a monetarist model for economie stabilization - research - federal

A Monetarist Model for Economie Stabilization*by LEONALL C. ANDERSEN and KEITH M. CARLSON

rjiI. HE MONETARIST VIEW that changes in the

money stock area primary determinant of changesin total spending, and should thereby be givenmajor emphasis in economic stabilization programs,has been of growing interest in recent years. Fromthe mid-1930’s to the mid-1960’s. monetary policy re-ceived little emphasis in economic stabilization policy.Presumed failure of monetary policy during theearly years of the Great Depression, along with thedevelopment and general acceptance of Keynesianeconomics, resulted in a main emphasis on fiscal ac-tions — Federal Government spending and taxingprograms — in economic stabilization plans. Monetarypolicy, insofar as it received any attention, was gen-erally expressed in terms of market rates of interest.

Growing recognition of the importance of moneyand other monetary aggregates in the determinationof spending, output, and prices has been fostered bythe apparent failure of stabilization policy to curbthe inflation of the last half of the l960’s. Sharplyrising market interest rates w’ere interpreted to indi-cate significant monetary restraint, while the Reve-nue and Expenditure Control Act of 1968 was con-sidered a major move toward fiscal restraint.

Despite these policy developments, total spendingcontinued to rise rapidly until late 1969, and the rateof inflation accelerated. Those holding to the mone-tarist view were not surprised by this lack of success

aOffering helpful suggestions throughout the study wereDenis Karnosky of this bank, William P. Yohe of Duke Uni-versity and visiting Scholar at this bank, 1969-70, andDavid Fand of Wayne State University. Susan Smith pro-vided programming assistance and Christopher Babb andH. Albert Margolis advised on statistical problems. Theauthors thank the following for their comments on earlierdrafts, without implying their endorsement of either themethods of analysis or the conclusions F. Gerard Adams,Philip Cagan, E. Gerald Corrigan, Richard Davis, Ray Fair,Edgar Fiedler, Milton Friedman and members of the Moneyand Banking Workshop at the University of Chicago, EdwardGramlieh, Harry C. Johnson, John Kalchbrenner, EdwardKane, Michael Keran, Allan Meltzer, Franco Modigliani,George Morrison, David Ott, Joel Popkin, Thomas Saving,Roger Spencer, Henry Wallich, Clark Warburton, ManfredWillms, and Arnold Zellner.

in curbing excessive growth in total spending, largelybecause the money stock grew at a historically rapidrate during the four years ending in late 1968. Eco-nomic developments from 1965 through 1969 were ingeneral agreement with the expectations of themonetarist view.

This article develops a model designed to analyzeeconomic stabilization issues within a frameworkwhich focuses on the influence of monetary expan-sion on total spending. Most of the major econometricmodels have not assigned an important role to themoney stock or to any other monetary aggregate.1

Furthennore, most econometric models contain a largenumber of behavioral hypotheses to be empiricallyestimated and integrated with each other, becausethey are designed to aid in understanding the deter-mination of many economic magnitudes. By compari-son, the model presented in this article is quite small.It is designed to provide information on the mostlikely course of movement of certain strategic eco-nomic variables in response to monetary and fiscalactions.

Frank de Leeuw and Edward M. Cramlieh, “The FederalReserve-MI’I’ Econometric Model,” Federal Reserve Bul-letin (January 1968), pp. 11-40, and “The Channels ofMonetary Policy: A Further Report on the Federal ReserveMIT Econometric Model,” Federal Re~~~erveBulletin (June1969), pp. 472-91; James S. Duesenberry, Gary Fromm,Lawrence R. Klein, and Edwin Kuh (ed), The BrookingsQuarterly Econometric Mode? of the United States (Chicago:Rand McNally, 1965), and The Brookings Model: SomeFurther Results (Chicago: Rand McNally, 1969); MichaelK. Evans and Lawrence R. Klein, The Wharton EconometricForecasting Model, 2nd Enlarged Edition (Philadelphia:University of Pennsylvania, 1968); Maurice Liebenberg,Albert A. Hirsch, and Joel Popkin, “A Quarterly Econo-metric Model of the United States: A Progress Report,”Survey of Cur,’ent Business (May 1966), pp. 423-56; DanielM. Suits, “The Economic Outlook for 1969,” in TheEconomic Outlook for 1969, Papers presented to the Six-teenth Annual Conference on the Economic Outlook at TheUniversity of Michigan (Ann Arbor: University of Michigan,1969), pp. 1-26. For a discussion of the role of money inthese models, see David I. Fand, “The Monetary Theory ofNine Recent Quarterly Econometric Models of the UnitedStates,” forthcoming in the Journal of Money, Credit, andBanking.

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~AL RESERVE SAI?or ST LOUIS - APRIL 1970

The model presented here is the authors’ own ver-sion of how monetary and fiscal actions influence theeconomy. Other economists (including those of ainonetarist persuasion) may prefer to develop certainaspects of the model in a different way. Two suchmodifications are presented in Appendix C. Themodel is considered open to revision, hut is presentedat this time with a view to stimulating others to joinin quantifying relationships that are generally asso-ciated with the monetarist view.

This article is divided into five major sections. Ageneral monetarist view of the response of spending,output, and prices to monetary and fiscal actions issummarized first. Next, the specific features of themodel are discussed within a formal framework ofanalysis. Statistical estimates of the model’s param-eters are presented in the third section. The fourthsection tests the performance of the model with sev-eral dynamic simulation experiments.. Finally, bysimulating the response of the economy to alterna-tive rates of monetary expansion, an illustration isprovided of how the model can be used for currentstabilization analysis.

