods of Construction of the Monetary Aggregates construction of the monetary aggregates begms with it A discussion of the demand deposit component of the money stock is next, followed by a descnpuon of the broader money stock measures, M 2 through M 5 Currency in circulation The currency component of the money stock is defined as all U S currency and com outside the Treasury, Federal Reserve Banks, and commercial banks This component accounts for roughly 25 per cent of the narrow money stock mec1sure, M 1 Daily data on currency m circulation outside the Treasury and the Federal Reserve System are reported to the Board on a regular basis Table I shows for the last day of 1975 the vc1nous items that make up the total of currency and com m circulation outside the U S Treasury and Federal Reserve Banks The bulk o[ currency c1nd com m circulation con5ists of Federal Reserve notes, followed by the fractional com (quc1rters, dimes, mckels, and so on) issued by the Trcc1sury Other relatively large components are silver dollars currently JSSued by the Treasury and U S notes issued by the Treasury m earher years A mmor TABLE 1 Currency m C1rculahon Outside the U S Treasury and Federal Reserve Banks, Year-End 1975 1 In mllbons of dollars Type of currency F R notes outstanding Fractional c01n Sliver dollars Silver ceruficates US notes FR Bank notes National Bank notes Gold cerllfica !es FR notes prior to 1923 series Total currency and com Less F R notes of other FR Banks and Treasury com held by FR Banks FR notes Com Held by the Treasury FR notes Com Total Amount 78 769 8,610 1,001 210 323 50 20 3 I 88,987 1,612 345 175 308 86,547 1 For a more detailed descr1pt1on of the components that make up total currency m c1rculat1on, see Banking and Monetary Sta11s11cs, 1941-1970 (Board of Governors of the Federal Reserve System, 1976), pp 615-16 https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 119 component, about $285 milhon, of assorted currency still outstandmg but m the process of retirement consists of silver certificates, Federal Reserve Bank notes, National Bank notes, Federal Reserve notes pnor to the 1923 senes, and gold certificates The currency component of the money stock measures excludes the vault cash (currency and com) held by commercial banks Smee vault cash of member banks can be used to meet reserve reqmrements, these holdmgs aie mcluded on reports submitted to the Federal Reserve for the determmauon of reqmred reserves, and are thus available on a dally basis Vault cash at nonmember banks must be estimated from quarterly or semiannual reports of condition of all commercial banks Lmes 2 and 3 m Table 2 show the estimated vault cash held at member and nonmember banks on average m December 1975 7 Estimates of vault cash held at nonmember banks a1e based on the ratio of vault cash of nonmember banks to vault cash of membe1 banks on cc11l report dates Currently, these benchmark relationslups c1Te avatlable for weekly c1verc1ges surroundmg call dates £om times each year Pnor to March 1976, they were c1vallable for four smgle days each year, pnor to March 1973 they were generally available only for June 30 and December 31 8 Estimates of the ratio of vault cash for ec1ch week between call report dates are based on c1 straight-hne mterpolation Weekly estimates of nonmember vault cash are then denved by muluplymg the est1mc1ted weekly ratio of vault cash by the rep01 ted weekly-average vault cash of member banks Monthly-ave1age vault cash 1s denved from a proration of the weekly estimates The ratio for the latest call report 1 Note that Table 1 shows currency and com com ponents for the last day of December 1975, while T dble 2 shows th<- monthly average for December 1975 of currency m c1rculat1on ancl vault cash at member and nonmember banks R Data for all commercial banks are ava1labk from call rcpolts fo1 Jun<- 30 and December 31 The other l\\O call~ provHk data for all mmred banks (Unmsured banks a1e a rdal!vdy ~mall wmponent of the total U S bankmg sy~tem ) 120 Improvmg the Monetary Aggregates Staff Papers TABLE 2, Construction of M, Monthly averages ID mtlbons of dollars, not seasonally ad.Justed Line, Item Contr1button December 1975 Source of data 85,847 Daily data reported by Federal Reserve Banks and Treasury Department Daily data reported by all member banks Esttmated, based on data reported by member banks and call report data Currency ID c1rculat1on 2 3 Less 4 5 6 7 Equals Currency component of M1 8 9 10 Member bank vault cash Nonmember bank vault cash Demand deposits at member banks1 Less F R float Plus Demand deposits at nonmember banks 8,097 2,649 75,101 155,722 3,096 62,082 Demand deposits due to foreign commercial banks 5,408 Demand deposits due to mutual savmgs banks 1,132 Daily data reported by all member banks Daily data reported by Federal Reserve Banks Estimated, based on daily data reported by small member banks and call report data Estimated based on SIDgle day (Wednesday) data for large banks and call report data for other banks Estimated, based on s1Dgle day (Wednesday) data for hrge banks and call report data for other banks Demand deposits due to banks tn terntones and possessions Cash items ID process of collection associated with foreign agency and branch transfers• 3,319 Daily data reported by foreign-related 1Dst1tut1ons ID New York City 12 Mi-type balances at foreign related mst1tut1ons ID New York City 3,025 Esumated, based on daily reporting for large 1Dstltut10ns and on reports for the last Wednesday of month for smaller 13 Deposits due to foreign oflictal 1Dst1tut1ons at Federal Reserve Banks Equals Demand deposits component of M, Money stock (M1)-<:urrency plus demand deposits adJusted 391 228,093 303,194 II 110 Esumated, based on call report data mstttuUons 14 15 1 Gross demand deposits less demand deposits due to U S Government and 1Dterbank deposits and cash items ID process of collection period is held constant until another call report is available Even though the currency component, defined as currency m circulation outside the Treasury and the Federal Reserve Banks less vault cash held at commercial banks, can be measured quite accurately, the defimt10n deviates by some unknown amount from a holder-record concept because it makes no allowance for currency lost or destroyed In addition, some of the currency may be held m safe-deposit boxes or sent out of the country Thus the published measure overstates the amount of currency m circulation m the Umted States No effort has ever been made to measure the currency "not in circulation," and any adjustment for it would be nothmg more than a guess Demand deposits component of money stock Data on the demand deposits component of the money stock are not so readily available https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 2 Daily data reported by Federal Reserve Banks Includes M, type deposits at Edge Act corporations as are those for the cuirency component and thus must be constructed from a number of sources These mclude data available each day and smgle-day data available weekly, monthly, and from quarterly call reports Nearly two-thirds of total demand deposits are accounted for by member banks, and data on these deposits are readily available on a daily basis from the Report of Deposits submitted by member banks for determmation of reserve requirements Because the purpose of this report 1s to measure deposits subject to reserve requirements, and not deposits to be mcluded m the money stock, a number of adjustments must be made m the basic data reported by member banks The demand depos1 ts component of domestic nonmember banks is derived from call report data and estimates based on dally deposits data reported by small member banks Deposits of other financial mst1tut1ons, and other adjustments to the deposits component of Mi, are derived from a number of sources Each component is discussed m detail below Sources of Data and Methods of Construction of the Monetary Aggregates Member bank demand deposits From the Report of Deposits, filed weekly by member banks, four items are used to construct the demand deposits component of the narrow money stock, M 1 Three of these Items aggregate to gross demand deposits U S Gove1nment deposits, demand deposits due to other commercial banks, and "all other" demand deposits (that 1s, demand deposits due to md1v1duals, partnerships, and corporations -domestic and foreign, State and local governments, nonp1ofit orgJ.mzat10ns, and so on) The fourth Item, cash items m the process of col1ect1on (CIPC), 1s deducted from gross demand deposits m the construction of the money stock All U S Government demand depos1 ts are excluded from the money stock and "all other" demand deposits are mcluded A problem anses m connect10n with demand deposits due to banks At the present time, demand deposits due to foreign commercial and mutual savmgs banks are mcluded m the money stock, and demand deposits due to domestic commercial banks are excluded Because these Items are not hsted separately on the Report of Deposits but are mcluded m the "due to hanks" component, alternative sources of data must be used to estimate the demand deposits due to foreign commercial banks and mutual savmgs banks included m the money stock The bulk of these deposits are held at large banks that report on them each week (Wednesday) as part of a detailed balance sheet These smgle-day weekly data, along with call report data for all commercial banks, are used to adjust the demand deposits data The calculat1on of the demand deposits at member banks included m the money stock begms with gross demand deposits From this figure total demand deposits of the US Government and those due to banks are deducted In order to av01d double countmg of demand deposits that are shown simultaneously on the books of two banks, CIPC are also deducted from gross demand deposits to denve the component of M 1 accounted for by the member bank demand deposits (see lme 5 of Table 2) https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 121 Smee CIPC can be deducted m computmg deposits subject to reserve 1eqmrements, It 1s J.lso available on a daily basis from the Report of Deposits CIPC shown on tlus report, however, is not b1oken down for items associated with private demand deposits and those associated with all other operat10ns of the bank It 1s known that gross CIPC overstJ.tes those items that should be deducted from the money stock deposits For example, cash Items assoClated with deposits due to banks, with US Government deposits, with redeemed coupons of US Government securities, and with bank ued1t cards are mcluded m the gross cash items data Past mvest1gat1ons and contacts with bank accountants suggest that the distortions noted above J.re not large f01 domestic transJ.ct10ns and that they 1emam fanly constant relative to total deposits A much more senous p1oblem, discussed m some detail below, concerns the s1gmficant p10port10n of the CIPC related to mterbank transfe1 s of funds, associated largely with the clearmg of Eurodollar transactions m the New York City money market between large member banks and more specialized mst1tut1ons engaged m mternJ.t10nal bankmg Such CIPC 1s added hack vu data collected chrectly from mternatlonal bankmg mst1tut10ns Federal Reserve fl,oat Federal Reserve float, which is very similar to CIPC, 1s also deducted fiom pnvate demand deposits m calculatmg M 1 (lme 6 of Table 2) This float 1s deducted because on some Items that are cleared through Federal Reserve Banks crecht 1s passed to the sendmg bank before the paymg bank has received the item and reduced deposits When the sendmg bank receives credit, the CIPC account 1s reduced on that bank's books even though deposit hab1ht1es on the books of the paymg bank have not been reduced The amount of double countmg m such mstances 1s reflected m the float created by Federal Reserve Banks rather than CIPC Deductions for both Federal Reserve and CIPC float serve to offset this double-countmg effect 122 lmprovmg the Monetary Aggregates Staff Papers Nonmember bank deposits Domestic nonmember banks account for the second largest deposit component of the money stock (hne 7 of Table 2) Data for nonmember banks are available four times a year from call reports In order to estimate their deposits for other periods, the ratio of the demand deposits of nonmember banks m M 1 to those of the smaller member banks is computed for each call report date A straight-lme mterpolation of this ratio ad1usted for changes m bank structure is made between call report dates 9 These estimated weekly rat10s are then apphed to weekly data on average deposits reported by smaller member banks m order to obtam weekly and monthly estimates of the demand deposits component of the money stock at nonmember banks Monthly-average estimates are derived from a weighted average of the weekly estimates Beyond the current call report date, rat10s are estimated based on a regression equation and Judgment 10 As new call report data become available, these estimates are revised and benchmarked to the umverse data available from the call report While demand deposits of member and nonmember banks account for the bulk of the demand deposits component of Mi, a number of additional adjustments must be made to complete construct10n of M 1 Demand deposits due to foreign commercial banks As mdicated m the discussion of the demand deposits of member banks, demand deposits due to foreign commercial banks are mcluded m mterbank deposits on the Report of Deposits Smee total demand deposits due to banks were deducted from gross deposits, further ad1ustments must be made to mclude deposits due to banks m foreign countries m 9 Changes m bank structure reflect shifts m bank reportmg status due to changes m Federal Reserve membership, mergers, and the like that affect the ratio of nonmember banks to small member banks 1 For a descnpuon of this process, see "Rev1s10n of the Money Stock Measures and Member Bank Deposits and Reserves," Federal Reserve Bulletin, vol 60 (Febru ary 1974), pp 81-95 ° https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis the demand deposits component of M 1 Estimates of these foreign demand deposits are based on weekly smgle-day (Wednesday) data for large banks and on call report data As part of a detailed balance sheet, on Wednesday of each week about 320 large commercial banks report the breakdown of their deposits, from which the demand deposits due to foreign commercial banks can be derived For nonweekly reportmg banks, which account for about 20 per cent of demand deposits due to foreign banks, estimates are based on call report data Estimates of the demand deposits due to foreign commercial banks mcluded m M 1 are constructed as follows For each call report the amount of demand deposits due to foreign commercial banks at nonweekly reportmg banks is calculated Between call report observat10ns, weekly estimates are derived from a straight-lme mterpolat10n After the most current call report date, the latest level of deposits at nonweekly reportmg banks is earned forward as a constant The total of weekly estimates for nonweekly reportmg banks and Wednesday data reported by weekly reportmg banks is then used as a proxy for the weeklyaverage level of deposits due to foreign commercial banks at all domestic commercial banks Monthly averages are prorations of the weekly data Deposits due to foreign commercial banks are a relatively small part of M 1 (lme 8 of Table 2) However, because these deposits, particularly as derived from Wednesday data for weekly reportmg banks, can be qmte volatile, they can have a sigmficant impact on the changes m M 1 both from week to week and from month to month Smee weekly reportmg banks account for roughly 80 per cent of these deposits, measurement error should be relatively small, except to the extent that the smgle-day Wednesday data are a poor estimator of the weekly-average level Demand deposits due to mutual savings banks Demand deposits due to mutual savmgs banks are also mcluded m the mterbank ac- Sources of Data and Methods of Construction of the Monetary Aggregates count on the Report of Deposits and thus deducted from gross deposits Estimates of deposits due to mutual savmgs banks, to be added back to the component of M 1 cons1stmg of demand deposits adJusted, are denved from the same sources as estimates of deposits due to foreign banks-that 1s, weekly reportmg banks and call reports Weekly estimates of mutual savmgs bank deposits at nonweekly reportmg banks are based on a stra1ght-lme mterpolat10n between call report dates These estimates plus Wednesday data for weekly reportmg banks ate used as a proxy for the weekly-average level, and monthly data are weighted averages of the weekly observat10ns The component compnsmg deposits due to mutual savmgs banks 1s small and relatively stable (see lme 9 of Table 2) In addition, weekly reportmg banks account for the bulk of such deposits, about two-thirds m late I q75 Thus any errors m est1mat10n of data from nonweekly reportmg banks are small and have httle impact on the total M 1 measure Demand deposits due to banks in territories and possessions Demand deposits due to banks m terntones and possess10ns are also denved from call reports However, these deposits must be estimated somewhat differently-from a special tabulation of the call report showmg balance sheet data fm banks located outside the Umted States, sometimes referred to as banks m "other areas " Included m tlus tabulation 1s an asset item, demand deposits due from US banks This Item 1s assumed to be eqmvalent to demand deposits due to banks m terntones and possess10ns mcluded m demand deposits due to banks on the books of U S commercial banks, and 1t 1s used as a proxy for such depos1 ts Weekly estimates of demand deposits due to banks m US terntones and possess10ns (hne 10 of Table 2) are derived from a stra1ghtlme mterpolat10n between call report dates Estimates between call report dates are earned forward as constants, and monthy-average estimates are derived from prorat10ns of the weekly figures Smee these deposits generally https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 123 are less than $100 million on call report dates, there 1s httle measurement error m this component Adjustments for cash-items bias CIPC, as reported by member banks on the Report of Deposits, excludes some items that should be deducted from demand deposits to avoid double countmg of money stock deposits, and 1t mcludes some Items that should not be deducted because they do not reflect double countmg An example of the understatement of CIPC 1s the "due from banks" bias Some banks, when forwardmg checks to a correspondent bank for collect10n, 1mmed1ately mcrease their due-from-banks account rather than their CIPC account Durmg part of the collect10n ptocess, such accountmg entnes result m an overstatement of the money stock because CIPC is understated and deduct10ns for double countmg are too small Duefrom-banks deposits are not deducted from gross deposits m calculat10n of the money stock Due-to-banks deposits, from the hab1hty mle of the balance sheet, are deducted from gross demand deposits If both due-to and due-from deposits were deducted, the money 5tock measure would be grossly understated No data exist to measure the amount of the overstatement of the money stock related to this bias, but 1t 1s generally thought to be relatively small and to grow proport10nally with the money stock Thus, while the level of the senes 1s biased upward, month-to-month and year-to-yea1 changes should not be senously affected The overstatement of CIPC and the assonated understatement of the money stock have been a much more senous matter, particularly m the late l960's and early 1970's In the sprmg of 1969, 1t was discovered that an mcreasmg volume of Euro-dollar transact10ns of large banks with their foreign branches had sharply expanded the dollar amount of items m the process of collect10n While drafts issued for the payment of such transfers ("London drafts" and "bills-payable checks") mcreased CIPC, they were not classified as deposits and the associated expans10n m CIPC resulted m 124 Improvmg the Monetary Aggregates Staff Papers unwarranted deductions from reported demand deposits m the estimates of the money supply 11 The deduction of CIPC associated with these Euro-dollar transfers also had the effect of reducmg required reserves To prevent such reductions, the Board changed Regulation D, effective July 31, 1969, to require that member banks mclude checks ongmatmg from transactions with foreign branches as deposits subject to reserve requirements To avoid a sigmficant break m the money stock senes associated with this change m Regulation D and to correct for the understatement of the money stock senes m previous periods, back data were revised The revisions to correct for Euro-dollar float were earned back to May 1967 Rev1S1ons for the first 7 months of 1969 weie based on weekly data obtamed from large banks covering bills-payable checks and London drafts ongmatmg from transact10ns with foreign branches Accordmg to these reports, the total amount of such mstruments mcreased from $1 8 billion m January 1969 to $3 3 billion m July, largely m the May-June period, when Euro-dollar borrowmgs rose sharply Revmons pnor to 1969 were mterpolated on the baSIS of the reported growth rate of CIPC relative to gross demand deposits These data mdicated that growth m cash items relative to demand deposits accelerated significantly about mid-1967 and agam about mid-1968 12 In the sprmg of 1970, additional problems with CIPC ansmg from mternat10nal transact10ns were uncovered Checks issued by Edge Act corporations and agencies and branches of foreign banks were recorded as CIPC on the books of domestic banks However, these checks were not picked up m the gross de- posit figures used m the construction of the money stock smce at that time liabilities of these mstitutions were not mcluded m the money stock The generation of CIPC without recordmg a counterpart liability for money stock deposits on the books of large New York City banks resulted m a downward bias of the level of the money stock This bias was even larger than the one corrected m the 1969 rev1S1on And because the issuance of such checks had grown rapidly durmg this penod, the measured growth m the money stock was also understated In order to correct for this downward bias m the money stock, data were collected from Edge Act corporations and U S agencies and branches of foreign banks, which served as a proxy for the amount of CIPC improperly deducted 13 On October I, 1970, mst1tut10ns began to report daily data that reflect the amount of mappropnate cash items mcluded m the total figure deducted from demand deposits (line 11 of Table 2) Smee that date, money stock measures have been ad jUsted for the CIPC bias by addmg back the amounts reported by foreign-related mstitut10ns (Subsequently, m early 1973, the money stock was also adjusted for CIPC bias generated by foreign mvestment corporations located m New York City) With reported data available from October 1, 1970, m order to avoid a break m the money stock senes, a method was needed to estimate the s1Ze of the bias pnor to that date To make correspondmg revisions m the back data, lt was necessary to estimate the amount of total cash-items bias mdirectly The sharp fluctuat10ns m cash items and m mterbank deposits that occurred on the books of the major New York City banks around certam "London drafts" and "bills-payable checks" were checks drawn by or on behalf of a foreign branch of a member bank on an account mamtamed by such a branch with a domestic office of the parent bank Until the change m Regulation D, effective July 31, 1969, such checks were not mcluded m officers' checks by the issumg bank 12 "Revmon of Money Supply Series,'' Federal Reserve Bulletin (October 1969), p 788 13 Smee Edge Act corporations are required to hold reserves agamst deposits, these mstltutions submit a weekly report similar to the report of deposits submitted by member banks The data from these reports not only reflected the cash items bias generated by Edge Act corporations but also a small amount of M 1 type deposits held at these mstltutlons Smee the cashitems bias and the M1 type deposits could not be separated, all of the Edge Act corporation ad1ustment was mcluded m the adJustment for cash items bias 11 