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SOME FACTORS AFFECTING SHORT-RUN GROWTH RATES OF THE MONEY SUPPLY Alfred Broaddus I. introduction Public interest in the monthly and weekly movements of the money supply’ has intensified since the early 1970’s. One manifestation of this interest is the extensive coverage of week-to-week and monthto-month changes in the money supply in the financial press. A second indication is the intense scrutiny of each new weekly or monthly money supply statistic by financial market participants. Indeed, one of the major current rituals in the markets is played out late every Thursday afternoon as investors across the nation hover around news wire machines awaiting the release of the latest weekly money supply figures. The increased attentidn to short-run money supply movements dates back to 1970 when the Federal Open Market Committee (FOMC), the Federal Reserve’s principal monetary policymaking body, began to place greater weight on achieving specific longerrun growth rates for particular monetary aggregates.” Under the current strategy of monetary policy,3 the FOMC periodically specifies desired longer-run growth rates (extending roughly a year ahead) for These growth objeccertain monetary aggregates. tives are publicly announced in quarterly testimony before one of the Congressional banking committees. At its monthly meetings the FOMC then reviews the state of the economy and compares the actual growth of the aggregates with their desired long-run paths. ‘There are several concepts of the money supply. and statistical series corresponding to each of these “monetary aggregates” are published regularly in the Federcrl Reserve Bulletin. This article deals exclusively with the short-run behavior of MI, the most narrowly inclusive aggregate, which is comprised of (1) currency outside the Treasury, Federal Reserve Banks, and vaults of commercial banks; (2) demand deposits at commercial banks other than domestic interbank and U. S. Government deposits. less cash items in process of collection and Federal Reserve float; and (3) MI is the foreign demand balances at Federal Reserve Banks. aggregate most closely watched by financial market participants and the general public. Also, much of the short-run variability of the more broadly defined aggregates (all of which include i%) is due to the variability of ML *This change in emphasis is evident in the evolving language of the FOMC’s directives to the Trading Desk at the Federal Reserve Bank of New York. Prior to 1970, the directives generally instructed the Desk to seek a desired condition in the money markets as indexed by interest rates or free reserves. Since 1970, in contrast, most directives have instructed the Desk to foster monw market and reserve supply conditions consistent with more rapid, slower, or unchanged growth of the monetary aggregates. *See Lomhra and Torte C41 for a current strategy of monetary policy. 2 detailed description ECONOMIC of the and Timothy Q. Cook Based, on this review the FOMC specifies short-run “tolerance ranges” for the growth rates of the aggregates over the two-month period covering the current and following months. The aim in setting these tolerance ranges is to define the near-term growth rates most likely to be consistent with achieving the existing long-run growth objectives. Consistency in this context, however, does not necessarily imply The short-run ranges can and often do equality. deviate numerically from the long-run objective either because the FOhilC is attempting to offset some unintended deviation in earlier months or because some temporary but foreseeable factor is espetted to affect short-run growth. In any event, once the short-run tolerance ranges are set, the FOhlC specifies a Federal funds rate range (normally from 50 to 100 basis points in width) believed to be consistent with short-run monetary growth within the bounds of the tolerance In this tactical framework, an emerging ranges. deviation of the actual two-month growth rates from the specified tolerance ranges might lead the Federal Reserve to alter the Federal funds rate (by increasing or decreasing the supply of nonborrowed reserves to member banks) in order to hold the growth rates Finally-a point of within the tolerance ranges. considerable importance-both the long-run monetary growth objectives and the two-month tolerance ranges are expressed in terms of seasonally adjusted annual rates of growth. It should be evident from this description of the Federal Reserve’s operating strategy that despite the longer-run time. horizon in which basic monetary growth goals are cast, the procedure by its nature tends to focus day-to-day attention on short-run monetary movements. First, from the standpoint of the Federal Reserve, the key tactical operating specification is the two-month tolerance range. Setting an appropriate range requires close attention to the numerous factors affecting current weekly and monthly growth rates. Further, incoming weekly and monthly data must be continuously tracked and evaluated against the criteria established by the toIerante ranges. Second, the procedure naturally stimu- REVIEW, NOVEMBER/DECEMBER 1977 lntes financial market interest in the short-run behavior of the aggregates. Given this procedure, these nlovements strongly influence market expectations regarding the likelihood that the Federal Reserve \vill seek a change in the Feder;~l funds rate that will in turn influence tlie lx-ices and yields of other financial instruments. ;is a I-esult. considerable resources \vitliin the markets are no\v devoted to “watching” hot11 the Federal Resell-e 2nd the money supply. Tlie major difficult). that arises in this institutional fr:liiie\vork is that short-run monetary data, even after seasonal adjustment. xe highly volatile. It is therefore difficult to project short-run movements, even for the immediate future, and equally difficult to evaluate incoming data. Cliart 1 illustrates this volatility. It conilx~res tlie originally published or “l)reliminar~“~ seasonally adjusted one- and twomonth ;\I1 grokvth rates (at annual rates) in 1975 and 1976 \vith the full year g-ro\vth rates during the surrounding 12-month period. Table I provides a ‘As evidence of this expectational impact. the corwlation coefficient between the chanse in MI announced Thursday and the char.re in the three-month Treasury bill rate the followins day was 26 over the 52 weeks of 19i6, which is statistically significant at the 5 percent level. z Throughout this article, first published covering the most recently revised be on the preliminary data both the Federal Keserve “preliminary” refers to the MI statistic a particular period. “Final” refers to statistic for a period. The emphasis will since it is the preliminary data to which and the financial markets react. 1 PRELIMINARY .’ 18 t The purpose of this article is to provide some insights into the difficulties inherent in interpreting the short-run behavior of the seasonally adjusted monetary aggregates and to provide a framework for The analyzing certain kinds of short-run swings. article lvill focus on variations caused by factors other than changes in basic underlying conditions in Chartl~“, I Ml GROWTH * Percqt 1 SHORT-RUN further illustration. It shows the standard deviations of the annualized preliminary one- and two-month l\iI, growth rates in each of the last ten years. The average standard deviation is 5.5 percentage points for the one-month growth rate and 3.8 percentage points for the two-month growth rate. Strikingly, the standard deviation of the one-month growth rates actually exceeds the average monthly growth rate in a number of years. This volatility of short-run growth rates relative to trend would not constitute a serious problem if it were possible to distinguish, on a current basis, between transitory changes in money growth and more permanent changes related to basic economic developments. Unfortunately, making such distinctions is an extremely difficult task. Consequently, the possibility always exists that the shortrun behavior of the monetary aggregates might mislead either the Federal Reserve or market participants observing and trying to anticipate Federal Reserve actions. _ I, d_ RATES COMPARED (SAAR) * TO LONGER-RUN GROWTH RATES I: A c i 1’6. ----- P-Month .---a FEDERAL RESERVE BANK OF RICHMOND 1 -Month - l-Year Table STANDARD DEVIATIONS PRELIMINARY I SHORT-RUN AND MEANS Ml GROWTH OF RATES (SAAR) One-Month Standard Deviation ~ Growth Rates -Mean Two-Month Growth Rates standard Deviation Mean 1967 6.7 6.6 4.0 6.6 1968 1969 4.9 3.6 6.5 1.9 3.7 2.1 6.1 2.1 1970 6.0 4.5 3.5 4.2 1971 6.5 6.1 5.5 6.3 1972 4.9 8.0 3.2 7.5 1973 5.1 5.6 4.1 5.4 1974 4.5 4.9 3.0 5.1 1975 7.7 4.7 5.4 4.7 1976 5.2 5.6 3.3 5.2 Average 5.5 Source: Federal Reserve 3.8 Bulletin. the economy. As indicated in the sections that follow, these noneconomic factors are responsible for a sub stantial portion of the observed illouth-to-moIltl~ and week-to-week variations in monetary growth rates. The next section of the article describes in general terms the various kinds of noneconomic factors that produce short-run movements in the preliminary XI, data. Special attention is devoted to movements that result from the nature of the procedures currently used to seasonally adjust the data. The third section illustrates some of the points made in the second section with specific examples of factors affecting The monthly M1 growth rates in recent years. fourth section provides further illustrations with The final reference to the weekly M1 statistics. section contains a brief summary of the article and presents a few conclusions. periods of several weeks. Moreover, seasonal adjustment techniques, despite notable improvemer, ts in recent ).ears. are far from perfect. Over long periods, variations in the M1 data related to both special adjustment problems should events and seasonal wash out. But factors such as these produce sharp fluctuations in short-run growth rates. It will be useful in organizing the discussion to distinguish two classes of variations : ( 1) movements that result from shortcomings in the method currently used to seasonally adjust the data and (2) irregular variations due to special nonrecurring events. Each of these two categories of factors will be addressed in turn. The focus throughout this section is primarily on the monthly data. Variations Due to Deficiencies in the Seasonal Adjustment Procedures Chart 2 shows the annualized monthly growth rates of ~of seasonally adjusted M1 in 1973, 1975, and 1976. It is evident from the chart that these growth rates are extremely variable, ranging from over 3070 to under -3070, and that they are dominated by recurring seasonal Inovenients. A glance at the chart suggests two of the major forces underlyin, 0 this seasonal movement : tax dates--April, in particular, \vheii individuals accumulate balances to pay income tnses-and the iticreased business activity during the Christnlas season. As described in Box I on 11. 5, the M1 data are seasondly adjusted with seasonal factors computed I)): the I<ureau of the Census’ S-1 1 Variant of the Census Metllotl I1 Seasonal Adjustment Program (referi-etl to below as X-1 1) Judgmental modifications are then made by the Federal Reserve staff in \ ,* i- : Money Growth Short-Run Movements Rates: A General in Description This section will discuss in general terms some of the noneconomic factors that produce variations in seasonally adjusted short-run Ml growth rates. Observed growth rates are no doubt related in some way to changes in economic conditions. But factors totally unrelated to current business conditions can cause significant variations in these growth rates. Special nonrecurring events can have an important effect on demand deposit balances in some cases over 4 ECONOMIC ;&g12” h~~“jl 3,; “- e pi NOT SEASbNALLY “ADJUSTED MONTHLY M, GROWTH RATES ~ II. Some Factors Affecting ” REVIEW, NOVEMBER/DECEMBER 1977 s” ,‘ Box I SEASONAL ADJUSTMENT OF THE MONEY As indicated in the text, money supply data are seasonally adjusted I)y the Federal Reserve staff using the Census Bureau’s S-11 Variant of the Census Method I I seasonal adjustment model, referred to belo\v simply as X-11. ITsing unadjusted data for a period of years, this ~notlcl generates a seasonal adjustment factor for each entry in the series: for example, for each individual month in a In determonthly series of money stock data. mining the final seasonal adjustment factors actually cmploycd in developing the published seasonally adjusted money supply series, the staff may alter the adjustment factors derived from the model where the staff’s knoxvledge of special circumstances affecting the X-11 factors suggests such What follows is a brief alterations are in order. description of some of the problems encountered (For a in applying X-11 to money supply data. detailed description and analysis of Federal Reserve procedures used in seasonally adjusting the money supply, see the accompanying article I)y Lawler.) Like most conventional seasonal adjustment procedures, X-11 assumes tllat the lcvcl of an unadjusted data series (call it Munad in the case of monthly money supply data) at any point in time reflects the combined influence of four underlying determinants: long-term trend movements (T), recurring seacyclical movements (C), regularly sonal movements (S), and irregular movements (I). The version of X-11 used the Federal serve assumes four determinants related to another in multiplicative, i.e., fashion: hl = T c X 2; I. this general one can two alternative under xvhich the unadjusted influences might supply data: a condition the pattern constant from to year seasonal influences (2) a where the changes from year to next. 111 iirbt case, multiljlicativc proportionate inlpact seasonal influon tlie data is hame for particular calendar (say, January) all of years covered the series. these condiany computed of seasonal factors, S, January, February, respectively, should constant over full span years covered the series. the second the proimpact of influences during given calendar changes over To rethese changes seasonal adjustment for each month should, general, change out year the next. has alternative modes designed deal with of these sets of As applied any set monthly data, X-11 model essentially a average seameans that adjustment procedure. seasonal adjustment are derived developing of (1) unadjusted data individual months example, June in the to SUPPLY: THE PROBLEM OF MOVING SEASONALS (2) average of months data on that Such a is calculated each individual in the The seasonal justment factor each individual is then by averaging ratio for month with ratios for corresponding calendar in other The two modes mentioned enter the as follows. the pattern seasonal influences the data believed to stable over a single adjustment factor derived for of the calendar months an average all of the ratios for that calendar month over the full series. If the pattern is believed to be changing over time, a moving average of such ratios, covering a more abbreviated time span, is used to compute a distinct adjustment factor for each individual month in the series. For the reasons given in the text, it is clear that the seasonal pattern of the unadjusted monthly money supply series is not constant but changes over time. Therefore the version of X-11 used to adjust the money supply data derives seasonal adjustment factors for each individual month in the series from a weighted 7-term moving average of the ratios in the corresponding calendar months of surrounding years. Where a month is in one of the terminal years of the series, the span of the moving average is reduced since data for a full centered 7-term moving average are not available. For example, the presently published adjustment factor for January 1973 (an example of what is called “final” data in the text) is derived from a weighted average of the January ratios for the years 19701976, inclusive. The presently published factor for January 1976 is derived from the four year period 1973-1976, inclusive. It is important to note that under this procedure, the factors used to seasonally adjust incoming data during the current year-the all important “preliminary” data to which both the Federal Reserve and the markets react-are derived from ratios of preceding years and do not directly reflect any changes in seasonal patterns in the current year.* For example, the seasonal factor used to adjust the January 1973 figure when the figure was initially released in early February 1973 was derived from the January ratios for the years 1969-1972, inclusive. Therefore, if the seasonal pattern is in fact changing in the current year, it is particularly likely that the procedure will distort the preliminary, i.e., current, data. Ironically, this is precisely the data of greatest importance to Fed policymakers and the markets. The discussion in the text describes some of the distortions that arise and shows that these distortions are a source of seasonal movement in the seasonally adjusted money supply data. * Strictly speaking the preceding year ratios procedure to anticipate small extent. FEDERAL RESERVE BANK OF RICHMOND weights attached to these might implicitly cause the current year changes to a 5 an effort to compensate for some of X-11’s deficiencies.” As indicated in the ljox, the purpose of se;lsonally adjusting lhf , is to eliminate the impact of seasonal forces, leaving only trend, cycle and irregular movements. In practice, however, the influence of seasonal forces is often not eliminated from tile preliminary seasonally adjusted M, data. A majoi reason for this residual seasonality is that X-l 1 necessarily relies solely on past data in calculating preliminary seasonal adjustment factors and therefore cannot take full account of changes in seasonal l)ehavior currently in progress, despite the program’s allowance for “moving” seasonnls described in tile Box. A variety of developments impact of seasonal particular month. tiutling of seasonal Consider hs, commodating, underlying the relative should capture there are changes in the For example, in 1955 the the program of nonwithheld example, shifting calendar position averfinal the seasonal First, events. fact, patterns average changes sonal event affecting changes the centered, that occur abruptly. change M1 occurred even the final adjusted might not adequately in On the other hand, well suited to dealing that a lasting Here, of the Easter since is not particularly assume gmdrta! by its very construction changes. such with permanent individual in the nioving after nioving on the money Federal income taxes was permanently shifted from March 15 to April 15. A contrasting example is the weighted seasonally adjusted data for that year.’ For this reason, the program is especially well suited to ac- seven-year in a As indicated on a given year in deriving age of data centered supply can change first the final data. S-l 1 uses a seven-year events final day for the payment continuously ally over :I period of years or abruptly. Moreover, tile inil)act of tliese changes on the preliminary (i.e.. first l)ul)lislietl) adjusted data for a particular month is likely to differ from tlleir impact on the final revised tlata for the month. The folloning paragr~plis will el:J)ornte these points. abruptly monthly capture As an in some senin 1973. data for 1973 the change since the holiday. Second, the relative magnitude of sctrsonnl force can change. The aggregate amom7t of individ- final data, derived from the seven-year centered moving average, would be based partly on experience ual or corporate taxes paid in a given month relative to the level of the money supply, for instance, might preceding deviate from the usual norm. This deviation during balances during periods wanage characterized their UIOIIE~ by recurring seasonal events can change. For example, improved corporate cash management practices have probabl) compressed the necessary lead-time for the accumLilation of cash balances prior to scheduled tax pay- ments. Finally, neza, seasonal events appear from time to time. In late 1972, for instance, the Federal government ments initiated at the beginning sizable revenue-sharing pay- of each quarter. 1972-all years the more of whether significant preliminary a permanent change in underlying seasonal forces occurs gradually or abruptly, the preliminary adjusted growth rates are likely to be distorted in the seiise that they will payments over the various periodic tax payment dates within the year. Third, the VUWULCY which in and bzrsincss firms 1970, 1971, and the change. Consider next data. Kegardless might be due either to a change in the total tax liability relative to M1 or to a change in the distribution of households the years probably differ systematically from revised data pub lished later. The reason for these distortions is that S-l 1 derives preliminary adjustment factors from actual data for years preceding the year in question. (See Box.) Consequently, the preliminary factors fail to capture lying seasonal viously the full effects of changes in underbehavior. Such distortions are ob- significant since it is the preliminary Ml data that condition current monetary the behavior of the financial markets. adjusted policy and The impact of these several changing seasonal forces on short-run seasonally adjusted Ml growth A couple of hypothetical examples clarify the nature of these distortions. rates is likely to vary, depending begimiing in 19S0, the unadjusted growth rates of hII in the month of October began to display a particularly on (1) might help to Suppose that whether the change is permanent or temporary and (2) if permanent, whether the change occurs gradu- g~~drtnl 0 See the accompanying article by Lawler for a description of these judgmental modifications. In making these modifications the staff faces many of the same difficulties anticipating changes in seasonal patterns encountered by the X-11 proaram itself. For this reason it is not clear that the modifications significantly improve the preliminary data. In any case, this article does not attempt to evaluate these modifications. 7 The term “final” may be slightly misleading in that money susplr data is always subject to further revision. The term is used hers, to refer to revised adjusted data available beginnina in the fourth year following the year to which it applies. Such data is seasonally adjusted using adjustment factors that are derived from actual data for the full seven-year period covered by the seven-term movins average in the X-11 program. 6 ECONOMIC REVIEW, but NOVEMBER/DECEMBER persistent 1977 decline due, perhaps, to a decline in the relative volume of business sales in that month. Suppose further that this trend persisted through the year 1990. Under these circumstances, the X-11 seasonal adjustment factor used to compute the prelinlinary seasonally adjusted growth rate in, say, October 19S5 would reflect the movement in M, in the years 19Sl-19%. Consequently, this preliminary factor would be biased upward and the preliminary seasonally adjusted growth rate In subsequent years the \voultl l)e understated.X October 19% gro\vth rate \vould be revised upward. The preliminary gro\vth rates for Octoijer in ensuing J’ears, ho\vever. would continue to differ systematically from revised gro\vth rates as long as the trend continued. Consider next an ab,-lip1 future change in a seasonal event such as, for instance. a hypothetical change in the deadline for iiidi~idual Federal income t;ls l~:tyinents from April 15 to May 15. Suppose that such :I cllange Ivent into effect in 19S6. In that case, beg-inning in 19SG the unadjusted growth of MI in April would be low \\hile not seasonally adjusted gro\vth in Slay would be high relative to the pattern in earlier years. Here, the preliminary seasonal adjListment factors for April and Llay 19SG would be I)asetl on i\l, I)ehavior over tlie 19S2-19S5 period. Consequently, the preliniinnry adjusted growth rate for April 19SG would proba1~1y I)e unusually low, \\-bile the R’lny 1924 growth rate \vould be significantly inflated. In the absence of further changes. however, the problem would tend to disappear by 1990 since by that year all of the data used in deriving the preliminary April and May adjustment factors would reflect the 19SG tax date change. Beyond the more durable seasonal developments discussed to this point, temporary changes can also affect short-run seasonally adjusted monetary growth rates. As ;L final ex;unple, suppose that Federal tax payments by individuals were unusually large relative to the level of Ml in April 19S3, but that in 19S3 and subsequent years, the payments fell back to more normal levels. In this case the preliminary seasonal adjustment factor for April 19S3, which would be based on 1979-1932 experience, would be low relative Hence, in the to the level of the tax payments. absence of some other ulwsual event tending to depress growth, the preliminary seasonally adjusted RiIl growth rate for April 19S3 would be relatively high. Further, the final revised data for this month would also show a relatively circumstances. RESERVE rate under these It should be clear from this discussion that the procedure presently used to seasonally adjust monetary data is itself an important potential source of short-run variations in adjusted monetary growth rates. Irregular Variations In addition of changing seasonal the seasonal adjustment growth patterns nonrecurring sonal movements to the working procedures, rates are also strongly irregular, no effort short-run influenced events. effects through M, at times by In contrast to sea- is made to remove such irregular movements from the adjusted Ml data. While the events underlying these movements are not always explanation examples fully understood, in many instances the is straightforward. One of the best of a large irregular movement in recent years was the bulge in Ml in May and June 1975 following the $9 billion disbursement of tax rebates and supplemental social Treasury to the public.!’ security payments by the It should be noted parenthetically that the distinction between ( 1) irregular movements and (2) the movements discussed above reflecting temporary changes in seasonal forces is not always clear. In the preceding section the example used to illustrate temporary seasonal forces was unusually large individual tax payments in one year. Some analysts might prefer to regard such an occurrence as an irregular event. The criterion adopted in this article is that events that recur with some definite periodicity are seasonal in nature, while other events are irregular. Whatever the distinction in principle, in practice both categories of events are likely to produce short-run movements in the seasonally adjusted M1 data, As indicated above, the X-11 program is unlikely to remove the effects of temporary changes in seasonal patterns from the seasonally adjusted data, and irregular movements are left in the adjusted series by design.‘” The following section illustrates the foregoing discussion with specific empirical examples from recent experience. !‘See Breimyer impact of the rates in 1975. and Wenninaer [z] rebntes on seasonally for empirical evidence adjusted monthly Ml on the growth ‘OIt might be added that both irregular movements and movements due to temporary changes in seasonal forces can present additional problems if they are mistakenly treated as permanent changes in In addition. computed seasonal patterns by the X-11 pro!zram. seasonal adjustment factors might be distorted by cyclical developSee Lawler 13, p. 241 and Poole and Lieberman [6, pp. ments. 325-3341. ‘The X-11 prozram does contain an adjustment designed to correct See r7, p, 161. partially for trend changes in seasonal behavior. As long as the chanaes continue nt roughly the same pace. however. the correction will be only partial, and the bias discussed in the text will persist. FEDERAL high growth BANK OF RICHMOND 7 III. Factors Affecting Short-Run Money Some Empirical Gradual Changes Christmas adjusted growth months prior following flects with during increased pattern for rises un- in the presumably transactions business and the reduced the holiday. The 2, the and falls in the months This demand Rates: Patterns: in Chart of M1 typically to Christmas Christmas. the holiday Seasonal As shown rate the rising associated after in Cycle Growth Examples activity re- balances prior to need for such balances The behavior this period forms a regular of unadjusted “Christmas M1 cycle” that appears to begin as early as late August, peaks in the first week of January, and reaches a trough in Chart 3 THE CHRISTMAS CYCLE Percentage increase in Not Seasonally Adjusted M1 From late August Trough Percent The net increase from the late late February.” August trough to the late February trough generalI> is roughly equal to the trend rate of iLlI1 growtll. Hence, the cycle is complete in the sense that the preChristmas seasonal rise has nashed out by the end of February. As suggested by Chart 3, the shape of the Christmas cycle has undergone :I sulMaiitia1 and fairI> continuous change since the mid- 1960’s. despite the fact that the typical percentage rise from the August trough to the January peak has been fairly stable. In particular, the c).cle has become narrower to\vartls the base, so that ;I greater part of the pre-Christmas rise now occurs in the November-December period, and a greater part of the post-Christmas runoff occurs in January. This information is convey-ed in a different way in Table II, which shows that the increase in the percentage of the post-Christmas runoff occurring in January has been remarkably persistent over the longer run. Similarly, except for 197G, the percentage of the pre-Christmas rise occurring in November and December has risen quite steadily. 1’ Of course, other seasonal forces affect the movement Christmas, however, appears to MI in this period. pattern of the unadjusted data over these months. Table - II 1963-65 THE CHANGING - ...-..... ,96*.,0 --- of unadjusted dominate the SHAPE OF THE CHRISTMAS % of Decline in NSA Ml Occurring in Jan. % of Rise in NSA ,441 Occurring in Nov.-Dec. 1973-75 1961 50.5 51.7 1962 51.3 47.9 1963 47.5 40.8 1964 40.5 61.9 63.4 1967 62.9 62.7 1968 67.5 67.3 1969 73.1 60.7 1970 71.6 81.4 1971 70.5 81.9 1972 71.7 77.7 1973 75.2 90.2 1974 77.6 87.0 1975 90.8 86.5 1976 ECONOMIC 41.0 50.1 1966 8 48.8 1965 SOUVX 62.7 82.6 Federal REVIEW, NOVEMBER/DECEMBER Reserve 1977 Board Release, CYCLE H.6. Table III SUCCESSIVE REVISIONS Ml GROWTH OF JANUARY RATES (SAAR) Published 1971 1970 --I_----- 1972 Growth 1973 Rates for 1974 1975 1976 1977 As of: 1970 9.0 1971 9.4 1.1 1972 9.2 2.8 3.7 1973 10.3 2.7 1 .o 1974 10.4 3.3 1.5 4.7 -3.1 1975 10.9 4.3 3.1 5.2 -2.7 1976 9.2 5.5 8.2 9.4 3.5 -5.1 1.2 1977 9.2 5.5 9.2 10.3 4.4 -4.2 2.0 +5.1 + .a 0.0 -9.3 5.4 Cumulative Revision +.2 Note: Source: +4.4 Diagonal Federal +5.5 shows Reserve +10.3 preliminary +7.5 growth rates for each yeor. Bulletin. The gradual change in the shape of the Christmas cycle since the mid-1960’s has probably been due at least in part to the steady rise in interest rates during this period. As Table 11 indicates, the cycle began to change in 1966, the year interest rates began their strong upward trend. The underlying logic here is straightforward. Higher interest rates have made it progressively more costly for business firms and households to hold Mt balances rather than alrertiative, interest-bearing assets. Hence, the buildup in Mt balances prior to Christmas has been progressively delayed. Further, after Christmas the public has attempted to convert the Mt balances acquired during the holiday period into interest-earning assets with greater speed. These efforts to economize on M1 balances have probably been aided by the proliferation of credit cards and a variety of other financial instruments permitting improved cash balance management. Whatever the cause, the gradually changing shape of the Christmas cycle has had a large impact on the seasonal adjustment factors for some of the Christmas cycle months. First, the final revised factors for these months have changed continuously from one year to the next since the mid-1960’s. For example, the January factor has declined steadily since 1965. More importantly, the preliminary factors and the preliminary adjusted growth rates for these months in recent years have been substantially revised with the passage of time. Consequently, the preliminary reported growth rates for these months have been nofably unreliable during the last several years. This is illustrated in Table III which compares the preliminary January seasonally adjusted growth rates with successive revisions. The cumulative revisions have been very large, frequently increasing the January growth rates by more than 5 percentage points and in one case by more than 10 percentage points. While a small part of these revisions might be unrelated to seasonal adjustment, it is clear that the preponderant share are due to revisions in the seasonal adjustment factors. The direction of the January revisions is consistent with the changing shape of the Christtnas cycle. As data for succeeding years becomes available, the progressively more rapid decline in M1 following the early January peak produces a lower January adjustment factor and a higher adjusted January growth rate.l’ Abrupt Changes in Seasonal Patterns: The Rise in Federal Income Tax Refunds Due to heavy overwithholding of Federal income taxes, the Treasury typically pays out sizable tax refunds to individuals during the first half of the year, primarily in the period from March through May. Since a large portion of these funds are initially deposited in demand deposits, they affect the level and growth rate of not seasonally adjusted Ml. For several years prior to 1973, the time profile of these disbursements was relatively stable, as was the total amount relative to the outstanding money supply. Consequently, the seasonal impact of the refunds on Mt was probably adequately captured by the X-l 1 seasonal adjustment factors. “Another example of a long-run trend in a seasonal force that had a large impact on a monthly seasonal factor was the rapid growth in nonwithheld individual income taxes paid in April. relative to the money supply, between the mid-1950’s and the mid1960’s. This growth in tax payments caused a steady seasonallr adjusted April M1, resulting in gradual increases in the April adjustment factor. See Lawler rise in not progressive 13. p. 261. Table IV INDIVIDUAL INCOME As Q Percent 1968 1973 4.9 4.9 8.5 1975 1976 9.0 9.0 5.9 1972 1974 6.2 6.4 1969 1970 1971 Note: TAX REFUNDS of Ml 8.4 1977 9.0 Ratios we total tax refunds for the year divided by not seasonally adjusted level of Ml in December of the preceding year. The figure for 1977 is an estimate. Source: Federal FEDERAL RESERVE BANK OF RICHMOND Reserve Bulletin. 9 the 1970-1972 1972 period growth on the one hand and the postSpecifically, of not seasonally June period adjusted has probably been stronger in the latter of the X-11 in the preceding section might expect this shift to distort sonally adjusted M, growth of this article, one the preliminary sea- rate over the March-June period in 1973, since this growth using the seasonal Ml in the March- On the basis of the discussion years.13 model period on the other. seasonal through adjustment 1972 only. downward based More specifically, pect X-11 to produce nary growth rate was calculated factors an upward on data one would ex- bias in the prelimi- rate over this period in 1973, leading revisions as additional high refund to years were use to calculate the 1973 seasonal adjustment factors.14 (As suggested in Section II, however, even the final adjusted surge in refunds 1973 data might reflect the abrupt to some extent since the final adjust- ment factors are based partly on pre-1973, low-refund year experience.) The same general process should .-.-.- 1970- 72 affect the 1974 and 1975 data. In fact, March-June the preliminary growth rates over the period in the years 1973, 1974, and 1975 have been significantly reduced by subsequent re-. visions. Annualized, seasonally adjusted M, growth from a base comprising and February the average of the Januar) to a terminal value comprising the average of the four months March through June has been revised downward on average by 2.49 percentage points for these years, a fairly dramatic indication figures of the magnitude of &I1 revisions that ca!n occur. It shows that the average revision of the Ml growth rate over this period was in the neighborhood of the typical 2 to 2yz percentage tween the upper and lower limits longer-run In 1972, however, increased withholding for numerous individual taxpayers went into effect, causing a sharp increase in refunds from $14 billion in 1972 to $22 billion in 1973. As indicated in Table IV, the result was an abrupt jump in total refunds from about 6 percent of M, to roughly 8% percent of M,. Chart 4 shows the monthly profile of the tax refunds relative to MI in the years following 1972 compared to The monthly the pattern in the 1970-72 period. profile of the disbursements was very similar (1) in the years 1973, 1974, and 1975 and (2) in 1976 and 1977. Consequently, these two sets of years are grouped together in Chart 4. Presumably, the abrupt increase in the level of refunds in 1973 altered seasonal patterns as between 10 ECONOMIC Ml growth point range be- of the FOMC’s targets. The precise implications of these downward revisions, however, is clouded by the fact that they might have been influenced and by ad lzoc judgmental by benchmark adjustments revisions made by the 1J June is included, even thouph the bulk of the refunds are paid before June, for two reasons. First, there is normally a lag between the receipt of refunds and their expenditure or conversion to Other Consequently, the daily average level of MI balfinancial assets. ances in June is likely to be affected by refund disbursements in May. Second, refund checks mailed in May (the refund data are reported on a mailing date basis) may not actually be cashed until JUWZ. 14 Note that the increase in the level of refunds tends to increase the daily average level of not seasonally adjusted Ml in each of the fsxxr Therefore, the impact of the months of the March-June period. refunds on any individual month’s growth rate depends on the profile of the refund flow. The discussion in the text refers to growth over the entire March-June period: i.e., the increase in the daily average level of Mt for the four-month March-June pwiod over the average daily level for some base period. REVIEW, NOVEMBER/DECEMBER 1977 staff of the Board of Governors as well as by changes in the underlying zX-l 1 seasonal adjustment factors. In order to abstract from these other factors, comparable growth rates were calculated using the factors generated by the X-l 1 model without any modification. First, unmodified X-l 1 seasonal adjustment factors were calculated these factors nary” using data through 1973 base). for 1974 and growth rates in a similar manner. magnitude changes of seasonal Patterns changes in the timing forces can In in seasonal and relaalso affect factors using 1975 were preliminary to “final” derived computed revisions Preliminary These rates were then compared rates for the same periods X-11 temporary tive Seasonal 1973 period (over a January-February The implied patterns, in durable a “prelimi- rate for the March-June March-June derived Changes to relatively 1972, and were then used to develop growth growth Temporary addition growth from unmodified data are -1.70 through percentage 1976. points in 1973, -1.56 percentage points in 1974, and -1.06 percentage points in 1975-an average revision of -1.44 percentage points. This analysis suggests that successive contributed changes heavily in the underlying X-11 factors to the revision in the published M1 data summarized To this point impact in the preceding the discussion of the increased paragraph.