General Monetarist ViewThe general monetarist viesv is that the rate of

monetary expansion is the main determinant of totalspending, commonly measured by gross nationalproduct (GNP ) .~ Changes in total spending, in turn,influence movements in output, employment, and thegeneral price level. A basic premise of this analysisis that the economy is basically stable and not neces-sarily subject to recurring periods of severe recessionand inflation. Major business cycle movements thathave occurred in tile past are attributed primarily tolarge swings in the rate of growth in the money stock.

This view regarding aggregate economic relation-ships differs from prevailing views which consideraggressive policy actions necessary to promote sta-bility. Monetarists generally hold that fiscal actions,in the absence of accommodative monetary actions,exert little net influence on total spending and there-fore have little influence on output and the pricelevel. Governsnent spending unaccompanied by ac-commodative monetary expansion, that is, financedby taxes or borrowing from the public, results in acrowding-out of private expenditures with little, if any,

2Ceneral references on the monetarist view are Karl Bmnner,“The Role of Money and Monetary Policy,” this Review(July 1968), pp. 9-24; David I. Fand, “Some Issues inMonetary Economics,” this Review (January 1970), pp.10-27, and “A Monetarist Model of the Monetary Process,”forthcoming in the Journal of Finance,

net increase in total spending. A change in the moneystock, on the other hand, exerts a strong independentinfluence on total spending. Monetarists conclude thatactions of monetary authorities which result inchanges in the money stock should be the main toolof economic stabilization. Since the economy is con-sidered to be basically stable, and since most majorbusiness cycle movements in the past have resultedfrom inappropriate movements in the money stock,control of the rate of monetary expansion is the meansby which economic instability can be minimized.

The theoretical heritage of the monetarist positionis tile quantity theory of money.8 This theory datesback to the classical economists (particularly DavidRicardo) in the early 1800’s. The quantity theory inits simplest form is characterized as a relationshipbetween the stock of money and the price level.Classical economists concentrated on the long runaspects of the quantity theory in which changesin the money stock result in changes only in nominalmagnitudes, like the price level, but have no influ-ence on real magnitudes like output and employment.

The quantity theory of money in its modem formrecognizes the important influence that changes inthe money stock can have on real magnitudes inthe short run, while influencing only the price levelin the long run. The modern quantity theory postu-lates that in the short run a change in the rate ofgrowth in money is followed with a moderate lag bychanges in total spending and output, while changesin the price level follow with a somewhat longer lag.~These changes in total spending, output, and pricesare in the same direction as the change in the rateof monetary expansion.

The modern quantity theory still accepts the long-run postulates of its older version. A change in therate of monetary expansion influences only nominalniagnitudes in the long run, namely, total spending(GNP) and the price level. Real magnitudes, notably

3The classic work on the quantity theory is Irving Fisher,The Purchasing Power of Money (New York: Macmillan,1911). For an extensive review of the quantity theoryliterature, see Arthur W. Marget, The Theory of Prices: ARe-examination of the Central Problems of Monetary Theory(New York: Prentice-Hall, 1938), volume II, pp. 3-133.

4Many of the ideas prevalent in current monetarist doctrinecan be found in the writings of Clark Warburton in the194O’s and early 1950’s. Many of his important articles havebeen reprinted in his Depression, inflation, and MonetaryPolicy, Selected Papers, 1945-1953 (Baltimore: The JohnsHopkins Press, 1966). See also Milton Friedman, (ed),Studies in the Quantity Theory of Money (Chicago: Uni-versity of Chicago Press, 1958), and Lloyd W. Mints,Monetary Policy in a Competitive Society (New York:MeCraw-Hill, 1951).

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FEDERAL RESERVE BANK OF ST. LOUIS APRIL. 1970

output and employment, are unaffected.8 Followingthe short-mn responses to a change in the rate ofmonetary growth, total spending and the price levelgrow at rates determined by the rate of increase inmoney, while output moves toward and resumes along-run growth path. Such growth in output is litheinfluenced by the rate of monetary expansion. In-stead, it is determined by grosvth in the economy sproductive potential, which depends on growth ofnatural resources, capital stock, labor force, andproductivity.

General Form of the ModelA summary of the model is presented in algebraic

form in Exhibit I, along with a listing of variablesclassified as to whether they are endogenous or exo-genous to the model (for a graphical illustration ofthe model, see Appendix B). This general form ofthe model summarizes its essential features, ignoringproblems of dimensionality and lag length.

Eqi.wti.i.ms of• t:he MoacS..Equation (1) is the total spending equation. The

change in total spending (AY) is specified as a func-tion of current and past changes in the money stock(AM) and current and past changes in high-employ-ment Federal expenditures (AE). Thisgeneral specification represents the re-duced form for that class of structureswhich has AM and AE as exogenousvariables. In this form the total spend-ing equation remains uncommitted asto structure; it is potentially consistentwith both Keynesian and quantity the-ory models.6 (The magnitude and sig-nificance of the estimated parametersdetermine whether the data conformmore closely to a Keynesian or a quan-tity theory).

