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FEDERAL RESERVE B A N K O F S T. L O U IS JUNE 1975 Two Stages to the Current Recession ............... 2 A M onetary M odel of N om inal Income Determ ination ...................................... ................ 9 V ol. 5 7, No. 6 Two Stages to the Current Recession NORMAN N. BOWSHER T HE pattern of economic developments since the X R ea l Product* fall of 1973 has seemed baffling to many. It has been a period of prolonged and deep economic recession combined with intensified inflation for a year. The re cession has had substantially different characteristics from the four previous recessions since 1950, including two distinct periods within the current contraction. S e a s o n a lly A d ju s t e d P e a k s -1 0 0 A v e r a g e o f 1968-71, 1 9 5 9 -6 , 1 9 5 6 -5 8 , a n d 1 9 5 2 -5 4 / ✓ In terms of causal forces, the recent downturn also differs from earlier contractions. All previous reces sions in the past twenty-five years were preceded by periods of pronounced monetary restraint. The current downturn, by contrast, was preceded, and accom panied for a time, by stimulative policy actions. As the downturn progressed, however, the growth of the money stock did slow markedly. In addition, develop ments which have hampered production — such as the higher price of oil, unfavorable weather condi tions, and the effects of price controls — have played a much greater role in the current downturn than in earlier recessions. This article reviews economic developments since the fall of 1973 and finds that some of the confusion concerning the current recession is eliminated if the period is divided into two stages. The first stage, which began in the late fall of 1973, was largely a response to constraints placed on aggregate supply. The second stage, which began in the early fall of 1974, reflected, in addition, a reduction in the growth of demand for goods and services. For this study, November 1973 is used as a tenta tive peak for the past expansion.1 It was the month of greatest industrial production, and in the following three months production declined. The second stage of the recession is postulated to have begun after Sep tember 1974. Industrial production and employment, 1There are, of course, differences of opinion with respect to the dating of the cyclical peak. Page 2 r J * ✓ V -/ t f 1 9 7 2 -7 5 \ 3 R D C)TR 5 3 3RD C)TR 5 7 \ \ 4 TH Q T R 6 9 1 4 TH Q T R 73 -4 1 1 1 1 I 1 1 1 1 -3 -2 -1 0 1 2 3 4 5 6 QUARTERS TO A N D FR O M PEAK * G r o s s n a t i o n a l p r o d u c t in c o n s ta n t d o ll a r s . L a te s t d a t a p lo t t e d : 1st q u a r t e r S o u rc e : U.S. D e p a rtm e n t o f C o m m e rc e which had risen, on balance, in the previous seven months, declined sharply after September. Compari sons are made with averages of periods just before and after the four preceding cyclical peaks, as se lected by the National Bureau of Economic Research. They are November 1969, May 1960, July 1957, and July 1953. COURSE OF THE RECESSION Production Total real output of goods and services has declined markedly throughout the recent economic contrac tion. In the first five quarters following the peak ( end ing first quarter 1975), real output decreased at a 6 percent annual rate, and available data indicate that FEDERAL RESERVE BANK OF ST. LOUIS the contraction probably has continued into the cur rent quarter. By comparison, in the four previous recessions, real output declined for only two quarters, on average, and by the fifth quarter output typically exceeded the previous cyclical high. Industrial production declined for three months after the 1973 cyclical peak, then increased slightly for the seven months from February to September 1974. During this period, production was bolstered by increased inventory demand as a result of anticipated shortages of many items and by anticipations of in ventory profits as prices jumped. However, from September 1974 to April 1975 industrial production again fell sharply at a 21 percent annual rate. JU N E 1975 ten-month period of earlier recessions, employment declined at an average 2 percent rate. Reflecting a marked rise in employment since mid1971, 65.2 percent of the non-institutional population of working force age (16 through 64) were employed in the third quarter of the current contraction (III/ 1974). On average, 62.7 percent held jobs at the four earlier cyclical highs. As the recession intensified in the period from last September to March, total em ployment decreased at a rapid 6 percent rate. Never theless, 63 percent of the noninstitutional population of working force age were employed in the first quar ter of 1975, or slightly more than had been employed at the peaks of the four earlier cycles. Total Em ploym ent M O N T H S TO A N D F R O M PEAK L a te s t d a t a p lo t t e d : A p r i l S o u rc e : U.S. D e p a r tm e n t o f L a b o r In the four previous recessions the pattern was for industrial production to contract for about nine or ten months. Thereafter, production turned up and rose, on average, at an 11 percent annual rate from the tenth to the seventeenth month, the stage comparable to the period of marked drop in the current cycle. Employment A distinctive feature of the current cycle has been the relatively high level of employment throughout much of the contraction. Total employment, which had risen a rapid 4 percent in the year preceding November 1973, continued to increase, but at a slower 1 percent annual rate during the first stage of the eco nomic downturn. By contrast, in the corresponding The unemployment rate remained relatively low until early last fall, but has risen abruptly since then. In the first two months after the peak in economic activity, the unemployment rate rose. Then, from the second to the ninth month after the turn (January to August 1974) the unemployment rate changed little, in marked contrast to pronounced increases in com parable periods of the earlier recessions. Since the ninth month, the trends have been reversed; the rate has risen sharply in recent months at a time when it usually remained on a high plateau. At the seven teenth month after the turning point (April 1975), the unemployment rate, at 8.9 percent, was higher than in any of the four previous recessions. The combination of high unemployment and a rela tively large percentage of the working age population Page 3 JU N E FED ER AL RESERVE BANK OF ST. LOUIS U n em p lo y m en t Rate P e o k s -1 0 0 Pea k s= 1 0 0 S e a s o n a lly A d ju s t e d go 1 i I I I i I I l 1 I l 1 I 1 1 1 -12 -9 -6 -3 0 3 l l 1 1 i 1 I 1 1 gO 6 9 12 15 18 M O N T H S TO A N D FR O M PEAK L a te s t d a t a p lo t t e d : A p r il S o u r c e : U .S . D e p a r tm e n t o f L a b o r employed reflects a rise in the participation rate in the labor force. A larger share of women have entered the labor force in the last several years, and more recently, second and third members of many households have sought jobs to meet the higher cost of living or to maintain income when another member loses a job. G e n e r a l Prices* P eaks= 1 0 0 120 r S e a s o n a lly A d ju s t e d P eaks= 1 0 0 ---------- 120 1975 average, during the final year of the four earlier eco nomic expansions and the first two quarters of re trenchment, general prices, as measured by the im plicit GNP deflator, rose at a 3 percent annual rate. From the second to the fifth quarters after the earlier cyclical peaks, overall prices increased at a slower 2 percent average rate. Despite the sharp and prolonged contraction, the rate of inflation in the most recent downturn did not behave as in previous recessions. For the period from four quarters before to two quarters after the most recent peak, general prices advanced at an 8.5 percent annual rate. From the second to the fifth quarter of the recession, the pace of inflation accelerated to 12 percent. In the fifth quarter, however, prices rose at a slower 8.5 percent pace, and preliminary indications are that the slowing has continued into the sixth quarter (11/1975). FIRST STAGE - NOVEMBER 1973 TO SEPTEMBER 1974 The contraction in production in the current reces sion, as noted above, has come in two distinct waves — the first from the November 1973 peak to Septem ber 1974 and the second from September 1974 to the present. The two periods of decline displayed sub stantially different characteristics and resulted from different causes. Therefore, in examining the recession it is useful to analyze the two periods separately, even though there is obviously an overlap of causes and effects. Demand Q U A R TE R S T O A N D F R O M PEAK * G r o s s n a t i o n a l p r o d u c t i m p l i c i t p r ic e d e f l a t o r . Growth in demand for goods and services, as indi cated by nominal gross national product, moderated after the 1973 peak, but remained rapid by historical standards for the first three quarters of the recession. From the fourth quarter of 1973 to the third quarter of 1974, total spending rose at a 7 percent annual rate. By comparison, even in the final year of economic expansion preceding the four earlier economic con tractions, total spending rose at only a 5.5 percent rate on average; then, in the first three quarters of recession the rise in spending slowed to a 0.3 percent rate. L a te s t d a t a p l o t t e d : 1 st q u a r t e r S o u rc e : U.S. D e p a r tm e n t o f C o m m e r c e Prices The rate of inflation has typically moderated after about two quarters of economic sluggishness. On Page 4 Policy Actions The unusual demand growth during the first three quarters of the current recession is partially explained by monetary developments. Monetary actions, as JU N E FEDERAL RESERVE BANK OF ST. LOUIS Total Spending on G o o d s an d Services* M o n e y Stock Q UARTERS TO A N D FR O M PEAK ‘ G ro s s n a t io n a l p r o d u c t in c u r r e n t d o lla r s . 