‘” has centered tax refunds on the on the prelimi- nary seasonally adjusted M, data over the MarchJune period. More broadly, there is evidence that the increased generally refunds in conjunction biased the preliminary with the X-l 1 model seasonally adjusted growth rates upward in the second quarter and downward in the third quarter in 1973 and subsequent years. Chart 5 shows the week-to-week movements of a ratio of three-month Ml growth trend growth justed and to longer-run on both a (preliminary) basis an unadjusted seasonally basis. The panel of the chart shows the movements prior to the abrupt panel shows increase increase the movements in the refunds. ad- upper in 1972, just in the refunds. The lower in 1973, just after If the increased the refunds to- gether with the X-l 1 model have in fact produced the biases mentioned above, one would expect a greater degree of (in this particular case positive) correlation between the unadjusted and adjusted movements of the ratio in 1973 than in 1972. The chart indicates rather clearly that the correlation is indeed considerably greater in 1973 than in 1972. Specifically, the correlation -.22 coefficient is .70 in 1973 compared to in 1972. to ‘6It is possible that these results are influenced the June 1975 tax rebate payments. Excluding analysis. however, does not greatly alter the results. some June FEDERAL extent from by the RESERVE BANK OF RICHMOND 11 Although seasonally adjusted M1 growth rates.‘” X-11 attempts to take account of lasting changes in the profile of seasonal forces influencing M, through the construction of moving adjustment factors, the model is simply not designed to deal effectively with temporary changes in these forces. Basically, the model treats such changes as though they were irregular movements in the not seasonally adjusted data. Consequently, most of their impact is probably passed on to the seasonally adjusted data. For example, since there is a positive relationship between the relative magnitude of April tax payments and the unadjusted lMl growth rate in April, unusually large April tax payments in a given year probably tend to inflate the seasonally adjusted April M1 growth rate in that year. A somewhat more esoteric example involves the timing of April tax collections by the Treasury. Individuals generally pay nonwithheld income taxes by check. Many of these checks are mailed close to the April 15 deadline. Individuals typically accumulate the balances needed to cover these checks at the time they are mailed, but the Treasury often takes two or three weeks to process the checks. Because of the huge sums involved, even a small variation in processing time can significantly affect average daily M1 balances in April and seasonally adjusted April M, growth rates.‘? A final example is a recent change in the procedures surrounding monthly social security retirement and survivors benefit (SSA) disbursements. Prior to mid-1976 all of these disbursements were made bj check. The checks were usually posted so that they would reach .their recipients on the third of the month. When the third fell on a Saturday, payment was made on that day even though some financial institutions are closed on Saturdays. If the third fell on a Sunday, payment was made on the preceding Saturday. In mid-1976 this schedule was changed in conjunction with the introduction of facilities permitting the direct deposit of some of these clisbursements through electronic media. Specifically, payments are now made on the preceding Friday when the third falls on either a Saturday or a Sunday.‘8 Since a sizable portion of the disbursements are converted into -R/I1 balances, these changes in payment In As indicated in Section II of this article. the distinction between (1) temporary changes in seasonal patterns and (2) irregular movements in not seasonally adjusted data is not always clear. Consequently. the choice of examples in this and the following subsections is somewhat arbitrary. 17 See Auerbach [ 11. lRThese changes apply ments by check, which total payment volume. 12 not only continue to direct deposits to account for but also well over ECONOMIC to payhalf of REVIEW, schedules have altered the seasonal behavior of not seasonally adjusted M, in these months for two reasons. First, the timing of the payments with respect to calendar dates has changed compared to earlier years. Second, since the payments are no\\ made prior to rather than after a holiday or a weekend, the funds are likely to be held in the form of Ai, balances for a longer period (specifically the one or two days of the holiday or weekend) before being spent or converted into other financial assets, thereby raising average daily balances and growth rates. Again, to the extent that these changes are ignored by seasonal adjustment procedures, they are likely to affect seasonally adjusted M, growth rates.‘” It is interesting to note that all of the conditions described in these examples were present in April 1977 when RI1 grew at a record annual rate of 19.7 percent. First, individual nonwithheld ta% payments were larger relative to the level of M, than in any other year since the Treasury began publishing these data in 1954. Second, Treasury processing of these payments appears to have been considerably slower than in the three preceding years perhaps due to the magnitude of the pnyn~ents.2n Third, April 3 fell on a Sunday so that social security payments were made on Friday, April 1. Finally, April tas refunds were unusually high, as shown earlier in Chart 4. These observations are not intended to imply that these factors explain all or even most of the unusually large prelitninary April 1977 M1 growth rate. They do illustrate, however, how temporary changes in seasonal forces can cloud the meaning of a specific preliminary monthly M, growth rate. The factors conIrregular Movements in M, tributing to short-run variations in seasonally adjusted Mt growth rates discussed thus far have all been related to changes in the underlying determinants of the seasonal behavior of M1. Irregular movements in seasonally adjusted growth rates, in contrast, result from special or unusual events. Some-times these events can be identified and anticipated. More often, unfortunately, they are neither identifi- “~The third has fallen on a nonbusiness day three times since the schedule chance went into effect: October 1976. April 1977. and The preliminary seasonally adjusted Mi growth rates July 19’77. (at annual rates) for these months were 13.7 percent. 19.7 percent. and 18.3 percent, respectively. These growth rates exceeded both trend growth and other monthly rrowth rates during the postchance period by wide margins. It is likely that the change contributed to these hiah prowth rates. although the extent of the effect cannot be specified precisely. ~1 This statement is based on a comparison of tax collections in April and in early May, respectively, using data published in the Trcasur?/ Zlullet,n. (The collection date is the date on which the Treasury actually clears a check.) This comparison indicated that a significantly higher proportion of total collections in 1977 occurred in May as opposed to April than in the three preceding years, strongly suggesting slower processing in 1977. NOVEMBER/DECEMBER 1977 al)le nor foreseeable. Consequently, movements in proper monetary policy response when the event is anticipated. seasonally adjusted M 1 growth rates due to irregular events resemble variations resulting- from changes in seasonal forces in that they complicate monetary fundamental policy IJ~ changes making it difficult in the trend rate of Ml from some transitory the conduct of The Weekly Data growth Up to this point this article has focused on shortrun movements in the ~zonthly M, growth rates. The Federal Reserve also publishes seasonally adjusted weekly Ml data. These data take the form of daily average balances over Federal Reserve “statement” weeks, which run from Thursday through Wednesday, inclusive. This section will extend the preceding discussion by describing some of the factors that influence the weekly behavior of M1. change. As suggested above, the most obvious recent change in M1 growth caused by an irregular event was the sharp acceleration in May and June 1975 due to the $9 billion of tax reljates and supplemental social security benefits paid during those months. In hindsight, it seems clear that while the FOMC expected these payments to enlarge growth rates over this period, the full magnitude of the impact was not anticipated. As a result, the FOMC appears to have concluded that the acceleration was attributable to a considerable extent to the expansion of business activity just beginning to gather steam at that time and put upward pressure on the Federal funds rate in order to restrain it. The R/I1 growth rate dropped abruptly in July, however, and remained minimal for several months, prompting the Committee to reduce the funds rate to its pre-rebate level in October and November.” The first point that needs to be made about the weekly M, data is that they are exceedingly volatile: the change in Ml this week-whether measured in dollars or as a percentage growth rate-is likely to be very different from the change next week. Chart 6 provides a visual demonstration of this point using preiiminary 1976 data. Each point on the graph shows the ratio of the dollar change in seasonally adjusted M, during a given week to a moving 53-week average of weekly changes centered on that week. As the chart indicates, there are both wide variations in weekly growth over the year as a whole and, in many instances, sharp fluctuations from one week to the next. A number of other recent swings in short-run seasonally adjusted M, growth rates can be linked to specific nonrecurring events. For example, the -3.2 percent rate of decline in December 1975 almost certainly resulted partly from the change in Federal Reserve Regulations Q and D permitting business firms to hold savings deposits. But while it is often possible to evaluate irregular variations in Ml growth in terms of specific events sucli as these after the fact, it is extremely difficult in most cases to specify the probable impacts on short-run growth rates in advance with any degree of quantitative precision. Obviously the absence of suc11 information makes the Chart 6 suggests that there is little if any atic relationship between weekly changes in of Ml-viewed either individually or over of several weeks-and longer-run trends in of M1 growth. “As events actually unfolded in May and June of 1975, the rise that took place in the money supply was much larger than the Federal Reserve staff had estimated would occur as a result of the rebate program. The inference we drew was that the demand for money was expanding rapidly quite apart from the rebate program. We therefore took mildly restrictive action toward the end of June to reassure the Nation that the Federal Reserve would not countenance monetary expansion on a sca:e that might release a new wave of inflation. Differences of judgment existed then-and still do-as to the appropriateness Let me say only that if we of that mild tightening action. erred. the mistake was technical in origin-that is, it grew out of the difficulty in making good estimates of the tax-rebate In any event, monetary growth impact on deposit growth. rates soon moderated, and we lost very little time in returning to an easier monetary stance.” RESERVE Nonetheless, as pointed systemthe level a period the rate out in the introduction to this article, the FOMC’s current procedures for implementing monetary policy tend to focus the attention of both policymakers and financial market participants on the weekly data. Apart from these procedures, though, the simple fact that the most recent weekly M1 figure is usually the latest information available regarding monetary developments quite naturally stimulates interest. The remainder of this section attempts to provide some perspective for evaluating the informational content of the weekly statistics. In general, the same kinds of factors that produce variations in the seasonally adjusted monthly R/I1 data also produce variations in the seasonally adjusted weekly MI data. Abstracting again from fundamental changes in underlying economic conditions, these factors are : (1) irregular events and (2) changes in the timing and magnitude of seasonal movements not captured by the seasonal adjustment factors used to adjust the data. :‘I The policy record for the FOMC meeting held May 20. 1975. refers explicitly to the Committee’s recoanition that short-run MI tolerance ranges in the May-June period should be relatively liberal to allow for the rebate effect. The ran&~ was set at 1 to 9% percent. The actual (preliminary) growth rate for the two-month period was 14.4 percent. See Board of Governors of the Federal Reserve System, This episode was later reviewed by Annual Report. 