Equation (2) specifies the change in the pricelevel (AP) as a function of current and past demandpressures (D) and anticipated price changes (AN).Demand pressure is defined in equation (3) as thechange in total spending minus the potential increasein output (V — X), The price equation is an alter-native to the standard short-run Phillips curve rela-tion generalized to include changes in total spendingand anticipated prices.7 (See Appendix A for furtherdevelopment of this relationship.)

Equation (4) defines a change in total spendingin tenns of its components, the part associated withchanges in the price level (AP) and the part asso-ciated with changes in output (AX) ~8 With AY deter-mined by equation (1), and AP by equation (2),AX can be derived from equation (4).

Equation (5) specifies the market rate of interest(R) as a function of current changes in the moneystock (AM), current and past changes in output

7See Roger W. Spencer, “The Relation Between Prices andEmployment: Two Views,” this Review (March 1969),pp. 15-21.

5The change in the price level, AP, and the change in output,AX, are defined in dollar units so that their sum is equalto the change in total spending, AY.

Exhb’t I

MODEL IN ALGEBRAIC FORM

Total Spending EquationM’... .. ~ AE ...AE

12 Price Equationf.(D .. .D’ r.

Demand Pressure Identityày X~ X.

1’; Total Spending IdenttyAy. ..Ap —Ax

(5;. InteresT Rate EquationR. -- I (AM.. Ax .. Ax .. Ap. AP’)

6 Anticipated Price Equationf,(AP . . Ap,

(7) Unemployment Rote EquationU’ . F 10,6’

(B) GNP Gap Identityx’. x,

C

Endogenous Variables , Exogenous Variables’

ày- &ange :~Iota’ spt’nd,r,q AM ‘. chnngL., n money stockI nominal ONPI Ar.” chango in higi’ employment

A P. . . c horign in p.~e cccl ION P price Feoera’ expendituresdetlatorl X - potential IfuII.empiaymentj

D demano ~rPsiJre a~tps.tAx ~hnr.’je in o,itpui (‘cal CNP)

R -. r’a,kct :r,lerexl rateanticipated change in p’ice tecel

Li’ unemployment r&eC- C-NP gap

Othe’. tli;sn

8See Milton Friedman, “The Role of ivlone-tary Policy,” American Economic Review(March 1968), pp. 1-17.

6For further discussion of the structural versusthe reduced form of a model, see MichaelKeran, “Monetary and Fiscal Influences onEconomic Activity .— The Historical Evidence,”this Review (November 1969), pp. 5-24;Edward M. Cramlich, “The Usefulness ofMonetary and Fiscal Policy as DiscretionaryStabilization Tools,” forthcoming in the Jour-nal of Money, Credit end Banking; andRichard C. Davis, “How Much Does MoneyMatter? A Look at Some Recent Evidence,”Federal Reserve Bank of New York, MonthlyReview (June 1969), pp. 119-31.

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FEDERAL RESERVE BANK OF ST. LOUIS APRIL, 1970

Equation (7) is the unemployment rate equationand is a transformation of the GNP gap (C), asdefined in equation (8), into a measure of unem-ployrnent relative to the labor force, This transforma-tion is based on “Okun’s Law.”1°

The workings of the model are summarized by aflow diagram (Exhibit II). Only variables in the cur-rent period are shown in the diagram; lagged vari-ables, with the exception of past changes in prices,are omitted. The relationship that determines totalspending is the fundamental one among those thatdetermine the endogenous variables of the model.Total spending is determined by monetary actions andfiscal actions (Federal spending financed by taxes orborrowing from the public), though no direct infor-mation is provided as to how such actions affectspending.

The change in total spending is com-bined with potential (full employment)output to provide a measure of demandpressure. Anticipated price change,which depends on past price changes,is combined with demand pressure todetermine the change in the price level.

The total spending identity enablesthe change in output to be determined,given the change in total spending

0For a detailed study of interest rates andthe Fisher eftect, see William P. Yohe andDenis S. Karnosky, “Interest Rates and PriceLevel Changes, 1952-69,” this Review (De-cember 1969), pp. 18-38.

50Arthur M. Okun, “Potential CNP: Its Meas-urement and Significance,” 1962 Proceed-ings of the Business end Economic StatisticsSection of the American Stetistical Associe-tion, pp. 98-104. Okun’s Law relates theCNP gap to the unemployment rate asfollows:

The number .03 is a productivity factorand 4 is defined as the unemployment rateconsistent with full resource utilization.

and the change in prices. This method of determin-ing the change in total spending and its division be-tween output change and price change differs frommost econometric models. A standard practice in econ-ometric model building is to determine output andprices separately, then combine them to determinetotal spending.

The change in output, the change in prices and inanticipated prices, along with the change in themoney stock, determine market interest rates. Theflow diagram shows that the market interest ratedoes not exercise a direct role in the model in thedetermination of spending, output, and prices.

To detennine the unemployment rate, the changein output is first combined with potential output todeternine the CNP gap relative to potential output.The GNP gap is then transformed into the unem-ployment rate.

The model has been presented in general form toshow the basic linkages postulated among money,Federal expenditures, prices, and output. The pur-pose of the following statistical section is to estimate

(AX), current price change (AP), and anticipatedprice change (AN). The price anticipations termis included to capture the Fisher effect.° The anti-cipated price function is defined in equation (6).Anticipated price change (AN) in the current pe-riod is assumed to depend on past price changes(AP).

— X~= .03(Ut — 4)Xt.

Page 10


the response of output and prices to monetary andfiscal actions, not to test a hypothesized structure.The focus is on the response in the short run — periodsof two or three years — but the long-run propertiesof the model also are examined.