1975 QUARTERS T O A N D FR O M PEAK L a te s t d a t a p l o t t e d : 1st q u a r t e r L a te s t d a t a p l o t t e d : 1st q u a r te r S o u rc e : U.S. D e p a r tm e n t o f C o m m e rc e measured by the growth rate of the money stock, were restrictive prior to each of the four earlier business cycle peaks. In each case the rate of money growth fell substantially below its trend rate of growth. This has been cited as a prominent causal factor in the cyclical changes in demand and subsequent reces sions. In the year preceding the current recession, the rate of monetary expansion slowed, but fell only slightly below its pre-1973 trend rate of 6 percent in the second half of the year. From the fourth quarter of 1972 to the fourth quarter of 1973, the money stock rose 6.3 percent. In the last two quarters of the most recent economic expansion (11/1973 - IV/1973) money growth did slow to a 5.3 percent annual rate. This break in the pace of money expansion probably contributed to the moder ation in the growth rate of total spending after the fourth quarter of 1973. After the recession began, demand growth con tinued for a time to be stimulated by monetary ex pansion. In the first two quarters of the current re cession (IV/1973 -11/1974), the money stock grew at a 6.7 percent annual rate, slightly above the trend rate of growth. Fiscal developments were also more expansive in the first stage of the current recession than in the cor responding periods of earlier recessions. In the year ending third quarter 1974, Federal Government ex penditures, on a national income accounts basis, jumped 16 percent. In the corresponding spans of the four earlier cycles, Federal spending rose an average of 4 percent. Even though tax receipts, bolstered by rising nomi nal incomes, rose sharply, Government expenditures exceeded receipts by a substantial margin in 1973 and 1974. The deficit in the national income accounts budget was $14 billion in these two years, compared with an average deficit of $6 billion in the correspond ing periods of the earlier cycles. Production Despite the relatively rapid growth in demand for goods and services in the first stage of the current recession, output declined. Total real output de creased at a 3.5 percent annual rate from the fourth quarter of 1973 to the third quarter of 1974. In the corresponding periods of the four earlier recessions, output declined at a 2.4 percent rate. The apparent paradox of substantial production cut backs in the face of rapidly expanding demand during the first three quarters of the current recession re flects a number of supply constraints which sharply increased production costs. In 1973, rates of produc tion were very high in many industries, and marginal costs rose rapidly with increased output. Then, the economy was struck by a number of adverse factors which reduced resource availability and raised costs. Page 5 FED ER AL RESERVE BANK OF ST. LOUIS Through monopolistic actions of producing nations and domestic price (and, therefore, production) con trols, oil supplies were cut back and energy costs increased sharply. Adverse weather conditions, both here and abroad, resulted in widespread crop failures and increased food prices. Depreciation of the dollar relative to other currencies raised domestic produc tion costs by increasing the dollar prices of imported goods, and caused significant shifts in demand for re sources. Compliance with environmental and safety laws consumed resources and added further to costs, while making adjustment to all the other changing forces much more difficult and costly. In addition, output was inhibited by marked changes in consumer spending and by price controls. The rapidly rising prices of certain items prompted consumers to shift consumption patterns, causing abrupt contractions in the demand for some items (such as autos) while intensifying upward pressures on prices of other commodities. Price controls, still in effect in early 1974, prevented firms from adjusting to increasing production costs. With fixed selling prices, production of many goods was no longer prof itable; some marginal facilities were closed, and plant expansions were postponed. As a result, production in related industries was hampered further by short ages for a time, and later by higher prices for inputs. These interferences in the productive process made the country poorer by reducing output capabilities. The adverse effects of these constraints were dis tributed through the economy by higher prices, a chief factor in the intensification of inflation during a period of recession. JU N E 1975 The money stock, after rising at a 6.7 percent an nual rate in the first two quarters of the recession, slowed abruptly to a 3 percent pace in the following three quarters (ending March 1975). In the earlier recessions money typically increased at an accelerated rate in the third through fifth quarters. A few months after money began accelerating in previous recessions, growth in demand also accelerated. A few months after money growth began decelerating during the current recession, growth in demand also decelerated. The first stage of the current recession, being caused in large part by constraints on supply, was unlike any of the earlier recessions, which were largely demand induced. However, the second stage, which has been fostered by a slowing in the growth of demand, is similar to the earlier experiences. Hence, for certain studies, comparisons of the period since last Septem ber with the periods immediately following the pre vious cyclical peaks have more relevance than com parisons which use the entire span of the current recession. At this second stage turning point, the growth rate in total demand for goods and services fell precipi tously from the aforementioned 7 percent rate in the first stage to the virtual plateau in the first two quar ters of the second stage. Between the comparable periods before and after the four earlier cyclical R e a l Product* Second Stag* of Current Decline Compared w itk Previous Recessions S e a s o n a lly A d ju s te d SECOND STAGE - SEPTEMBER 1974 TO DATE A v erag e of 1969-70, 1960-61, 1957-58, and 1953-54 i / Demand As the effects of some of the supply interferences were diminishing last fall, production was severely hampered a second time by a marked slowing in de mand for goods and services. Total spending, which had risen at a 7 percent annual rate in the first three quarters of the recession, decelerated sharply last fall and declined in the first quarter of this year. By com parison, in the four previous recessions spending rose at an average 0.3 percent rate in the first three quar ters, but at an accelerated 9 percent rate in the fourth and fifth quarters. With the reduction in demand growth, it was not feasible to maintain existing pro duction levels, and sharp cutbacks occurred. 6 Digitized forPage FRASER V -/' \ 1974-75 3RD TR.53 3 R D G T R .5 7 4TH QTR '69 1 3 R D QTR. 74 1 1 1 I I 1 ! 1 ! 0 1 2 3 4 5 6 QUARTERS FROM TURN *G ro ss n a tio n a l product in constant d o lla rs. Source: U.S. Department of C o m m erce FEDERAL. RESERVE BANK OF ST. LOUIS JU N E In d u stria l Production Total E m p lo y m e n t Second Stage of Current Decline Compared w ith Previous Recessions Peaks= 100 105 r Peaks= 100 105 S e a s o n a lly A d ju s t e d 100 1975 Second Stage of Current Decline Compared w ith Previous Recessions ^ A v e r a g e o f 1 9 6 9 -7 0 , 1 9 6 0 -6 1 , 1 9 5 7 -5 8 , 100 V and 1 9 5 3 -5 4 \v \ N \ \ \ \ \ \ \ \ 95 95 \ ' N " ' ' \ 1 9 7 4 -7 5 90 90 JU L 5 3 JU L ' 5 7 M A r-6 0 NOV 69 \ \ 74 SEP 85 \ . . . ---- -------- ..................... 