1975. P. 197. Chairman Arthur Burns of the Federal Reserve in testimony before the Senate lludget Committee March, 1977: FEDERAL even IV. to distinguish or cyclical problematic BANK OF RICHMOND 13 Jirly *_ Aug.” Oct. -~ Nov. Dec.” 4 Box II SEASONAL ADJUSTMENT The technique used to seasonally adjust the weekly Ml data is essentially an extension of the procedure used to develop monthly seasonal adjustment factors. Indeed, the weekly adjustment factors arc derived directly from the seasonally adjusted monthly data as follows. First, the adjusted monthly data are centered at mid-month, and a provisional seasonally adjusted level for each stateis derived by interpolation of the ment week* monthly series. Second, so-called “original” ratios of the unadjusted weekly data to the provisional adjusted weekly data are derived for each statement week, and, through interpolation of these statement week ratios, “offset” ratios are derived for weeks ending on days other than a Wednesday. Following these calculations, a ratio exists for each individual day in the entire data series, covering the calendar week ending on that day. Third, a weighted moving five-year average of these ratios is calculated for each statement week in the series. This calculation uses the ratio for the statement week in question along with the “original” or, * Statement weeks are Federal weeks running from Thursday lowing Wednesday. Reserve through reporting the fol- OF THE WEEKLY Ml DATA where necessary, the “offset,” ratios for corresponding calendar weeks in the four surrounding years, with truncation of the average for terminal years in tile series. For example, the weighted average used in calculating the currently published factor for the statement week ending March 7, 1973, is based on the ratios for the calendar weeks ending h,Iarch 7 in the years 1971.1975, inclusive. The average used in calculating the currently published factor for the statement week ending March 3, 1976, is Ijased on the ratios for corresponding \veeks in the years 19741976. inclusive.) This third step is designed to take account of moving weekly seasonality and resembles the procedure used to take account of moving seasonalit) in the derivation of the monthly factors. (See Box I on p. 5.) Fourth, the average of the weekly ratios for a given calendar month is adjusted to approximate closely the corresponding monthly seasonal adjustment factor. Fifth, these ratios are judgmentally adjusted by the Federal Reserve staff. It should be clear even from this brief summary that the weekly seasonal adjustment factors are subject to the same kinds of limitations as the monthly adjustment factors and for roughly the same reasons. J 14 ECONOMIC REVIEW, NOVEMBER/DECEMBER 1977 Irregular Events As we have seen, irregular events can have a sizable effect on monthly M1 growth rates. They can also have a marked impact on the weekly data, particularly if the event is of relatively short duration. Two illustrations from recent experience are relevant. In late January 1977, the eastern and midwestern portions of the United States experienced the most severe winter weather in several decades, disrupting production and sales activity in these areas. Seasonally adjusted M, fell a total of $3.0 billion over the two statement weeks ending January 26, compared to declines of only $100 million and $700 million in the corresponding periods in 1976 and 1975, respectively. It is likely that the unusual weather was partly responsible. R4ore recently, there was a precipitous $5.0 billion increase during the statement week ending July 20, 1977. The magnitude of the rise contrasted sharply with the moderate growth typical of mid-July. While the full explanation for this increase is unclear, the July 13 power failure in New York City, which disrupted interbank settlements there, may have been a contributing factor. While it is sometimes possible to anticipate irregular events such as these, they are more often not anticipated, leading in some instances to substantial market reactions. Changes in the Magnitude and Timing of Seasonal Gains As in the case of the monthly data, short-run swings in the adjusted kveekly data are also caused by changes in the magnitude and timing of seasonal movements not captured by the seasonal “Distortions” adjustment factors. of the adjusted weekly data of this sort result from inherent deficiencies in the procedures used to derive weekly seasonal adjustment factors similar to those discussed in Section II of this article with respect to the derivation of the monthly adjustment factors. (The procedure for seasonally adjusting the weekly h4, data is outlined briefly in Box II on 11. 14.) There is evidence that the distortion of the preliminary adjusted weekly data clue to these deficiencies is sizable. The results of one recent study suggest that the mean absolute revision of the preliminary adjusted data, espressed il! terms of annualized growth rates, is on the order of 13 percentage points.‘“” Two specific cases are discussed below. Enstcv Week Since the week containing the Easter holiday varies from year to year over an al,prosimately four calendar week span, the timing of this seasonal influence on the unadjusted weekly M, data L” See Wood , especially Table II. Table V RATIO OF WEEKLY Ml LEVEL TO CENTERED FIVE-WEEK AVERAGE IN WEEKS SURROUNDING (Seasonally Week 1 ----__- EASTER Adjusted Dote) Week 2 Week 3* Week 4 Week 5 Date of Easter Sunday 1968 0.999 0.998 1.009 0.997 0.995 April 14 1969 0.997 0.998 1.011 1.005 0,996 April 1970 0.992 0.990 1.018 1.005 0.999 6 March 29 1971 1.001 1.008 1.006 0.997 0.990 April 11 1972 1.000 0.997 1.003 1.001 0.998 April 1973 1 .ooo 1.003 0.994 1.001 1.000 April 22 2 1974 1.001 1 .ooo 1.003 1.000 0.998 April 14 1975 0.999 0.999 1.000 1.001 1.000 March 30 1976 0.998 1.005 1.004 0.996 0.998 April 18 1977 0.991 1.005 1.004 0.999 1.004 April 10 preliminary data. * Includes Note: .SOWC.% Easter Sunday. Ratios are calculated Federal Reserve using Bulletin. The weekly seasonal adjustment proalso shifts. cedure described in the Box makes no allowance for these shifts.“3 Consequently, one would expect that the seasonal adjustment factor for the week containing Easter would typically be too small, and, correspondingly, the reported seasonally adjusted M, level in that week would be too large. The data in Table V tend to support this assertion. Each entry in the table is the ratio of the seasonally adjusted M1 level for the indicated week to a five-week average of weekly levels centered on that week. Ratios are reported for the Easter week and the two surrounding weeks in each of the last ten years. In five of the years, the Easter week ratio is the largest of the five ratios. It is the second largest in four of the remaining five years, strongly suggesting a systematic upward bias affecting that week. Cllangcs in the Intra~uonthly Seasonal The second example involves the effect of a somewhat more general phenomenon on the behavior of the seasonally adjusted weekly data: namely gradual changes in the seasonal behavior of the unadjusted data z&l&z a calendar month. To the extent such change does in fact occur, it would tend to introduce an intra- “Since the week containing Easter is known well in advance. its seasonal effect on the weekly Ml data could presumably be anticipated throulrh judgmental adjustments to the preliminary seasonal adjustment factors. The evidence supxnarized in Table V, however. indicates that if judgmental adjustments have been made. they have not been adequate. FEDERAL RESERVE BANK OF RICHMOND 15 ------ ,960 -‘-.--,9&j --- 1968 --- 1968 . . . . . . ..-... ,972 - 1976 - 1976 monthly seasonal movement into the preliminary adjusted weekly data in a manner analogous to the impact of the Christmas cycle on the adjusted monthly data.24 There is ample evidence that intramonthly seasonal patterns change. The two panels of Chart 7 depict the intramonthly pattern of the not seasonally adjusted MI data during four separate years spanning a 16-year period for the months of July and August. These months were selected since they are less influenced than other months by tax dates and other events that might obscure the evolution. While this evolution has by no means proceeded at a steady pace, a careful examination of both panels of this chart suggests that there is now relatively greater strength in the data during the first half of the month and a sharper decline during the second half. Comw Bee 16 Section III, pp. 8-9. ECONOMIC parable data for other months suggest that a similar change may be occurring in these moriths.“5 While this evolution is not as neat and persistent as the similar gradual change in the Christmas cycle affecting the monthly data, it does appear to be influencing the behavior of the adjusted weekly data. Chart 8 provides evidence supporting this contention. The chart shows the average change in preliminary seasonally adjusted Ml for statement weeks ending on a given calendar day of the month over the 12 months of 1976, smoothed by a moving average. The chart clearly indicates an upward bias in the seasonall) adjusted movement of Ml in the first half of the month and a downward bias in the second half of the month, a pattern consistent with the evolution of the SThe cause changes in and receipts, ing factor. of this evolution the intramonthly however, are in REVIEW, NOVEMBER/DECEMBER 1977 Systematic is not entirely clear. pattern of Treasury disbursements all likelihood an important eo‘otribut- procedures to capture fully the impact of changes in the seasonal behavior of Ml, especially when such changes are actually in progress. Specifically, the discussion has indicated that the observed variation in short-run growth rates has been produced by forces as broad and persistent as the apparent longerrun change in the seasonal demand for M1 balances during the Christmas season and the abrupt change in the level of Federal income tax refunds in 1973 to such seemingly innocuous developments as the recent change in the timing of monthly social security disbursements and year-to-year variations in the time required to process tax payments. 71 Moving Average -2 ‘_ -3 - IIIIIIIIIIIIIIIILLL 2 4 6 8 10 12 14 16 18 20 22 24 26 28 3 Day of the Month . * (. _. : F The dotted line is the average change in the Note: seasonally adjusted money supply for all statement weeks in 1976 that ended an the day The solid line is a centered $-day plotted. moving average of the points on the dotted I Jinr, So&w: Federal Reserve Board Release, H.6: intramonthly pattern of the not seasonally data illustrated in Chart 7. adjusted Monetary economists, both inside and outside the Federal Reserve, frequently point out that too much attention is paid to monthly and weekly M, growth Short-run growth rates are important, howrates. ever, because the Federal Reserve’s current procedure for implementing monetary policy on a day-to-day basis makes them important. As pointed out in the introduction to this article, preliminary estimates of current two-month Ml growth rates are one of the major factors determining policy actions under existing operating procedures. Federal Reserve policymakers are well aware of the existence of short-run disturbances of the kind discussed in this article. The problem faced by policymakers-and by financial market participants attempting to anticipate Federal Reserve policy-is that the immediate causes of short-run M1 growth rate variations are not usually apparent on a current basis. But the appropriate policy response to sucli movements depends critically on the conditions causing them. Suppose, for esample, that M1 growth over a two-month period exceeded the desired longerIf it were clear that this divergence rerun rate. flected an increase in the demand for transactions 1)alnnces due to excessive final demand for goods V. Conclusion and services FEDERAL RESERVE in the economy at large, policymakers know that the acceleration should be resisted. Conversely, if the increase were obviously the result of some temporary disturl~nnce likely to wash out in This article has attempted to identify and esplnin some of the factors that produce the high degree of observed variability in short-run seasonally adjusted Ml growth rates. Sonic of this varial)ility undouhtedly results from fundamental changes in economic conditions that produce changes in the underlying demand for and supply of n1, balances. A large part of the olzerved variation, however, appears to have little ‘ro do with economic conditions, and it is with these noneconomic determinants that this article has lIeen concerned. In particular. the article has argued that many short-run swings in M, growth rates result frolli ( 1 ) special events that occur irregularly or (2) the inability of existing seasonal adjustment woultl the near future, policymakers would presumably pursue ;I steady policy course. The principal implication of the analysis in this article is that making such determinations on a current basis with any degree of certainty is always difficult and often impossible. As the preceding sections have attempted to demonstrate, a wide variety of factors unrelated to basic economic trends can and do affect short-run Ml growth rates, particularly the preliminary growth rates that actually determine policy actions. BANK OF RICHMOND 17 Unfortunately, no simple, this problem-either servers-is likely circumstances, individual pears the not times incoming Beyond however, promising presented seasonally changes and short-run the more Under analysis of rates In in this article with M1 patterns tactical ol)- policy. Any lqontl data each appar- suggests seasonal any printe these or market approach. adjusted (2) to solution growth (1 ) with in these the question lies eclectic in short-run familiarity of the year spective forthcoming. and most the analysis policyrnakers be close that a detailed ating to fluctuation to be the ticular, in for mechanical patterns at certain ongoing or pro- can assist in evalu- of evaluating fundamental incoming issue detailed current of the implementing difficulties short-run doul)ts sl)out cedure. of this R/l1 data, however, such as the esisting short-run short-run growth in n very one, rates systenlatic for improving these where.