Estimation of the ModelThe general form of the model indicates those

variables that are included in each equation. Estima-tion requires selection of the algebraic form of theequations and the techniques to be used inestimnation.

Each of the equations of the model is estimatedby ordinary least squares. Lag structures, with oneexception, are estimated by the Almnon lag technique.The reported relationships reflect considerable ex-perimentation with the number of lags and the de-gree of the polynomial.” The sample period startswith 1933 for the spending equation and with 1955for all the others. The data are quarterly and, withthe exception of interest rates, are seasonally adjusted.

Criteria used in the selection of the equationswere minimizing the standard error of estimate andeliminating serial correlation in the estimated resid-uals. In addition, the signs and statistical significanceof the estimate’d coefficients received consideration,along with the pattern of the lag distribution. Sincethese criteria frequently could not be satisfied simul-taneously, an elemnent of subjectivity was present in-selecting the “best” equation.

The change in total spending is specified as afunction of current and past changes in the moneystock (demand deposits and currency held by thenonbank public) and in high-employment Federalexpenditures (expenditures on goods and services plustransfer payments adjusted to remove the influenceof variations in economic activity on unemploymentbenefit payments)~The choice of the particular equa-tion (Table I) is based on previous work by Andersenand Jordan.’2 Implicit in this choice is the assump-tion that the change in the money stock is an exog-enous variable. ~kmore complete model would specifya mechanism whereby the money stock is determinedby actions of the monetary authorities, the public,and the banking system.

‘‘For discussion of the use and interpretation of the Almonlag technique, see Keran, p. 10.

‘tm

Leonall C. Andersen and Jerry L. Jordan, “Monetary andFiscal Actions: A Test of Their Relative Importance inEconomic Stabilization,” this Review (November 1968),pp. 11-24. See also Keran, pp. 5-24.

Table ITOTAL SPENDING EQUATION

$qmp)e Period: 1/1953 P1/1969Conaretrsts 4th Degree Polynomial(en or 0,ms—e 0)

4At 267 2 mAMt + 2 esAs R

2’ .66

(3.46) ~ ° SE 384OW— L75

in — 122 (273) 00— 56 ( 2.57)en, = ISO 17-34) at — .45 ( L437mm 162 (425) ez 01 ( 08)in — 87(3657 ea .43 ( 318)en .06 ( .12) e — 54 ( 2477

2,,, 557 (8067 Ze 05 ( 17)

rabol a C ndAT dolla ehng ntotal p dinglOMP non ntpe I

‘n qu,u’te S

E_j on, eJ,an n money took aqua ,

En dlrchan -nh,h-ompoyo,etPe am p thtu‘nq

No - tattOo pp wuheach a es oncoeffse cab1, pareti, E’, be 05 at nun hda unsent

,ablewh , epbunedhyv ian nth undpendtna’abl Eu U, tanad ro I, ‘ma fl-Wihobu atm in

The pattern of thc coefficients indicates a largeand rapid influence of monetary actions on totalspending relative to that of fiscal actions.” Changesin high-employment expenditures, with the moneystock held constant, first have a positive influenceon total spending, but the influence becomes signifi-cantly negative after three quarters. Fiscal actions,unaccompanied by changes in money, have little neteffect on CNP over five quarters.’4 For short periods,and for extended periods in which the rate of changeof Federal expenditures is either accelerating or de-celeratirig, fiscal effects are significant. The estimatedcoefficients for changes in money and changes inFederal expenditures are in general agreement withthe monetarist view of the response of total spendingto these two variables.

The specification of the total spending equation, asshown in Table I, has been criticized as being incom-

‘3

Andersen and Jordan tried several measures of fiscal actionsin their basic equation. The best results were obtained byusing only high-employment expenditures, rather than thehigh-employment surplus or both high-employment ex-penditures and receipts. They justify their choice by ap-pealing to the notion that financing expenditures by borrow-ing from the public and taxes have essentially the sameimpact on total GNP. For some results that contradict thoseof Andersen and Jordan, see E. C. Corrigan, “The Measure-ment and Relative Importance of Fiscal Policy,” forthcom-ing in Federal Reserve Bank of New York Monthly Review.It should be repeated that, a priori, specification of thetotal spending equation was sufficiently general as to beconsistent with a numher of theories of CNP detennination,

‘-‘Andersen and Jordan, p. 18, indicate that these results areconsistent with a “crowding-out” theory of eftects of gov-ernmnent spending.

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FEDERAL RESERVE BANK or sr LOUIS -— - — APRIL 1970

plete in that it allegedly ignores the effects of interestrates on velocity.’5 However, since the spendingequation is a reduced form, such effects are embodiedin the coefficients of money.’°

flUIItCS

The total spending equation is the cornerstone ofthe model, providing its monetarist character. Thefocus of this paper, hosvever, is on determining thedivision of the change in total spending betweenprice and output changes. Price changes are estimatedas a function of (1) current and past demand pres-sure, and (2) anticipated price change.

Demand pressure — As a measure of demand pres-sure on prices, the change in total spending is relatedto the potential change in output (GNP in constantprices).’7 These two variables, when combined,provide a measure of the economy’s demand for goodsand services relative to its capacity to supply goodsand services, The change in prices is specified as apositively related linear function of this measure ofdemand pressure (see Appendix A).