0 3 6 9 85 12 M O N T H S FR O M TURN peaks, demand growth decelerated nearly the same amount, averaging a drop of 6 percentage points. Production, Employment, and Prices Total real output of goods and services fell at a 10 percent annual rate from the third quarter of 1974 to the first quarter of 1975. In the first two quarters of the four earlier recessions, real output declined at an average 4 percent rate. Industrial production dropped at a 21 percent rate from September 1974 to April 1975, compared with an average 11 percent rate in the first seven months of the earlier recessions. Total employment declined at a 6 percent rate from Sep tember to April, whereas it decreased at an average 2 percent rate in the comparable earlier periods. Prices continued to rise rapidly for a time after the second stage of the recession began, the rate of in crease has now slowed. From September to November 1974, consumer prices rose at a rapid 12 percent an nual rate, about the same pace as in the first stage. Then, from November to April 1975 prices rose at a reduced 7 percent rate. In the earlier recessions, in creases in consumer prices decelerated less than two percentage points at the seventh month, on average. The greater and quicker reduction in the rate of infla tion in the second stage than in earlier recessions reflects the greater severity of the current economic decline, some dampening price effects from the first stage recession, and a dissipation of the short-run price effects resulting from removal of wage-price S o u rc e : U.S. D e p a r tm e n t o f L a b o r controls, the dollar devaluation, and the markup of oil prices. SUMMARY AND CONCLUSIONS The current recession has been severe by post World War II standards, with output contracting by a greater magnitude and for a longer period than in any of the four previous recessions experienced since 1950. Not only has the current contraction been deep and prolonged, but it has been, in effect, two reces sions. The first, induced largely by constraints on sup ply, had characteristics which differ strikingly from prior experience. Previous recessions were preceded, and accom panied for a time, by a slow ( relative to trend) rate of money growth. By contrast, money expansion in the current cycle continued to be rapid, except for a brief period, through the first two quarters of the recession. However, from the second quarter of 1974 to the first quarter of this year, the rate of money growth slowed markedly. Fiscal actions, on the other hand, have been expansive since a quarter before the current cyclical peak. Total spending for goods and services rose substan tially during the first three quarters of the current recession, pausing only moderately after the cyclical peak. However, spending growth slowed significantly Page 7 FEDERAL RESERVE BANK OF ST. LOUIS after the third quarter of the contraction, causing the recession to enter the second stage. Until last fall, the chief cause of the downturn came from the supply side. The nation’s ability to produce was reduced by increased energy costs, unfavorable weather, costs of environmental and safety programs, the impact of dollar devaluation, and the effects of price controls. The quantity of goods and services available for consumption thus declined. Much of the current recession and the persistence of inflation have reflected the process of adjustment that the economy has been making to the constraints placed on production. Recovery from the current recession depends on the overcoming or removal of constraints on supply. Elimination of wage and price controls was a signi ficant step in attaining greater output, since produc Digitized forPage FRASER 8 JU N E 1975 tion tends to expand when profits are enhanced. With normal weather, agricultural production should in crease, placing downward pressures on the price of food. While some adjustment to the higher cost of fuel has taken place, a full adjustment will take addi tional time. Economic recovery is also dependent on a pick-up in demand growth. In view of the projected sizable Federal deficits, and the probable monetary creation that will occur in financing them, total demand is likely to receive a substantial boost from fiscal and monetary developments in the near future. Since Jan uary the money stock has again risen sharply. Expan sionary developments are now welcome, because demand is inadequate. Yet, a stimulation of demand in excess of the ability of the economy to produce would likely result in a re-intensification of inflationary pressures at a later date. A Monetary Model of Nominal Income Determination LEONALL C. ANDERSEN D u RING the past several years the Federal Re serve Bank of St. Louis has presented a number of empirical studies demonstrating a strong and pre dictable response of nominal gross national product ( GNP) to changes in the nation’s money stock. These studies found that changes in the secular trend of the money stock are the prime determinant of changes in the secular trend of GNP. They also found that short-run changes in GNP are related to similar changes in the money stock. On the other hand, changes in Government spending were found to have only a temporary short-run influence on changes in GNP. A number of other studies, using variations of the approach of the St. Louis studies, have yielded similar empirical relationships. The St. Louis studies related changes in nominal GNP directly to current and past changes in the money stock and in high-employment Government expenditures. No underlying set of relationships was specified. Instead, the empirical relationship was pre sented as the reduced-form of an unspecified struc ture of the economy. This article sets forth a theoretical model consist ing of a set of postulated relationships which form a basis for the relationship of nominal income (GNP) to the money stock and Government expenditures. The theoretical properties of this model are similar to the empirical relationships found in the St. Louis studies. The parameters of the model are estimated for the period from first quarter 1955 to fourth quarter 1973. Empirical tests fail to reject the theory as an explanation of nominal income determination in the sample period. THEORETICAL MODEL This section develops a model of nominal income determination which is based primarily on a prominent NOTE: This presentation was given as part of the Lawrence H. Seltzer Memorial Lecture Series at Wayne State Univer sity, Detroit, Michigan, May 21, 1975. theory of the influence of changes in the money stock on income.1 At times, however, assertions different from those in the prominent theory are made. It is also asserted that the responses of holders of money balances to changes in the dependent variables are in relative terms; that is, rates of change or percent discrepancies. The model, therefore, is expressed in log-linear form. Desired Nominal Money Balances The theory underlying this study is based on the assertion that households and business firms desire nominal money balances to conduct market transac tions and to hold as a store of value. Specifically, the desired amount of nominal money balances, in the aggregate, depends on the perceived price of newly produced final goods and services, perceived nominal income, the expected rate of inflation, yields on alter native financial assets, and the technical efficiency of the economy’s system of making money payments.2 Since holders of money balances do not have perfect information regarding market opportunities, and since there exist costs of both collecting information and conducting market transactions, the desire to hold money balances depends on the perceived, instead 1For statements of this theory, see Milton Friedman, “The Demand for Money: Some Theoretical and Empirical Re sults,” Journal o f Political Econom y (August 1959), pp. 327-351; “A Theoretical Framework for Monetary Analysis,” Journal o f Political Econom y (March/April 1970), pp. 193238; and “A Monetary Theory of Nominal Income,” Journal o f Political Econom y ( March/April 1971), pp. 323-337. 2For various asserted forms of the money demand function, see David E. W. Laidler, The D emand For M oney: T he ories and E vidence (Scranton: International Textbook Com pany, 1969). For an excellent statement of the “conventional view” of the money demand function, see Stephen M. Goldfeld, “The Demand For Money Revisited,” Brookings Papers on Econom ic Activity —■3 (1 9 7 3 ), pp. 577-638. Also see John T. Boorman, “The Evidence on the Demand for Money: Theoretical Formulations and Empirical Results,” in John T. Boorman and Thomas M. Havrilesky, Money Sup ply, Money Demand, and M acroeconomic M odels (Boston: Allyn and Bacon, Inc., 1972), pp. 248-291, and Stephen Rousseas, Monetary Theory (New York: Alfred A. Knopf, 1972). Page 9 JU N E FED ER AL RESERVE BANK OF ST. LOUIS of the actual, price of goods and services and nominal income. Given the influences of the other factors, the amount of nominal money balances demanded is posi tively related to the perceived price of newly pro duced final goods and services. Given the influences of both perceived price and the other factors, the amount of money balances demanded is positively re lated to the amount of goods and services that per ceived nominal income can purchase. It is asserted that the response of holders of money balances is of the same magnitude with regard to both perceived price and the amount of goods and services that perceived nominal income can purchase. The desire for nominal money balances, therefore, is form ulated in terms of perceived nominal income only (Equation l ) . 