“G would appear further is well de- evaluating is bound to raise operating pro- that focuses largely rates without relating to desired have that longer-run Suggestions fashion. procedures It in of any growth growth monetary issue The preceding inherent the effectiveness on nnnualized these for analysis the scope of this article. scription deserve M1 data. procedures been tllese made else- suggestions attention. data, of appro- 20 See, for example, Poole [Sl. References 1. Surge in Ml Laid to Auerbach, Irving M. “Recent IRS Delay in Processing Taxes.” The Money Manager, May 16, 1977, pp. 4-5. 5. Poole, William. “Interpreting the Fed’s Targets.” Brookings Papers on Economic (1st quarter, 1976), pp. 247-259. 2. Breimyer, F. and Wenninger, J. “An Estimation of the Effect of Treasury Tax Rebates and Social Federal Reserve Security Supplements on M1.” Bank of New York Research Paper No. 7611, March 1976. 6. Poole, William and Lieberman, Monetary Control.” Brookings Activity, (2nd quarter, 1972), 7. 3. “Seasonal Adjustment of the Lawler, Thomas. Money Stock: Problems and Policy Implications.” Economic Review, Federal Reserve Bank of Richmond, (November/December 1977)) pp. 19-27. Bureau of the U. S. Department of Commerce. Census. The X-11 Variapzt of the Census Method 1’1 Seasonal Adjustment Progrum, by J. Shiskin, A. II. Young, and J. C. Musgrave. Technical Paper No. 15. Washington, D. C.: 1967. 4. Lombra, Raymond E. and Torto, Raymond G. “The Strategy of Monetary Policy.” Economic Review, Federal Reserve Bank of Richmond, (September/ October 1975), pp. 3-14. 8. Wood, Cynthia W. “Money non~ic Commentary, Federal land, May 16, 1977. 18 ECONOMIC REVIEW, NOVEMBER/DECEMBER 1977 Monetar:y Aetivitbf, Charles. “Improving Papevs ox Economic pp. 293-335. Stock Revisions.” EeoReserve Bank of Cleve- SEASONAL ADJUSTMENT OF THE MONEY STOCK: Problems and Policy Implications Thomas A. Lawler The short-run behavior of the seasonally adjusted money stock has received increased attention from l~olicyniakers. economists, and financial analysts in recent years. Quarterly, monthly, and even weekly changes in the adjusted money stock are scrutinized carefully. Recently, however, some economists have questioned the adequacy of the method used to adjust the money stock for seasonality, and therefore the quality of the seasonally adjusted data itself.’ Since the Federal Reserve considers short-run movements in the seasonally adjusted money stock in formulating monetary policy, seasonal adjustment problems may adversely affect the Fed’s ability to achieve its policy goals. The purpose of this article is to discuss some of the problems associated with adjusting the money stock for sensonality. The article begins \vith a brief discussion of the general principles of seasonal adjustNest, it examines the method currently used ment. to adjust the monthly money stock (defined here as or currency plus demand deposits) for seasonality. Finally, it discusses the policy implications of inadequate seasonal adjustment. hz,, then it may not be offset within a year, and, in the absence of any policy action, may affect long-run money growth. Seasonal Adjustment Methods There are various seasonal adjustment techniques available. Most of these assume that an original time series (0) can be broken down into separate components, namely the seasonal component, the trend-cycle component, and the irregular component. The seasonal component (S) embodies the intrayear pattern of variation that recurs regularly from year to year. The trend-cycle component (C) is made up of long-term trend and cyclical movements. The irregular component (I) reflects the influence of short-run erratic fluctuations. A seasonally adjusted series is composed of the trendcycle and irregular components, the seasonal component having been filtered out. Experience indicates that for most economic time series, including the money stock [7, pp. 4-71, these components are related in a multiplicative fashion (i.e., 0 = c x s x I).” Ratio-to-Moving Average Method The most widely used multiplicative method of seasonal adjustment is the ratio-to-moving average niethod.3 For a monthly series the basic steps of this method are: Purpose of Seasonal Adjustment The purpose of seasonally adjusting a time series is to separate from that series any short-run variations that tend to recur at the same time each year. In this way longer-term movements as well as unusual short-term fluctuations can be distinguished from these systematic intrayear The distinction between seasonal and movements. nonseasonal movements is important, as the policy implications of the two types of movements may differ. For example, the reaction of the Federal Reserve to a change in short-run money growth \vill generally depend on whether that change is perceived as being consistent with some long-range money growth target. If 3 short-run change in money growth is due solely to seasonal forces, then it will be offset later in the year, with no effect on long-run money growth. Conversely, if the change in money growth is caused by nonseasonal influences, ‘E.g., see IS], Cl?]. 1. A 12-month centered moving average of the original series is constructed so that short-run intrayear movements are averaged out and the trend-cycle component can be estimated.4 The average must be centered because a 12-month average falls between the sixth and seventh months, and therefore cannot be associated with either. For example, the midpoint of a 12-month average from January to December, inclusive, falls between June and July. Similarly, the midpoint of a 12month average from February to January, inclusive, falls between July and August. However, the average of these two 12-month averages is centered on the month of July. Therefore! centering a 12month moving average on a specific month is accomplished by taking the average of each two consecutive 12-month averages. ‘This c+s+1. 2 A good numerical is in contrast discussion example, to an additive relationship, of the ratio-to-moving is given in [ZI. 4 A moving average is simply an average period at a time. dropping one term and ClSl. FEDERAL RESERVE BANK OF RICHMOND average where method, that moves forward adding another. 0 with = a one 19 The X-11 Prqrnm The basic steps of the X-l 1 program are described in the Box on page 23.” The: X-l 1 program is an iterative process that can br broken down into three stages. In the first stage 2. preliminary seasonally adjusted series is obtained using a method similar to the ratio-to-moving aveT-age procedure described above, with an additional step limiting the influence of extreme irregular movements on computed seasonal factors. In the second stage a weighted average of this preliminary season- 2. This centered average is then divided into the original series, and the resulting ratios are known as seasonal-irregular (S-I) ratios. 3. A moving average of these S-I ratios is computed separately for each month (i.e., a separate average of the S-I ratios for January, the S-I ratios for February, etc.) so that irregular movements are averaged out. This average estimates the seasonal component, or seasonal factor, for each month. The use of a moving average of the S-I ratios allows for a seasonal aattern that changes gradually over time. The t&e span over which these S-I ratios are averaged depends on how fast the seasonal pattern is assumed to change -the more stable the assumed seasonal pattern, the longer the span. If the seasonal pattern is believed to be constant over time, then the seasonal factor for each month is the average of all S-I ratios for that month. 4. These seasonal factors are divided original series to obtain a seasonally series. ally adjusted of the trend-cycle average yields does a simple into the adjusted the original better Note that the seasonal factor in any time series is simply the ratio of the unadjusted value to the adjusted value of the series. Therefore, a seasonal factor (converted to an index number) greater than 100 indicates that seasonal influences are tending to push the series above the yearly average, while a factor below 100 indicates that the series is depressed by seasonal influences. Seasonal Adjustment 1 plots monthly ponents, of the Money Stock Chart the seasonally unadjusted and adjusted money stock series (Ml) and its two comdemand deposits and currency, from 1970 to 1976. The chart indicates that the unadjusted money stock series is subject to significant seasonal variation, deposit the greater component. seasonally adjusted part deriving However, from the demand it is movement series that commands tion of most analysts and policymakers. describes adjust the monthly The Fed separately mand deposit in the the atten- used by the Federal the method This section Reserve to M1 series for seasonality. adjusts components of the currency hll for and de- seasonal vari- ation. Seasonal factors are first computed for each Ml component using the Bureau of the Census’ X- 11 Variant of the Census Method II Seasonal Adjustment Program (hereafter simply X-11). The X-l 1 is based on the ratio-to-moving average method described above, although it is more complicated. The output of the X-11 is then reviewed by the Board of Governors’ staff, and modifications are made when deemed appropriate. The modified seasonally adjusted currency and demand deposit series are added together to obtain the seasonally adjusted money stock. The two steps, the X-11 and judgmental modification, are discussed in more detail below. 20 ECONOMIC REVIEW, series is calculated estimate a smoother 12-month series, to obtain component. trend-cycle centered of the true curve moving and is generally representation a revised This weighted than average thought of to be a underlying trend- cycle component. In the third stage this revised estimate of the trend-cycle component is used to obtain revised calculations for the irregular the seasonal series. and the seasonally component, component, adjusted Jrrdglltcntal iZlodifiration Once the X-l 1 program has generated seasonal factors for each component of the money stock series, the Board of Governors’ staff reviews the X-11’s output, and any factor which in its judgment does not represent true seasonal influences is modified.” These final modified season;>1 factors are divided into the original series to obtain the final seasonally adjusted series. These judgmental modifications can either increase or decrease the smoothness of the X-11 adjusted series, and, depending on the circumstances, either type of modification may be justified. One justification for judgmental modifications that smooth the series stems from the X-11’s use of 5- and 7-term moving averages to separate the seasonal from the irregular component [see Box, steps 3, 7, 11, and 131. The use of these moving averages assumes a smooth, continuous change in seasonal patterns. If something occurs that would abruptly change the seasonal pattern of the series (such as the shift in the tax filing date from March 15 to i\pril 15 in 195.5), the X-l 1 would only reflect this change gradually. In such a case there seems to be good reason to modify the X-11 generated seasonal factor to reflect this change. This type of modification tends to smooth the series, since the change in the unadjusted series caused by the shift in seasonal patterns is reflected in the seasonal factor. On the other hand, a &For a more 8 Ot course, factors over detailed description these modifications any l&month period NOVEMBER/DECEMBER 1977 see [ZOI. especially are constrained must still sum pp. in that to 12.000. 8-11. seasonal Chart 1 Ml TOTAL AND COMPONENTS 1970-76 $ Billions 320 NOT SEASONALLY ADJUSTED (N.S.A.) 300 300 - 280 - 260 - 240 - ----- SEASONALLY ADJUSTED (S.A.) I 220 200 DEMAND DEPOSITS 180 60 CURRENCY possible justificnfion for jiidgmentnl modifications that decrease the smoothness of the seasonally adjusted series is that the 5- and 7-term moving averages of the S-I ratios conqxttetl I)y X-1 1 may not be long enough to ayerage out sufficiently the influence of relatively large nonseasonal movements (i.e.. those nonseasonal nlovements that are large but not thrown out as estreme). If it npl)ears that a large nouseasonal movement in the money stock series for ;I given month (such as the June 19i.5 jump in MI caused 11) the tax r&ate) has untlul~~ influenced the S-1 1 generated seasonal factor for that month, then it seems jnstifinl)le to alter that seasonal factor. This type of modification makes the series less smooth, as the nonseasonal movement in the series is no Iongel compensated for by the seasonal factor. Ml seasonally adjusted by S-11 alone, from 1970 to 1976.’ Also plotted is the difference between the two gro\vth rates. The chart shows that while the two growth rates generally move together, judgmental changes have often significantly affected the published A4I growth rates. The correlation coefficient of these t\vo growth rates is only S67, which suggests that judgmental decisions play a significant role in determining the final published rates of growth. To determine the net effect of these judgmental modifications on the smoothness of the M, series, the standard deviation of each of the two growth rate series was calculated. For the period 1970 to 1976, the two standard deviations are almost identical, suggesting that over the whole period judgmental changes did not alter the smoothness of the series (though as Chart 2 indicates, judgmental changes Impact of Judgmental Modifications Chart 2 plots the monthly annualized rates of growth of MI seasonally adjusted by the I3oard of Governors and FEDERAL RESERVE i The X-11’s default options demand deposit series using BANK OF RICHMOND were data used from to adjust 1965 to the currency 1976. and 21 - SEASONALLY ADJUSTED BY X-11 ALONE ---4 SEASONALLY ADJUSTED BY BOARD OF GOVERNORS 1970 I I I I -1OI 1971 1972 I I I 1973 1974 1975 *CONTINUOUSLY COMPOUNDED ANNUAL RATES. L Sburce: Federal Reserve Bulletin. have at certain times smoothed the series and at other times made the series less smooth) .R Iio~\.If just the 197576 suhperiod is considered, ever, the standard deviation of the pul~lishetl 14 1 growth rates (5.5) is sul~stantially greater than that of the X-l 1 generated growth rates (3.5)) meaning that judgmental changes decreased the smoothness of the M, series in that suhperiod. Chart 2 also shows that judgmental modifications have been larger in these two years. One ‘possible reason for modifying the X-11’s seasonal factors for 1975 and 1976 in this fashion involves the X-11’s use of data before antl. when available, after a given year in determining seasonal factors. Since 1975 and 1976 are the two end years for the series used in this article, sufficient year-ahead data are not available to compute 5 and /‘-term moving averages of S-I ratios centered in these years. As noted in the description of the X-l 1 [see Box], relatively higher weights are assigned to end year data to compensate for this lack of future This procedure increases the chance of the data. 8 The standard deviation of the MI growth rate for the period 1970 to 1976 seasonally adjusted by the Board of Governors is 4.27, while seasonally adjusted by X-11 it is 4.31. The standard deviation is a valid measure of the relative smoothness of the two series because by definition their trends are the same. 22 ECONOMIC S-l 1 incorporating nonseasonal movements into the seasonal factors for the end years. Apparently the staff at the I!oartl of Governors thought that the large nonseasonal movements in the M1 series in 1975 and 1976 (especially in January 1975 and April 1976) \vere at least partly incorporated into the X-l 1 seasonal factors, and they modified the seasonal factors to take account of this possil)ility. Unfortinlately, these judgmental decisions do not alw:~ys ljerfcctly compens:~te for deficiencies in the X-l 1, It is extrenlely difficult to (letermine preciz;ely the effect :I gixven occurrence will have on seasonal factors, or what portion of the X-l 1 seasonal factors rq)resents the “true” seasonal pattern and what l)ortion reflects nonseasonal influences. Shortcomings of the Present Method There are a nunll)er of shortcomings of the present seasonal xljustment method. These shortcomings are inherent in almost all seasonal adjustment techniques. Therefore, in discussing the prol,lems associated with the currently used seasonal adjustment process, this article does not mean to imply that the present process is a “bad” one, or that there exist other methods that are unambiguously better. REVIEW, NOVEMBER/DECEMBER 1977 Box BASIC STEPS OF THE X-l 1 SEASONAL ADJUSTMENT PROGRAM -tllis time \vith extreme values replaced as tlescribed in step 6-to obtain modified first-round seasonal factors. Again, these seasonal factors are ;ctljustctl to sum to 12.000 over any IL-montll period. 8. Tl~ese nlodificd first-round seasonal are divided into the original scrics to get liminary seasonally adjusted series. 3. .\ \vciglltctl .i-!crnl 111ovilq avcrs,qe of tllese for S-l rati<,h (\vitll \veights 220.127.116.11.1 ) is computed cacl~ of tile 11 calc~ltlar liloirtl\5 ~cl)aratel?; to aver;16c out tllc illilucllcc of irrc~ular lllovements and to ol)taill iir.<t-round cstinlatcs of the ieaional factors. ‘l‘lie ,151: of a nloving average yield5 a tli5tillct bca‘l‘hus, soll:ll factor for cacll lilnnth of cacl1 year. the iir>t-round SK,WII~I iwor fur. SLY. January 1973 is tlerivetl frown 111~ five January S-I Iratio\ for tile years 1971 to 1075. inclu5ivc. 9. A special weighted moving average (the socalled Hentlcrson average) is applied to this prcliminar) seasonally adjusted series to ol,taiu ;I revised cstimatc of the trelltl-cycle componcnt.~’ The span of this moving average depends on the variability of the irregular component relative to that of tile trcntl-cycle component. with the more A preirregular the series, the longer the span. liminary estimate of the variability of the irregular relative to the trend-cycle is obtained using a 13month Henderson average [ZO, p. 341. I-niortunatcly. sufficient year-alleatl tlat;c arc not at the end of a titllc series available for tllc 2-years ITor ex:1n1ple. a to calcu!nte tllis J-term avcragc. .i-tern1 average cclltcretl in 1976 rcrluire> S-l ratios for 197-1 through lY78. inclusive, wllilc ior this article 1976 is tllc last year for \vhich data arc available. To conlpcllsate for tllc lack of future data, the S-l I wcigllts the availal)lc S-I ratios (which for 1076 factors are the S-l ratios for 1974. lY75, and 1976) more hea:~ily than if future data xverc For csample. in calculating the firstavailable. round seasonal factor for January 1976 (\vith data through 1976). ti~c January 1976 S-I ratio is given a \veight of .107. wllilc in computing the first-round scaso~lal factor for January 1973. the January 1973 S-l ratio is given a weight of only .333 [?O, p, 611. 10. This revised trend-cycle into the original series to obtain seasonal to get an factors estimate 12. These revised seasonal factors are divided into the S-I ratios to get new estimates of the irregular component, and the S-I ratios are modified for extremes by the same method as described in step 6. (a) greater than 2.5, it is considered an extreme value. and the corresponding S-I ratio is removed and replaced hy an average of the two nearest preceding and t\vo nearest follo\ving full \veight (i.e.. unmodified) S-I ratios for that month: then the corresponding is given full weight; 13. A weighted 7-term moving average of these modified S-I ratios is computed separately for each month to obtain the X-11’s final seasonal factors. (Of course, these factors are adjusted to sum to 12.000 over any 12.month period.) S-I 14. These final seasonal the original series to obtain ally adjusted series. 2.50 and I..;, a linearly graduated Cc) bet\vccn \velght I)et\vccn 0.0 and 1.0 is assigned to the irregular, and the corresponding S-I ratio is replaced with an average of the ratio times its assigned weight and the two nearest preceding and t\vo nearest following full lveight S-I ratios for that month. ing :\ xveighted j-term is again calculated S n+1= FEDERAL RESERVE S, = the ‘* A Henderson squares of the discussion of age see , moving average of the S-l separately for each month BANK factors are divided into the X-11’s final season- 15. Preliminary seasonal year are estimated from where This graduated treatment of extremes is designed to limit the influence of unusually large irregular movements on seasonal factors. 7. ratios is divided S-I ratios. Sufficient year-ahead data are not available for the 3 year> at the end of the series to compute this 7-term average. For example, a 7-term average centered in 1976 needs data from 1973 to 1979. inclusive. and (as of the end of 1976) data from lY77 to 1979 are not availaljle. To compensate for this lack of future data, the X-11 weights the available S-I ratios (for 1976 factors, the ratios for 1973 through 1976) more heavily than if future data For example, in computing the xvcrc available. revised January 1976 seasonal factor, the January S-I ratio for 1976 is given a weight of 283, while in computing the revised January 1973 seasonal factor the January 1973 S-I ratio is given a weight of only ,200 [20, p. 611. 6. .-\ nlo\ring i-year (60-month) standard deviation [a) of these irregular component estimates is calculated. and the irregulars in the central year of the j-year period are tested against 3.5, Irregulars greater than 2.50 are removed, and the moving j-year standard tlcviation is again computed If the irrcgtilar for 3 nlonth in the central year is: (I,) less tllan 1.5, ratio for that month estimate revised 11. A weighted 7-term moving average (with lvcights 1,2,3,3,3,2,1) of these S-I ratios is computed separately for each month to oljtain revised seasonal factor estimates. Thus, the seasonal factor for. say, January 1973 is derived from the seven January S-I ratios for the years 1970 to 1976. inclusive. -1. These factors arc atljustctl to hum to 12.000 in ratio form. or 1,200 in index numl)er form. over any ll-month period so that year-to-year cllanges in the series are unaffected [20. p, 911. 5. The<e adjusted first-round are tlividctl into the S-I ratios of the irregular component. factor; a pre- OF RICHMOND s, + seasonal factors for the the formula %(S, factor - upcom- s,-11, for year n. average minimizes the sum third differences of a series. the merits of the Henderson especially Chapter III. of the For a aver- 23 Moe&zg Scaso~2nl Option One prol~leni alrend) alluded to involves the X-1 l’s use of 5 and 7-term moving averages to separate the seasonal component Some critics have from the irregular conil~onent. argued that the seasonal pattern of the nioney stock has been quite stable over time, and therefore that the )(-l l’s use of these relatively short moving averages only serves to smooth the money stock series excessively. Poole and Lieberman [ 17, 1). 327j argue that the use of the S-l l’s moving senson:J option to adjust the money stock is justifiable only if the money stock’s seasonal factors e.\;hibit a recognizable trend. Chart 3 plots M, seasonal factors (unndjusted Ml/adjusted M,) separately for each month over the period 1947 to 1976. The chart indicates that the factors for some months do display a clear trend. However, it also shows that for periods where no recognizable trend is present, seasonal factors for some months still vary significantly from year to year. Thus, the evidence suggests both that a niovii~g seasonal model is warranted, and that the present method overly smooths the series. This behavior of the X-11 seasonal factors reflects the trade-off that exists between adequately allowing for moving sensonality and preventing nonseasonal movements from being incorporated into seasonal factors. The length of the moving average used reflects the adjuster’s judgment on this trade-off. Other evidence that suggests that the current method of seasonal adjustment is unduly smoothing the money stock series is given by Kaufman and Lombra [S] . Using spectral analysis, a statistical technique that decomposes a series into periodic (e.g., seasonal) movements, they find that the seasonal adjustment process flattens out the series at nonseasonal frequencies, “which indicates excessive smoothing of the series” [S, p. 1516J. SJaifts ipa Seasonal Yew-Em1 Revisions Another shortcoming involves the year-end revisions of the money stock necessitated by the use of the X-l 1. The X-l 1 uses data several years before and, when available, after a given month to determine that nionth’s seasonal fator. Unfortunately, sufficient future data are not available for end years in the series to calculate the 5 and 7-term moving averages of the S-I ratios used to compute seasonal factors [see Box, steps 3 and 11 J. At the end of each year, the newly availab’ie data for that year are entered into the X-l 1, and revised seasonal factors are obtained for these end years. These revised factors frequently differ sig‘/See the accompanying article discussion of some of the factors bulge in MI in 1976 and 1977. PRELIMINARY ECONOMIC by Cook believed and Broaddus to have caused VERSUS REVISED Ml GROWTH [l] the for a April RATIES 1975 (2) (1) Preliminary M 1 Growth Rates Pattcms Another problem occurs when the seasonal pattern of a time series The X-11 is not designed to changes abruptly. handle sharp, discontinuous shifts in the seasonal pattern, and judgmental changes are seldom able to correct the X-11 deficiencies perfectly. Failure to take such shifts into account can cause computed seasonally adjusted series to exhibit unexplained variability. The recent behavior of the IvI, series may be an example of a seasonal pattern shift. In April of both 1976 and 1977, the monthly seasonally adjusted M1 growth rate jumped unexpectedly, with the annualized growth rate being almost 15 percent in April 1976 and 20 percent in April 1977. Suppose the seasonal pattern in the demand for M, shifted abruptly in 1976 in such a way that money demand 24 rose in April relative to the other months. The X-l 1, with its /^-term moving average of S-I ratios, would not fully capture this shift until 1979, since the X-1 1 c:Jculatetl seasonal factors for April in 19TG and 1977 are derived from data hefore this hypothetical seasonal pattern shift occurs in 1976. Therefore these factors will understate the true seasonal conil)onent for April in 1976 and 1977, causing the reported seasonally adjusted growth rate to overstate the true seasonally adjusted growth rate. Whether these unusually high April movements in M1 are actually the result of a shift in the seasonal pattern of the demand for money, however, remains to be seen.L) January -11.8 February -5.1 3.4 March Revised Ml Growth Rates* (2) - (1) Difference ~6.7 0 -3.4 - 1.7 11.0 9.3 April 3.4 3.4 0 MOY 11.3 11.3 0 -4.6 June i a.7 14.1 July 2.0 3.7 1.7 August 2.9 5.3 2.4 1.6 - .4 September 2.0 Ociober -2.4 November 12.2 December --.8 - 2.8 *Revisions Source: made Federal REVIEW, NOVEMBER/DECEMBER 9.0 -3.3 in Jonuary Reserve 1977 1976. Bulletin. 