Demand pressure, Dn, is defined as:

Dr = Al, _(Xr, — Xn_,),

where AY, is the change in total spending in quartert; X”, is potential (full employment) GNP in 1958prices in quarter t; and X,_, is real GNP in theprevious quarter.’8 Given the GNP gap, defined asX~’, X,—,, the larger is the change in total spending

(AY,), the greater is the spillover into higher prices.Given ~Y,, the larger is X”~— X,—,, the greater isthe expansion of output and the less the spilloverinto higher knees.

In addition to current values, past values of thedemand pressure variable are included in the priceequation. The purpose of including past values is toallow for lags in th0 detennination of prices in re-

sponse to changing de,nand. Furthennore, the impactof changing demand through changing input pricesand costs of production is given a chance to operateby including lagged values for the demand pressurevariable,

Anticipated Price Change — The other independentvariable included in the price equation is’’~inieasureof anticipated price change (AP’n). The purpose ofincluding this variable as a factor influencing currentchanges in the price level is to allow anticipations offuture price movements to influence the decisions ofmarket participants. Since such a variable is not

bI 1

ANTICIPAT 1) PRICE DEFtNFTIONp from Løng T us late oat Rote Eq eStee)

‘ Pl1~

4) 01 5]

ps 02 py 08p 03 p 06 p, 06p 0 p 36 p—04p 06 r ~ pa 03p-—04 06 p,r 2p .07 pa 7 Pi 96

yrabolaa Ctee I s oil a a

15

a S haagemnawr 01 (10 00)

4 ~n namlo en e tat I t

(0 40 mutat (ON? mu p’eea) luqu

observable, it has to be constructed. This is accom-plished by assuming that anticipations about futureprice changes are formed on the basis of past priceexperience.

The measure of price anticipations used in thisstudy is a by-product of estimating long-term marketinterest rates.’° Yohe and Karnosky showed thatlong-term market interest rates respond to price an-ticipations of borrowers and lenders, since commit-

‘~‘Forother ways of handling expectations, see Appendix Con alternative price equations.

tmmSee Paul S. Anderson, “Monetary Velocity in EmpiricalAnalysis,” in Controlling Monetary Aggregate,-, Proceedingsof the Monetary Conference held on Nantucket Island(June 1969), pp. 37-51, and the discussion of that paperby Leonall C. Andersen, pp. 52-55. See also Henry A.Latand, “A Note on Monetary Policy, Interest Rates andIncome Velocity,” Southern Economic Journal (January1970), pp. 328-30.

‘6See A. A. Walters, “Monetary Multipliers in the U. K.:1880-1962,” Oxford Economic Papers (November 1966):

‘7This measure was apparently first used by Ray Fair ofPrinceton University. See his “The Determination of Ag-gregate Price Changes,” forthcoming in the Journal ofPolitical Economy. For a similar specification of a priceequation, see Milton Friedman, “A Theoretical Frameworkfor Monetary Analysis,” also forthcoming in the Journalof Political Economy. See also a paper by William Considineof Stanford University, “Public Policy and the CurrentInflation,” prepared as a part of a summer intern programat the U.S. Treasury Department (Septe,nber 5, 1969).

‘-5

The series on potential output is based on that used bythe Council of Economic Advisers. Currently, potentialoutput is estin,ated to be rising at a 4.3 per cent annualrate. For alternative estimates of potential output, seeFair, “The Determination of Aggregate Price Changes.”

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FEDERAL RESERVE BANK OF St. LOUIS APRIL, 1970

ments to borrow and lend funds nec1uirc’ an assessmentof anticipated changes in the priee level for the periodof the loan. The problem consists of isolating this

price effect on market intc’rest rates from factors in-

fluencing the real rate.

In the process of constructing a measure of antici-

pated price change, past changes in prices are ad-justeci by a summary measure of current c’eononlicconditions. Since price changes tend to lag changesin total spending, the degree of resource utilizationas measured by the unemployment rate is used asa leading indicator of future price movements.’°Forexample, if unemployment is rising relative to thelabor force, decision-making economic units wouldtend to discount current inflation in forming anticipa-tions about future price move,nents. Reflecting thisconsideration, the price change in each quarter isdivided by an index of the unc-inplovment rate ap-plicable to that quarter. Thus the measure of priceanticipations would be less for a given inflationrate accompanied by high or rising unemploymentthan when unemployment is low or falling.

The specific definition of price anticipations isshown in Table II. The weights and the length of thelag period were obtained from the estimated long-tenn interest rate equation.2’

Estimated price equation — The estimated priceequation is shown in Table III, where AP, is definedas the dollar change in total spending due to pricechanges in quarter t. The influence on prices of thedemand pressure variable, D—,, is significant andpositive for five quarters but very small thereafter.22

The pattern of influence is one of steady decay, \Vith70 per cent of the total effect of demand pressuretaking place in the first three quarters and 95 percent in the first five quarters.

Anticipated price change, represented by AP5,,is a significant determinant of current price change.

‘0For purposes of exposition the unemployment rate was notincluded in the definition of anticipated price change inExhibits I and II.

2tThe price expectations variable as shown in Table II isscaled in dollar units. This transforn,ation is ,nade becauseprices are estimated as the dollar change in total spendingdue to price changes.