https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis Sources of Data and Methods of Construction of the Monetary Aggregates holidays-such as Easter and Christmas-when European and U S bankmg practices with respect to workmg days diverge, provided a basis for estimatmg the magmtude of the cashitems bias In those hohday penods when New York City banks were open and European banks were closed, the declme m cash items typically exceeded the declme m money stock deposits by several bilhon dollars The difference reflected a drop m mterbank deposits attnbutable to the collection of checks issued the day before the European bank hohday by agenoes, branches, and Edge Act corporations Tlus difference 1s a 10ugh measure of the amount of bias assooated with the mternational operations of such mstitutions The Euro-dollar market was closed on the hohday abroad and the flow of overmght transfers was mterrupted, but banks m New York City remamed open and collected outstandmg checks When these checks were collected, cash items declmed sharply At the same time, New York City banks debited "due to banks"-that 1s, due to agenoes, branches, and Edge Act corporations-for an equivalent amount of check clearmgs agamst their balances The balances due to banks declmed by an amount approximately equal to the residual declme m cash items Thus the hohday declme m balances due to banks was about equal to the volume of cash items generated by these mstitutions m their normal daily transactions Cash items and balances due to banks returned to normal quickly followmg the hohday Over the hohday, the ehmmation of Euro-dollar cash items resulted m an "unbiased" measure of net deposits, as denved from bank records The declme m balances due to banks was measured on each Good Fnday back to 1959, and on Boxmg Day (observed as a holiday m Britam on the day after Chnstmas) back to 1966, to provide benchmarks for ad1ustmg the back data for cash-items bias Ratios of the total bias to known Edge Act deposits were mterpolated between the holiday benchmarks, and the estimates of bias for mtervenmg weeks and months were denved by multiplying these https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 125 estimated ratios by figures on Edge Act deposits The adjustment for cash-items bias remams a component of the construction of the money stock However, the advent of new methods of transferrmg funds m New Y01 k City-the Clearmg House Inte1 bank Payments System (CHIPS) m Apnl 1970 and the Paper Exchange Payment System (PEPS) m eaily 1972 -ehmmated much of the cash-item~ bias Banks and other mstitutions usmg these fac1hties were required to record all of their transactions 1n interbank accounts, either as due to banks or due from banks, thus ehm1natmg any cash-items bias from transactions related to CHIPS or PEPS For a short time afte1 the 111tio<luction of CHIPS, a few banks 111 New York City failed to account properly for the transfers through that system This problem was soon resolved, however, and back data were collected to correct for errors 1t had caused Currently, the bulk of Emo-dollar transfers that ong111ally generated cash-items bias are handled through CHIPS Transfers outside CHIPS cont111ue to create a bias, however Generally, tlus bias 1s small and relatively stable While rare, the cash-items bias can 111crease to a very s1gmficant factor when there 1s a failure of the CHIPS faohty Ad1ustment for Regulation J In late 1972, a change m the Board's regulations governmg check collection procedures (Regulation J) required a one-time ad1ustment to the data on the money stock to avoid a break 111 the senes Pnor to that change, many banks were on a "deferred payment" basis m remutmg to the Federal Reserve for checks presented to them for payment That 1s, when the Federal Reserve presented checks to a payee bank for payment, remittance m 1mmed1ately available funds was not due until the followmg busmess day Payee banks, nonetheless, were able to reduce their customers' demand deposit accounts on the day the check was presented by the Federal Reserve For one day the bank would carry the hab1hty m Improvmg the Monetary Aggregates Staff Papers 126 a nondeposit account ("other habihties"), remittance due to the Federal Reserve Because the demand deposit account at the payee bank was reduced before the correspondmg cash item or Federal Reserve float was reduced, the level of the money stock was understated by the amount of these remittance payments The change m Regulation J, implemented m November 1972, reqUired former deferredpayment banks to remit for checks presented by the Federal Reserve for payment on the day of presentauon The earlier remittance by the affected banks resulted m the disappearance of this source of bias, and a one-tlme mcrease m the money stock on the day the change was implemented To avoid this break m the series, the remittance-payments bias was estimated usmg data collected from Federal Reserve Banks and regression analysis For the pe11od I 966-72, the adJustment to the money stock was based on the reported credits to member and nonmember transit accounts at Federal Reserve Banks For the period 1959-65, the adJustment was derived from an estimated and simulated regression equauon for transit-account ciedits based on reported data for 1966-72 14 The effect of these estimates was to raise the level of the money stock about $300 million m January 1959 and about $4 5 billion m December 1972 Other M1 components The net of the components discussed above --currency, demand deposits of member and domestic nonmember banks, Federal Reserve float, and the cash-items bias adJustmentaccount for 98 pe1 cent of the total money stock, M 1 The remamder of the money stock deposits are distributed among a number of financial mstitut10ns, primanly foreign related, and nearly all of them are m New York City (see Imes 12 and 13 of Table 2) While 14 For a complete descnpuon of the adjustment process, see the appendix to "Rev1s10n of Money Stock Measures," Federal Reserve Bulletin (February 1973), pp 66-69 https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis each mstitution accounts for a relatively small port10n of the total money stock, their deposittype habihtles are mdistmgUishable from demand deposit habihues of commercial banks and therefore rightly belong m an aggregate U S money stock measure 15 The deposit-type habihties of several of the remammg mstltuuons have been folded mto the money stock measures smce 1970 As each mst1tut1on was folded m, estlmates of money stock deposits back to 1959 were denved Deposits of U.S. branches of foreign banks Deposits of U S branches of foreign banks have always been considered part of the U S money stock Pnor to I 973 these deposits were mcluded m the nonmember bank estlmates derived from the call report Like domestic commercial banks, U S branches of foreign banks are reqUired to file call reports, but only twice a year In late 1972, the Board began to collect smgle-day data from branches each month In most months, these observatlons were as of the last Wednesday of the month In June and December these reports were for the last day of the month and comcided with the call report date Begmnmg m January 1973, smgle-day monthly data were used to estimate deposits at U S branches of foreign banks Weekly estimates were denved from straight-lme mterpolations between the smgle-day monthly data In Apnl 1975, the Board began to collect daily data on deposits from branches of foreign banks located m New York City Smee then these daily data have been used to measure the contribution to M 1 of demand deposits at US branches of foreign banks 15 Demand deposits of mutual savmgs banks, which are not mcluded m any of the measures of the money stock, should also be mcluded m M1 when they are clearly subject to withdrawal on demand In total, all mutual savmgs banks reported demand deposit h.tb1h ties of about $1 b1l110n at the end of 1975 The bulk of the~e deposits was m escrow accounts, however, and was not generally subject to withdrawal on demand Sources of Data and Methods of Construction of the Monetary Aggregates Mi-type balances of agencies of foreign banks in New York City By State law, agencies of foreign banks located m New York City are not permitted to hold demand deposits However, these mstitutlons have credit habihues to customers' accounts, which serve the same funct10n as demand deposits The 1970 rev1S1on of the money stock measures mcorporated credit habiht1es reported by these mst1tut1ons mto the money stock Agencies of foreign banks are reqmred to file monthly reports with the New York State Commissioner of Bankmg From early 1970 to Apnl 1973 these monthly reports were used to estimate the amount of habihues akm to the money stock held at U S agencies of foreign banks Pnor to 1970, estimates of such deposits were denved from end of-year summary tabulations published by the New York State Commissioner of Bankmg Agam, weekly observat10ns were denved from 5tra1ght-lme mterpolations between end-of-year or monthly smgle-day data Smee M,-type deposits at these mstitut10ns were relatively small pnor to 1970, esumatmg errors fo1 this component must also be small, despite the limited mformauon available for estimatmg back data Smee Apnl 1975, agencies of foreign banks m New York City, hke branches of foreign banks, have reported data on M 1 -type deposits on a daily basis These data are currently used m the construct10n of the money stock measures M 1-type balances of international investment corporations m New York City Internat10nal mvestment corporat10ns chartered by the State of New York, and located m New York City, also hold Mctype balances to the account of customers that are mcluded m the money stock measures Such balances at these mstitutlons, only about $800 million at the end of 1975, can be used m the same manner as demand deposits at other mstitu- https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 127 t10ns and thus belong m an aggregate money stock measure Balances at these mst1tut1ons were first mcluded m the money stock m February 1973 Histoncal data were estimated based on data denved from rep01ts of the New York State Comm1ss10ner Qf Bankmg From November 1972 to Apnl 1975, M 1 -type deposits of foreign mvestment corporations were estimated based on monthly smgle-day data similar to those i eported by agencies and branches of foreign banks Smee Apnl 1975, foreign mvestment corporations have reported daily data to the New York Federal Reserve Bank, which are currently used m the construction of the money stock senes Deposits due to foreign offecial accounts at Federal Reserve Banks Smee 1962, deposits due to foreign official accounts at Federal Reserve Banks (that is, due to foreign governments, central banks, ,md mternattonal mstituuons) have been mcluded m M 1 The reason for the mclus10n was that these deposits "may be used for mvestment or other expenditures m much the same way as foreign demand balances with commercial banks " Data for the5e accounts are reported daily by Federal Reserve Banks Their mclus10n has httle effect on the change or the level of the money stock senes Broader money stock measuresM2 through M. In the October 1960 descnpuon of the construction of the money stock, the discuss10n centered entirely on the narrow money stock, M 1 There was an oblique reference to the fact that "other financial mstruments perform m varymg degrees some of the funct10ns of money, particularly the store-of-value funct10n, but no other mstrument peiforms all of [the funct10ns]" As our financial system changes, new mstruments such as NOW (negotiable orders of withdrawal) accounts, telephomc transfer of funds, overdraft arrangements, and negotiable certificates of deposit lmprovmg the Monetary Aggregates Staff Papers 128 TABLE 3 Construction of M2 through M5 Monthly averages m mtlhons of dollars, not seasonally ad.Justed Line, item Money stock, Mi Time and savmgs deposits at member banks Time and savmgs deposits at nonmember banks 2 3 Plus 4 Less 5 6 7 8 9 10 11 Contnbutton, December 1975 Time deposits due to banks Time deposits due to US Government Large denommatton ($100,000 or more) negotiable CD's Equals Money stock, M, Plus Thnft mstttutton deposits Equals Money stock, Ma Money stock, M, Money stock, M, (CD's) have blurred the distmctton between demand deposits and other hqmd assets Consequently, the Board has periodically reviewed and broadened the money stock concepts it publishes on a regular basis The first such broader concept was M 2-M1 plus time and savmgs deposits at commercial banks other than negotiable CD's m denommations of $100,000 or more issued by large weekly reportmg banks Later, M 3 , M 4 , and M 5 were added Table 3 shows the construction of these broader money stock measures Money stock, M2 The construction of M 2 parallels very closely the construction of M 1 so far as the member and nonmember bank components are concerned (see Table 3) In addition to the currency and demand deposit components of M 11 M 2 mcludes time and savmgs deposits at all commercial banks other than large negotiable certificates of deposit and all deposits due to the U S Government and domestic commercial banks The measure mcludes time deposit habihties of branches of foreign banks but not time deposits of Edge Act corporations and other foreign-related mstituttons (There is no theoretical reason for mcludmg the demand deposits of these latt~r mstitutions m M 1 and excludmg them from M 2 Importance and https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 303,194 337,186 122,302 9,300 575 83,462 669,345 424,936 1,094,281 752,807 I, 177,743 Source of data See Table 2 Daily data reported by all member banks Estimated, based on dally data reported by small member banks and call report data Estimated, based on smgle day (Wednesday) data for large banks and call report data for other banks Estimated, based on smgle day (Wednesday) data for large banks and call report data for other banks Smgle day (Wednesday) data reported by large banks Smgle day data for last day of month for mutual savmgs banks, savmgs and loan assocIat1ons, and credit umons M, plus large denommation negotiable CD's at large banks M, plus large denommation negotiable CD's at large banks data availability have been the criteria Historically, these latter mstitut10ns held a relatively small amount of time deposits) Figures for total time and savmgs deposits of member banks are available from the Report of Deposits submitted by these banks for purposes of settmg reserve reqmrements, but time and savmgs deposits of nonmember banks must be estimated on the basis of call reports The method used is similar to that for estimatmg demand deposits at nonmember banks, that 1s, the rat10 of nonmember time and savmgs deposits to the ttme and savmgs deposits of smaller member banks is derived from the call report data, weekly ratios <1re estimated by straight-lme mterpolation between call report dates, ad1usted for changes m bank structure, and these estimated rat10s are apphed to the weekly time and savmgs deposits reported by smaller member banks Adjustments to eliminate time and savmgs deposits due to the U S Government and to domestic commercial banks are derived from data for weekly reportmg banks and the call report Negotiable CD's m denommations of $100,000 or more issued by large weekly reporting banks are deducted from total time and savmgs deposits m computmg M 2 16 For 16 Smee all large negottable CD's and all time de posits due to the US Government and to domestic Sources of Data and Methods of Construction of the Monetary Aggregates this purpose monthly-average estimates a1e based on a weighted average of the Wednesday figures as reported by large weekly reportmg banks A detailed descript10n of the construction of the historical CD series 1s presented below Money stock, Ms The Ma money stock 1s defined as M 2 plus deposits at mutual savmgs banks, savmgs and loan shares, and credit umon shares Because of the limited data available for these mst1tut10ns, the Ma series 1s published only monthly Time and savmgs deposits at mutual savmgs banks are reported as pa1 t of the balance sheet data accompanymg the monthly "Research Analysis" of the Nat10nal Assoc1at1on of Mutual Savmgs Banks (NAMSB) 17 These data are based on a sample of 338 mst1tut10ns of a total of 470 for the entire mdustry Accordmg to the NAMSB, the mst1tut10ns m the sample hold more than 90 per cent of all savmgs bank deposits The sample estimates geneially are available 6 to 7 weeks followmg the end of the month Twice a year, m June and December, the NAMSB collects data from all savmgs banks and revises the prelimmary numbers for those months accordmgly Unless June and December rev1s10ns are large, the first published numbers for other months are not changed Total savmgs capital at savmgs and loans rs taken from a monthly release of the Federal Home Loan Bank Board (FHLBB), "Selected Balance Sheet Data, All Operatmg Savmgs and Loan Associat10ns " These data are estimated by the FHLBB staff on the basis of smgleday, end-of-month reports from all savmgs and loan assoc1at1ons msured by the Federal Savmgs and Loan Insurance Corporation commercial banks are subtracted from time and savmgs deposits, some time deposits-large negotiable CD's issued to the U S Government or other banks-are deducted twice No estimates of this double deduction are available, but It 1s thought to be qmte small 11 This total excludes checkmg, club, and school ac counts Mutual savmgs banks held a total of about 1:,600 mdhon m such accounts m late 1975 https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 129 Such assoc1at10ns hold about 97 per cent of all mdustry deposits Usually, prelimmary data are received with a 4-week lag, and final data become available I month later "Credit Umon Stat1st1cs," a monthly release by the Nat10nal Credit Umon Admm1st1at1on (NCUA), rs the source of data on credit umon shares These data are estimated from an end-of-month sample of about 6 per cent of all credit umons, holdmg approximately 30 per cent of the deposits of these mst1tut10ns Figures are generally available with a I-month lag and are 1ev1sed ammally to mcorporate benchmark data derived from endof-yea1 1eports filed by all operatmg Federal cred1 t umons Data on mutual &avmgs banks, Sa\mgs and loan associat10ns, and credit umons are rep01 ted for a smglc day each month, usually the last Smee the M 1 and M 2 numbers are essentially monthly averages, two successive month-end figures for thrift mst1tut1ons are averaged m an effort to obtam consistent series For example, the published figure for the month of June for the thrift deposits component of M, would be the average of the end-of-May and end-of-June data reported by these 111st1tut1ons These "monthly average" data are then added to M 2 to construct M 3 A techmcal problem arises as the money stock measures are expanded to mclude the hab1ht1es of mutual savmgs banks, savmgs and loans, and credit umons Ideally, one would hke to consolidate the hab1lit1es of these 111st1tut10ns with those of commercial banks For example, when the deposrt hab1ht1es of savmgs and loan assoc1at1ons are added to M 2 , the deposit hab1ht1es of banks due to savmgs and loans should be deducted to net out mtermst1tut10n deposits The same rs true for mutual savmgs banks and credit umons Such consohdat1on already exists with the nettmg of mte1 bank demand deposits m the construction of M 1 Unfortunately, because of the way the data on thrift mst1tut1on deposits are collected and reported, such consohdat1on rs, m most cases, qmte difficult and reqmres add1t10nal data and a great deal of estimation 130 lmprovmg the Monetary Aggregates Staff Papers Thus the Af 3 measure 1s essentially a combination of the liabilities of banks and thrift mst1tut1ons rather than a consolidation Negotiable certificates of deposit Negotiable time certificates of deposit became important as a money market mstrument m early 1961 At that time several large money market banks m New York City began to offer CD's m readily marketable form to their corporate depositors At about the same time, securities firms announced that they stood ready to buy and sell CD's m open tradmg The practice was soon taken up by other banks and other dealers In early 1964 the Federal Reserve System began to gather weekly data on the volume of negotiable CD's m denommat10ns of $100,000 or more outstandmg at large weekly reportmg banks The panel of weekly reportmg banks has been revised once, at the begmnmg of July 1965 The resultmg break m the senes was relatively large The old panel of banks reported outstandmg CD's of $15,203 million while the new panel of banks reported outstandmg CD's of $15,587 million, a difference of about 2½ per cent To avoid a break m series, and to make the prev10us data comparable with the new, the reported weekly data for the penod January 1964 through June 1965 were mcreased by 2½ per cent Data on negotiable CD's pnor to January 1964 were estimated based on a survey conducted m late I 962 and early 1963 The survey showed that at the end of 1960 large-denom1nat10n CD's ($100,000 or more) issued by banks totaled about $800 million By the end of 1961 the total had nsen to $2 9 b1lhon, and by late 1962 1t had reached $5 6 billion, a sixfold mcrease m JUSt 2 years These totals mcluded all large CD's, negotiable and nonnegotiable Several assumpt10ns were made m the process of estlmatmg large negotiable CD's outstandmg for the penod 1961 to 1963 The first was that no negotrable CD's were outstandmg at the end of 1960 Second, the $830 https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis million of large nonnegotiable CD's outstandmg at the end of 1960 were replaced by negotiable CD's durmg 1961 on a stra1ght-lme path Third, the growth m total CD's, negotiable and nonnegouable, from $800 milhon to $2 9 b1lhon m 1961 was estimated by straight-lme mterpolauon of the log of the begmnmg and endmg values Thus the week-to-week dollar mcreases were greater at the end of the period than at the begmnmg The difference between the estimated total series and the estimated nonnegotiable CD series was used as the estimate of large negotiable CD's for the year 1961 For 1962 and 1963, estimates were made usmg stra1ght-lme mterpolatron between the logs of the 1961, 1962, and 1963 year-end values, $2 9 b1lhon, $5 6 b1lhon, and $9 8 billion, respectively Weekly observatrons were derived, and monthly estimates were based on the proratrons of the weekly data Smee 1963, when Wednesday observations became available, they have been averaged to obtam a rough proxy for the weekly-average level of CD's consistent with the weeklyaverage measurement of M 1 and M 2 Estimates of the monthly-average level of large negotiable CD's are derived from prorat10n of estimated weekly-average levels 18 Money stock, M4 and Ms The broader money stock measure, Jv1. 