3 A continuing rise in the price of goods and services results in a given amount of nominal money balances held as a store of value commanding, over time, a decreasing amount of goods and services. Given the influences of the other factors, the amount of money demanded is negatively related to the rate of inflation expected to prevail in the future (Equation l ) . 4 Other financial assets are substitutes for money bal ances as a store of value, and they yield a rate of return. These rates of return, with constant, per ceived prices for goods and services, are measured in terms of real rates of interest. To the holder of a financial asset, the real rate of interest is the annual percent increase in the amount of goods and services, at current prices, that a given dollar value of a finan cial asset will command over the term to maturity. With the influence of other factors held constant, the amount of money demanded is negatively related to real rates of return on alternative financial assets. It is asserted that the dominant substitutes for money as a store of value are short-term financial ^Ignoring the other factors, In M° = a i In Pp + «2 In = a i In Pp + <*2 ln Yp - a 2 In Pp. By assertion ft 1 = therefore, ln M° = a j ln Yp. Friedman in “A Monetary Theory of Nominal Income” asserts that for all practical purposes <*1 = c*2 = 1. In this study the only assertion made is that « i = a.%. The validity of this assertion is tested later in the study and the hypothesis that the two responses are identical cannot be rejected. Friedman’s asser tion that they both equal unity is also tested and is rejected. 4It is important to note that there are two different influences on the amount of money balances demanded related to the price of newly produced final goods and services. One is the positive influence of the perceived price level for the current period, and the other is the negative influence of the ex pected rate of change in the price level over the relevant future. Page 10 1975 assets and that the time horizon upon which expecta tions of the rate of inflation are based is the same for money balances as for these assets. It is generally accepted that the nominal rate of interest on a finan cial asset is the sum of the real rate of return and the rate of inflation expected over the term of the financial asset. The nominal short-term interest rate, therefore, is presumed to capture the negative influence on the amount of money demanded of both the real short term interest rate and the expected rate of inflation (Equation 1). The technical efficiency of the system of making money payments is defined as the average amount of money balances required to be held to conduct a given nominal volume of transactions. With the influences of other factors held constant, the amount of money demanded is negatively related to the technical ef ficiency of the system of making money payments ( Equation 1). In other words, the smaller the amount of money balances technically required to be held to conduct a given dollar volume of transactions, the smaller is the amount of money demanded. (1) In M* (t) = <*o In E(t) + <*i ln Yp (t) + (*2 ln r(t). <*0 < 0, <*1 > 0, and <*2 < 0. M° = desired nominal money balances. E = technical efficiency of the payments system. Yp = perceived level of nominal income. r = nominal short-term interest rate. Adjustment of Spending by Households and Business Firms The nominal stock of money is assumed to be ex ogenous, determined by the monetary authorities. Therefore, holders of money balances, in the aggre gate, cannot adjust their holdings when a discrepancy occurs between actual and desired money balances. Instead, it is asserted that individual holders of money balances attempt to add to (reduce) money balances by reducing (increasing) their rate of spending on goods and services. Such an adjustment continues un til desired money balances are brought into equality with actual money balances. It is assumed that the rate of change in the dollar volume of spending by households and firms on newly produced final goods and services from both domestic and foreign sources is proportional to the percent dis crepancy between actual and desired money bal ances.5 It is also assumed that the response of spend ing is distributed over time (Equation 2 ). 5This specification of the adjustment process is a marked de parture from that specified in other studies. Some specify FED ER AL RESERVE BANK OF ST. LOUIS (2) d l " Yd = X [In M(t) - In M* (t)]. dt M = actual nominal money balances. d In dt = rate of change in spending by households and business firms for newly produced, final goods and services. X = speed of adjustment. 0 < X ^ o°. The larger is X , the faster is the speed of adjustment. X = 00 is instantaneous adjustment. Combining Desired Money Balances and Adjustment Process The preceding assertions regarding the demand for nominal money balances and the adjustment proc ess are now combined by substituting equation (1) into equation (2 ). The result is that the rate of change of nominal spending by households and business firms is related to the level of actual nominal money bal ances, the technical efficiency of the payments sys tem, the level of the nominal short-term interest rate, and the perceived level of nominal income. (3) d ln Yd = \ [In M(t) - a 0 In E(t) dt <*1 ln Yp(t) - <*2 ln r(t)]. Definition of Nominal Income Nominal income is defined as total value added (that is, factor payments) in the domestic production of new final goods and services. Total nominal spend ing on domestic product is also equal, by definition, to value added. Nominal income, accordingly, is equal to nominal spending for both domestic and foreign product by domestic households, business firms, and all units of government, plus nominal spending by foreigners for domestic product, less domestic nomi nal spending for foreign produced goods and services. (4) Y(t) = Yd(t) + G(t) + X(t) - IM(t). Y = nominal income. Yd = spending by household and business firms for both domestic and foreign product. G = spending by all units of government for both domestic and foreign product. X = spending by foreigners for domestic product. IM = domestic spending for foreign product. that the actual money stock changes in response to a dis crepancy between actual and desired money balances; others specify that “real” money balances change; and others spe cify that the short-term interest rate changes. See references in fn. 2 for specific examples of these other specifications. For discussion of the importance of the specification of the adjustment process in empirical research, see; A. A. Walters, “The Demand for Money — The Dynamic Properties of the Multiplier,” Journal o f Political Economy (June 1967), pp. 293-298, and D. R. Starleaf, “The Specification of Money Demand — Supply Models Which Involve the Use of Dis tributed Lags,” Journal o f Finance (September 1970), pp. 743-760. JU N E 1975 Domestic Spending for Foreign Product Domestic nominal spending for foreign product is assumed to be a constant proportion of total nominal spending in the economy. (5)6 (t) = IM(t) = 6. Yd (t) + G(t) + X(t) Dynamic Form of the Model The model, up to this point, involves the change in the level of income in response to changes in the level of the money stock, or in Government spending, or in foreign spending on domestic product, or in the short-term interest rate, or in the technical efficiency of the payments system. All of these variables, how ever, are continuously changing over time. The model is differentiated with respect to time to reflect the response of households and business firms to those variables which are continuously changing. In its dynamic form, the rate of change in desired money balances is related to the rates of change in the technical efficiency of the payments system, in the short-term interest rate, and in perceived income. d in M" dt d ln E dt d ln YP d in r dt dt (1 ) ---- ----- = ag--- ---- + <*! ----------+ a2 The change in the rate of change in nominal spend ing by households and business firms is proportional to the discrepancy between the rate of change in actual money balances and the rate of change in de sired money balances. (2 ') d2 ln Yd dt2 d ln M dt d in M* dt The statement