22M/hen the price equation is estimated with the componentsof D,~ separated, the coefficients for the AY, portion arenot statistically significant at the five per cent level, im-plying that the gap portion, (XF, - X,,), explains most ofthe changes in AP,. However, there may be eollinearityproblems which influence the estimated coefficients. Fur-the,’more, the D,_u form is used because, theoretically,it is a measure of excess demand (see Appendix A),

~Iat tIm

PRICE EQUATION

Sample Period I 1955 IV 1949Conur met uS Oo9r a Pofynotaucd

- (4— 01

du_0)

A~ 270 , do,, 86AP R 87(70) ‘ (855 SE 107

0~W 141

4 02(263 Cs 01 (186)4 02 ~633} 6 11 81& 0 (66) 4 09 fLI4 0 (29)

8 aI ii e,nt C I I

d ‘e n a rS

an n I a Ce’,a t

S ~I s I t

on I P ‘

tub a I ut

.5 tat 8 11,t 1’ ‘

mn, I,, n ‘.m2k ni n

Webaa!

Though significant the measure of the impact of thisvariable should not be taken too literally because itsconstruction indicates that it cannot really be viexvedindependently of the demand pressure van ible. ‘~ Theinfluence of the e tno variables should perhaps b’viewed in combination rather than as independentand separate influences.’4

Determination of output — Given AY as deter-mined by the total spending equation and ~P fromthe price equation the dollar change in total spending due to output changes defined as can bedcnved from the follouing identity:

AY, — Al’ + AX, (P — P -,) (X X—,).The cross product term is a sumcd equal to zero.25

Thus,AX, = AY, — AP,.

23From the standpoint of the model as a unit, price an-ticipations are important only in determining the divisionof total spending between prices and output, not the level(or change) of spending itself. To allow for the possibledirect influence of price expectations on total spending, thespending equation was estimated with the price anticipa-tions variable. l’he coefficient of the price anticipationsvariable was not significant for this specification.

2’There is, however, some evidence that the price anticipa-

tions variable may he interpreted as an independent andseparate influence. When the price equation is estimatedwithout Al’

51, the sun, of the coefficients on I),—, is only

slightly more than shown in Table HI and the standarderror is increased considerably.

~“The value of this cross-product term was calculated from1953 to the present and provide-s ample justification for

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FEDERAL RESERVE BANK OF ST LOUIS APRIL 1970 I

The unemplo> mnent rate pla\ s a role in the modelrepresenting the moms b ~shieh past prices arc ad-justed to Like into account van inc economic condi-tions in the formation of mtic’ipated price changes.To estimate the unemplo~mcnt rate thc unc mplos -

ment rite ms regrc ssedl on curm c-nt and lagged v’tlucof the GNP gap expressed as a per ct nt of potentialGNP. This equition is estimated b\ uneonstninedoielinarx least square , md is shoss n in Tmble Ps

Toble IV

UNEMPLOYMENT RATE EQUATION

Sample Penad I 1955- lV/1969

U 39004

Gu 280 i R2

92(72.50) (ItO) (680) SE .30

OW 60

Smbi r ,Iuine,IaU un ,nj$oyn, a a p teat u labor orce n uarter C

a ‘ .0

X pots loutput n u etc

eutu ION? nIOsp, ),aqurtert

Nc,t’’’sas, emma th much ~ mo yea teteel adbypanth ituq,prnt a tnnth p tv uabl bib is Ii aChy arm ton x helndpendetvrub S-b tb adade ofti, elms 0~14,I, nr n\at n ta t

the assumption that it he equated to zero for purposes ofthe model here. Also note that AP, is defined in dollar units,that is, as (P, — P,—,)X,_1, not (Pm — Pt—,). AX, is de-fined analogously.

tm0Thomas Sargent, “Commodity Price Expectations and the

Interest Rate,” Quarterly Journal of Economics (Febniary1969), pp. 127-40, and Yohe and Karuosky, pp. 31-34, 38.The eytin,atcd interest rate equations also contain adummy variable (0 for 1955-60 and 1 for 1961-69). Thesignificance of tl,is dnmn,y variable indicates a shift ofstructure within the sample period. Questions can be raised

Tnblc V

LONG-TERM INTEREST RATE EQUATION

Sample Period: 1,1955 - IV 1969

Con,trninls’ 2nd Oeqree Polynomiallx ‘: 0. p I ‘~ 0; x,; ‘. p:; . . 0)

1.28 CaM.- 1.42Z ‘ . x X.

l5.20) ).. 3.53) 111.01)R

2.92

I p. (p ... ) 5.E .28U, ~ D.W._.69

x. .02 I 385) .0! ( 2.6)) , 0] I 1.38).02 ( 4.35) s. ‘.01 1 2.27) x,: ._ 01 I 1.28)

- 02 1 4.44) x .01 I 2.01) x’,,_ ( 1.20).02 I 4.08) x, — .01 I 1.80) x’:. ..: 1 1.13)

- 02 I ~5~1 x: 01 ( 1.64) xi’. ::. ( 1.07)

0213031 x,i . .01(1.501 .x. .201 2.88!

p. 021 1.23) p.. ‘‘.08(1713) pn.....Oó( 9.29)

F: :._ 031 305) p; ...08fl4.49! p:, 061 8891

p~—.O415.96) p- . .08 (1264) p~.n.04( 8.57)

p 06 (1082) p.’ :‘ .08 (11.37) p 03 ( 8.30)pi — .06 (17.34) p .08 (10.47) p 02 ( 8.0?)p. . .07 119661 p;i mO? I 9.81) Ip 96 (1904)

‘‘‘.1ICr.. i)....’ly’,’t. . ,..,:,,;rIIc.’.u’L,.’’,:r.,:,: Idili’

‘1, ;L:I,.’,;Ij sat, I.: rime,,’ nra.,,..: k si,,,.,- I

‘I., ‘‘i.’ijIi~.’V’i, nh. ,‘,,‘,,‘.,,t,’r S I’, ‘s I I,’:,:, . I’ u’t.’iI 1 ‘:1 . 1%, I

,‘LtL,.Ii’•iis:.a,Ii,~~jiI’L.t ‘eN I’I,.