4, 1s derived by addmg CD's, derived as described above, to M 2 This measure corresponds 10ughly to all private deposits at commercial banks plus currency m circulat10n It excludes US Government deposits and net mterbank deposits The M 4 measure 1s published on both a monthly-average and weekly-average basis 1s It should be noted that large denommat10n non negotiable CD's serve the same purpose as negotlable CD's In addilion, lt is not difficult for large banks to convert a nonnegot1able CD to a negollable mstrument Thus M 2 might logically be computed by deductmg all large time deposits from total time and savmgs deposits 1f h1stoncal data were available It is only recently, however, that the Board has collected any data on total large time deposits In December 1975 large lime deposits at commerc1al banks totaled about $158 I billion and large negotiable CD's totaled about ~83 5 billion Sources of Data and Methods of Construction of the Monetary Aggregates The M 5 measure, the broadest one published by the Board, 1s derived by addmg CD's to the Ms measure It mcludes not only the private deposits of all commercial banks but also the deposits of thrift mstitutions (mutual savmgs banks, savmgs and loan assoc1at10ns, and credit umons) Like Ms, M 5 1s published only as a monthly average Seasonal adjustment of the monetary aggregates The measurement of the seasonal component 1n any economic time series 1s difficult, and this 1s especially true of the money stock The money stock 1s mfluenced not only by normal seasonal swmgs but by other economic factors The irregular component of the series H large and highly volatile Moreover, changes m the financial system, such as shifts m tax collectron schedules, m disbursement dates for large government transfer payments, and m the form m which the public holds Its hqmd assets ,tffect the seasonal pattern over time Some of these changes are abrupt and new seasonal patterns develop qmckly, but a few years of data are reqmred to establish the new seasonal pattern for most changes Some of the changes evolve over a considerable period, 1 esultmg m contmuously sluftmg seasonal factors that also are measured only with a lag In some mstances, several factors may be workmg simultaneously to change the seasonal pattern, some havmg cumulative effects and others offsettmg one another with unpredictable net impacts The existence of these changmg mfluences makes measurement of 5easonal patterns m the money stock imprense and subJect to revisron, especially for the most recent years The various components of the money stock -currency, dem,md deposits, time and savmgs deposits other than large negotiable CD's, large negotiable CD's, mutual savmgs bank deposits, savmgs and loan shares, and credit umon shares-are all seasonally ad3usted separately The published adjusted measures are aggregates of these seasonally adjusted com https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 131 ponents Most of the components are published along with the aggregate All of the monthly seasonally adjusted series are denved usmg the Census Bureau's X-11 seasonal ad3ustment method 19 A multiplicative movmg-seasonal variant of this program 1s used to update seasonal factors each year, and the results are reviewed and m some mstances modified Judgmentally m an effort to take account of known factors affectmg seasonals, random disturbances, or policy-mduced changes m the series Usually the published senes 1s close to the X-11 results For all scnes the monthly seasonal pattern 1s denved fii st and the weekly seasonal factors ,ue forced to agree with the monthly seasonal factors In other words, the weighted averages of the weekly seasonal factors for any month must equal the monthly seasonal factor, withm a small range of tolerance Experience suggests that the monthly seasonal patterns are more 5t<1ble than the weekly ones, because they are mfluenced less by irregular movements m the data and because factors causmg shifts m mtramonthly patterns tend to average out over the month While there 1s always considerable uncertamty about the validity of current weekly seasonal factors, they are anchored to the more stable monthly seasonal factors, and the seasonally ad1usted weekly and monthly data will average about the same levels over a penod of several weeks The Board's weekly seasonal adJustment program is es5entially a ratio method Seasonally ad1usted monthly data are centered at midmonth, and estimates of seasonally adJusted weekly values are generated by a 5tra1ght-lme mtei polatron between these values The unadJusted weekly data are divided by these estimated adJusted values to obtam an estimate of the seasonal irregular component of the senes The mtramonthly pattern of these iatios is smoothed, first by a 3 x 3 movmg average of the seasonal-irregular 1 atros calculated for all the weekly obserrn For a desc11pllon of this program, see "The X-11 Vanant of the Census Method II Seasonal Adjustment P10gram," Bureau of the Census Techmcal Paper 15 (Government Pnntmg Office, 1965) 132 Improving the Monetary Aggregates Staff Papers vatlons over recent years, and then by a Judgmental modification to take account of any apparent shifts m the mtramonthly pattern Differences between the predetermmed monthly factors and the average of weekly factors are distributed to the weekly seasonal factors so that the latter agree on average with the former After deriving unadJusted aggregates for the currency and demand deposits component of M 11 each component series is seasonally adJUsted separately Seasonal factors for currency and demand deposits are computed and reviewed as described above The ad1usted series are then aggregated to derive adJusted M 1 All of the raw data, whether or not adJusted, are estimated to millions of dollars, and the aggregation of seasonally ad1usted data is also done at this level However, these estimates are not considered accurate to the nearest milhon so, for publication, all series are rounded to the nearest tenth of a billion dollars Thus rounding differences frequently appear between the published series on components and on aggregates Derivation of seasonally adJusted time and savings deposits m M 2 is more complex Fust, large negotiable CD's are subtracted from total time and savings deposits at all member banks and the residual senes on member bank time and savmgs deposits is seasonally adjusted Second, seasonal factors are derived for ad1usting total time and savings deposits at small member banks A seasonally adjusted senes on total time and savings deposits for nonmember banks is derived by applymg the expansion factors described above to total time and savings deposits at small member banks, seasonally ad1usted Next, the seasonally adJusted senes on total time and savings deposits less negotiable CD's at member banks is aggregated with the seasonally adJusted total time and savings deposits of nonmember banks From this aggregate, time and savings deposits due to the U S Government and domestic commercial banks, not seasonally adjusted, are subtracted (There is no measurable seasonal m these deposits) The result is an adJusted time and savings deposits component of M 2 https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis that parallels the adJusted demand deposits component of M 1 in excluding deposits due to the U S Government and other commercial banks Seasonally adjusted M 2 is the aggregate of seasonally ad1usted currency, demand deposits, and time and savings deposits other than large negotiable CD's Mutual savmgs bank deposits, savings and loan association shares, and credit union shares-components of Ma-are also seasonally adjusted by the Board First, the reported end-of-month data for each series are seasonally adJusted These numbers are then averaged, as explamed above, to approximate a monthly-average series, which is added to seasonally adJusted M 2 to derive Ma Because weekly data are not available for thnft deposits, only a monthly-average senes on Ma can be constructed Large negotiable CD's are also seasonally ad1usted, both monthly and weekly Seasonal factors are especially difficult to denve for this senes, however, because of the large trend and cyclical components Durmg the early and mid-1960's, when CD's first became an important financial asset, the senes was highly dommated by trend In the late l 960's and early 1970's, CD's-because of Regulation Q ceilings on mterest rates-were heavily mfluenced by monetary policy and the level of market mterest rates These two factors are extremely difficult to untangle m derivmg seasonal factors for the senes The seasonal factors from the basic X-11 program are used with only mmor Judgmental review Seasonally adjusted, monthly-average CD's are aggregated with ad1usted M 2 and M 3 to denve ad1usted monthly-average M 4 and Ms, respectively Seasonally adJusted weekly-average CD's are aggregated with adjusted M 2 to denve adjusted weekly-average M 4 Weekly-average Ms is not available Conclusion The measures of monetary aggregates currently constructed and published by the Board are derived from a wide variety of data sources The data have been revised and re- Sources of Data and Methods of Construction of the Monetary Aggregates fined several times over the yea1 s, as new data sources developed or as measurement problems reqmred the collect10n of additional data Nevertheless, all of the sen es on the money stock are still only approximations of the conceptual, holder-record measures mtended Problems of double countmg, inconsistency m accountmg entnes, dnd smgle-day https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 133 versus daily-average data all have an impact on the accuracy of the senes The longer the time span, the less senous are such data problems However, those who use the money stock measures for short-run analysis should be ,Lware of the extent of est1mat10n 1eqmred m the construction of the senes and of the shortrun volatility mhe1ent m the clat.a https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 135 An Alternative Method for Calculating M 1 Anton S Nissen and Darwin L Beck This paper revises and updates the study originally prepared for the Advisory Committee and contains information not available to the Committee when it made its report The Advisory Committee on Monetary Statistics mcluded as one of its recommendations a new, simpler process of handlmg mterbank deposits and cash items m the process of collection when consolidatmg data from different financial mstitut10ns, m order to ehmmate certam biases and to obtam a more accurate measure of M 1 and other aggregates " 1 The Committee made this a tentative recommendation because of large statistical differences between a prehmmary construct of the new series and the money stock then bemg published by the Federal Reserve The Committee also recommended that the Board staff mvestigate the new series further and resolve the differences between the two measures The Committee assumed that these differences would be resolved and that the new method, while still not perfect, would be a more accurate measure of the actual money stock Smee the Committee report, the staff of the Federal Reserve has made an mtensive effort to reconcile the differences between the two series This paper presents the mformation available to the Committee at the time of its report and mcorporates additional mformat10n collected by the staff smce the report was published First, mmor biases m the published money stock measure have been uncovered These biases were corrected m 1976, and at the same time, the staff improved the miual estimates of the alternative money stock measure 2 For contmmty, data on the current and alternative money stock measures and mterbank deposits as they were origmally made available to the Committee are presented m Tables l and 2 These tables also show sources of subsequent rev1S1ons to the series, the final alternative series, and the money stock series now bemg published The differences between the two series are described m this paper Information available at the time of the Committee rtport md1cated that, despite the large discrepancy between the two series, the alternative method of constructmg the money stock was an improvement over the current method 3 Assumptions were that further re search would explam the differences and that the alternative measure would prove to be superior Further research has not resolved the differences, however, nor 1s 1t clear which method of constructmg the money stock IS superior, both measures can be affected by changes m bankmg regulations, and both can be affected by changes m accountmg procedures The problem 1s one that 1s mherent m manv economic time series Often, economic series derived from different data sources provide different measures of the same variable There NoTE-Anton S Nissen 1s a member of the staff of the Federal Reserve Bank of New York and Darwm L Beck 1s on the staff of the Board's D1v1S1on of Research and Statislics 1 Improving the Monetary Aggregates Report of the Advisory Committee on Monetary Statistics (Board of Governors of the Federal Reserve ~System, 1976), p 3 2 "Rev1S1on of Money Stock Measures," Federal Re serve Bulletin, vol 62 (February 1976), pp 82-87 For a detailed descnpl!on of these revmons, see the ap pend1x 3 In December 1974 the level of the current money stock measure was $8 0 b1lhon higher than the level of the alternal!ve measure on a monthly average basis, and about i5 5 b1lhon on an end of month basis https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 136 Improving the Monetary Aggregates Staff Papers TABLE 1. Comparison of Alternative and Current M1 Measures In millions of dollars, not seasonally ad.Justed Ava!lable to the Advtsory Committee on Monetary Statistics Year-end Alternative M1 Current M, Alternative M1less current M1 (I) (2) 147,771 148,767 154,553 156,984 161,241 172,218 180,581 185,756 198,545 214,929 222,869 234,067 248,164 272,492 289,834 301,321 (3) 1,016 966 1,343 788 1,057 127 320 718 1,027 552 508 -4,579 -3,396 -5,892 -6,250 -6,504 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 19752 19762 148,787 149,733 155,896 157,772 162,298 172,345 180,901 186,474 199,572 215,481 223,377 229,488 244,768 266,600 283,584 294,817 Adjustment To alternative M1for mapprol?natc Regulation J adjustment To current M, for reesumat1on of cash items bias Adjusted alternative M, (5) (4) -500 (6) 148,287 149,133 155,196 156,972 161,398 171,345 179,801 185,274 198,272 214,081 221,877 227,888 243,068 266,600 283,584 294,817 309,349 326,520 -600 -700 -800 -900 -1,000 -1,100 -1,200 -1,300 -1,400 -1,500 -1,600 -1,700 800 900 -2,600 -2,600 -1,600 -500 -1,000 Adjusted current M11 Adjusted alternative M1 less current M1 (7) 147,771 148,767 154,553 156,984 161,241 172,218 180,581 185,756 198,545 215,729 223,769 231,467 245,564 270,892 289,334 300,321 313,913 332,660 (8) 516 366 643 -12 157 -873 -780 -482 -273 -1,648 -1,892 -3,579 -2,496 -4,292 -5,750 -5,504 -4,564 -6,140 'See footnote 8 on p 138 •As revtsed and pubhshed m early 1976 a1 e, for example, statistical discrepancies between gross n<1t1onal product and national mcome accounts, between household and manhour employment surveys, and between different measures of the balance of payments A similar unresolved stausucal discrepancy appears to exist between the current and alternative money stock senes The currently pubhshed money stock senes has been ad1usted £01 breaks associated with regulatory changes and for ma1or biases assonated with convcnt10nal bank accountmg The alternative money stock has also been adJusted for I cgul<1tory changes, and 1t 1s not distorted by accountmg procedures as 1s the current money stock Further mvest1gat1on suggests, however, that the alternative money 5tock measm e 1s affected by other data prob- TABLE 2 Interbank Demand Deposits and Cash-Items Bias AdJustment In milhons of dollars, not seasonally ad1usted Available to the Advisory Committee on Monetary Statistics Deposits Year end I I Due to Due from Due to banks banks du!el:om (1) 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 19751 19761 13,445 14,882 15,900 14,058 13,460 15,718 16,016 17,195 19,029 21,566 23,651 26,713 28,357 30,616 32,630 41,089 (2) 12,429 13,916 14,473 13 230 12,403 15,153 15,519 16,416 18,002 20,208 21,675 24,932 26,048 33,424 35,932 43,915 1 See footnote 8 on p 138 https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis (3) 1,016 966 1,427 828 1,057 565 497 779 1,027 1,358 1,976 1,781 2,309 -2,808 -3,302 -2,826 To due Adjust from ment Net mterbank less to remove for cash cash-items Regulation items bias J d1scon ttnmty bias (4) 84 40 438 177 61 806 1,468 6,360 5,705 3,084 2,948 3,678 (5) 1,016 966 1,343 788 1,057 127 320 718 1,027 552 508 -4,579 -3,396 -5,892 -6,250 -6,504 After adjustment for Regulation J and reesttmatton or cash items bias Adjustments (6) 500 600 700 800 900 1,000 I, 100 1,200 1 300 1,400 1,500 1,600 1,700 To cashitems bias for re esu matton (7) 800 900 -2,600 -2,600 -1,600 -500 -1,000 Deposits I Due to Due from banks banks (8) 13,445 14,882 15,900 14,058 13,460 15,718 16,016 17,195 19,029 21,566 23,651 26,713 28,357 30,616 32,630 41 089 38,625 41,033 (9) 12 929 14,516 15,173 14,030 13,303 16,153 16,619 17,616 19,302 21,608 23,175 26,532 27,748 33,424 35,932 43,915 39,433 42,350 I Due to du!?:om (10) 516 366 727 28 157 -435 -603 -421 -273 -42 476 181 609 -2,808 -3,302 -2,826 -808 -1,317 Adjustment Net mterbank less for cash- cash items items bias bias (II) 84 40 438 177 61 1,606 2,368 3,760 3,105 1,484 2,448 2,678 3,756 4,823 (12) 516 366 643 -12 157 -873 -780 -482 -273 -1,648 -1,892 -3,579 -2,496 -4,292 -5, 750 -5,504 -4,564 -6, 140 An Alternative Method for Calculating M 1 lems The lack of umformity among banks m accountmg for mterbank deposits causes d1stort10ns m the accounts that reflect demand deposits due to and due from banks, data senes that are important m the construct10n of the alternative money stock For example, changes m accountmg practice associated with the 1mplementat10n of the Paper Exchange Payments System (PEPS) m 1972 are believed to have caused a serious d1stort1on m the alternative money stock measure Construction of the alternative series The narrowly defined money stock, M 1 , has two ma1or components-demand deposits adJUSted and currency m circulat10n outside the Treasury, the Federal Reserve, and commercial banks 4 The first component 1s mtended to measure pnmanly the net demand deposit hab1ht1es of commercial banks m the Umted States to both domestic private nonbank customers and to all foreign customers, bank and nonbank At present, this component 1s calculated by subtractmg cash items m the process of collect10n, as shown on the books of commercial banks, from so-called "other demand deposits," which consist of demand deposit hab1ht1es due to depositors other than the U S Government and banks 5 However, a number of stat1st1cal problems m this basic procedure cause biases m the senes When possible, adJustments have been made to correct for such bias, but for the purposes of this paper, three data problems are important First, cash items m the process of collect1on mclude items drawn agamst accounts outside of other demand deposits Second, some checks drawn agamst accounts recorded m other demand deposits and still m the process of 4 Smee the currency component 1s common to the two money stock measures, 1t 1s not discussed m this paper 5 In add1t10n to cash items m the process of collection, Federal Reserve float also 1s subtracted Cash items m the process of collection represent pnmanly checks m the process of collection for which the collectmg agent has not yet granted credit Federal Reserve float also represents checks still m the process of collect10n, but for which the Federal Reserve has passed credit even though 1t has not yet collected from the banks on which the checks were drawn https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 137 collection are not reported m cash items m the process of collect10n And third, other demand deposits, as used m the money stock calculauons, do not mclude all deposits due to money stock holders The first problem-cash Items drawn agamst deposits that are not mcluded m the money stock-anses m connection with a large volume of checks drawn agamst due-to-banks accounts by agencies and branches of foreign banks, foreign bank-owned mvestment compames engaged m bankmg, and Edge Act corporat10ns m New York City 6 Most checks are drawn m the course of transferrmg funds related to mternauonal financial transact10ns and typically are deposited m New York City commercial banks on the day they are drawn The New York City banks carry the checks deposited as cash Items m the process of collect1on, a procedure that results m an overstatement of cash Items for money stock purposes and a consequent understatement of M 1 This d1stort10n was first discovered early m 1970 Smee late that year, data have been collected on the amounts of outstandmg checks drawn by the agencies and branches of foreign banks, foreign bank-owned mvestment compames engaged m bankmg, and Edge Act corporat10ns m New York and have been used to correct for this so-called "cash-Items bias " 7 The second problem 1s that many banks forward checks to correspondent banks for collect10n and immediately post them as demand deposits due from banks rather than as cash items Thus, other things being constant, the amount of cash Items deducted m calculatmg 6 Other items mcluded m cdsh Items-such as checks drawn on US Government accounts, food stamps, redeemed savmgs bonds, credit card slips-also violate the assm;npt1on Studies conducted by the Federal Reserve md1cate that the problem of checks drawn on U S Government accounts 1s small, but no data are available on the size of the other problems D1scuss1ons with banks md1cate that 1t would be virtually 1mposs1ble to have these items recorded m separate accounts 7 While discovered m 1970, the cash-items bias first developed on a much smaller basis around the m1dl 960's Smee actual data on outstandmg checks were not available until the late 1960's, adJustments to account for the earlier bias were estimated as descnbed m the Federal Reseroe Bulletin, vol 56 (December 1970), pp 892-93 138 lmprovmg the Monetary Aggregates Staff Papers demand deposits adjusted is smaller than it should be (and the amount of demand deposits adjusted is larger) until the checks are received and either charged directly agamst a deposit dccount by the correspondent or entered on its balance sheet as cash items and forwarded for collection The resultmg overstatement of M 1 -referred to as the "duefrom-banks bias"-was recogmzed by the Federal Reserve System committee that had developed the money stock measure m the late 1950's However, smce the overstatement was <tssumed to be relatively small on average and to change relatively slowly over time, the basic money stock calculation has not been adjusted to correct for this bias As mdicated, the tlurd problem is th<tt other demand deposits do not mclude all relevant money stock deposits In particular, this deposit category does not mclude demand deposits due to foreign commercial banks or domestic mutual savmgs banks, so an adjustment has to be made to "other deposits" to mclude the deposits due to these mstitutions The only data av<til<tble upon which to base such adjustments are smgle-day, Wednesdayas opposed to daily-average-data reported by weekly reportmg banks and call report data <tva1lable four times a year These estimated data are mcorporated mto the money stock calculations The three problems were considered at an early meetmg of the Advisory Committee on Monetary Statistics, and an alternative method for calculatmg the money stock was suggested Briefly, the alternative was to mclude, along with other demand deposits, all demand deposits due to banks (foreign and domestic) ,md to deduct, along with cash items m the process of collection, demand deposits due from domestic banks m computmg the demand deposits adjusted component of M 1 The alternative method was believed to have three advantages First, it would ehmmate the cash items bias and the consequent need for correction of data to adjust for that bias In this mstance, the deposits due to banks agamst which the currently mappropriate cash items are drawn would be mcluded m the deposits https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis total from which the cash Items would be deducted Second, the alternative method would ehmmate the due-from-banks bias because, by deductmg both cash Items and demand deposits due from banks, the use of the due-from <tccount by b<tnks forwardmg checks to correspondents for collection no longer would result m the bias Fm<tlly, Wednesday and call report data would no longer have to be used to estimate demand deposits due to mutual savmgs banks and foreign commercial b<tnks, smce such deposits would be mcluded on a daily-average basis as a part of demand deposits due to banks A prion the level of the money stock senes constructed by the alternative method w.15 expected to be slightly lower than the present senes, reflectmg ehminat10n of the due-from-banks bias, but changes m the two senes over any penod of timeexcept perhaps short ones-would be essentially the same In 1esponse to the Committee's suggestion, an alternative money stock senes was con5tructed on a monthly-average basis for the 1968-74 penod, and on a smgle-day basis, December 31, for the 1959-74 penod (Table I) 8 Comparison of the two revised senes for December 31 (columns 6 and 7) mdicated that a pnon expectat10ns were not borne out 9 As can he seen m column 8 of Table l, the differences between the currently published and the alternative money stock were contrary to expectations m the early years and much larger than expected m the later years Moreover, large discontmmties appear m 1968, 1970, and 1972 A further effort was made to explam these differences Essentially, the procedure used to