1.6 -3.2 - .5 nificantly from the preliminary factors, and often affect the previously published MI growth rates. The accompanying table lists the 1975 seasonally adjusted annualized monthly rates of growth of MI published both before and after the January 1976 year-end revisions. Absolute differences in the before and after monthly growth rates vary from 0 to almost 6% percentage points, with an average absolute deviation of about 2.2 percentage points. Most of this clifference can be attributed to revisions in the seasonal factors (as opposed to revisions in the underlying data). Kaufman and Lombra believe that “the sizable difference between ‘final’ data (employed by the model-builders) and the ‘preliminary’ data (viewed by the policymakers) introduces a significant distortion into estimates of policy impacts” [S, p. 1525] Scasoml Relationships A~uo~lg Series Another problem with seasonal adjustment involves the way in which the money stack and other economic variables are seasonally adjusted on a variable-to-variable llasis, without regard to the relationship between seasonal changes in one series and seasonal changes in other series. Marc Nerlove notes that : Seasonal variations have causes and insofar as these causes are measurable they should be used to explain changes that are normally regarded as seasonal. Indeed, seasonality does not occur in isolated economic series, but seasonal and other changes in one series are related to those in another [15, p. 2631. This is especially important because the money stock is a policy-controlled variable-i.e., the actions of the monetary authorities influence the seasonal pattern of the money stock. Therefore, if the policy objective of allowing the money stock to exhibit seasonality is to affect the seasonal pattern of some other economic variable, then knowledge of the structural relationship between seasonal movements in the two series would be desirable. “Unfortunately, the nature of ratio-to-moving average techniques and post-war monetary tion” policy [S, p. For example, its inception . I combine to obfuscate such informa- 1523]. the implicit has been policy of the Fed since to reduce or eliminate interest rate seasonality (arising from a natural seasonal in the demand for money) by allowing the money supply to vary seasonally. However, the method used to seasonally adjust the money stock does not take into account the structural relationships among seasonal movements in the money stock, interest rates, and factors affecting the seasonal in money demand. Indeed, one of the reasons that the present adjustment is inadequate in handlin g abrupt seasonal pattern shifts is that it fails to take into account the relation- FEDERAL RESERVE BANK OF RICHMOND 25 ship between abrupt changes in those factors affecting the money seasonal and the money seasonal itself. Sensomlily irr Polir~~ .ilctio,zs One final shortcoming discussed here is that since the money stock is a policy-controlled variable, any seasonality in the Fed’s policy actions may affect the seasonal factors calculated by the X-l 1. For example, if the Fed increases its money growth targets at the same time of the year in successive years, then the X-l 1, with its moving seasonal option, may incorporate these policy movements into its seasonal factors in subsequent revisions. Thus seasonality in policy actions, whether accidental or otherwise, may cause changes in computed money seasonal factors that are not due to any change in the underlying seasonal pattern of the demand for money and credit. Poole and Lieberman [17, p. 2361 believe that the seasonal behavior of policy actions has been affecting money seasonal factors. Seasonality and Monetary Policy As mentioned in the beginning of the article, the purpose of seasonal adjustment is to enable the user of a time series to differentiate between seasonal and nonseasonal movements. However, the above discussion suggests that the present method used to adjust the money stock sometimes has trouble separating seasonal from nonseasonal movements. For the Fed to be able to determine what portion of the current movement in the money stock is due to seasonal forces, the seasonal factors used to adjust the money data should reflect the true seasonal pattern in the demand for money and credit. In other words, nonseasonal movements should not influence the seasonal factors, while shifts in the seasonal pattern of money and credit demand should be fully reflected. However, the factors used to adjust current money stock data are probably the least likely to satisfy these criteria, since they are based solely on past money stock movements. These seasonal adjustment problems can affect Federal Reserve policy. To understand how, it is necessary to have some idea of the Fed’s short-run strategy of monetary policy.lO Each month the Federal Open Market Committee sets a tolerance range for the two-month growth rate of the seasonally adjusted money stock and a tolerThe seaance range for the Federal funds rate.ll sonaliy adjusted money growth rate is allowed to fluctuate within this tolerance range in order to limit 10 The following simplified. For 11 The Federal lend each other 26 description of the a fuller discussion funds rate reserves. is the Fed’s short-run strategy see 131 and [Ill. rate at which commercial ECONOMIC is Holvever, if the two-month interest rate variability. money growth rate appears to be moxing outside of the tolerance range, the Fed may react by changing its funds rate target so that longer-run control of the money stock can be achieved. The Fed’s money growth tolerance ranges are stated in seasonally adjusted terms, and the factors used to adjust the money stock are calculated by the method described above. Unfortunately, these computed factors may not reflect the true seasonal forces affecting the demand for money and credit in the current year. If they do not, then the seasona!lJ, adjusted money growth rate may exhibit fluctuations that are due solely to faulty seasonal adjustment.‘:! These adjustment problems increase the difficulty of setting short-run money growth targets that are compatiljle !,oth with some longer-run money target ant! Adjustment problems with interest rate stability. also complicate the Fed’s taslc of deciding how to react to a given short-run change in money growth. For example, suppose that the seasonally ndjustec! M, growth rate in a given month is either very high or very low, causing the two-month money growtll If the rate to move outsitle of its tolerance range. change in money growth is due to faulty seasonal adjustment, then any corrective action by the Fed will have to be reversed later in the year, producing WInecessary fluctuations in short-term interest rate:;. However, if the Fed does not react to this change in money growth by changing its funds rate target, and the change in money growth is really caused not by seasonal adjustment problems, but by, say, a cyclic:-d shift in the demand for money, then deviations from target money growth rates may cumulate, and sonle longer-run target may be missed. Thus season,4 adjustment problems must be added to that long list of factors complicating monetary control. Conclusion This article has shown that adjusting the money stock for seasonality is no trivial matter. Despite its high degree of sophistication, the X- 11 program employed to seasonally adjust the money stock is far from flawless. The Board of Governors’ staff recognizes that the X-11 is not perfect and Even the attempts to correct for its deficiencies. Board staff, however, cannot always distinguish between seasonal and nonseasonal movements in the money stock, especially in current money stock movements. If the estimated seasonal factors for the current year imperfectly reflect the influence of actual seasonal forces, then the seasonally adjusted over- banks REVIEW, 12 For specific examples of affected reported seasonally and Broaddus [l]. NOVEMBER/DECEMBER 1977 how seasonal adjustment adjusted money growth problems have rates, see Cook money data will exhibit some spurious volatility caused by the imperfections. Considering the Fed’s dual policy goals of (a) long-run stability in money growth, and (b) short-run stability in money market interest rates, these seasonal adjustment problems can complicate the task of determining the proper policy response to any given short-run movement in the seasonally adjusted money stock. References Marris, Stephen N. “A Technical Survey of Problems and Methods of Seasonal Adjustment in Europe and North America, with Special Reference to United States Bureau of the Census Method II.” Seasonal Adjustment on Electronic Computers. Washington, D. C.: Organization for Economic Development, 1960, pp. 35-78. -. in Census Electronic 15. Cullison, William E. “A Seasonally Adjusted World-The Census Seasonal Adjustment Technique.” Monthly Review, Federal Reserve Bank of Richmond, (August 1970), pp. 2-8. MacCauley, Frederick R. The Smoothing of Time Series. New York: National Bureau of Economic Research, 1931. 13. Broaddus, Alfred and Cook, Timothy Q. “Some Factors Affecting Short-Run Growth Rates of the Money Supply.” Economic Review, Federal Reserve Bank of Richmond, (November/December 1977). 2. 12. 14. 1. Analysis of Seasonal AdNerlove, Marc. “Spectral Econometrica, (July 1964)) justment Procedures.” pp. 241-286. “Monetary Objectives and Davis, Richard G. Monetary Policy.” Quarterly Review, Federal Reserve Bank of New York, (Spring 1977), pp. 29-36. Diller, Stanley. The Seasonal Variation of Interest Rates. NBER Occasional Paper 108. New York: National Bureau of Economic Research, 1969. Friedman, Mi!ton. A Program for Monetary bility. New York: Fordham University Press, Sta1960. and Schwartz, Anna J. A Monetary History of the United States: 1867-1960. A National Bureau of Economic Research Study. Princeton : Princeton University Press, 1963. 7. 16. Organization velopment. Computers. Seasonal Adjustment of MIFry, Edward. Czcr)zxtly Published and Alternative Methods. Staff Economic Studies 87. Washington, D. C.: Board of Governors of the Federal Reserve System, 1976. Herbert M. and Lombra, Raymond E. “Short-Run Variations in the Money Stock.” Southcy?z Economic Journal, (February 1977), pp. 15151527. 11. 19. “Causes of Seasonal Variations in InRates.” Monthly Review, Federal Reserve of Kansas City, (February 1974)) pp. 3-12. Lombra, Strategy Federal October and DeElectronic Committee on Monetary Statistics. Report 18. Advisory of the Committee. Improving the Monetary Aggregates. Washington, D. C.: Board of Governors of the Federal Reserve System, 1976. Variations in Interest Kohn, Donald L. “Seasonal Rates.” Monthly Review, Federal Reserve Bank of Kansas City, (November 19’73), pp. 3-10. 10. ----. terest Bank for Economic Cooperation Seasonal Adjustment on Washington, D. C.: 1960. and Lieberman, Charles. “Improv17. Poole, William ing Monetary Control.” Brookings Papers on Economic Activity, (2nd quarter, 1972), pp. 292342. 8. Kaufman, 9. “The Treatment of Moving Seasonality Method II.” Seasonal Adjustment on Computers, pp. 259-309. Shiskin, Julius and Eisenpress, Harry. Adjustment by Electronic Computer NBER Technical Paper 12. New York: Bureau of Economic Research, 1958. Seasonal Methods. National of Commerce. Bureau of the 20. U. S. Department Census. The X-11 Variant of the Census Method II Seasonal Adjustment Program, by J. Shiskin, A. H. Young, and J. C. Musgrave. Technical Paper No. 15. Washington, D. C.: 1967. Raymond E. and Torto, Raymond G. “The of Monetary Policy.” Economic Review, Reserve Bank of Richmond, (September/ 1975), pp. 3-14. , The ECOXOMIC :: b Richnlond. REVIEW is produced Slrbscriptions Public Relations. 23261. Arficles by the Research Department of the Federal Reserve Bank of Address inqztiries to Bank and are available to the public witlzolft charge. Federal Reserve Bank of Richmond, if source P. 0. 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