:11:11,,: j’,!,.,r ii, ru;~t’‘5. (,N; ,:,‘‘I,,’.

~J, ,4 I;’.i.’: of ‘i’’rn,,’,~r’. ‘i us:’ it,’la—,’ 4

Ni,’: i ;‘‘,:‘c’nr’ra-a, s’h,’,u’l L,’,,,,’i.C’’rII’,’,’i’ . tI.’•I “elit’’. ii,.’ ‘‘‘‘~I .. ee:ai’.’n,’, Li’,. ,j’’p’.i,,I,’n’

I I~_L’~iiii’i.i’i I’~. ‘,,‘a,i’,’’,. Ifli’ ‘i,j,’i.,’,’.,’i,t~‘tI’’ul,l . . 0,, .5 ?l.t~t’i:’nd. . I~55

10,1. .,

I UI

Inte~ee~tRatesInterest rates do not function explicitly in the model

as a part of a transmission mechanism running fromchanges in the money stock to output and prices.The estimated long-term interest rate equation playsa vital role in the mnodel, however, providing the in- Long.term interest rate — The long-term marketformation to calculate the measure of price rate (RL,) is measured by the rate on seasoned cor-anticipations. porate Aaa bonds. Changes in output and prices

Market interest rates are specified to depend on (adjusted for unemployment) lagged for 17 quarterscurrent and past rates of change of output (*), the provide the most satisfactory results. The estimatedcurrent rate of change in the money stock (kr), and equation for the long-term rate is shown in Table V.current and past rates of change in prices(~) ad- The results reflect, in a general way, the viewjusted by an index of the unemployment rate. This stressed by monetarists that a change in the rate ofspecification draws on Sargent’s work, which was cx- monetary expansion influences market interest ratesplored further by Yohe and Karnosky.2° in three stages.27 First, the liquidity effect of an

_____________________ — increase in the rate of clmange of the money stock

about this procedure, but it is felt that a price expecta-tions variable should not be constructed on the basis of usample period containing only an expansion like 1961-69.Including the dumn,y variable leaves unexplained thatfactor (or factors) which changed the relationship, but itdoes provide a way of estimating a set of coefficientson prices that is based on a sample period reflectingvarying economic circumstances.

27See Friedman, “The Role of Monetary Policy,” p. 6.

Page 14


on market interest rate is negmti e. Second an in-ereise in the rate of monetary expansion influencesthe rate of change in output \vheh in turn has apositive influence on market interest rates. Finallyan increase in nione grossth influences the rate ofchange in pr’e’es xvhic’h ha a positive effect on mar-ket interest rates.

Short-term interest rate Thc shoit term inteme strate (R” ) nhich is estimited is the foui- to six-monthcommeeeial paper mate. The equation i shosvn’ inTable VI. Price changc’s ame found to enter signmficantly for a shorter lag pci mod thin in the lom —ternirate equation Also the sho t tcmm rate, as measuiedby the foui- to six month commercial papem mate ismuch mole sensitive to changes in output md themoney stock than is the long-term rate as mneasuredby the rate on semsoned coi pot ate Aaa bonds.

Table VI

SHORT TERM INTEREST RAT EQUATION

Sample Period 1/1955 IV/1969

Coestr~osts 2nd Degree Polynomial

(xi ILp Cmxii pit 01

0 10RSi~ 113 l7Mt 92Zt Zx’X +~p (~‘ )

314)( 636) (5-03) i 0 0 t~R

290

$ .47DW_ 69

xo — 08 1 810) pa 04 ( 91)x SB ( 89fl pi — 04 ( 1.53)

*2 — 08( 897) p = 09( 8.26)

* — 08 ( 845) p — 14 (18.52)

1(4 —08(7.83) — .17 (1317)

— Q7( 725) pn — AS (1029)

*6 _,07(676) p — .19(8S2)*7 = .06 ( 6-36) p — 18 8.14)

xc _~O5(6S2) p — .15(764)xp 03 ( 575) pa — 11 ( 730)xo_ 02( 5.52) po_ 06( 704)

201, — JI ( 824) Zpm — 127(1689)

Symbols are deSnedB o - to e -Inn th commercial paper te in qu ne

t~t~— annual Is of ehang in macmice teak ‘a quarter

Z—du,mmmnyva bme,nqarte (G:f 1/19 IVI 0nOt! I/191-IV/199)

a nua rate of hen a outpu (ON? in 198 prices)in quarter t—m

annum t o ehang ON? C flat.ar (19 100) inqua,-te

U j/4 inC of unniplyrnn a apereen flab nrc(be (flinqerte t

Note t’ ~ appear with ach r me ye Thc,enh eselo edbyparoh B’ theprcr,to an ion nth depenenvarable hi h expl n by ear ation in 4k in p nd ntvanale.S.E., the madam-den ofihe em DW1be Durbin W teen taCt em

.tiesuoase •tmi I’ ia.etara /tet/:O.5;~

The pattern of the coefficients in the equationsprovides information about the time response of totalspending, output, and prices to monetary and fiscalactions. The equations indicate that monetary actionsgenerally affect total spending with a tsvo- to three-quarter lag. A change in the rate of growth of totalspending is accomnpanied by a simultaneous changein the rate of growth of output, and it is not untilthree quarters later that the response of prices to achange in demand pressure builds to 70 per cent ofthe total. The response of prices to a change in totalspending is yet slower when there are anticipationsof a high rate of inflation.