calculate the alternative money stock series was to add demand deposits due to domestic banks to the current money stock series, and to subtract both demand deposits due from banks and the adjustment for cash-items bias from It s Call report data for December 31, 1975 and 1976, available smce the Committee completed Its report, are also shown e The focus was on the December 31 senes smce the monthly-average senes contam large estimated components for nonmember banks An Alternative Method for Calculating M 1 This procedure 1s eqmvalent to addmg net interbank deposits and subtracting the adJustment for cash-items bias In attempting to explain the unexpected differences between the two senes, therefore, attention was concentrated on the behavior of net interbank deposits and the adJustment for cash-items bias Data on net interbank deposits and the adJustment, as ongmally presented to the Committee and as later revised, are shown m Table 2 The 1959-67 period The 1959-67 penod presents a mixed picture, but 1f allowance 1s made for the vagaries of smgle-day data and the uncertainty of h1stoncal adJustment for the alternative measure, the currently published and the revised alternative money stock senes track about as expected (column 8, Table 1) Durmg this penod, the levels of the two senes differ by less than $1 0 billion and annual growth rates differ, on average, by less than ¼ of a percentage pomt Nevertheless, there are some unexpected differences between the two senes Smee the adJustment for cash-items bias was negligible durmg most of this penod, the mterbank deposits must be responsible for the difference The alternative money stock exceeded the current money stock early m the 1959-67 penod (Table I), reflecting an excess of deposits due to banks over those due from banks and contrad1ctmg the expectation of a bias m the current money stock measure ansmg 1n deposits due from banks As noted earlier, the poss1b1lity of a duefrom-banks bias m the current money stock senes had been suggested by a System committee m the late 1950's 10 The committee The due-from banks bias, 1t will be recalled, was hypothesized to anse because some banks forwarded checks to correspondents for collection and wrote up immediately the1r deposits due from banks Because of unavoidable lags m transportmg such checks to correspondents and m postmg by the correspondent banks to cash items m the process of collection and deposits due to banks, the cash items deduction from money stock deposits was thought to be understated, the money stock to be overstated, and deposits due from banks to exceed deposits due to banks 10 https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 139 noted that, at least smce the m1d-1950's, deposits due to banks had exceeded deposits due from banks by almost $1 billion The committee report hypothesized that some banks did not post checks forwarded to correspondents for collection immediately to a due-frombanks account as had been assumed m adJUstmg for the due-from-banks bias Rather, the committee suggested, the checks were posted to the cash-items account and held there until not1ficat10n was received from the correspondent that they had been collected, then the cash-items account was reduced and the due-from-banks account was increased Smee the checks bemg collected by correspondent banks appeared on the correspondent's books durmg the collect10n penod as deposits due to banks, this phenomenon was believed to explam the excess, on balance, of due-to accounts over due-from accounts Wlule this explanation appears plausible, there 1s no practical way to check its h1stoncal validity If this explanat10n 1s correct for the early penod, the data md1cate that around 1964 either a shift m accounting practices or some other structural change caused deposits due from banks to grow more rapidly than deposits due to banks From 1964 to 1968, deposits due from banks consistently exceeded those due to banks, but generally by ever-smaller amounts (column 10, Table 2) Dunng this penod there were no known changes m accountmg practices or m structure that would explam the shift m the relationship between deposits due to and deposits clue from banks Thus the data do not establish the supenonty of either senes over tlus penod The 1968-71 period The 1968-71 penocl was a time of rapid expans10n m transfers of funds through the New York Clearing House by agencies and branches of foreign banks, foreign bank-owned investment compames engaged m banking, and Edge Act corporat10ns located m New York City These transfers of funds were related pnmanly to expanding Euro-dollar transac- 140 t10ns As column 11 of Table 2 shows, the adJustment for cash-items bias, a proxy measure for the volume of these transfers, 1s estimated to have mcreased rapidly dunng this period In makmg transfers of funds through the Clearing House, the vanous mst1tut1ons mvolved typically would make deposits m New York City correspondent banks, thus leadmg to mcreases m cash items m the process of collection and demand deposits due to banks on the books of those correspondents Other tlungs constant, one would expect an mcrease m the excess of deposits due from banks over deposits due to banks that would roughly equal the mcrease m the adJustment for cash-items bias However, accordmg to the data available, this did not happen Over the 1968-71 penod, the adJustment for cash-items bias mcreased nearly $3 2 billion, while net mterbank deposits (deposits due to banks less those due from banks) mcreased less than $1 0 billion This discrepancy accounts for the sharp rise m the difference between the current and the alternative series From 1959 to 1967, deposits due to banks and those due from banks mcreased, on average, $700 million and $800 million, respectively, per year From 1968 to 1971, these yearly mrreases rose to $2 4 b1ll10n and $2 1 billion, 1 espect1vely The mcreased growth m the deposits due to banks 1s explamed m part by the mcreases m transfers of funds through the Clearmg House by foreign-related mst1tut1ons m New York City What 1s unexplamed, and what ultimately causes the differences m the money stock series, 1s the acceleration m the growth of deposits due from banks Could tlus growth reflect an mcrease m the so-called due-from-banks bias? That 1s, were more banks usmg a due-from-banks account rather than a cash-items account when forwardmg checks for collect10n? If so, the alternative senes might be a better measure of the money stock Smee hanks had no known reason to shift their accountmg practices at this particular time, 1t 1s assumed that some other, unknown, factor accounted for the change Whatever the cause, there appears to be a break m the alternative money stock measure, and given the sIZe of the https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis Improvmg the Monetary Aggregates Staff Papers change, 1t most probably reflects bias m the series either before or after the change During the 1968-71 period the alternative money stock measure would not have been so susceptible to the problem of cash-items bias as was the current money stock The cashitems bias m the current money stock was, however, 1dent1fied and corrected, albeit with a lag It 1s not certam that the alternative series was affected over this period by a bias from deposits due from banks, but because of the peculiar and unexplamed movement m the deposits due from banks, that poss1b1hty cannot be d1sm1ssed At this pomt m time, 1£ there 1s a bias m the alternative measure, 1t can be neither identified nor corrected Thus, for the 1968-71 period, as for the 1959-67 period, neither money stock measure 1s clearly superior to the other The 1972-74 period In 1972 the relat1onsh1p between demand deposits due to banks and demand deposits due from banks slufted sharply, by nearly $3 5 billion, and then remamed roughly constant through the end of 1974 (Table 2, column 10) Whereas prior to 1972 demand deposlt5 due to banks had exceeded demand deposits due from banks, at the end of 1972 deposits due from banks exceeded those due to bank5 by about $2 8 billion Of that amount, about '$1 7 billion (-$2 0 billion m due to, and -$0 3 billion m due from) reflected the change m the Federal Reserve's Regulat10n J m November 1972 11 When Regulation J was changed, banks had to remit funds to the Federal Reserve on the day checks presented by the Federal Re5erve were received (Pnor to the change, banks did not remit funds until one busmess day after receipt of the checks from the Federal Reserve ) Member banks actmg as correspondents for nonmember banks that did not have a deposit account with the Federal Reserve also were requued to remit 11 For a more detailed d1scuss1on of the impact of the change m Regulation J on the current and alternative money stock, see the appendix An Alternative Method for Calculating M 1 funds one day earlier for checks presented for collection by the Federal Reserve to nonmember banks Because the nonmember banks for the most part had already been accountmg for deposits due from banks one day before actual remittance to the Federal Reserve by their correspondents, when payment was speeded up a day the due-from accounts at these banks were mostly unaffected, whereas the due-to accounts at the correspondent banks declmed The source of the remammg part of the shift m the differential between due-to and due-from accounts m 1972 1s not certam However, It seems to stem from the mtroduction by the New York Clearmg House m February of that year of the Paper Exchange Payments System (PEPS) PEPS was an arrangement under which a large number of agencies and branches of foreign banks, foreign bank-owned mvestment compames engaged m bankmg, and Edge Act corporations located m New York C1ty met at the New York Clearmg House each day to exchange debit and credit advices arismg from transfers of mternational-transaction funds The purpose of PEPS was to obviate the need to receive and deposit each day large volumes of checks drawn on (or payable through) member correspondents of the New York Clearmg House Although the accounts reflectmg deposits due from and due to banks at the Clearmg House banks were affected by PEPS, any specific accountmg conventions that would have led to the change m the due-to-due-from relationship have not been 1dent1fied Thus, the 1mt1ation of PEPS does not necessarily account for the remamder of the 1972 shift The s1m1lar timmg of these events, however, 1s difficult to ignore and gives credence to the susp1c1on that the explanation hes m PEPS Both the current and alternative series were adJusted to avmd a break m series when Regulation J was changed m late 1972 Thus, assummg that the ad1ustments were reasonably accurate, there 1s no reason to expect thatWI th respect to the effects of the change m Regulation J-one series 1s any better than the other However, the current series has reqmred a larger adjustment than the alterna- https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 141 t1ve because It was subject to bias from two types of accountmg practices associated with remittances to the Federal Reserve, whereas the alternative series was sub1ect to a smaller bias from only one of these practices To the extent that the 1972 shift m the due-to-due-from relationship was caused by factors other than the change m Regulation J, the Federal Reserve staff 1s unable to make any Judgments as to the relative quality of the current and alternative M 1 series over the 1972-74 period The staff has not been able to 1dent1fy with any degree of certamty those factors and how they affected the various accounts on banks' books that bear on the calculations of the two money stock measures Even 1f the shift were related to the advent of PEPS, there 1s still the question of what were Its effects on deposits due to and due from banks, and hence which of the two money stock series was affected W1thout firm evidence, however, more defimtive statements cannot be made at this time Summary The difference between the current and alternative money stock measures contmued to grow m the 1975-76 period (Table I, column 8) This growth, however, did not accelerate sigmficantly, and the relationship between the two measures did not shift noticeably after the apparent break between 1971 and 1972 Thus, the later data provide no additional mformat10n that might help to explam the large differences between the two series A review of the construction of the two senes mdicates that both measures can be distorted by regulatory changes and by changes m accountmg practices The alternative measure appears to be particularly susceptible to changes m accountmg procedures associated with mterbank deposits While attemptmg to reconcile the differences between the two series, the Board staff became more acutely aware of mstances when timmg or mterbank accountmg variations could lead to discrepancies between deposits due to and due from banks for the commercial 142 lmprovmg the Monetary Aggregates Staff Papers bankmg system as a whole Of course, what 1s important to an md1v1dual bank 1s not that the book balances show its deposits due to and due from other banks to be equal at dny pomt m time, but rather that they can be reconciled These mterbank accountmg vanat1ons can, however, mJect senous bias mto the alternative money stock measure At this pomt 1t 1s not known 1f the alternative money stock contams such biases or not The comc1dence of some of the sharp changes m the differences between the two senes and of known changes m interbank accounting suggests that such biases exist On the other hand, except for the bias ansmg from deposits due from banks, which 1s still believed to be small, the current money stock measure has no known or suspected biases The differences m levels created by tlus form of bias https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 1s not important for policy purposes, and the 1mt1al presumpt10n that this bias evolved rather slowly on average with httle attendant effect on monetary growth rates, wluch are more important than levels for pohcy purposes, appears to be vahd When biases have developed m the past, they have been found and qmckly corrected In conclus10n, neither method of constructmg the money stock discussed m tlus paper 1s clearly superior As with other economic data senes, analysts should be awdre that these statistical d1screpanc1es exist and that any con~truct10n of the money stock 1s only a near dpprox1mat10n of the "true" money stock Data on the money stock, regardless of the method of construct10n, reqmre careful and constant momtormg to avoid senous d1stort10ns m the senes 143 Appendix: Adjustments to Money Stock Measures In constructmg the alternative money stock measure and comparmg 1t with the current measure, two data problems were uncovered The first related to a m1sesumation of the cash-Items bias associated with the transfer of funds by foreignrelated mstitut1ons m New York (primarily Euro dollar transfers), and the second related to an mappropriate adjustment to the alternative measure associated with the change m Regulauon J m 1972 After discovery of the problem of cash-Items bias, additional data were collected as necessary and new estimates of the cash-Items bias associated with foreign related funds transfers were derived The revised estimates of cash-items bias were folded mto the published money stock data m 1976 The reasons for this revmon are described below The impact on mterbank deposits and the current money stock of transfers of funds at the New York Clearmg House for foreign-related msututions m New York C1ty was first discovered m the sprmg of 1970, when there was a huge unexplamed bulge m the money stock Investigation showed that this bulge was caused by a large declme m cash items m the process of collection at New York City banks on Good Friday, which contmued unchanged over the weekend This declme m cash items was matched not by a declme m other demand deposits, however, but by a declme m deposits due to banks Further mvestigation revealed that London banks were closed on Good Friday, while U S banks were open 1 With London banks closed, there was thought to be little or no activity m the Euro-dollar market-which gave rise to most of the transfers discussed above-so that few, 1f any, new borrowmgs were mltlated or outstandmg ones repaid W1th New York C1ty banks open, however, all the transfers associated with Euro-dollar borrowmgs and repayments that had been m1t1ated on the precedmg day cleared out of the p1pelme 1 On December 26, Boxing Day, London banks are also closed and U S banks are open, which leads to the same phenomenon that occurs on Good Friday In those years when December 26 falls on a weekend, there 1s, of course, no impact on domestic money stock data https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis As a result, deposits due to banks at New York C1ty banks (specifically due to agencies, branches, and Edge Act corporations makmg the transfers) declmed sharply, along with cash Items m the process of collecuon If usual accountmg pro cedures had been followed by the agencies, branches, and so forth, the problem with the money stock could have been corrected by foldmg m balance-sheet data reported by these msutuuons However, convenuonal accountmg practices had not been followed at most of these mstitutlons, so their balance-sheet data were not adequate to correct the current money stock Instead, some proxy measure was needed Thus, begmnmg m late 1970, daily data on officers' checks outstandmg of these mstitutions were collected for tlus purpose For the period before actual data are ava1lable, a method for esumatmg the impact of the transfers of funds at the New York Clearmg House on the current money stock had to be devised Given the explanation for the declmes m deposits due to banks and cash Items around Good Friday and Boxmg Day, the size of these declmes was determmed to be a good measure of the cash-Items bias Thus, estimates of the cash-Items bias for earlier periods were based on mterpolat1ons between "benchmark" data derived from earlier holiday declmes m deposits due to banks A s1m1lar mterpolat1on was made for the penod between Good Fnday 1970 and early October 1970, when the m1trnl "hard" numbers reported by agencies, branches, and so forth became available As suggested by the behavior of the cash-Items adjustment, the total of the first actual numbers received m October 1970 was much larger than the estimate for Good Fnday, and 1t remamed much larger, with some modest further growth mto 1971 The difference between the Good Fnday estimate and the actual numbers was not suspect, however, smce there were other md1cat1ons that activity m the Euro dollar market was expandmg rapidly Because of the mterpolauon between the estimate for Good Friday and the first actual numbers m 144 Improving the Monetary Aggregates Staff Papers October, however, the adjustment for cash Items bias grew rapidly m 1970 In 1970 Boxmg Day was on a Saturday, so the declme m the deposits due to banks could not be checked agamst the adjustment for cash-Items bias unul Good Fnday 1971 When the check was made, the reported declme m the adjustment exceeded the declme m deposits due to banks by perhaps $3 b1lhon to $3 5 bilhon As will be discussed later, about $2 billion to $2 5 bilhon of the difference appeared to reflect an overstatement of the actual adjustment, while $1 0 bilhon was the amount by wluch the declme m deposits due to banks underestimated the cash-Items bias One part of the overstatement m the reported data on cash-Items bias denves from the fact that, m some mstances, contrary to assumpt10ns, checks received by agencies, branches, and so forth were not bemg deposited m New York City banks on the day of receipt In particular, the checks were not bemg deposited until early the followmg day Given these delayed deposits, the checks did not appear as cash Items on the books of New York C1ty banks on the day of receipt by the agencies or branches Nonetheless, the checks were reported by the agencies, branches, and so forth that had wntten the checks as a part of the bias-adjustment numbers, and so they were mcluded m the adjustment Data collected on the amounts of delayed deposits suggest that the daily flow of "m1ssmg" cash Items and the consequent overstatement of the adjustment for cash-Items bias was about $2 0 bllhon m 1971 Another part of the overstatement of the adjust ment for cash-items bias may be caused by the fact that some checks drawn by agencies, branches, and so forth were deposited m the same New York City banks on which they were drawn In these circumstances, the offset to the credit of the depositor's account was an immediate debit to the account of the mst1tut1on that drew the check At the same time, however, the amount was reported by the agencies, branches, and so forth drawmg the checks as part of the statistics for the adjustment for cash-Items bias, and It was mcluded m the adjustment No data are available on the extent of this particular problem, although the agencies, branches, and so forth have suggested that the percentage of their total checks outstandmg that were deposited m the banks on which they were drawn was "small"-perhaps $500 million m 1970 The estimates of the cash items for Good Fnday and Boxmg Day are understated because not all https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis foreign bankmg offices active m the Euro-dollar market are closed on those days Smee data on the cash-items bias were first collected, a residual amount of checks-about $1 0 b1lhon-never disappears m the reported adjustment for cash-items bias, even when European banks are closed for holidays Presumably these checks give nse to a need for a contmued adjustment Smee the checks are still m the p1pelme, however, there 1s no declme m deposits due to banks to match these checks, and the estlmatmg procedure, usmg Good Fnday and Boxmg Day declmes m deposits due to banks, understates the true level of the necessary adjustment After cons1derat1on of all the foregomg details, new estimates of the cash-items bias were denved m 1976 and folded mto the h1stoncal money stock senes For the penod 1968-74, the magmtude of these rev1S1ons for the la5t day of each year ranged from -S2 6 billion to 5900 million For earlier penods the adjustment was neghg1ble The second data problem was an mappropnate adjustment to the origmal alternative senes asso oated with a change m Regulation J m late 1972 Tlus mappropriate adjustment, wluch raised the level of the senes for 1959-71, resulted from the method used to construct the ongmal alternative 5eries The alternauve M 1 was calculated by usmg current M 1 as a base That 1s, alternative M 1 wa5 constructed by addmg demand deposits due to domestic banks to the current M 1 series and rnbtractmg demand deposits due from banks and also the origmal adjustment for cash Items bias This calculation 1s the same as addmg net mterbank de posits and subtracting the cash-Items bias from current M 1 In late 1972, current M 1 was adjusted upward for the period extendmg back to 1959 2 That adjustment compensated for what was termed the "remittance payment bias" that persisted untll November 1972, when the Federal Reserve's Regulat10n J was changed For the current money stock, the entire adjustment made at that time was appropriate For the alternative M 1 , however, part of that ad1ustment was not appropriate, but 1t was inadvertently mcluded m the ongmal estimate because the estimate used the current money stock measure as a base The reason for the different treatment 1s described below Pnor to November 9, 1972, payments for checks presented by the Federal Reserve to banks outside Federal Reserve ewes were not due to the Federal 2 Federal Reserve Bulletin, vol 61-77 59 (February 1973), pp An Alternative Method for Calculating M 1 Reserve until the busmess day after presentation Even so, banks reduced their customers' demand deposit accounts on the day the checks were presented, and as an offsettmg entry banks mcreased an other-habiht1es account, "remittance due to Federal Reserve " In addition to followmg general accountmg conventions, banks wanted to reduce their deposit habihties as soon as possible m order to mmimize reserve requirements other habiht1es are not subject to such reqmrements Reductions m demand deposit accounts generally occurred before the reducuon of the correspondmg cash Items or Federal Reserve float Because the