combining the adjustment process and the factors influencing desired money balances is accordingly modified. /0,\ d2 ln Yd dt2 ^ r d ln M dt (3 /--------- —AI - «2- d In E dt a i ■d In «o - YP dt d ln Z-l dt Substituting equation (5 ) into (4) and differentiat ing with respect to time, the rate of change in nominal income is equal to the weighted sum of the rates of change of spending for product by domestic house holds and business firms, domestic units of govern ment, and foreigners. (4,) d J n Y = W l(t)_d dt dt / % d In G + W2(t) ---- ;---- + W3(t). d ln X dt dt Wi(t) = [1 - 6 ] J ^ L ;W 2 (t) = [ l - B] ^ > ; Y (t) Y(t) and W3(t) = [ 1 - 6 ] Y(t) Page 11 FED ER AL RESERVE BANK OF ST. LOUIS JU N E 19 75 Summary of Variables Dynamic Equilibrium State The endogenous variables of the model are the change in the rate of change in nominal spending by households and business firms, the rate of change in desired money balances, and the rate of change in nominal income. It will also be developed in sub sequent analyses that the rate of change in the per ceived level of nominal income is an endogenous variable related to past rates of change in nominal income. The exogenous variables are the rates of change in actual money balances, in the short-term interest rate, in the technical efficiency of the pay ments system, in Government spending on goods and services, and in foreign spending on domestic product. The relationships of the model (Equations 3', 4', and the weights) together with the three dynamic equilibrium conditions (Equations E -l through E-3) are used to solve for the dynamic equilibrium state of the endogenous variables.7 In the dynamic equili brium state, taking into consideration the postulated signs of the coefficients, the rate of change in nominal spending by households and business firms is posi tively related to the rates of change in actual money balances, in the technical efficiency of the payments system, and in the nominal short-term interest rate, and is negatively related to the rates of change in government spending and exports (Equation ES-1). The rate of change in nominal income is positively related to the rates of change in actual money bal ances, in the technical efficiency of the payments system, and in the nominal short-term interest rate (Equation ES-2). The model is one of partial analysis, inasmuch as the nominal short-term interest rate is an exogenous variable. There is no provision for feed-back effects on the rate of change in nominal income. These effects would emanate from changes in exogenous variables which change the rate of change in the short-term interest rate, either by induced changes in the real interest rate or in the expected rate of inflation. Conditions for Dynamic Equilibrium Dynamic equilibrium is defined as the state in which all of the variables are changing at constant rates.6 This occurs when the rates of change in actual and desired money balances are equal. Three condi tions are required for this equality to be fulfilled — changes in the rates of change in nominal spending by households and business firms and in nominal in come equal zero (E - l and E -2), and the rates of change in nominal income and in the perceived level of nominal income are equal ( E -3 ). (E -l) rl2 I n Y<i - - ■- = 0. dt- (E-2) d2 1---Y- = 0. dt2 d In YP d In Y (E-3) dt dt BThe definition of equilibrium as constant rates o f change is a marked departure from the standard literature in monetary economics, other than some growth models. The standard analysis defines equilibrium as constant levels of the endo genous variables. The equilibrium conditions for the standard analysis would be that desired and actual levels of money balances are equal, that the rates of change in spending by households and business firms and in nominal income equal zero, and that the perceived level of nominal income equals the actual level. Thus, in the standard analysis there is both stock and flow equilibrium. In the dynamic form in this study, however, equilibrium is defined as constant rates of change in both stock and flow variables. Page 12 1 d In M d In E d In i «0---:------ «2 dt dt Wi(t)<*i dt dt d In G d ln X , - W2(t) W3(t) dt dt d In Y d In M d In E d In r , (ES-2) «o ■ «2 ---:--- 1dt <*l ~ d t dt dt (ES-1) d In Yd A Change in Dynamic Equilibrium State An existing dynamic equilibrium state is disturbed, in this model, by two types of events. One type is the initial creation of a discrepancy between the rates of change in actual and desired money balances. Factors initiating such a discrepancy are changes in the rate of change in actual money balances or changes in the rate of change in desired money balances. This latter change can result from changes in the rate of change in either the technical efficiency of the payments system or in the short-term interest rate. The other type of equilibrium disturbance is a change in the rate of change in government spending or in foreign spending for domestic product, which initiates a change in the rate of change in nominal income. Fol lowing both types of disturbance, a new equilibrium state is achieved when the rate of change in nominal income has changed to the extent that the rate of change in desired money balances is brought into equality with the rate of change in actual money balances. 7This analysis and the one immediately following is for partial equilibrium only inasmuch as the interest rate is exogenous. The model only considers the influence of exogenous shocks on the choice between money and new production and not on the choice between money and existing assets. JU N E FEDERAL RESERVE BANK OF ST. LOUIS For example, starting from dynamic equilibrium (that is, all variables changing at constant rates) as sume there is a maintained increase in the rate of change in actual money balances, with the rates of change in the other independent variables remaining as they were. First, there occurs a positive discrep ancy between the rates of change in actual and de sired money balances, resulting in an increase in the rate of change in nominal spending by households and business firms. As a result, there is an increase in the rate of change in nominal income. This latter in crease, in turn, results in an increase in the rate of change in perceived nominal income and thereby in the rate of change in desired money balances. As a result, the discrepancy between the rates of change in actual and desired money balances is nar rowed and the rate of change in spending by house holds and business firms decreases. This decrease reduces the rate of change in nominal income from what it was initially. This process continues until there is equality between the rates of change in actual and desired money balances. In the new dynamic equilibrium state, the rates of change in spending by households and business firms and in nominal income are higher than their starting equilibrium values (ES-1 and ES-2). In another example, starting from equilibrium, as sume there is a maintained increase in the rate of change in government spending, with rates of change in the other independent variables remaining the same. The first response is an increase in the rate of change in nominal income which produces an increase in the rate of change in perceived nominal income. This results in an increase in the rate of change in desired money balances. As a consequence, there is a negative discrepancy between the rates of change in actual and desired money balances, resulting in a subsequent decrease in the rate of change in spending by households and business firms. This is accompanied by a decrease in the rates of change in nominal income and in per ceived nominal income, which, in turn decreases the rate of change in desired money balances. This process continues until the rate of change in desired money balances equals that of actual money balances. In the new dynamic equilibrium state the rate of change in nominal income is the same as it was be fore the increase in the rate of change in government spending (E S-2). The rate of change in spending by households and business firms has been permanently decreased (E S-1), offsetting fully the initial increase 1975 in the rate of change in nominal income generated by the increase in the rate of change in government spending. The length of time required for achieving the new equilibrium state depends on (1 ) the speed of re sponse of the rate of change in spending by house holds and business firms to a discrepancy between the rates of change in actual and desired money balances and (2 ) on the length of time required for the rate of change in perceived nominal income to respond fully to past rates of change in actual nominal income. The time path to a new equilibrium — whether it oscillates or moves only in one direction — depends on the response characteristics of the relationships