hab1hty for remittance payment was not carried m a money stock deposit account, the amount deducted for these Hems was too large for money stock purposes and the level of the series was understated When Regulation J was changed, the total amount of checks for which remittance was speeded up by one busmess day was esumated at around $4 0 billion The acceleration m remittance eliminated the write-up of other hab1ht1es Thus, the contraseasonal declme m other hab1lit1es at member banks that immediately followed the change provided a measure of the part of the $4 0 b1lhon that was concentrated at member banks-roughly $2 0 billion The remamder reflected faster remittance from nonmember banks through correspondents Banks that do not have accounts at the Federal Reserve remit through correspondent banks that do have such accounts Prior to November 1972, these banks could follow either of two accountmg procedures First, they could, upon receipt of a cash letter from the Federal Reserve, reduce their customer accounts and the deposits due from domestic banks The next day, when the correspondent remitted to the Federal Reserve, 1t would reduce an account reflectmg deposits due to banks Given these transacuons and other thmgs bemg unchanged, deposits due to banks would always exceed deposits due from banks In the alternative procedure, nonmember banks could use essentially the same procedure as member banks, writmg down customer demand deposits and mcreasmg other habiht1es for I day On the followmg day, when the correspondent bank remitted to the Federal Reserve and reduced deposits due to banks, the nonmember banks would write down deposits due from banks and other habdmes Under this accountmg procedure, deposits due to and due from banks remamed m bal ance each day To the extent that the second ac- https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 145 countmg method was used, the contraseasonal declme m other liabilities at nonmember banks after the change m Regulauon J should provide a measure of its magmtude Other hab1hues at nonmember banks showed a contraseasonal declme of only about $300 m1lhon Subtractmg this $300 milhon from the $2 0 billion remittances through correspondents by nonmember banks leaves $1 7 billion This 1s a rough estimate of the amount by which deposits due from banks were reduced 1 day prior to the reducuon m deposits due to banks 3 Smee neither other liabilities nor deposits due from banks are used m calculatmg the current money stock, adjustment for both transactions was appropriate m order to avoid a break m series after the change m Regulauon J For the alternative measure, however, m whose construction net mterbank deposits were used, adjustment was appropriate only for the other liab1hues related to member banks' remittances for their own accounts and to nonmember remittances through correspondents when similar accountmg procedures were followed No adjustment 1s necessary m the alternative series for the remittances associated with the early reduction of deposits due from banks In fact, because the alternative money stock measure used the current measure as a base, the Regulation J adjustment was mcluded m both series The result was that alternative M 1 as origmally calculated was overstated by the amount of the mappropriate adjustment for remittance-payment bias A new estimate of the overstatement of the alternative M 1 was derived by usmg the late-1972 estimate of $1 7 billion as a benchmark and reducmg this level by $ I 00 m1lhon each year back to I 959 This 1s not a satisfactory procedure, but unfortunately, there 1s no better way to make this adjustment Regardless of how the adjustment is made, 1t is sufficiently small and would be spread over a sufficiently long period of time that year-toyear distortion should be mmor The adjustments for the current and alternative money stock for the last day of each year from 1959 to 1974 are shown m Table I m the text As md1cated, the adjustments for cash-items bias were folded mto the published money stock series m 1976 3 The practice of wntmg down amounts due from banks before remittance by correspondents might have been un necessarily costly for nonmember banks because of lower deposits that could be used to meet nonmember State reserve reqmrements, and there is no economic explanation for its use https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 147 Developing Money Substitutes: Current Trends and Their Implications for Redefining the Monetary Aggregates Steven M Roberts This paper was completed tn January 1977 It has not been revised to include any deposit or other data available since late 1976 Nor has any attempt been made to inc01porate any regulatory or legal changes afjecting the monetary aggregates that have been made since late 1976 In recent years the distmct10n between demand deposits and savmgs deposus at both banks and nonbank depositary mst1tut10ns has become mcreasmgly blurred The dnvmg force behmd the regulatory and mstitut10nal mnovat10ns leadmg to this development has been greater compeuuon for funds among financial mst1tut10ns, which m turn has resulted m expanded payments services and lugher mterest returns to deposit owners For example, depositary mnovauons that have emerged withm the last few years mclude negotiable orders of withdrawal (NOW) accounts m New England, telephomc and thirdparty transfers from savmgs accounts, credit umon share drafts, and electromc transfers of funds by means of customer bank commumcat10n termmals (CBCT's) As a result of these and other mnovauonswhich suggest evolvmg savmgs-based transfer systems-the tradit10nal meanmg of the narrow money stock (M 1), defined as private demand deposits at commercial banks plus cur- NoTE-The author, formerly of the D1vmon of Research and Statistics, 1s currently Chief Economist, Com m1ttee on Bankmg, Housmg and Urban Affairs of the US Senate He would like to thank Paul Boltz, Edward Ettm, David Lmdsey, Raymond Lombra, Darrel Parke, John Paulus, and John Williams for comments on early drafts of this paper https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis rency m the hands of the public, as bemg representative of the economy's media of exchange or cash balances, has been somewhat eroded While the usage is thus far relatively small, it can be expected that an mcreasmg volume of fund transfers may be made from mterest-bearmg accounts, and M 1 as currently defined may account for a smaller proport10n of total transact10ns m the years ahead Consequently, monetary pohcy formulat10n might appropriately consider and evaluate movements m a broader array of monetary aggregates that exphcitly recogmze the development of savmgs-based transfers and other recent developments The Board of Governors of the Federal Reserve System and the Federal Open Market Committee, through Chairman Burns' recent series of congress10nal testimomes on monetary pohcy, are already on record as havmg targets for the growth of several monetary aggregates, mcludmg M 11 M 2 , and M 3 1 However, lt should be recogmzed that the ume deposit components of M 2 and M 3 have specific maturities and stnct regulat10ns regardmg redempt10n pnor to maturity that make them both relatively ilhqmd compared with savmgs deposits and M 1 and not really representative of transact10ns balances, although they may be considered near-money reposi1 These testimonies are published m the Federal Reserve Bulletin on a regular basis and also appear m the Annual Report M 2 1s defined as averages of daily figures for M1 plus time and savmgs deposits at all commercial banks other than negotiable certificates of deposit (CD's) of $100,000 or more at large weekly reportmg banks Ms 1s defined as M2 plus the average of the deposits at the begmnmg and the end of the month at mutual savmgs banks, savmgs and loan assocmlions, and credit umons 148 tones for precautionary or speculative funds 2 Also, m recent years there has been a tendency for small-denommation time deposit funds to become mcreasmgly concentrated m the longer maturities because mterest ceilmgs and rates paid on such matunues make them relatively more attractive, vis-a-vis market instruments, than the shorter-maturity time deposits Thus, the inclusion of longer-maturity time deposits m M 2 and Ma has resulted m monetary aggregates that mclude, m addition to M 1 , both hqmd (savmgs) and ilhqmd deposits In add1t10n, the meanmg of M 2 and Ma as currently defined may also be distorted by the current treatment of large-denommatlon (over $100,000) time deposits The current definit10n of "other time and savmgs deposits" -which are added to M 1 to obtam M 2-is total time and savmgs deposits less negotiable certificates of deposit (CD's) m denommat10ns of $100,000 or more at weekly reporting banks 3 This definition of other time ,md savmgs deposits means that M 2 includes not only those large-denommat10n ume deposits at weekly reporting banks that are not m the form of negotiable CD's but also all large-denommation time deposits, whether negotiable or not, at all other banks Recently available data suggest that movements of other time and savmgs deposits, as currently defined, may be significantly mfluenced by large-denommatlon deposits that tend to move hke negotiable CD's at weekly reporting banks and do not parallel the behav10r of consumer-type (small-denommat10n) deposits Thus, not only do M 2 and M 3 contam long-term maturity deposits, which are unlikely to be used as part of the payments mechanism, but M 2 also contains both small2 The penalty £01 early withdrawal of a time deposit under Regulation Q (Section 217 4 as amended July r,, 1973, applicable to all time deposit contracts entered mto after that date) 1s that mterest paid on the amount withdrawn may not exceed the savmgs deposit ce1hng 1ate and that 3 months' mte1est 1s fo1fe1ted The Fed eral Deposit Insurance Corporation (FDIC) and the Federal Home Loan Bank Board (FHI BB) have s1m1 Jar regulations for the depositary msutuuom under theu 1unsd1ct1on a Weekly reportmg banks are the approximately 320 large commercial banks that report detailed balance sheets to the Federal Reserve System each week https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis Improvmg the Monetary Aggregates. Staff Papers and large-denomination deposits, with the latter behaving differently from the former over the business cycle It should also be noted that nonbank thnft institutions-that is, mutual savmgs banks (MSB's), savmgs and loan associations (S&L's), and credit unions-have been relatively more active than commercial banks m developing and marketing savmgs-based transfer services for their customers 4 These services include not only telephonic and third-party transfers but also direct transfers between consumer and business savmgs deposits as payment for goods and services by means of remote terminals Commercial banks have been able to offer similar services only smce 1975 The development of savmgs-based transfers at nonbank thnft institutions suggests that the Federal Reserve will need more extensive and more timely data on deposits at such mst1tut1ons m order to monitor developments m the more broadly defined stock of "money" used for payments 5 The remainder of this paper reviews these developments m more detail and considers their imphcauons for redefining the monetary aggregates One sect10n focuses on the recent 1 egulatory changes and financial innovations that have led to the development of money substitutes Some of the new money substitutes will be described and, whenever possible, data on the dollar amounts outstanding and on rate of growth will be presented The analysis will indicate the causes for the recent changes Another sect10n discusses two problems re4 The term nonbank thnft mst1tut1ons will be used m the remamder of this paper to denote MSB's, S&L's, and credit umons taken as a group 5 More timely and extensive data from the FDIC pertammg to demand deposits at nonmember banks have been recommended as necessary to the Federal Reserve's central monetary policy function m Improving the Monetary Aggregates Report of the Advisory Committee on Monetary Statistics (Board of Governors, 1976) Begmnmg with the March 1976 call report, the FDIC agreed to collect 7 days of deposit data from non member banks m order to provide weekly average benchmark data rather than smgle-day data In add1 uon, the FDIC has agreed to remst1tute the callee Uon of weekly data from a sample of about 575 nonmember banks Data from a s1m1lar sample of nonmember banks was collected on an expenmental basis from the summer of 1974 to the sprmg of 1975 Developing Money Substitutes latmg to the current defimt10n of "other" time deposits that are mcluded m M 2 The creat10n of longer-maturity, small-denommat10n time deposit categories under Regulation Q has changed the maturity structure of these time deposits sigmficantly This 1s true of time deposits at S&L's and MSB's and thus affects the current defimuon of M 3 also In addition, this sect10n discusses the mclus10n of largedenommat10n time deposits m the defimuon of M 2 and M 3 The final section draws on the mitial port10ns of the paper and suggests several ways m which current defimt10ns of the monetary aggregates nught be modified at some future date Recent regulatory changes and financial innovations and the development of M1 substitutes Substitutes for transact10ns balances held m the form of currency or demand deposits have existed for a long time However, It 1s only w1thm the past several years that regulatory changes and financial mnovauons have resulted m new means of fac1htatmg payments for goods and services Today payments may be made through deposits held at banks and nonbank thnft mst1tut10ns without directly mvolvmg currency or demand deposits F1om an mst1tut10nal pomt of view, the smgle most important factor mfluencmg the development of savmgs-based transfers 6 1s the proh1b1t10n of mterest payments on demand deposits legislated m the m1d-1930's 7 In the 1950's and 1960's the pubhc-part1cularly the busmess sector-sought to reduce non-mterestheanng claims m favor of highly hqmd earnmg assets that could be easily transferred mto ,t payments medmm, these claims-money market assets 5uch as Treasury bills, commernal paper, and negotiable CD's-were generally available only m large denommat10ns A 6 Savmgs-based transfers 1s a term that will be used m this paper to denote payments mvolvmg an m1t1al or duect transfer from mterest-beanng deposits, ~hares, and so forth 7 Section 19 of the Federal Reserve Act a~ amended by the Bankmg Act of 1933 https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 149 second important mst1tut10nal factor leadmg to savmgs-based transfers has been the statutory monopoly of demand deposit powers by commercial banks Tlus monopoly has led to vigorous efforts by nonbank thnft mst1tut10ns to develop payments alternatives that they can offer to their customers as substitutes for demand deposlls It 1s clear that the nonbank thnft mstitut10ns as an mdustry have been more mnovauve m the payments area because they have been forced to compete with banks tor payment-type deposits 8 Although nonhank thrift mstltutions m general may not issue payment-type deposits, commercial banks may not pay mterest on the1r demand deposits 9 Thus, as the thrift mstitut1ons have mtroduced money substitutes, commercial banks-seemg the1r compeuuve advantage erodmg-have sought changes m reguL1t10ns m order to make bank savmgs deposlt5 ea5ier to transfer In the past 5 years there have been sigmficant changes 1elatmg to ownership and transfer of savmgs deposits at banks Innovc1t1om and regulatory changes made m the penod smce 1970 that affect components of M 1, M 2 , and MJ are shown m Table I If these types of mnovat1ve changes contmue-as seems hkely, given both their rapid recent mcrease and the changes that will be mduced by activity under electromc fumh transfer systems (EFTS)-the ba5ic monetary aggregates may have to be redefined to mclude m M 1 or some new aggregate all, or part, of the new demand deposit 5uhst1tutes The remainder of tins sect10n provides speofic mformat10n relatmg to several of the recently developed money substitutes NOW accounts A NOW account 1s a savmgs deposit that pe1m1ts the owner of the deposit to withdraw s 5&.L's and MSB s have, of course, been given ~ome compct1t1ve advantage over banks 1n the time and savmgs deposit markets because of the ¼ percentage pomt mterest ceilmg advantage they enJoy 9 Appenchx l provides a State by State rundown of t1ansfcr powers of State chartered thnft mstltutions Improving the Monetary Aggregates Staff Papers 150 TABLE 1: Innovations and Regulatory Changes Since 1970 Change Date of change Sept 1970 June 1972 Sept 1972 July 1, 1973 July 5, 1973 Nov 1, 1973 Jan 1, 1974 Jan 1974 Early 1974 Aug 1974 Nov 27, 1974 Dec 23, 1974 Apr 7, 1975 Apr 16, 1975 Sept 2, 1975 Nov 10, 1975 Jan 16, 1976 Feb 27, 1976 Mar 15, 1976 May 26, 1976 S&L's were permitted to make preauthonzed nonnegotiable transfers from savmgs accounts for household-related expenditures 1 State-chartered MSB's m Massachusetts began offermg NOW accounts State-chartered MSB's m New Hampshire began offenng NOW accounts Federal regulatory authont1es mtroduced a 4-year time deposit (ce1lmg free) with a mm1mum denom1nat10n of $1,000 Federal Reserve amended Regulation Q to modify penalties for early withdrawal of time deposits Interest rate cedmgs were imposed on 4-year $1,000 mm1mum time deposits (7¼ per cent for banks and 7½ per cent for S&L's and MSB's) All depositary mst1tut1ons m Massachusetts and New Hampshire (except credit umons) were authonzed by the Congress to offer NOW accounts 2 Accounts s1m1lar to NOW's, but non-mterest beanng, offered by State-chartered thnfts m additional States through the year 3 First Federal Savmgs and Loan, Lmcoln, Nebraska, mstalled customer bank commumcat1on termmals (CBCT's) m two Hmky Dmky supermarkets, allowmg its customers to make deposits to or withdrawals from savmgs accounts Such withdrawals can be used to pay for merchandise purchased from the stores The First Federal system, known as Transmat1c Money System (TMS), 1s now bemg franchised to other S&L's Money market mutual funds (MMMF's) came mto existence on a large-scale basis These funds, which mvest m money market instruments, allow their shareholders to redeem shares by checks drawn on accounts estabhshed at designated banks, by wife transfer, or by mad Federal credit umons were permitted to issue credit umon share drafts, which are check-hke mstruments payable through a commerc1al bank 4 Commercial banks were permitted by Federal regulatory authonUes to offer savmgs accounts to domestic State and local government umts Federal regulatory authont1es mtroduced a 6-year time deposit, mm1mum denommat1on $1,000, with a 7½ per cent ce1hng for banks and 7¾ per cent ce1lmg for S&L's and MSB's Member banks were authonzed by Federal Reserve to make transfers from a customer's savmgs account to his checkmg account upon telephomc order from the customer The FHLBB broadened its 1970 action to allow S&L's to make preauthonzed th1rd-party nonnegotiable transfers for any purpose Commercial banks were authorized by Federal regulatory authontles to make preauthor1zed thirdparty nonnegotiable transfers from a customer's savmgs account for any purpose Commercial banks were authonzed by Federal regulatory authont1es to offer savmgs accounts to partnerships and corporations operated for profit, hm1ted to $150,000 per customer per bank The Federal Reserve adopted an mtenm pohcy for access to System-operated automated cleanng houses (ACH's) that md1cated that ACH transfers could "ongmate from any account havmg thirdparty powers, for example, savmgs, NOW, and share draft accounts," as well as from demand deposit accounts Federal leg1slat1on authonzmg NOW accounts m Connecticut, Mame, Rhode Island, and Vermont became effective The Federal Reserve and the FDIC proposed for comment an amendment to Regulation Q to permit banks upon request of a customer to cover overdraft of a demand deposit account by automatic transfer of funds from the customer's savmgs account At this wntmg the rule change has not been made All State-chartered S&L's and MSB's m New York were granted consumer demand deposit powers pursuant to Chapter 225 of the laws of 1976 i Authonty contamed m the Housmg Act of 1970 2 Pubbc Law 93-100, signed August 16, 1973 • According to Manlyn G MathIS, "Thnfts contmue to gatn tn third-party payment plans," Banking, vol 66 (December 1974), pp 32-38, non-mterest-beanng NOW's were offered by at least some thnfts m Connecttcut, Delaware, Indiana, Maryland, New Jersey, New York, North Carolma, Oregon, Pennsylvama, Rhode Island, and Utah In 1975 several other States enacted legislatton pernuttmg https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis State chartered mstitutions to offer sinular accounts These States mclude Illmois, Mame, Nebraska, and Vermont See Appendix 1 for a list of transfer powers authonzed for State chartered mstitutions • Secllon 721 3, Rules and Regulallons of the Nallonal Credit Union Adnumstrallon (NCUA), estabbshed rules for expenmental pilot programs for electromc funds transfers (EFT) that mclude share draft plans Developing Money Substitutes funds by wutmg a negotiable order of withdrawal-hence the acronym NOW 10 The withdrawal document is a negotiable draft that can be used to make payments to tlurd parties, essentially like a check drawn on a bank demand deposit This f01m of savmgs account came mto bemg followmg a rulmg by the Massachusetts Supreme Judicial Court on June 12, 1972, that found no restriction m the State charter of MSB's prohibitmg withdrawals from savmgs accounts through the use of NOW drafts State chartered MSB's m Massachusetts soon entered the NOW market, and m September a savmgs bank m New Hampshire began to offe1 NOW's after havmg dete1mmed that, as m Massachusetts, there we1e no statutory 1cstnct10ns on the manner of withdrawal from savmgs accounts Immediately, State-regulated savmgs banks m the two States held a competitive advantage over Federally charte1ed or msmed mstitutions, which could not offer NOW accounts These mstitut10ns sought relief from Federal agencies, which led to congressional legislation (Pubhc Law 93-100), signed mto law August 16, 1973, authonzmg all depositary financial mstitut10ns (except crecht unions) m Massachusetts and New Hampshire to offer mterest-beanng deposits on which negotiable mstruments of withdrawal could be drawn As a result of this legislation, 1egulations by the Federal Reserve, the FHLBB, and the FDIC authorized NOW's for Federally chartered depositary msututions m Massachusetts and New Hampshire as of Janu,n y I, 1974, limited exclusively to mdividuals and nonprofit orgamzat10ns 11 The three agencies agreed to impose a umform interest rate ceilmg of 5 per cent on NOW's and to restnct the advertisement of such accounts to Massarhusetts and New Hampshire Outstandmg NOW balances at vanous types 10 Much of the material m this subsecl!on 1s based on the work of my colleague John W1lhams 11 From November 1974 until authonzatton was with drawn m Apnl 1975, State and local governmental umts were permitted to hold NOW accounts at commercial banks https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 151 of depositary mstitut10ns m Massachusetts and New Hampshire from September 1972 to December 1975 are shown ml able 2 Growth m NOW accounts has been 1apid throughout the penod Table 2 ,tlso shows market shares, which h.tve changed conmlerably over time and have not as yet stabilized fully Ongmally, MSB's-wh1ch p10nee1ecl NOW accountsdommatecl the market, but more recently commc1 cial banks h,tve entered the NOW ma1ket aggressively, and then share of that market has grown veiy iap1dly A few commercIJ.l hanks have converted all eligible savmgs acwunts to NOW's, and some have notified customers that their demand deposits are ehg1ble foi conveis10n to a NOW account Table 3 compa1es some of the characteristics of NOW accounts at competmg mstltutions as of Decembe1 31, ICJ75 Most mstltutions were paymg 5 pe1 cent mte1 est on a day-of-depositto-day-of-withdrawal basis A maJonty of these mst1tut10ns also compounded mterest dally or contmuously and offe1ed free NOW drafts The lugher proport10n of free drafts at nonbank mstitut10ns suggest5 that they see NOW accounts as a means of clrawmg funds from commercial bank demand depo~1 ts-that