comprising the model. EMPIRICAL FORM OF THE THEORETICAL MODEL The theoretical model consists of three relation ships. One is for the change in the rate of change in spending by households and business firms ( Equation 3 '). The other two are the identity for the rate of change in nominal income (Equation 4 '), and the weights involved in this identity. The theoretical model is next given an empirical form which pro vides the basis for testing whether or not the theory can be accepted. This section presents the empirical model and the following section uses it to test the theory. Data Problems A major data problem is involved in developing the empirical form of the model — the theory is in terms of changes in time which are infinitesimally small while data on the variables are available only for discrete points in time separated by a month or a quarter of a year. A linear approximation in discrete time is used — the first difference of natural loga rithms of a variable between two discrete points in time is presumed to approximate its rate of change (Appendix). Another data problem exists inasmuch as there are no measurements of the technical efficiency of the payments system or of the perceived level of nominal income. It is assumed that, on average, the technical efficiency of the payments system increases at a con stant rate (Appendix).8 The second problem is solved 8Examples of developments which are usually presumed to have increased the efficiency of the payments system ( a reduced amount of money balances required to carry out a given volume of money payments) over the sample period Page 13 FED ER AL RESERVE BANK OF ST. LOUIS by em ploying a procedure presented by Philip C agan.9 According to this procedure, the rate of change in perceived nom inal incom e can be approxim ated by a w eighted average of past rates of change in actual nominal incom e (A p p end ix). In this procedure, the w eights sum to unity. Estimated Parameters of the Model Only the param eters of the relationship explaining the change in the rate of change in spending for product by households and business firms are esti m ated; the other relationships are identities. Tw o ver sions of this relationship are estim ated. O ne is based on the assertion th at desired money balances are posi tively related to perceived price and the amount of goods and services that perceived nominal incom e can purchase, w ith no assertions regarding the m agni tudes of response. T h e other one is based on the assertion th at the m agnitude of response of desired m oney balances is the same w ith regard to perceived price as w ith regard to the am ount of goods and services th at perceived nom inal incom e can purchase — the perceived incom e form ulation used in the theoretical discussion. T h e general forms of these two relationships are as follow s: (A) A in Yjl — A in Y ^ n +a 3 2 i = 1 (B) Ain Y = ao + a i A in Mt + a.2 A in rt , _ n Wi Ain Pt-i + a4 1 Wi Ain Qt-i + £ t. i = 1 — Ain Y j! j =bo + bi Ain Mt + b£ Ain rt + b 3 £ W i Ain Yt-i + 8 t. i =1 Ain Yf1 —Ain Y td_[ = change in the rate of change in spending by households and business firms for product. a,, and bo = response to the average rate of change in the technical efficiency of the payments system. Ain Mt = rate of change in nominal money balances. Ain rt = rate of change in nominal short-term interest rate. X wi Ain Pt-i = weighted sum of past rates of change in *=1 price. X W i Ain Qt-i = weighted sum of past rates of change in 1= 1 the amount of goods and services that nominal income can purchase. X Wi 1= 1 Ain Yt-i = weighted sum of past rates of change in nominal income. Et a random error term. are the introduction of faster means of transferring funds and the adoption of improved methods of managing money balances. See George Garvy and Martin R. Blyn, The V eloc ity o f Money (New York: Federal Reserve Bank of New York, 1969), pp. 207-218, for further discussion of this point. !'Phillip Cagan, “The Monetary Dynamics of Hyperinflation,” Studies in the Quantity Theory o f Money, ed. Milton Fried man (Chicago: University of Chicago Press, 1956), pp. 31-41. Page 14 JU N E 1975 Ordinary least-squares regressions, using quarterly data from first quarter 1955 to fourth quarter 1973, are used to estimate the parameters of equations A and B. Spending by households and business firms is measured by the sum of consumption plus investment in the national income accounts. Nominal income is measured by nominal GNP.10 The price level is measured by the GNP deflator, and the amount of goods and services that nominal income can purchase is measured by nominal GNP divided by the price deflator. Two definitions of money are used. One (M j) is the sum of demand deposits and currency held by the nonbank public. The other one (M 2) is Mt plus time and savings deposits at commercial banks, other than large, negotiable certificates of de posit. The short-term interest rate is measured by the 4- to 6- month commercial paper rate. Two zero-one dummy variables are included for the average influ ence of major strikes on income, with D j equaling one for the quarter of a strike and D2 equaling one for the quarter following a strike.11 A test was performed for a structural change in the model (Appendix). For M! such a change is alleged by some analysts to have occurred after the fourth quarter of 1966 when a change in the trend growth of the ratio of GNP to Mx is observed. A similar change in the trend growth of the ratio of GNP to M2 occurred after the fourth quarter of 1961. In both cases the structural change hypothesis was rejected. A statistical procedure (Appendix) was next used to select the appropriate number of lagged changes in the price level, nominal income, and in the amount of goods and services that nominal income can pur chase; four lagged terms were deemed appropriate. The estimated parameters of equations A and B are reported in Tables I and II. EMPIRICAL MODEL AS A TEST OF THE THEORY The empirical model is used to test whether or not the theory of nominal income determination advanced earlier can be accepted. The part of this theory re garding the determination of nominal spending by households and business firms carries specific implica10In national income terms, the definition of nominal income used in this study is the sum of consumption, investment, government expenditures, and exports less imports. This sum should be adjusted for depreciation and indirect busi ness taxes, to be identical to value added. It is assumed that variations in these two magnitudes will have little influence on the outcome of this study. 1'The major strikes in the sample period were: steel III/1959, autos 1V/1964, and autos IV/1970. FEDERAL RESERVE BANK OF ST. LOUIS JU N E Table I 1975 Table II Regression Results* Equation Independent V a riab le Regression Results* (A ) Equation m2 - 1 .9 9 6 (- 3 .7 6 5 ) - 1 .9 4 7 (- 3 .6 3 7 ) d2 2 .2 5 9 (3 .9 7 8 ) A in Mt .6 8 5 (4 .0 0 3 ) Mj m2 Dl - 1 .9 3 0 ( - 3 .7 4 4 ) d2 2 .3 8 0 (4 .3 2 6 ) - 1 .8 8 6 ( - 3 .6 1 6 ) 2.041 (3 .6 3 0 ) A in Mt .701 (4 .5 2 7 ) .5 7 2 (4 .3 0 9 ) V a ria b le (2 .2 5 7 ) 1.921 (3 .3 2 1 ) .5 3 4 (3 .8 1 4 ) .0 3 2 (3 .0 9 6 ) A in Q t- i - .7 9 7 ( - 5 .2 5 0 ) - .7 9 9 (- 5 .1 8 2 ) A in Y t _ i c < M l, Dl - .2 4 9 ( - 1 .9 0 5 ) - .2 0 8 ( - 1 .5 8 0 ) A in Yt -2 A in Qt _3 .2 6 3 ( 2 .0 5 1 ) .2 3 8 (1 .8 4 2 ) A in Q t _4 - .2 7 8 ( - 2 .3 4 1 ) - .301 ( - 2 .5 1 8 ) A in P t-i - .91 8 (- 2 .1 0 5 ) A in Pt-2 - .5 5 8 ( - 1 .1 9 3 ) - .811 ( - 1 .8 5 5 ) - .5 9 2 ( - 1 .2 5 4 ) A in Pt-3 .1 4 3 ( .2 9 8 ) .0 2 2 A in rt 7 a A in Pt_4 .251 ( .6 0 6 ) .2 3 2 ( .4 7 9 ) .2 7 4 ( .6 5 7 ) Constant 1 .0 7 4 (3 .0 7 8 ) .7 7 2 (2 .1 3 5 ) R2 .5 6 9 .561 SEE .8 7 5 .8 8 3 DW 2 .0 0 9 2 .0 3 7 ♦Numbers in parentheses are t-values. tions regarding the estimated coefficients reported in Tables I and II. If the estimated coefficients are con sistent with the implied coefficients, at the five per cent level of statistical significance, this part of the theory is accepted. The model as a whole constitutes the theory of nominal income determination. This theory is tested by the ability of the empirical model to forecast nominal income.12 Relatively small root mean squared errors in forecasting nominal income are taken as evidence that the theory of nominal income determination can be accepted. Testing Implications of Theory Regarding the Responses of Households and Business Firms It was asserted in the theoretical section that the response of holders of money balances is of the same 12A more appropriate test would be to solve for the reducedform of the model, and then to test whether the estimated coefficients of this equation are consistent with those implied by the theory. The reduced-form is a nonlinear equation with variable coefficients, which poses some very difficult problems