is, via the ,tbsorption of clearmg costs as a nonprice means of competitive advantage Table 4 shows how charges pei draft and activity per month have changed smce January 1974 Accounts with free draft privileges are typically the most active Furthermore, NOW account activity has mcrea5ed consideiably as more mst1tut1ons offer free drafts 12 On February 27, 1976, congressional legislation authorinng NOW accounts m Connecticut, Mame, Rhode Island, and Veimont became effective Although little mformat10n is yet available regardmg the newly authorized NOW markets, it appears that commercial banks entered this market more rapidly than did thrift mstituuons durmg the first month of expanded 12 For add1ttonal mformauon on NOW account act1v1ty m 1974 and 1975, see John D Paulus, "Effects of NOW Accounts on Costs and Earnmgs of Commercial Banks m 1974-75," Staff Economic Studies 88 (Board of Governors of the Federal Reserve System, 1976) Improvmg the Monetary Aggregates Staff Papers 152 TABLE 2 Outstanding Balances and Shares-NOW Accounts Dollar amounts ID thousands Date Commercial banks All offermg 1nst1- T ota I tullons Massa- I chusetts I Share of HNew amp- total shire NOW's Share Savtngs and loan assoc1at1ons Share of of New total MassaNew Hamp- total chusetts Hamp- NOW's shire NOW's Total shire Mutual savmgs banks I Total M assachusetts I I I 1972-Sept Oct Nov Dec 11,094 22,386 34,823 45,272 11,004 22,386 34,823 45,272 11, 0'.14 22,386 34,363 44,522 -460 750 1973-Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec 60,726 73,451 86,118 94,606 102,045 108,381 113,418 117,005 120,223 130,361 136,872 143,254 60,726 73,451 86,118 94,606 102,045 108,381 113,418 117,005 120,223 130,361 132,872 143,254 59,661 71,975 84,162 92,341 99,633 105,688 110,486 113,852 116,259 125,873 131,795 138,028 1,065 1,476 1,956 2,265 2,412 2,693 2,932 3,153 3,964 4,488 5,077 5,226 1974-Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec 143,190 150,447 165,157 174,682 180,637 191,229 204,646 232,386 249,033 270,813 293,305 312,576 2,556 4,338 6,588 9,689 11,052 13,771 17,919 32,955 39,253 46,776 55,994 65,249 2,274 3,857 5,916 8,458 9,296 11,156 14,175 28,450 33,597 40,245 48,563 56,989 282 481 672 1,231 1,756 2,615 3,744 4,505 5,656 6,531 7,431 8,260 02 03 04 06 06 07 09 14 16 17 19 21 139,779 143,764 154,007 157,412 159,591 164,733 171,503 180,335 187,721 197,758 206,764 213,661 134,832 138,453 147,845 150,309 151,510 155,946 161,544 169,119 175,340 184,830 192,577 200,083 4,947 5,311 6,162 7,103 8,081 8,787 9,959 11,216 12,381 12,928 14,187 13,578 98 98 93 90 90 86 84 78 75 73 71 68 855 2,345 4,562 7,581 9,994 12,725 15,224 19,096 22,059 26,279 30,547 33,666 855 2,345 4,325 6,913 8,351 11,089 13,223 16,781 19,314 23,316 26,689 29,747 237 668 I, 143 1,636 2,001 2,315 2,745 2,968 3,858 3,919 01 02 03 04 05 07 07 08 09 10 10 II 1975-Jan Feb Mar Apr May June July Aug Sept Oct 339,982 395,190 449,638 472,864 514,018 580,331 630,402 670,790 713,419 761,967 796,533 839,339 82,861 107,481 137,519 150,999 172,653 210,838 233,513 256,992 289,308 305,214 325,519 359,023 73,517 96,647 124,706 136,165 155,318 185,923 201,607 217,936 235,029 254,821 271,691 302,112 9,344 10,481 12,813 14,834 17,335 24,195 31,096 39,056 45,279 50,393 53,828 56,911 24 28 31 32 34 36 37 38 39 40 41 43 220,725 236,580 262,797 268,571 283,322 304,633 327,417 337,684 351,612 368,271 378,792 386,560 206,797 221,506 246,259 250,780 263,978 283,134 303,805 213,117 324,005 338,580 347,145 356,319 13,928 15,074 16,538 17,791 19,344 21,499 23,612 25,567 27,607 29,691 31,647 30,241 65 61 58 57 55 53 52 50 49 48 48 46 36,396 41,482 49,322 53,294 58,043 64,860 69,472 76,114 81,499 88,482 92,222 93,756 32,369 37,215 43,980 47,185 51,388 57,315 61,554 67,519 72,407 78,785 81,863 84,168 4,027 4,267 5,342 6,109 6,655 7,545 7,918 8,595 9,092 9,697 10,359 9,598 II II II II II II II II II 12 12 II Nov Dec Norn -Monthly data are released by the Federal Reserve Bank of Boston SouRCE -John D Paulus, "Effects of NOW Accounts on Costs and Earmngs of Commercial Banks m 1974-75," Staff Economic Studies 88 (Board of Governors of the Federal Reserve System, 1976} authorization This development 1s s1gmficantly different from the experience m Massachusetts and New Hampshire Almost all of the mst1tut1ons that offered the new accounts were paymg the ce1lmg rate of 5 per cent, although relatively few were offermg free drafts The TABLE 3 Characteristics of NOW Accounts, by Type of Institution, December 31, 1975 In per cent Interest Institution Commercial banks Mutual sa vtngs banks Sa vtngs and loan assocta t1ons All mst1tut1ons https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis Contmuom From day dally of deposit 5 per cent orcomto day of poundmg withdrawal Free drafts 96 97 45 86 73 98 30 77 99 97 69 69 92 89 82 63 total of the newly authorized NOW balances m the four States as of March 31, 1976, amounted to only $43 mtlhon Commercial bank savings deposits From November 1974 to March 1976 the Federal bankmg authorities made four regulatory changes, and proposed a fifth, which have greatly expanded the poss1b1ht1es for substitut10n of savmgs deposit balances for balances now mcluded m M 1 , particularly demand deposits These changes have been of two types (I) to allow for expanded ownerslup of savmgs deposits, and (2) to permit banks to offer their customers new services that would fac1htate the use of savmgs deposits for transact10ns purposes Developing Money Substitutes 153 TABLE 4 NOW Account Actmty and Charges Charges per draft (per cent of 1ssumg msutuuons) Month Free 1974-Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec 32 31 35 34 34 33 34 42 53 56 60 61 5 2 1 0 8 5 5 5 7 0 4 7 1975-Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec 62 64 66 66 66 64 65 67 65 65 65 63 1976-Jan Feb Mar I 10¢ 17 18 16 16 16 18 18 15 14 12 JO 10 I 15¢ I Other• Drafts per account dunng average month• 5 4 4 5 2 5 5 8 4 3 9 8 50 45 42 42 40 40 39 31 21 19 16 12 0 4 7 0 7 5 9 2 8 9 I 5 5 5 7 8 7 7 10 10 11 12 14 0 8 4 3 5 1 5 1 9 6 9 7 7 7 8 8 8 8 8 8 8 8 9 3 0 8 5 5 I 5 0 2 8 9 5 3 0 0 6 2 4 7 2 6 8 3 5 8 9 8 2 7 7 6 2 5 6 5 1 4 7 3 9 3 7 3 6 40 4 0 10 10 8 9 8 7 6 5 5 5 5 6 8 4 6 6 8 9 7 6 9 8 7 0 18 17 17 17 19 22 22 23 24 24 24 26 0 4 8 7 3 6 9 3 9 8 9 5 9 8 10 10 10 10 10 9 10 10 10 11 3 8 0 5 4 4 3 8 3 7 2 0 63 4 61 6 54 9 3 4 3 7 3 4 5 1 5 3 5 S 28 0 29 5 36 2 10 7 10 3 II 6• 1 Includes a combmat1on of free drafts plus a charge for each draft over a specified number, and free drafts m exchange for a specified mm1mum balance ' Excludes accounts with no act1V1ty durmg the month 3 Includes NOW accounts m Connecticut, Mame, Massachusetts, New Hampshire, Rhode Island and Vermont Domestic governmental umts were first permitted to hold savmgs deposits at commercial banks m November 1974 Effective November 10, 1975, commerCial banks were permitted to offer savmgs accounts to partnerships and corporat10ns, hm1ted to J150,000 per customer per bank These accounts have grown more qmckly than ongmally ant1npated and by the end of March 1976 amounted to about $2 r:i bilhon at the weekly reportmg banks and $5 4 billion at all msured commercial banks Authonzat10n to make telephomc transfers from savmgs to demand deposits and pre,mthonzed third-party nonnegotiable transfers directly from savmgs deposits provides banks the opportumty to offer their customers more convement methods for usmg savmgs deposits to make payments Because these savmgs-based ~erv1ces are new, 1t 1s difficult to gauge with any degree of certamty their quantitative impact on M 1 The direction of impact, however, 1s clear these services, 1f widely offered and utilized, would tend to reduce further the d1stmct10n between demand and savmgs deposits, and thus would erode the s1gmficance https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis of M 1 and would alter its relauonslup to the gross national product Compeuuon from thnft mst1tut1ons and the proh1b1uon of mterest payments on demand deposits suggest that commercial banks will offer these new services based on customer demand It 1s difficult to quantify the extent to which these new savmgs transfer services a1e bemg used, however, through mformal surveys and momtormg of developments by the Federal Reserve Banks and the FHLBB, 1t appears that telephomc transfer services are hemg offered on a fairly wide geographic basis by both large and small banks and also by S&L's Preauthonzed third-party nonnegotiable transfer services do not appear to be widely offered On March 15, 1976, the FDIC and the Federal Reserve issued a proposal to allow banks to offer automatic overdraft protection from savmgs accounts by means of preauthor11ed transfers from savmgs to cover overdrafts If adopted, tlus new service would be complementary to those savmgs-based transfer services already perm1ss1ble Such a service, Improving the Monetary Aggregates Staff Papers 154 pnced to compete with consumer overdrafts by takedowns of Imes of credit, could be widely marketed by banks, has the potential for consumer acceptance, and could mduce expanded use of complementary services If these developments were to take place, the average size of demand deposit accounts would tend to declme It should be emphasized that overdraft services would be an add1t10nal factormdeed, an extremely important one-tendmg to mcrease the relative importance of savmgs deposits m the payments process, while reducmg the s1gmficance of M 1 as tt 1s currently defined Money market mutual funds Money market mutual funds (MMMF's) are a fairly new form of mvestment company, the first was orgamzed m 1971, and others began operat10n m 1974 It was not until after the period of nsmg mterest rates m early 1974 that the MMMF's began to grow rapidly m number and dollar s12e As Table 5 shows, between January and December 1974 the number of money market funds mcreased from 4 to 30 and net assets of the mdustry grew from less than $200 million to about $2 5 b1lhon The number of funds mcreased through I 975, although the dollar amount of assets stabilized at about $3 6 billion as market mterest rates declmed Designed basically as cash management vehicles, these funds provide shareholders with an mterest return that vanes with rates m the money market They typically mvest m mstruments that are issued m large denommat10ns such as Treasury bills, large-denommat10n CD's, bankers acceptances, and commercial paper, while reqmrmg shareholders to mvest relatively small m1tial amounts such as $500 to $1,000 Shares m these funds can be purchased and redeemed easily, often without transaction charges Management fees of the funds are also relatively low Because of the high hqmd1ty of shares, near-market rate of return, zero or near-zero transact10n costs, and low management fees, shares m money market funds provide an attractive substitute for both demand and savmgs deposits offered by depositary mstitutions Most of the funds calculate and pay dividends on a daily basis, shares can be redeemed by check or wire transfer at little or no cost, .i.nd most funds have no sales charges The check redemption feature 1s especially mterestmg The shareholder may receive a book of ordmary checks from a bank (designated by TABLES Growth m Money Market Mutual Funds January 1974--March 1976 Change over month (mtlltons of dollars) Assets (mtlltons of dollars) 1974-Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec 4 6 6 7 8 10 13 17 18 22 26 30 174 208 244 303 412 542 792 1,106 1,393 1,860 2,208 2,439 34 36 59 109 130 250 314 287 467 348 231 19 17 24 36 31 46 39 25 33 18 10 5 3 2 0 6 1 6 9 5 7 5 1975-Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec 32 35 36 37 38 39 40 40 42 42 46 47 3,042 3,501 3,786 3,862 3,911 3,795 3,694 3,787 3,750 3,723 3,645 3,645 604 458 285 76 49 -116 -101 93 -37 -27 -19 -59 24 15 8 2 1 -3 -2 2 -1 -1 8 1 1 0 3 0 7 S 0 7 5 6 9 0 7 3 6 S S8 6 4 5 1 5 7 6 0 62 6 1 S 6 S 6 1976-Jan Feb Mar 48 48 48 3,701 3,736 3,719 56 35 -17 - 1 5 9 5 5 3 5 0 5 1 https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis Growth rate (per cent per month) Average yield (per cent per month) Number of funds Month 8 8 7 8 10 10 11 11 11 10 9 9 6 1 8 7 0 2 2 3 3 5 4 0 155 Developing Money Substitutes the particular fund) and can use these checks to make payments However, arrangements often specify mm1mums such as $500 per check When the check 1s presented to the payee bank, the bank, actmg as the shareholder's agent, mstructs the mutual fund's transfer agent to redeem a sufficient number ot shares m the shareholder's account to cover the amount ot the check This procedure allows the shareholder to earn mterest on his mvestment until payment 1s made to the bank In a similar manner, shareholders with a large amount of funds mvested can arrange for wire transfer of funds both out of and mto their share accounts at their commercial banks The ease with which shares may be purchased and redeemed with mm1mal transactions costs suggests that the MMMF's make extremely good mvestments for cash management purposes In fact, a large proportion (about 40 per cent) of all accounts are owned by mst1tutional mvestors that use them to mcrease cash management efficiency But both consumers and households may find MMMF's to be useful substitutes for demand, savmgs, and time deposit balances, and consequently they are another factor altenng the relat1onsh1p between market rates and the monetary .tggregates, and between the aggregates and gross national product Credit union share drafts 13 I Credit umon share drafts are a new type of payment mstrument and thus are neither widely known nor widely used However, there are approximately 23,000 credit umons m the Umted States, with total assets of about $35 billion, and 1f the current rapid growth of credit umon shares contmues, the potential impact on M 1 and M 2 of widespread use of share drafts will be large A share draft 1s a negotiable payments mstrument drawn on the 1ssmng credit umon but payable through a commercial bank It 1s 1a Add1t10nal mformation may be obtamed from Savings and Loan News, vol 97 (April 1976), and "Share Drafts The Fust Six Months" (report of the Credit Umon National Association, 1975) https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis one form of the legal payments mstrument known as "payable-through drafts " U nhke a check that 1s drawn directly on the deposit hab1hty of a commercial bank, a credit umon share draft 1s drawn on the credit umon that has established a cleanng arrangement with the "payable-through bank " In the clearmg process, these drafts are treated the same as checks until they are received by the payablethrough bank, which notifies the credit umon as to the drawer, the amount, and the debit to the credit umon's account at the bank for payment of the drafts The credit umon will then debit the shareholder's account The important pomt 1s that mterest will be paid on the shareholder's funds until the draft 1s cleared and the .tccount 1s debited In many respects share draft accounts are hke NOW accounts and have the same advantages over non-mterest-paymg checkmg accounts As Table 6 md1cates, the number of ned1t umons now offermg such accounts 1s only about 1 per cent of the total, but the recent growth rate has been 1mpress1ve as early problems have been resolved As md1cated above, share draft plans have been authonzed for Federal credit umons by the National Crecht Umon Admm1strat10n (NCUA) only smce August 1974 In order to make the share draft attractive to their shareholders, many credit umons are not, at least at this time, chargmg for drafts With mterest on share accounts m many cases above the maximum that commercial banks, S&L's, and MSB's can pay on savmgs deposits, share draft accounts are an attractive payments alternative Shareholder knowledge of, and demand for, share draft pnv1leges are the key unknown elements at this time Changes affecting the time deposit components of M2 and Ma The prev10us section focused on recent regulatory changes and financial mnovatlons that have mduced the creat10n of new substitutes for M 1 Savmgs deposits, which are mcluded m the "other time and savmgs" component Improvmg the Monetary Aggregates· Staff Papers 156 TABLE 6• Share Drafts at Credit Uruons Month Credit umons offenng drafts Federal I State• I Credit umons approved to offer drafts• Drafts drawn per month• (thousands) Federal ' Total I Total Federal credit umons offenng share drafts I Amount drawn Shares subJect to h withdrawal by draft per month per mont Thousands of dollars 1975-May June July Aug Sept Oct Nov Dec 5 6 11 16 27 53 65 81 7 8 15 17 19 19 29 37 12 14 26 33 46 72 94 118 12 29 54 81 96 120 143 170 15 20 26 32 51 184 106 179 23 33 44 59 91 144 171 278 1,100 1,200 1,800 2,100 3,100 4,500 5,600 9,300 2,208 3,471 3,972 5,028 6,759 9,453 12,111 14,395 1976-Jan Feb Mar 108 118 131 55 63 59 163 181 190 189 203 223 189 247 375 304 399 575 12,300 13,939 20,846 23,092 29,718 37,879 1 Data for State-chartered credit unions mclude an mcomplete mdustry sample • Federally chartered, mcludes those now offenng drafts 'Partially esllmated by the Nauonal Credit Umon Adm1mstra11on SOURCE -NCUA of M 2, have been sigmficantly affected by recent regulatory changes This section analyzes two changes m the time deposit component of "other time" deposits First, the effect of penalties for early withdrawal and the estabhshment of higher mterest rates for the newly created, longer-maturity time deposits with small mmimum denommations are discussed Second, the mclusion of some large-denommation time deposits withm the current definition of other time deposits will be exammed Longer-maturity, consumer-type time deposits Two recent changes m the Federal regulations governmg mterest payment on deposits by depositary 'mstitutions have affected the composition and meaning of the time deposit components of M 2 and M 3-penalties for early withdrawal of time deposits and the establishment of higher mterest rate ceilmgs on newly created, longer-maturity time deposits 14 The former decreases the liqmdity of time deposits because the dollar value of the penalty mcreases as the maturity date approaches The latter has lengthened the maturity composition of other time deposits because of the relatively attractive rates paid on longermaturity deposits It also has decreased the 14 Much of the mformauon m this sect10n 1s based on work done by Gerald N1ckelsburg, while a member of the research staff of the Board of Governors https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis ove1-all hqmdity of other time deposits and reduced the substitutability between smalldenommat10n time deposits and demand deposits Time deposits have become more like securities and less hke deposits In July 1973 the Federal Reserve amended Regulation Q to modify the structure of mterest penalties for withdrawal of time deposits prior to maturity, the FDIC made a correspondmg change m its regulations One reason for this change was to make the penalties for early withdrawal of time deposits the same for banks and for thrift mstitutions The penalty for early withdrawal was established as (1) the forfeiture of 3 months' mterest and (2) for the remamder of the period durmg which the withdrawn amount was held, the 1eduction of the rate paid to the regular passbook rate 15 In addition to the establishment of the modified penalty, banks were also reqmred under Regulation Q to describe fully and clearly by written statement how the penalty provisions apphed to time deposits Table 7 provides an example to illustrate the penalty for early withdrawal of a 4-year $1,000 time certificate of deposit It displays the mcreasmg dollar cost of withdrawal of the deposit prior 15 The rule for early withdrawal m effect before July 1973 permitted a bank to pay a time deposit before maturity only m an emergency, when the withdrawal was necessary to prevent great hardship to the depositor In such cases, the depositor forfeited accrued and unpaid interest for a penod of up to 3 months Developing Money Substitutes 157 TABLE 7 Penalty for Early Withdrawal of a $1,000, 7 ¼ Per Cent, 4-Year Certificate Dollars, except as noted Year and quarter Imputed value 1f held to matunty Value 1f withdrawn pr10r to matunty 1 Penalty for early withdrawal Effecllve rate of return 1f withdrawn at given date' (per cent) 1-1 2 3 4 1,018 1,036 1,055 1,074 12 58 37 49 1,000 1,012 1,025 1,037 00 50 16 97 18 24 30 36 12 08 21 52 2 49 3 33 3 74 2-1 2 3 4 1,093 1,113 I, 113 I, 154 97 80 99 53 1,050 1,064 1,077 1,090 95 08 38 85 43 49 56 63 02 72 61 68 4 4 4 4 00 16 28 37 3-1 2 3 4 1,175 1,196 1,218 1,240 46 77 46 54 1,104 1,118 1,132 1,146 48 29 27 42 70 78 86 94 98 48 19 12 4 4 4 4 44 50 54 58 4-1 2 3 4 1,263 1,285 1,309 1,332 03 92 23 96 I, 160 1,175 1,189 1,204 75 26 95 82 102 110 119 128 28 66 28 14 4 4 4 4 61 64 66 69 '$1,000, plus mterest actually earned, calculated as follows loss of 90 dws' (I quarter's) mterest, with mterest paid for remamde1 of the penod actually held at the passbook rate of 5 per cent, com pounded quarterly 2 Annual percentage rate assummg quarterly compoundmg to matuuty as the maturity date approaches The calculations assume an interest rate of 7¼ per cent compounded quarterly if the deposit is held for the full 4-year contract life The p,mbook rate is assumed to be 5 per cent, also compounded quarterly The penalty represents the "cost of hqmd1ty" imposed by the current regulations The effective rate of 1 eturn if an early withdrawal is made is shown m the last column Also m July 1973, the Federal Reserve, the FDIC, <1.nd the FHLBB created a new time deposit category with a 4-year maturity and J. lugher ceilmg rate than had previously been <1.vailable These 4-year certificates were at that time, and are still, quite popular since they bear a 7¼ per cent rate ceilmg for banks and a 7½ pet cent ceiling for MSB's and S&L's 16 As a result, substantial shiftmg of funds from ~horter to longer maturities began in July 1973 The shifting was reinforced in Decemhct 1974 by the introduction of a 6-year ume rn Ongmally, the 4 year deposits with mm1mum de 11ommat1ons of $1,000 had no mterest ce1lmgs and were known as "wild card" or "topless" certificate~ However, followmg complamts from many depo~1tary mstilut10ns that note competition was adversely affectmg their lendmg rates, the Congress made clear Its desue that ce1lmg rates be established for the 4 year certificates I:ffect1ve November I, 1973, the Federal agencies imposed mterest rate ce1lmgs on these deposits of 7¼ per cent for banks and 7½ per cent for S&L'~ and MSB's https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis deposit maturity category with ceiling rates of 7½ per cent for b<1.nks and 7¾ per cent for S&L's and MSB's As shown m T <1.ble 8, which presents data on time <1.ml savings deposits by maturity for rommerCIJ.l b,mks, the trend toward a lengthened matunty d1stribut10n of time deposits ts fairly easy to identify Similar mformauon is given for MSB's m Table 9 and for S&L's in Table 10 At each type of inst1tut10n, the longerm<1.turity, small-denommauon time deposits have grown at a considerably more rapid pace than have the shorter-maturity certificates In fact, outstanding small time deposits with matunues of less than 2½ years declined or remamed constant m absolute sIZe and declined 1 elative to total 5mall-denommat10n ume deposits except for the latest observat10n-Janu<11 y 1976-when market mtere5t rates were low t elative to time deposits The most rapid growth occurred m small-denommauon time deposits with maturities of 4 years or more 11 17 Tht:, S&L data a1e reported as remammg maturity, and thus the 4 year accounts represent only recent ~ales of certificates for each survey By the time of the next survey, those 4 year certificates previously mued ,\Ill have lc~s than 4 years remammg to ma tuuty and thus will be counted m the 2 to 4 year matunty category This explams a large part of the growth m accounts with 2- to 4-year rcmammg maturity Improvmg the Monetary Aggregates Staff Papers 158 TABLE 8 Time and Savmgs Deposits at All Commercial Banks, 1973-76 Savings Date Total I Small ume I f~~rs over Total savings and small time 48,510 9,956 3,181 45,554 13,262 12,954 41,422 15,663 21,027 37,741 17,365 28,786 36,372 19,500 35,956 36,506 20,453 42,070 238,532 245,987 255,267 264,149 291,514 317,417 118,487 132,309 158,185 169,267 153,816 144,223 104,173 119,298 148,580 157,557 135,975 124,300 14,314 13,011 9,605 11,710 17,841 19,923 67 65 62 61 65 69 33 35 38 39 35 31 29 32 36 36 31 27 4 3 2 3 4 4 to 11 to 2'/212 to 41 I Up 1 year years years 1 /2 Total NOW Other Total 130,584 na 130,584 130,923 3 130,920 137,307 17 137,290 141,122 83 141,039 158,515 234 158,281 171,321 394 170,927 107,948 115,064 117,960 123,027 132,999 146,096 46,301 43,294 39,848 39,135 41,171 47,067 37 35 33 33 36 37 30 30 29 28 30 32 13 11 10 10 9 10 4 Large ume Total 1 year to I and I Up 1 year over Millions of dollars 7-31-73 1-31-74 7-31-74 1-31-75 7-31-75 1-31-76 357,019 378,296 413,452 433,416 445,330 461,640 7-31-73 1-31-74 7-31-74 1-31-75 7-31-75 1-31-76 100 100 100 100 100 100 Per cent of total 37 na 35 * 33 * 33 * 36 * 37 * 3 4 4 4 4 4 14 12 10 9 8 8 I 3 5 7 8 8 n a Not available * Less than O 5 per cent of total NoTE -Data from FR Quarterly Survey of Time and Savtngs Deposits, Weekly Cond1t1on Report of Large Commercial Banks and Domestic Subs1d1anes, Reports of Deposits of Member Banks, Report of Condition of All Commercial Banks (call report)-Large Denommatlon Time Deposit Supplement The denommational breakdown of time deposits-under and over $100,000--1s available twice each year on the June and December call reports begmrung December 31, 1973 The matunty breakdown oflarge time deposits 1s taken from the monthly Survey of Negotiable CD Maturity Structure at Weekly Reportmg Banks, and 1t ts assumed that all other large time deposits have the same maturity structure A special survey m February 1975 provided evidence for this assumption The weekly reportmg bank data provide mforma t1on on large negotiable CD's, and smce 1975 on all large time deposits The maturity d1str1but1on for most small time deposits 1s , eported four times per year m the Survey of Time and Savmgs Deposits These data are for md1v1duals, partnerships, and corporations only Details may not add to totals due to rounding All data are m ongmal maturity Savmgs deposits at S&L's and MSB's declmed m relative, though not nommal, amounts durmg this period Savmgs deposits at commercial banks, however, experienced a large percentage mcrease This mcrease may be due to the convemence factor of havmg savmgs and demand accounts at the same mstltuttons, while longer-maturity time deposits are more hkely to be placed at the mstitution offermg the lughest yield The relative mcreases m the longer-maturity categories, coupled with their relatively ilhqmd nature due to the penalty cost for withdrawal prior to maturity, suggest that not only are those deposits quahtat1vely different from savmgs deposits but also they are qmte un- TABLE 9, Time and Savmgs Deposits at FDIC-Insured Mutual Savmgs Banks, 1973-76 Savmgs Date Total I Small time I Total NOW Other Total f~rs over Total savmgs and small tune 5,954 2,046 5,183 7,596 5,328 11,525 5,360 14,372 5,431 17,962 5,639 19,985 82,122 83,511 84,064 85,248 91,949 97,061 694 711 99 99 99 99 99 99 1 1 1 1 1 1 to 11 to 2½ 12½ to 41 I Up I year years years 4 Large time Total I Upto 1 year year I 1over and Mtlhons of dollars 7-31-73 1-31-74 7-31-74 1-31-75 7-31-75 1-31-76 82,496 83,977 84,607 86,070 92,643 97,772 59,300 56,694 56,305 56,341 60,267 62,207 7-31-73 1-31-74 7-31-74 1-31-75 7-31-75 1-31-76 100 100 100 100 100 100 72 113 140 172 221 327 401 59,187 56,554 56,133 56,120 59,940 61,806 22,822 26,816 27,759 28,907 31,682 34,854 72 28 32 33 34 34 36 1,439 13,383 1,433 12,605 I, 191 9,715 1,304 7,871 1,394 6,895 1,728 7,502 374 466 543 822 143 213 334 638 482 485 231 253 209 184 212 226 Per cent of total 68 67 65 65 64 * * * * * * 68 67 65 65 63 * Less than O 5 per cent of total NOTE -Aggregate MSB deposit data are avat!able as I-day figures for the last day of each month The matunty dtstnbut1on of these deposits 1s reported four times a year, on the same day as the commercial bank STSD, m the FDIC Quarterly Survey of Most Common https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 2 2 1 2 2 2 16 15 11 9 7 8 7 6 6 6 6 6 2 9 14 17 19 20 * * * 1 1 * * * * ** * Rates of IPC Time and Savtngs Deposits m FDIC-Insured Mutual Savmgs Banks Details may not add to totals due to roundtng All data are m ongmal matunty Developing Money Substitutes 159 TABLE 10 Savmgs Deposits at FSLIC-Insured Savmgs and Loan Assoc1at1ons, 1973-76 Passbook savmgs Date Total Term savmgs Matunty Total NOW Other Total Total passbook and small term savings Size Uptol 1110212103½ year years years 1 I years 3½ 1 Small I Large M1lhons of dollars 9-30--73 3-31-74 9-30--74 3-31-75 9-30--75 3-31-76 207,997 228,842 231,721 249,491 270,133 294,912 99,667 104,504 102,763 109,399 116,819 124,557 9-30--73 3-31-74 9-30--74 3-31-75 9-30--75 3-31-76 100 100 100 100 100 100 48 46 44 44 43 42 0 4 19 44 72 98 99,667 104,500 102,744 119,356 116,747 124,459 108,330 124,339 128,957 140,092 153,315 164,091 48 46 44 44 43 42 52 54 56 56 57 56 58,856 66,672 59,999 53,867 56,800 54,276 34 254 22,072 18,408 17,443 20,613 38,388 6,088 13,405 30,954 17 110 55,577 46,146 9,132 22,100 19,596 21,672 20,325 25,281 105,671 120,904 125,218 134,752 148,024 158,502 2,659 3,435 3,740 5,340 5,290 5,589 205,338 225,408 227,980 244,151 264,844 283,059 3 6 13 19 21 16 4 10 9 9 8 9 51 53 54 54 55 54 I 2 2 2 2 2 99 99 98 98 98 96 Per cent of total •• • •• 28 29 26 21 21 18 16 10 8 7 8 13 1 These maturity breaks are those used by the FHLBB * Less than O 5 per cent of total NOTE -Aggregate days are reported as I-day figures for the last day of each month The maturity breakdown of savmgs capital 1s reported m the FHLBB Serm-Annual"'survey of Selected Interest/ D1v1dend Rates and Account Structure, for March and September of each year These data are reported as remammg maturity and no attempt was made to convert to ongmal maturity Details may not add to totals due to roundmg All data are m remammg matunty hkely to be used for transactions purposes Portfolio theory suggests that the hqmd1ty of these longer-maturity deposits makes them more hke secunues, and thus complementary to, rather than substitutes for, hqmd assets In order to evaluate movements m the monetary aggregates relative to economic act1v1ty, some consideration might be given to segregatmg longer-maturity deposits from those deposits that might be more readily usable for transact10ns purposes by the depositor small-denommatlon time deposits, wluch are subject to mterest ce1lmgs, and, therefore, rates on large-denommat10n time deposits tend to be sticky, so that such deposits are sens1t1ve to market rates of mterest 18 To the extent that the time component of M 2 mcludes la1ge-denommat1011 time deposits, M 2 and MJ a1e more heterogeneous measures As currently defined, the time deposit component M 2 consists of total time and savmgs deposits at all commercial banks less large negotiable CD's at weekly reportmg banks Tlus defimt1011 was ongmally adopted 111 large part because no data on large-denommatlon time deposits other than CD's were readily available In add1t1on 1t was felt that negotiable CD's at large banks accounted for a s1gmficant share of the volume of, and the volat1hty m, total large time deposits However, the d1stmct1on between negotiable and nonnegotiable deposits may be largely techmeal smce 1t 1s reported that many banks permit convers10n from one form to the other Moreover, the exclus10n of such deposits from Large-denomination time deposits In addition to the mclus1on of both shortand relatively long-maturity time deposits m the other time components of M 2 and M 3 , these aggregates mclude varymg amounts of time deposits m denommat10ns of $100,000 or more that further distort their conceptual meamng Changes m large-denommat10n time deposits often reflect changmg bank aggressiveness m seekmg funds Smee they are exempt from the Regulation Q ce1lmg, these deposits have offermg rates that vary with market rates Also, a bank's aggressiveness m seekmg funds through large-denommat10n time deposits will depend on its deposit flows, loan demand, relative rate on other sources of funds, and so forth These deposits often behave differently from https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 18 Thrift institutions tend to have relatively ins1gmficant levels of large denomination time deposits Thus the large time deposits in M 2 and Ma come mainly from large negotiable and nonnegotiable time deposits issued by nonweekly reporting banks and nonnegotiable deposits issued by weekly reporting banks 160 lmprovmg the Monetary Aggregates Staff Papers M 2 and M 3 merely because they are habihties of large rather than small banks is somewhat arbitrary The growth of large-denommat10n time deposits at all banks-regardless of whether they are m negotiable or nonnegotiable form-is different from that of small-denommation time deposits For example, m some periods movements m the other time component of M 2 were not consistent with observed patterns of thnft deposit flows This suggests that either the demand for small-denommation accounts at thnft msututions is different from that for similar accounts at banks, or that changes m the nonexcluded large-denommauon time deposits have been obscurmg the movements m small-denommat10n time deposits As noted below, the evidence supports the second hypothesis While the mclus10n of large-denommation time deposits m the other time and savmgs deposit data has been of concern for some time, evaluation of the quantitative sigmficance of such deposits has been hampered by the sparseness of the data Although the data now available are still extremely limited and can be analyzed only under very gross assumptions, they do shed some hght on the magmtude of the problem Begmnmg m June 1973, when margmal reserve reqmrements were imposed on all large time deposits above a $10 million base, the approximately 900 member banks affected by these reqmrements began to report the total amount of their time deposits m denommations of $100,000 or more on a daily-average basis 19 The volume of these deposits reported was surpnsmgly large At large weekly reportmg banks the volume of negotiable CD's ranged between $58 billion and $67 billion m the latter half of 1973 Dunng that same penod other large time deposits at all member banks ranged from $30 billion to $40 billion Recogmtion of the existence of a sigmficant 10 Data were also gathered on large denommatlon time deposits at all member banks as part of the special monthly survey conducted from October 1973 to June 1974 to momtor the growth m 4-year certificates at commercial banks https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis amount of large-denommat10n time deposits that were not counted as CD's led the Federal Reserve to collect data on total large-denomination time deposits from its large weekly reportmg bank sample begmnmg m January 1975 These data permit comparison with data on large-denommat10n time deposits dVailable from special supplements to the June and December call reports smce December 1973 20 With these data as a base, Table 11 shows some very rough estimates of both other time and savmgs deposits and M 2, with estimates of total large-denommation time deposits-not JUSt negotiable CD's at weekly reportmg banks -removed for each month of 1975 Also shown are other time deposits and M 2 as currently defined A comparison of the adjusted seneskeepmg m mmd that the data are only rough estimates-with the senes as currently defined suggests that movements m large-denommation time deposits sigmficantly mfluence M 2 21 As 20 The December 31, 1975, call report was taken on a Wednesday, allowmg for a direct comparison with \\eekly reportmg bank data, which are always for Wednesdays, the last day of the bank statement week A comparison of large time deposits reported on the <-all and on the weekly report turned up many reportmg errors on both reports This suggests that problems still exist with the data on large time deposits and that any estimates based on either the weekly 1eportmg bank sample or the call report should be recogmzed as crude Unfortunately, smce the supple ment to the call report on large denommallon time deposits was mtroduced m December 1973, no June or December call date other than December 1975 was on a Wednesday This makes 1t more difficult to detect 1eporting errors 21 The ad Justed senes m Tables 11 and 12 were con structed by subtractmg total large denommatlon time deposits from total time deposits, both not seasonally ad1usted, and then applying the seasonal factors for other time and savmgs deposits at all commercial banks The series on large time deposits 1s based on data from the call report, the survey of time and savmgs deposits, the report of deposits when margmal reserve reqmrements were imposed, and the weekly re porting data senes It should be recogmzed that the crude method of seasonal adjustment used m con structing the adjusted other time and savings deposits and the ad1usted M2 senes bestows on them certam characteristics, which are difficult to quantify How ever, m the absence of suffiaent data to derive seasonal factors for these adJusted senes, a Judgment was made that 1t was better to use these data, constructed by the best method ava1lable, than to use data not seasonally adjusted The point I wish to illustrate is that movements of M2 as currently defined and of M 2 less all Developing Money Substitutes 161 TABLE 11 Other Time and Savmgs Deposits, M2, and Large-Denommatmn Time Deposits at Weekly Reportmg Banks, 1975 Othert1me and savmgsl Month Other lime and savtngs, adjusted' Large denommauon time M2• M2, • adjusted Total Seasonally adJusted annual growth rates, monthly averages (per cent) (I) Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec 12 13 9 JO 15 18 14 6 6 10 11 7 0 0 6 3 I 4 0 4 0 4 9 9 (2) 14 26 13 21 21 29 24 8 2 11 18 13 0 7 3 I 7 I I 9 9 I 7 7 (3) 4 7 9 6 13 16 9 5 4 5 10 3 I 2 3 I 4 5 5 7 2 I 8 I Negotiable Other I I Ra 110 of other to total Levels, last Wednesday of the month, not seasonally adjusted (b1Ihons of dollars) (4) 3 12 13 II 16 21 3 7 2 5 13 5 I (5) 8 8 I 7 4 5 5 I 3 2 8 5 128 125 124 120 119 116 114 114 117 116 116 116 (7) (6) 6 0 8 3 6 3 8 6 4 7 I 5 91 87 89 84 83 82 81 81 84 83 83 82 3 9 0 2 5 0 2 2 7 3 3 8 37 37 35 36 36 34 33 33 33 33 32 33 (8) 4 I 8 I 1 3 6 3 2 4 8 7 29 30 29 30 30 29 29 29 28 29 28 29 1 Total time and savmgs deposits less large denommat1on negotiable time deposits at weekly reportmg banks 2 Total lime and saVIngs deposits less all large denommatwn time deposits 3 M1 plus other lime and savmgs deposits • M1 plus adjusted other lime and savmgs deposits can be seen in column 8, the behav10r of l.11ge-denominat1on time deposits other than negotiable CD's at weekly reporting banks appears to be similar to that of CD's the rat10 of nonnegotiable to total large-denomination time deposits is fairly constant-that is, the two senes move together In order to examine further the relat10nshi p between the components of total large time deposits and total time deposits at the weekly reporting banks, weekly data available since January 1975 were examined The simple correlat10n coefficient between negotiable CD's and all other large-denominat10n time deposits was calculated to be O 84 in levels (0 24 in first differences) More important, the correlat10n between other large-denominat10n time deposits and small-denommatlon time and ~avings deposits was found to be negauve, -0 90 m levels and -0 68 in first differences These conelat10ns suggest that at the weekly reporting banks the behav10r of negotiable CD's and that of all other large-denommat10n time deposits are similar, and that largeclenominat10n time deposits other than nelarge denomination time deposits are different To the extent that the seasonal factors for other time and sav mgs deposits as currently defined were used to adJust "ad1usted" other time and savmgs deposits, any bias 1m parted to the data because of the seasonal ad1ustment should be toward greater, rather than le~~. s1milanty m behav10r between the senes https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis TABLE 12 Growth Rates of Other Time and Savmgs Deposits and M 2 before and after AdJustment to Exclude LargeDenommatlon Time Deposits Quarterly averages, seasonally ad1usted annual rates Quarter 1973-Q4 1974-Ql Q2 Q3 Q4 1975-QI Q2 Q3 Q4 Other time and savmgs 1 12 13 9 8 8 9 12 12 9 5 0 I 3 4 9 5 6 I Other tune and savmgs, ad1usted 2 2 IO 3 I 5 13 22 19 II 9 3 I 7 6 0 3 4 I MEMO M,' 8 9 7 6 6 5 10 10 6 9 6 5 4 4 6 2 I I Ma• ~d1usted 4 8 4 3 4 6 14 13 6 I 0 4 I 7 5 4 0 8 Nonbank time and savmgs 6 7 7 5 4 6 10 16 18 14 6 7 I 3 7 6 6 3 2 1 Total time deposits less large denommatlon negotiable CD's at weekly reportmg banks 2 Total time deposits less estimated total large denommat1on time deposits 3 M, plus other time and savmgs deposits as defined m note I • M1 plus adjusted other time and savmgs as defined m note I r. Deposits '\t S&L's MSB's and CU's got1able CD'~ behave inversely to smalldenominat10n time deposits Tlus supports the hypothesis that banks manage all large-denominat10n time deposits, not JUSt negotiable CD's Fm.illy, Table 12 compares M 2 and other time deposits with correspondmg adjusted ~e11es that exclude all large-denominat10n time deposits on a quarterly-average basis from 1973 Q4 to 1975 Q1 22 Fm comparison pm22 Sec note 21, which dl\Lllbcs the data and thl. mcthocl med to estimate large ttmc dcpo~Its The dat,t ~hould be viewed as rough estimates 1athcr than actual mlasuted stocks 162 poses, the nonbank thrift deposit component of Ma is also shown Even on a quarterlyaverage basis, removal of large-denommation time deposits from M 2 results m an adjusted ~eries that is qmte different from M 2 as currently defined For example, during each of the last three quarters of 1974, the adjusted M 2 series grew much more slowly than M 2 as currently defined and then grew more qmckly through all of 1975 This difference is understandable, of course, smce the series on other time and savmgs deposits as currently defined is qmte different from the series on other time and savmgs with total large time deposits removed The correlat10n between M 2 and "adJUSted M/' is only O55 m levels, about the same as the correlat10n (0 49) between other time and savmgs as now defined and nonbank time and savmgs More important, the correlation between the adjusted series on other ume and savmgs deposits and the series on nonbank time and savmgs deposits is O92 Inasmuch as the components of these deposit series are characteristically similar, it is not surprismg that their movements are highly correlated Possible recomposition of the monetary aggregates The regulatory changes and financial mnovat10ns discussed 1n the precedmg sect10ns suggest that the characteristics of the components of the monetary aggregates, as currently defined, have been altered greatly m the past few years to become more heterogeneous The pace of change has been rapid, and the distmction between time deposits and savmgs deposits is more clearly defined now than prior to 1973, conceptually, demand and savmgs deposits are more similar The components of time deposits have become more distmct m themselves as longer-maturity, small-denommat10n deposits with higher mterest rate ceilmgs have been created and as banks have mcreased their use of all large-denommatlon time deposits-not JUSt negotiable CD's-as a flexible source of funds Because recent changes either have already affected the behavior of the monetary aggre- https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis Improvmg the Monetary Aggregates Staff Papers gates or are expected to do so, 1t is appropriate to consider how current defimtions might be altered to reflect evolvmg developments Two defimtional changes are suggested by the prev10us discuss10n First, the development of savmgs-based transfer systems and the hqmdity of savmgs deposits relative to time deposits other than negotiable CD's suggest that some combmation of M 1 and savmgs deposits at banks and thrift mstitutions might be considered to represent transactional balances Second, the changmg maturity structure of small-denommauon time deposits and the behavior of large-denommat10n time deposits suggest that the defimtion of other time deposits, excludmg savmgs, ought to be reconsidered Such a defimtional change would affect M 2 and Ma and the higher-numbered M's but would have no effect on M 1 The possible permutat10ns and combmations stemmmg from these two types of defimtional changes are fairly large Therefore, the remamder of this paper focuses not on every possible type of monetary aggregate that might be considered but more broadly on the two ma1or categories of change At present the extent to which regulatory changes and mnovations relatmg to savmgs deposits have affected, or will affect, the monetary aggr_egates is unclear Money transfers will m the future mvolve both demand and savmgs deposits, and so long as the prohibition of mterest payments on demand deposits remams, easily faohtated transfers from savmgs will make those deposits a highly attractive transactions asset Currently, savmgs deposits have a small but growmg role m the payments mechamsm, with a large potential for further growth Historically, the motives for holdmg M 1 balances and savmgs deposits have been different, and therefore movements m these two variables have been different Although both are directly related to mcome and mversely related to market mterest rates, flows of funds mto and out of savmgs deposits have been determmed primarily by the relationship between the ceilmg on the savmgs deposit mterest rate-the "own" rate-and short-term market Developing Money Substitutes rates-competmg rates In addit10n, until recently the transact10ns costs for transferrmg funds between savmgs deposits and M 1 -type balances have been s1gmficant, often mvolvmg such mconvemences as personal presentation of a passbook at the depositary mstltution This fact suggests that, although statistical ,malysis of historical movements m an aggregate that combmes M 1 and savmgs deposits may provide some msight as to the appropriateness of such a defimtion at this time, the dec1S1on to mclude savmgs should probably rest on evidence that mdicates the ongomg substitution of savmgs for demand deposits m the payments mechamsm 23 Recent changes suggest that substitution is takmg place m the payments mechamsm and that the conceptual differences between savmgs deposits and M 1 balances have m fact already been reduced NOW accounts, which are available m New England, are essentially savmgs deposits that can be transferred to a third party by written draft Share draft accounts at credit umons are similar to NOW's, although there are legal differences between them Both types of drafts are legal payment mstruments, as are commercial bank checks However, such accounts allow the depositor to earn mterest on the funds subject to draft until payment 1s made, whereas demand depos1 ts earn no mterest As mentioned earlier, several types of savmgs-transfer systems, md udmg telephomc transfers from savmgs to demand deposits, third-party nonnegotiable transfers directly from savmgs, and pomt-ofsale transfers from savmgs, have been developed The first type appears to have gamed widespread acceptance among banks, S&L's, and MSB's, although the actual volume of use of the transfer arrangements 1s difficult to measure At some pomt, consideration must be given to creatmg a new monetary aggregate by mergmg mto M 1 those deposits that are close substitutes for M 1 balances Current mformation suggests that NOW accounts, share draft 23 Appendix 2 presents the results of some recent staff analysis of M1 plus savmgs usmg h1stoncal data https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 163 accounts at credit umons, and checkmg accounts available at State-chartered thrift mstitutions would be the first categories of M 1 substitutes that might be considered exphc1tly as transactions balances Such balances can be qmte easily identified and measured, so foldmg them mto current M 1 should present only mmor problems The next category of deposits thc1t can be considered as a substitute for M 1 is savmgs deposits at banks and thrift mst1tutions from which transfers can be 1mt1ated As savmgs-based transfer systems contmue to develop and spread, the subst1tut10n of savmgs deposits for demand deposits can be expected to take place and thm what may evolve 1s one or more monetary aggregates composed of currency, demand deposits, saHng~ deposits c1gamst which some form of negotuble draft can be drawn, and all other savmgs