of estimation. The forecasting test was therefore selected. (B ) Independent A in rt .0 2 0 (2 .1 8 3 ) .0 3 0 (2 .9 7 4 ) - .7 8 2 ( - 5 .2 4 2 ) - .2 7 4 (- 2 .1 6 4 ) - .781 ( - 5 .1 5 7 ) A in Yt - 3 .2 2 6 (1 .8 4 6 ) .1 9 7 ( 1 .5 9 2 ) A in Yt -4 - .3 0 9 ( - 2 .7 3 9 ) - .3 1 5 ( - 2 .7 6 5 ) Constant 1 .1 5 2 (3 .7 8 5 ) .911 (2 .7 9 2 ) - .2 2 5 (- 1 .7 5 9 ) R2 .5 8 0 SEE .8 6 4 .8 7 4 DW 2 .0 3 6 2 .0 4 9 .5 7 0 ♦Numbers in parentheses are t-values. magnitude with regard to perceived price as with re gard to the amount of goods and services that per ceived nominal income can purchase. Therefore, the theoretical formulation was in terms of perceived nominal income. This assertion implies in Equations A and B that for each lag the coefficients for the rates of change in price, in the amount of goods and services that nominal income can purchase, and in nominal income are equal. This implication was tested and could not be rejected at the five percent level of statistical significance (Appendix).13 As a result of this test, estimates of the coefficients of Equation B are used for the balance of this study (Table II). The theory of determination of nominal spending by households and business firms implies that all of the coefficients in Equation B are statistically signifi cant from zero at the five percent level and that they have the following signs: b0, bi, and b2 are positive and b3 is negative.14 All of the estimated coefficients in Table II are statistically significant from zero at the five percent level and have the implied signs. The 13The proposition that the elasticity of desired money bal ances with respect to the perceived level of nominal income equals unity was tested and rejected ( Appendix). The proposition that this elasticity is greater than unity was accepted. 14These implied signs are derived by applying the postulated signs for Equations 1' and 2' to Equation 3'. The magni tude of b3 is derived by adding the coefficients on the lagged income terms. Page 15 FED ER AL RESERVE BAN K OF ST. LOUIS empirical evidence is consistent with the implications of this part of the theory, which is, therefore, accepted. Testing Theory of Nominal Income Determination A test of the theory of nominal income determina tion is the ability of the empirical form of the model to forecast nominal income with relatively small root mean squared errors. This forecasting ability of the model is determined by dynamic simulations. In a dynamic simulation actual values of the quarterly rates of change in money balances, in government spending plus exports, and in the nominal short-term interest rate are used. At the start of the simulation, actual lagged rates of change in nominal income are used, but, subsequently, simulated rates of change are incorporated. Two types of simulations are performed — ex post for the sample period and a number of ex ante simulations beyond various sample periods. The simulation model consists of Equation B (Table I I ), Equation (4 '), and the definition of the weights. Using the discrete-time linear approximation to rates of change in Equation (4 '): Ain Yt = Wt Ain Y td + (1-W,) Ain Z,. W ,= (1-6) Y ^ Yt-i Z = government spending plus exports. 5 = ratio of imports to total spending on product. The ratio is held constant at its average value in the sample period. Ex post simulations are used to ascertain the ability of the model to capture movements in nominal in come over the sample period. The root-mean-squarederror (R M SE ) for the quarterly rates of change of nominal income (expressed as annual rates) is 2.85 percentage points using M2 and 2.95 using M2. Al though the errors in the quarterly rates of change ( expressed as annual rates) are quite large, the errors tend to be offsetting over the sample period. In the fourth quarter of 1973, the error in the level of nomi nal income was 0.36 percent using M, and 0.33 per cent using M2. Over the sample period, the RMSE for the quarterly levels of nominal income is 1.57 percent using Mx and 2.07 percent using M2. Ex ante simulations are used to determine the abil ity of the model to forecast nominal income beyond a sample period, with known values of the exogenous variables. The coefficients of Equation B are estimated for the sample period from first quarter 1955 to fourth quarter 1961. The coefficients are then re-estimated for the sample period from first quarter 1955 to fourth quarter 1962. This procedure of lengthening the sam Page 16 JU N E 1975 ple period by four quarters is continued until fourth quarter 1973, the terminal date. Dynamic simulations are then performed for the eight quarters following each sample period. The simulated annual rate of change in nominal income over the first four quarters and over the entire eight quarters are calculated. For the set of first four quarters, using all the post sample periods, the RM SE’s of the annual rate of change in nominal in come are 1.59 percentage points using Mx and 1.40 using M2. For the set of eight quarter periods, the RM SE’s are 0.99 percentage points using Mx and 0.82 using M2. For each post sample period, the simulated level of nominal income is calculated for the fourth quarter and the eighth quarter. The RM SE’s are then cal culated for the set of all post sample periods. Using M1; the RMSE in the fourth quarter level of nominal income is 1.59 percent and using M2 is 1.40 percent. For the eighth quarter level, the RMSE is 1.98 per cent using Mx and 1.64 percent using M2. The ex ante simulation results indicate that the empirical model forecasts the level of nominal income with relatively small RM SE’s, compared with fore casts from nine major econometric models of the U.S. economy. Carl F. Christ, in reviewing the ex ante forecasting performance of these models, concluded, “All have RM SE’s for real and nominal GNP that are 1 percent or less for one quarter ahead, and 3 percent or less for five or six quarters ahead.”15 The model presented in this study, which is based on a markedly different theory than eight of these nine models, fore casts nominal GNP with smaller RM SE’s than several of the large scale econometric models of the U.S. This forecasting evidence thus leads to acceptance of the theoretical model of nominal income determination. CONCLUSIONS A theoretical model of nominal income determina tion was developed, based on a set of postulates re garding the behavior of households and business firms. The central postulate is that the rate of change in nominal spending by households and business firms for newly produced final goods and services responds to a discrepancy between the rates of change in actual and desired nominal money balances. On the basis of the empirical tests, the theoretical model was accepted as representing the determination 15Carl F. Christ, “Judging the Performance of Econometric Models of the U.S. Economy,” International Econom ic R e view (February 1975), p. 64. FEDERAL RESERVE BANK OF ST. LOUIS JU N E of nominal income in the period 1955 -1973. The estimated coefficients of the empirical model have the signs implied by the theory. In addition, ex post and ex ante dynamic simulations indicate that it fore casts nominal income with relatively small errors. The empirical results mentioned in the introduction of the St. Louis reduced-form equation relating changes in GNP to changes in money and government spend ing are consistent with the theoretical properties of the model presented in this study. These theoretical properties are developed in the section which dis cusses the changes in the dynamic equilibrium state. A theoretical property of the model is that a change in the trend growth of nominal money balances changes the trend growth of nominal income. An other theoretical property is that short-run changes in the growth of nominal balances result in short-run 1975 changes in the growth of nominal income. A third theoretical property ( based on partial analysis) is that changes in the growth of government spending exert a short-run, but not a long-run, influence on growth of nominal income. Thus, there is “crowding-out” of spending by households and business firms, but only in partial equilibrium analysis. Since the desire to hold money balances is negatively related to the short-term interest rate, the financing of the growth of government expenditures by issuing debt may have a positive influence on growth on nominal income. The estimated interest elasticity of desired'money balances is very small (about .03); therefore, for debt financing to have much of an influence on growth of nominal income, the elasticity of the interest rate with respect to government debt must be very large or the increase in debt outstanding must be exceedingly large. APPENDIX Data Problems The linear approximation of rates of change in dis crete time is given by the following: d In Y 1 dY v . v -------- = ---------- --- In Yt - ln Yt-l. dt Y dt The technical efficiency of the payments system is assumed, on average, to increase at a constant rate given by the following exponential growth function: E(t) = aebt; or ln E(t) = ln a + bt. e = the base of natural logarithms, b = constant rate of growth, a = beginning level of E. of change in nominal income and the rate of change in the perceived level of nominal income. d2 ln YP = dt- ——-------- dt' d ln dt Y _ d ln YP , dt = th e c h a n g e in th e ra te o f c h a n g e in th e p e r c e iv e d level of nominal income. f3 = the adjustment coefficient. O < 0 =s The larger is A. the faster is the speed of adjustment. According to Cagan’s procedure, the rate of change in the perceived level of nominal income can be approxi mated in discrete time by the following: A in Ytp = d -e-'3 ) I i = 0 (l-e-0) I A in Yt-ie’^ . e -& = l. i = o t = an index of time. Differentiating with regard to time yields: d In E A variation of Phillip Cagan’s procedure is used for ap proximating the rate of change in the perceived level of nominal income. It is assumed that changes in the rate of change in the perceived level of nominal income are proportional to the discrepancy between the actual rate In the discrete time form of the model, it is asserted that the rate of change in perceived nominal income is that at the beginning of the period. The index (i), there fore, runs from 1 to T. Instead of assuming, as Cagan did, various values of P and then using their implied values for Ain Y [ directly in the regression equation and se lecting the one which has the largest R2, the coefficients for each lagged income term were estimated directly. Four lagged changes in nominal income (the lag struc ture used in this study) implies that (5 = 1.15, with the Page 17 FEDERAL RESERVE BANK OF ST. LOUIS JU N E implied weights ( 0.68, 0.22, 0.07, and 0.02) summing to 0.99. The estimated coefficients for the four lagged income terms, given their standard errors of estimate, are approxi mately consistent with those implied by these weights. Test for Structural Change A test of the hypothesis of a structural change in the coefficients of the model is performed by introducing a zero-one dummy variable into equation (A ) of the text. This equation is used rather than Equation B, which incorporates a special assumption regarding the param eters on perceived price and the amount of goods and services that perceived nominal income can purchase. The dummy variable has the value of zero in the M, equation from first quarter 1955 to fourth quarter 1966, and then a value of one to fourth quarter 1973. It has a zero value in the M2 equation from first quarter 1955 to fourth quarter 1961, and then a value of one to fourth quarter 1973. Two forms of equation (A ) are estimated. One is the original specification. The second one has all the original variables, but adds the dummy variable itself (to meas ure a change in the constant) and the product of the dummy and each of the original variables (to measure a change in the regression coefficients).1 If the estimated coefficients for these added varia bles are not statistically significant from zero, the struc tural change hypothesis is rejected. An F test is con ducted to test the null hypothesis that all the regression coefficients of the added set of variables are equal to zero. If the calculated F value is less than the critical F value, at the five percent level of significance, the null hypothesis is not rejected. Since the number of lagged AlnQ and AlnP terms have not been specified at this point, the test for structural change was conducted for lag specifications from one quarter to ten quarters (Table A ). For every length of lag, the calculated F value is less than the critical value. As a result, the hypothesis of a structural change in both the M j and M2 equations is rejected for each of the lag structures examined. Table A Test For Structural C h a n g e Equation Calculated F Mj m2 J 1.6 4 1 .6 7 2 .3 6 2 1.45 1.34 2 .1 7 C ritical F ( .0 5 ) 2.05 3 1.58 1 .54 4 1.05 1.42 1.98 5 .9 9 6 .8 7 1 .1 7 .91 1.93 1 .90 7 .8 2 .9 3 1.89 8 .7 5 .98 1 .89 9 .7 5 1.21 1.91 10 .83 1 .1 2 1.91 18 Digitized forPage FRASER Determination of Lag Structure A statistical procedure is used to determine the ap propriate number of lagged AlnQ and AlnP terms in equation (A ). Each equation (M , and M2) is estimated eleven times, first with no lags and then increasing the length of lag for AlnQ and AlnP by one quarter until ten sets of the two lagged terms are included. The F test is used to test the null hypothesis that the two estimated coefficients for each a d d e d lag are zero. If the cal culated F value is greater than the critical value, at the five percent level of significance, the null hypothesis is rejected. Table B shows that the null hypothesis is re jected when lags one and four are added, but not when any of the other lags are added. Table B Test of Lag Structure Equation Each Added Lag (A ) Calculated F C ritical F (.0 5 ) Mj m2 1 1 6 .8 8 16.92 4 .0 0 2 1 .1 9 .8 9 4 .0 0 4 .0 0 3 .4 5 .1 6 4 4.11 4 .8 3 4 .0 0 5 .2 0 .2 0 4 .0 0 6 1 .0 2 1.00 4 .0 0 7 .2 4 8 1 .24 .2 6 1.41 9 .3 9 2 .3 0 .3 0 4 .0 0 4 .0 4 2.78 4 .0 4 10 Lags 1-4 5 -10 6 .3 7 .91 4 .0 0 6 .0 9 2 .5 3 1.01 2 .2 9 The F test is next used to test the null hypothesis that as a set all the coefficients for lags one to four are equal to zero. This test, at the five percent level, rejects the null hypothesis (Table B ). A similar test is conducted for the coefficients as a set for lags five to ten, when lags one to four are included in the regression. In this second test the null hypothesis cannot be rejected (Table B ). On the basis of these results, four lagged AlnQ and AlnP terms are considered to be appropriate. Table I in the text presents the estimated coefficients for this speci fication, equation (A ). (A ) Number of Lags 1Except D i and Do. 19 75 Test of Equal Response Hypothesis The hypothesis that the response of desired nominal money balances is the same with regard to both per ceived price and the amount of goods and services that nominal income can purchase is tested by imposing a linear constraint on equation (A ). An F test is used to test this constraint. If the calculated F value for the con straint is less than the critical value, at the five percent level of significance, the proposition is accepted. Assuming that the weights in forming Ain Q d and Ain Pp are equal for each lag, the equal response hypo thesis implies that for each lag the estimated coefficients for AlnQ and AlnP are equal. Since by definition FEDERAL RESERVE BAN K OF ST. LOUIS JU N E Table C Test of U nitary Elasticity Hypothesis Regression Results Mi m 2 Dl - 2 .0 3 5 (- 3 .8 6 4 ) - 2 .0 2 2 (- 3 .7 0 8 ) d2 2 .4 8 6 (4 .4 2 4 ) 2 .0 9 5 (3 .5 5 0 ) A in rt .0 1 5 (1 .6 7 2 ) .0 2 5 (2 .4 3 8 ) A in Y t _ i - A in Mt - .6 9 6 (- 4 .7 2 3 ) - .6 4 5 ( - 4 .2 7 6 ) A in Y u 2 - A in Mt - .2 3 0 ( - 1 .7 9 7 ) .2 6 4 (2 .1 1 8 ) - .1 4 8 ( - 1 .1 2 9 ) - .2 1 3 (- 2 .0 0 7 ) - .1 8 4 ( - 1 .6 8 0 ) .571 (4 .0 6 3 ) .0 4 0 (.3 5 6 ) A in Yt -3 - A in Mt A in Yt -4 - A in Mt Constant .2 4 0 (1 .8 5 9 ) R2 .5 5 8 .5 2 6 SEE .8 8 7 2 .0 4 5 .9 1 8 DW 2 .0 2 7 ♦Numbers in parentheses are t-values. Ain Q t + AlnPt = Ain Yt, the coefficients on each set of lagged AlnQ and AlnP terms are constrained to be equal 1975 by specifying AlnY terms (Equation B ). Table II of the text presents the estimated coefficients for equation B. Regression results for this equation are tested against those for equation (A ). The calculated F value are .58 for and .64 for M2. The critical F value is 2.53, there fore, the equal response hypothesis is accepted in both cases. These results also lead to the acceptance of the assumptions made regarding the equality of weights in forming Ain Qp and Ain Pp. A frequent hypothesis in monetary economics is that the elasticity of desired money balances with regard to nominal income is unity. Since the weights sum to unity, the hypothesis implies that the coefficient an money in equation (B ) is equal to, but opposite in sign, the sum of the coefficients on the lagged AlnY terms. This con straint is imposed on equation (B ) by dropping the AlnMt term and subtracting AlnMt from each of the lagged AlnY terms. The regression results are reported in Table C and are tested against the results for equation ( B ) . The calculated F value for M j is 4.57 and for M„ is 7.99. The critical value of F is 4.00; therefore, the propo sition that the elasticity equals unity is rejected in both cases. The estimated elasticity of desired money balances with regard to perceived nominal income — 1.62 for M x and 1.97 for M ,, — is derived by dividing the sum of the coefficients on the lagged income terms by the coefficient on money and changing the sign. Page 19