that can directly or md1rectly be utilized f01 makmg payments Just when such defimt1onal changes ought to be made 1s unclear The proportion of savmgs deposits used for transactional purposes at this time 1s small but growmg, and 1t 1s hkely that some s~vmgs will always be used for the trad1t10nal reasons-that is, as a temporary abode of purchasmg power Unless some method can be devised to distmgmsh clearly the t1ansact10nal from the nontransact10nal components of ~avmgs deposits, 1t would be better to mclude all savmgs m a new Mi-type aggregate, rather than ignore the mcreasmg use of such deposits Savmgs deposits that can be readily used to make paymentsthat 1s, for transactions purposes-should be mcluded m the defimuon of M 1 But not all savmgs deposits are transact10nal m nature The suggested mclusion of all savmgs deposits raises the question of whether the traditional d1stmction between deposits at commercial banks and at thrift mstitut1ons should be mamtamed or dropped The necessity for such a d1stmct1on seems to be fadmg as the thrift institutions contmue to assert their presence m the payments mechamsm Their expanded role has been recogmzed by the Federal Reserve's mterim access pohcy to System ACH's (adopted m January 1976), which mdicated lmprovmg the Monetary Aggregates· Staff Papers 164 raises certam problems that have been noted earlier For example, what is the appropriate maturity break for separatmg security-type, small-denommation deposits from other small time deposits? From a conceptual standpomt, 2½ years is not much shorter than 4 years, however, it is sigmficantly less than 6 years The ch01ce of the breakmg pomt could be dictated by data availability Prior to July 1973 all small-denommatlon time deposits with miual maturities of 2 years or more were subject to the same mterest rate ceilmg It is unlikely that a large share of deposits subject to that ceilmg had maturities of 4 years or more Moreover, data collected after the mtroduct10n of 4-year certificates m July 1973 are reliable and so, on the basis of data considerations, the most reasonable maturity break would be deposits with an miual maturity of less than 4 years compared with those with an miual maturity of 4 years or more With large-denommauon deposits, most of the problems are related to data availability and comparability through time Data available before 1973 are scanty and may not permit accurate estimat10n of total large time deposits Thereafter, data are better but still allow only crude estimates of total large time deposits In order to see how much the exclus10n of longer-maturity small time deposits and all large time deposits affects the profile of the growth of M,, available data were used to create new aggregates, as shown m Table 13 The that ACH transfers could "origmate from any account havmg third-party payment powers" without distmgmshmg between commercial banks and thrift mst1tut10ns The discussion m the section on recent regulatory changes suggested that the "other time" deposit component of M 2 suffers from at least two conceptual problems The first problem is that longer-maturity small-denomination time deposits are relatively less hqmd compared with those with the shorter maturities, yet it is the longer-maturity deposits that have paid the highest mterest rates and, therefore, have attracted relatively more funds than the shorter deposits The 4- and 6-year deposits are more hke securit1es than deposits and, therefore, can be expected to behave differently from the other maturities The second problem stems from the fact that other time deposits contam large time deposits other than negotiable CD's at weekly reportmg banks, and accordmg to recently obtamed evidence, these deposits behave hke negotiable CD'sthat is, banks manage such deposit habihties by seekmg to mcrease them when funds are needed and allowmg them to run off when funds are not needed In both cases, it is not unreasonable to categorize both types of time deposits conceptually as bemg different from 5mall-denommat1on time deposits with short matuntles that are, in many portfolios, "temporary abodes for purchasmg power " Redefinmg Mi along these conceptual Imes TABLE 13. Companson of M2, M~, and M?, Not Seasonally AdJusted, 1973-76 I Levels (b!lhons of dollars) Date 7 /31/73 1/31/74 7 /31/74 1/31/75 7 /31/75 1/31/76 M, 551 581 597 619 647 674 I 1 1 8 5 8 1 Mi 496 502 606 511 537 550 I 7 2 9 1 8 3 M'' 486 489 491 492 518 529 8 0 2 7 3 8 I Annuahzed percentage changes M, IO 5 7 9 8 9 7 3 1 I I Mi 2 I I 10 4 2 9 3 9 6 I M~' 9 9 6 10 4 4 4 NoTE -When possible, data are for the date shown If they are unava!lable, data for the closest day were used The following defimt1ons are used M, = Mi plus total time and savings deposits less negotiable large denomination CD's at weekly reporting banks (current M,) M; = M2 less all large denommat1on time deposits at all commerctal banks and small time deposits with maturities of 4 years or more M;' = M, less all large-denommatlon time deposits at all commercial banks and small time deposits with matunties of 2 ½ years or more https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis Developing Money Substitutes data are not seasonally adJusted and are smgleday estimates correspondmg to dates of the Survey of Time and Savmgs Deposits (STSD) 24 For most of the time penod shown m Table 13, the growth rates of the newly defined M 2type aggregates were s1gmficantly different from those for Mi a~ It 1s currently defined Moreover, Mi defined to exclude large time d.nd longer-matunty small time deposits exlub1ted substant1d.lly lower growth rates m each penod except for July 1975, when mflows to l4 Some <latJ. are for the Wednesday closest to thL <late of the STSD https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis 165 other time and savmgs deposits were pnmanly m the form of savmgs deposits The apparent differences m growth among M 2 , M;, and Mr are stnkmg, and the causes for the differences can easily be traced Table 13 suggests that growth m M 2 as currently defined may give m1sleadmg 1mpress1ons of changes m the mix of the public's holdmgs of deposits that serve as a temporary abode of purchasmg power More important, 1t 1s clear from the table that the behavior of the time deposit components excluded from the M; and Mr vanables IS s1gmficantly different from that of the remammg components 166 Appendix 1: Third-Party Payment Powers of State-Chartered Thrift Institutions The regulatory changes that have expanded the third-party payment powers of Federally chartered thrift msutut10ns do not, m general, automaucally apply to similar msutuuons that have been chartered under the laws of the States m which they are located A number of States have bankmg laws that provide for parity m payments powers, and consequently, m those States all thrift msutuuons generally can now offer authorized telephonic transfer and preauthorized third-party nonnegouable transfer services to their customers When parity does not exist, some mstituuons have broader payment powers than Federally chartered thrift mst1tuuons Bankmg laws m many States are not specific about payment powers, and thus the msutuuons depend on case-by-case rulmgs by the State bankmg authority In order to ascertam the status of State-chartered thrift mst1tut1ons m the payments mechanism, a special survey of State bankmg authorities was conducted on a State-by-State baS1S m June 1976 The results of that survey are summarized m Table A-1, which reports data on five types of payment powers checking accounts, NOW accounts, credit union share drafts, telephonic transfers, and preauthorized nonnegotiable transfer services The checkmg accounts are non-mterest bearmg and are md1stmgmshable from checkmg accounts at nonmember banks m terms of the payments mechanism clearmg process In some States these have existed for a long ume and remam today because of grandfather clauses m ex1stmg laws In other States the checkmg powers are fairly new, resultmg from efforts by State legislators to provide thrift mst1tut1ons m their States with powers similar to those https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis of commercial banks Interest-bearing accounts agamst wluch written drafts may be drawn are primarily m two forms-NOW accounts and credit umon share draft accounts ~ he former are available primarily m New England, although some thrift mstttuuons m Delaware apparently can offer accounts very much hke NOW's Many States permit their credit umons to offer share draft accounts A ma1onty of States have laws that permit thrift msutuuons to offer transfer services to owners of savmgs accounts Table A-1 shows two types of savmgs-based transfer services telephonic transfers from a ~avmgs account at a thnft mstituuon to a checkmg account at a commercial bank, and preauthorized nonnegouable transfers (b1ll-paymg services) In those States whose bankmg laws are silent about the power of thnft msutuuons to offer such services State bankmg authoriues have usually allowed such services upon request by thnft msutuuons w1thm their 1urisd1cuon The State bankmg authorities were also asked m the survey whether they expected State laws to be mtroduced or amended m the near future to allow State-chartered thrift msutuuons to offer add1t1onal third-party payment powers The predommant response was that State leg1slat1on would follow smt should Federal laws be modified to allow expanded payment powers for thrift msutuuons In States m which compeuuon among financial msutuuons for deposits appears to be strong, however, the State legislatures are hkely to consider the quest10ri of expanded payment powers m the near future Those States mclude New Jersey, Pennsylvania, M1ch1gan, W1sconsm, Mmnesota, Montana, and Nebraska Developing Money Substitutes 167 TABLE A-1. Third-Party Payment Powers of State-Chartered Thrift Institutions, June 1976 State Alabama Alaska Arizona Arkansas Cahfomta Colorado Connecticut Delaware Flonda Georgia Hawaii Idaho Ilhnots Indiana Iowa Kansas Kentucky Louisiana Mame Maryland Massachusetts Mtchtgan Mmnesota M1ss1ss1pp1 Mtssoun Montana Nebraska Nevada New Hampshire New Jersey New Mexico New York North Carohna North Dakota Ohto Oklahoma Oregon Pennsylvanta Rhode Island South Carohna South Dakota Tennessee Texas Utah Vermont Vtrgmta Washtngton West Vtrgmta Checking accounts MSB MSB, S&L MSB, S&L MSB, S&L MSB MSB, S&L MSB CU share drafts cu cu cu cu cu S&L MSB silent silent (,U MSB, S&L CU, MSB, S&L cu cu cu stlent cu Telephonic transfers Preauthortzed nonnegotiable transfers parity parity parity panty S&L silent silent MSB parity panty S&L S&L S&L parity parity anty ~ &L S&L CU silent stlent stlent silent MSB, 1-&L silent MSB, S&L CU, S&L CU, S&L stlent S&L MSB stlent parity silent MSB, S&L MSB MSB, S&L S&L MSB stlent MSB, S&L stlent MSB, S&L stlent silent MSB, S&L MSB, S&L W1scons1n Wyommg CU = credtt untons MSB = mutual savmgs banks S&L = savtngs and loan assoc1at1ons https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis NOW accounts cu cu cu cu cu cu cu cu silent cu cu stlent cu cu parity stlent MSB partly MSB, S&L S&L CU, S&L parity partly MSB, S&L MSB parity MSB, S&L S&L CU, S&L S&L cu stlent stlent silent panty CU, MSB CU, MSB, S&L silent silent partly silent partly MSB, S&L panty silent MSB, S&L parity partly silent MSB, S&L parity Panty = State-chartered mst1tut1ons have the same powers as Federally chartered mst1tut1ons Stlent = law does not say, pennttted tf approved by bankmg authonty 168 Appendix 2: Savings Deposits at Banks and Thrift Institutions as Transactions Balances For a number of reasons, savmgs deposits at commercial banks and thnft msutuuons-or more precisely, a growmg proportion of such depositshave come to be used as transactions balances rather than simply as repositories of mterest bearmg hqmd assets The secular uptrend of mterest rates has raised the opportunity cost of idle, non-mterestbearmg deposits, mducmg holders of such bal ances to seek out convement alternatives In add1uon, regulatory changes perm1ttmg telephonic transfers between savmgs deposits wherever held and demand deposits at commercial banks, and nonnegotiable transfers to third parties at both banks and thnft msututions, have facilitated the uuhzauon of savmgs deposits for such purposes The authonzation of savmgs deposits for profitmakmg enterprises has widened the scope of users of such accounts to mclude relatively more soph1st1cated depositors These developments suggest the possible need for the formulation of a broader transactions vanable than M 1 While M 2 , M 1 , and still more comprehensive aggregates can be studied for their 1mphcauons for the general hqmd1ty of the economy, they do not purport to be transactions balances An aggregate broader than M 1 but not so broad as M 2 (which mcludes time deposits) might be appropriate to reflect the changmg habits of the pubhc regardmg transactions balances Four such aggregates are exammed here demand deposits plus savmgs deposits at all commercial banks (DD+ SB), 1 M 1 plus savmgs deposits at all commercial banks (M1 + SB), demand deposits at all commercial banks plus savmgs deposits at banks and thnft msutuuons (DD + SB + ST),2 and M 1 NoTE -Paul Boltz prepared this appendix The comments of Raymond Lombra, John Paulus, and Steven Roberts were very helpful m the wr1tmg process 1 Though technically not broader than M , DD+ SB 1s 1 evaluated as a separate aggregate smce the developments m the payments mechanism toward mterest bearmg transactions balances may have had only a mmor mfluence on the demand for currency Excludmg currency serves to focus the results on the subst1tutab1hty between demand and savmgs deposits 2 Thrift mst1tut1ons mclude S8cL's, MSB's, and CU's https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis plus savmgs at banks and thnft msutuuons (M1 + SB+ ST) The prmc1pal ob1ecuve of the analysis 1s to compare the broader monetary aggregates with M 1 m tradmonal money demand equations to determme whether the addition of savmgs deposits to the money stock strengthens or weakens the mfluence of GNP (as a proxy for transactions) In add1uon, savmgs deposits themselves are regressed as the dependent variable m money demand equations m order to 1denufy what, 1f any, relauonsh1p exists among these variables This analysis 1s part of a complex issue that extends well beyond the demand for money A change m the defimt10n of M 1 to account for all deposits that can be used for transact10ns balances necessarily has 1mplicat10ns for the defimuons of Mi and of the broader aggregates as well In add1t10n, any redefimuons of the monetary aggre gates along structural Imes may complicate the conduct of monetary policy 1f the new aggregates are less subject to the control of the monetary authority than their predecessors The lmkages be tween real economic activity and the newly defined aggregates may still be evolvmg and may be difficult to specify, further comphcatmg the determmauon of monetary pohcy The basic structural form of the estimated money demand equations hypothesizes the monetary aggregate to be a function of mterest rates, GNP, and the aggregate itself lagged one penod 3 The ordinary least squares regressions were run m log form and m real terms, the deflator bemg the consumer pnce mdex The Cochrane-Orcutt techmque was used to ad1ust for senal correlation The results of the regress10ns are summarized m Tables A-2 and A-3 Savmgs deposits at banks (SB) can be shown to bear a s1gmficant relation to GNP durmg the 9year penod from 1966 Q3 to 1975 Q2 (Equation I m Table A-2) The penod of observation was ~hortened to the most recent 5 years to evaluate 1 The source of !he data was the data files of the FRBMIT-Penn quarterly econometric model Developing Money Substitutes 169 TABLE A-2 Coefficients of Variables m Demand-for-Money-Type Equations for Savmgs Deposlts 1 Independent vanables Equation I 2 3 Intercept - 119 (- 52) 376 ( 42) 046 ( 05) I Lagged dependent vanable 863 (20 06) 971 (4 68) 795 (5 27) I Treasury bill rate - 075 (-8 44) (-3 (-3 074 80) 059 87) Regression sta t1st1cs Rate on savings I deposits I 035 (1 84) 05J_ (I 19) GNP 119 (2 79) - 027 (- 112) 146 ( 75) Standard error I R.2 0086 972 0089 960 0090 959 1 The dependent vanable 1s savmgs The period 1s 1966 Q3 to 1975 Q2 for Equation 1, and 1970 Q3 to 1975 Q2 for Equations 2 and 3 The numbers m parentheses are I stausucs For a one tailed test at the 95 per cent confidence level, the critical value of the I-statistic 1s I 76 for the shorter per10d (1970 Q3 to 1975 Q2) and I 70 for the longer period (1966 Q3 to 1975 Q2) whether the relationship between savmgs deposits and GNP has strengthened m recent years and to evaluate the changmg effects of mterest rates, which reached unprecedented levels m recent years It was found that the relat1onsh1p between savmgs deposits at commercial banks and GNP4 deteriorated mto ms1gmficance m the most recent period (Equat1ons 2 and 3 of Table A-2) It appears from these equations that the trend rate of growth of such deposits and market mterest rates were the prmc1pal determmants of savmgs deposit movements m recent periods The "own" rate on savmgs deposits 1s itself an ms1gmficant explanator of movements of savmgs accounts m Equation 2, but this may be rat1onahzed by the lack of variation (because of mterest rate ceilmgs) m the savmgs deposit rate after 1970 Removal of the savmgs deposit rate m Equation 3 only slightly improves the performance of GNP m the equation, which m any event remams ms1gmficant Equat10ns m Table A-3 show M 1 , DD+ SB, DD+ SB+ ST, M 1 + SB, and M 1 +SB+ ST run m similar money demand equations for the period 1966 Q3 to 1975 Q2 and 1970 Q3 to 1975 Q2 M 2 and Mg are also shown for reference to still broader aggregates The equations estimated over the shorter period are labeled "a" and those for the longer period are denoted "b " The results m Table A-3 md1cate that the rate on savmgs deposits 1s an ms1gmficant determinant of the broader aggregates DD + SB and M 1 + SB, though a s1gmficant explanator of DD and M 1 The hkely reason 1s that the rate on savmgs deposits 1s an "own" rate for SB but a competmg rate for M 1 and DD These opposite mfluences cancel each other when the savmgs deposit rate 1s used to explam DD + SB or M 1 + SB The equations also show that although SB Itself 1s not s1gmficantly explamed by GNP over five recent years, the relationship of DD and M 1 to GNP 1s not s1gmficantly weakened by the add1t1on of SA The coefficients of GNP are s1gmficant m a one tailed test at d 95 per cent level of confidence m all the equations with DD, DD + SB, M 1 , and M 1 + SB m Table A-3 In deed, the relationship of GNP 1s more s1gmficant, though only margmally, to DD + SB than to DD alone m both periods shown (Equations 4a, 4b, 5a, and 5b) The add1t1on of all savmgs deposits at banks and thrift mst1tut1ons to DD and M 1 creates broader aggregates that bear a stat1st1cal relationship to the mdependent variables used m the regressions, a relat1onsl11p that 1s s1m1lar to M 1 or DD alone The bank rate paid on savmgs accounts 5 remams s1gmficant for both periods shown for DD+ SB+ ST and M 1 + SB + ST Also, GNP 1s a highly s1gmficant explanator of the broader aggregates Indeed, the s1gmficance of GNP as an mdependent variable 1s strengthened by the addition of savmgs deposits to DD, and the relationship between GNP and M 1 1s about the same Comparmg these aggregates to M 2 and Mg shows that DD plus savmgs deposits and M 1 plus savmgs deposits have a more consistent relationship to GNP than M 2 or M 3 • The ch01ce of GNP as the appropriate scale variable IS open to questlon, and personal mcome or some other com prehens1ve flow variable of the economy could arguably be substituted for 1t m these equations However, smce m fluencmg GNP 1s an objective of monetary policy, It was used as the scale variable throughout https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis If at present there exists a transactional component m savmgs deposits, Its behavior 1s apparently swamped by the movements of the level of savmgs deposit~ mduced by changes m mterest • A series on the average rate paid by thrift mstltutlons for savmgs deposits (excludmg time deposits) was not avail able for testmg lmprovmg the Monetary Aggregates· Staff Papers 170 TABLE A-3. Coefficients of Variables m Demand-for-Money Equations for Six Concepts of Money 1 Independent vanab\es Equation' Defimt1on of money 4a DD 4b DD Sa DD+ SB Sb DD+ SB 6a M, 6b M, 7a M,+SB 7b M,+sB Sa M, Sb M, 9a M, 9b M, - Intercept I Money vanablc lagged I Treasury bill rate I Regression sta t1st1cs Rate on savm11s deposits I GNP Standard erro1 I R• - 223 (- 47) 378 (I 66) 830 (6 90) 790 (8 46) (-1 (-2 031 83) 022 53) (-1 (-2 059 62) 072 90) 179 0078 960 125 (2 07) 0071 956 - 325 (- 08) 269 (I 38) 647 (3 84) 835 (13 80) (-2 (-6 040 62) 041 84) (-1 (-1 060 53) 026 58) 314 (2 lO)l 112 (2 67) 0070 964 0063 969 - 062 (- 13) 505 (2 23) 747 (5 12) 681 (6 JS) (-1 (-2 028 81) 019 63) (-1 (-3 055 74) 068 35) 226 (2 30) 198 (2 86) 101 ( 25) 310 (1 57) 622 (3 25) 810 (11 65) (-2 (-6 037 58) 039 67) (-1 (-1 051 42) 025 60) 322 (2 04) 130 (2 75) 722 ( 76) I 170 (2 25) 844 (6 13) 751 (8 31) (-3 ( -6 037 69) 044 81) - 003 (- 49) 009 ( 65) - 045 (- 07) 211 ( 59) I 029 (8 54) 910 (11 17) (-3 (-6 038 17) 046 40) - 017 (- 87) 002 ( 11) (I 98) 0064 960 0057 971 0064 965 0056 974 197 0047 990 305 (2 74) 0050 996 (I 40) - 034 (- 21) 0056 992 156 0054 997 (I 32) • The numbers m parentheses are I stattst1cs The esttmatton pe11od 1s 1970 Q3 to 1975 Q2 for cquJt1ons 11belcd "•" and 1966 Q3 to 1974 Q2 fm cqu1t1ons labeled "b" 2 rates Thus, aggregate savmgs deposits alone ,ire not as yet transaction.ti m character to a discernible degree, nontransacttonal savmgs deposits apparently still dommate movements m the senes Moreover, It 1s not possible to estimate with prec1s10n the mm1mum proportion of savmgs that must become transactional m character before bemg recogmzed m trad1t1onal money demand analysis If savmgs deposit growth 1s whipsawed m commg penods by d1smtermedtat1on followed by large mflows, then the transactional component of savmgs will be largely obscured On the other hand, 1f nontransactlonal savmgs accounts follow a steady path of growth, a relatively small transactional component-say, IO to 20 per cent of savmgs-may be adequate to be perceived m many demand equations The analysts also suggests that a broader aggregate than M 1 constructed only from deposits at commercial banks may not adequately summarize the available transactional hqmdtty m the economy DD plus bank savmgs deposits and M 1 plus bank savmgs deposits did not have a s1gmficantly weaker relattonshtp to GNP than did DD or M 1 alone, but the mterest rate payable on savmgs deposits was predictably found to be pos1uvely related to SB but negatively to M 1 and DD The contrary mfluences render this rate an ms1gmficant explanator of DD+ SB or M 1 + SB as 1t affects https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis the parts of the aggreg,tte differently Thus, an important rate m an M 1 equ,ttlon ceases to be ~1gmficant m an equ.tuon relatmg DD+ SB or M 1 + SB to other mterest rates and GNP The elasticity of demand with respect to this savmgs deposit rate could be very !ugh when market rates are near ce1hng rates The hqmdity of thnft savmgs deposits 1s unquestionably comparable to that of bank savmgs, and the 1usuficatton for hm1tmg an M 1 -type trans actions aggregate to bank deposits 1s conceptually weak when bank savmgs deposits are mtroduced Moreover, the mclus10n of all savmgs deposits, rather than bank savmgs deposits alone, results m an aggregate with s1gmficant and more consistent relauonslups to the bank rate on savmgs deposits and GNP The hkely explanation for the rate's remammg s1gmficance ts that It affects the M 1 and '>T components the same way-negattvely-overcommg the opposite mfluence on SB The strength and consistency of the relat10n of GNP to the movements of these aggregates are comparable to those of M 1 , and m recent pertods better than those of M 2 , though neither DD plus all savmgs nor M 1 plus all savmgs clearly dommates DD or M 1 alone The results are, however, suggestive of the need for a contmumg exammatton of the conceptual and empmcal Justtficauons for the present defimuons of the monetary aggregates https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis https://fraser.stlouisfed.org Federal Reserve Bank of St. Louis