The spending equation (Table I) indicates thatabout half of the total response to a change in mone-tary growth occurs in the first two quarters, andabout 80 per cent in the first three quarters.

The pattern of coefficients in the price equation(Table III) indicates that the effect of a change intotal spending is reflected first in output and later inprices. Operating through the demand pressure vari-able, about a fourth of the response of prices to achange in total spending is in the first quarter, whichis about two quarters after the change in monetaryactions. Over 70 per cent of the price response isin the first three quarters, and 95 per cent in thefirst five quarters. The response of the price level tochanges in total spending is also influenced by antici-pated prices. The greater the anticipated rise in prices,the longer delayed is the response of the price levelto a decline in the rate of change in total spending.

Tests of the Model’s PerformanceThe equations of the model are to be viewed as a

unit, and the specification of the model is such thatgiven the change in money (AM), and the changein high-employment expenditures (AE), the modelcan be solved in the following sequence: for thechange in total spending (~Y), the change in theprice level (~P), the change in real output (AX),the unemployment rate (U), and the long- and short-term interest rates (R’~and R5).

The explanatory power of each of the equationsshown in Tables I-VI may he acceptable by conven-tional standards, but this provides no guarantee thatthe model will perform satisfactorily as a unit. Thereare interdependencies in the model that have to betaken into account when evaluating the complete

Page 15

FEDERAL RESERVE BANK OF St LOUIS APRIL, 1970

model. Of interest in evaluating the model as a unitis the implied pattern for the endogenous variableswhen only an initial set of lagged endogenous varia-bles and the time paths of the exogenous policyvariables (money stock and high-employment Federalexpenditures) are assumned known. To conduct sucha test, several dynamic simulation experiments wereperformed. These simulations take the form of cx postdynamic simulations and an cx ante dynamicsimulationY8

An cx post dynamic simulation is confined to thesample period from \vhich the estimated relation-ships are derived. Actual values for all current andlagged exogenous variables are used, but only initialactual values for the lagged endogenous variablesare used. The model generates solution values forthe endogenous variables in the first simulation pe-riod, xvhich are then used to generate solution valuesfor the second period, and so on for each succeedingperiod.29 A comparison of these calculated time pathsfor the endogenous variables with their actual timepaths enables one to formulate some judgment as tohow well the niodel performs as an interdependentunit in tracking the movements of certain strategiceconomic variables.

Ex post dynamic simulations were conducted forseveral subperiods within the sample period (1955-69). The results for the entire sample period aresummarized in Chart I on thenext page. When simulations areconducted for subperiods withinthe 1955-69 period, the patternof movement as shown for thewhole period simulation tendsto hold, but the levels are closerto the actual values at the be-ginning of each subperiod.

ables quite well during the 1955-69 period. Sincecriteria for judging the performance of the model insuch a simulation have not been developed, any con-clusions are necessarily subjective,30 The tendency forthe model to avoid diverging sharply from the actualpath for extended periods is an especially importantfeature. Such a feature provides some basis for trust-ing the tracking ability of the model over severalquarters, even if on a quarter-by-quarter basis it mayappear to be off the mark.

To gain additional information about the predictiveperformance of the model, a comparison is made withan cx post simulation from another model. Results ofan cx post simulation for 1963 and 1964 have beenpublished for the Wharton model. The results for themodel are compared with those of the Wharton modelin Table VII.

The period 1963-64 includes the 1964 tax cut, which,according to the Wharton model, is considered animportant factor influencing economic developmentsin 1964. However, the St. Louis model, which doesnot emphasize such fiscal actions, did about as well,on average, for the years 1963 and 1964 (see TableVII). The main difference to be remembered in eval-uating these simulations is that the St. Louis modelcontains three primary exogenous variables, whilethe Wharton model contains forty-three.

:uoSee Robert H. Rasche and Harold T. Shapiro, “TheFEB. - M.I.T. Econometric Model: Its Special Features,”American Economic Review, Papers and Proceedings (May1968), p. 142.

Chart 1 indicates that themodel tends to track the move-ment of the endogenous van-25

For a discussion of the differentways of assessing the trackingability of econometric models, seeCarl F. Christ, “Econometric Mod-els of the Financial Sector,” forth-coining in the Journal of Money,Credit, and Banking. For a dis-cussion of simulation proceduresand results with an income-expen-diture model, see Evans and Klein,pp. 50-69.

tm9See de Leeuw and Gramlich, “TheChannels of Monetary Policyp. 485.

Page 16

Toble VII

ALTERNATIVE EX POST SIMULATIONS: ACTUAL MINUS PREDICTED1

Comparison of Wharton and St. Louis Models for 1963-64Nominal GNP

2Real GNP’ Price Level Unemplolmen? Rate’

Wharton St. Louis Wharton St ouk Wharton St .ois Wharo.i St tours

1963. I 4.6 0.4 3.9 0.4 01 02 09 0.3II 0.2 0.3 0.4 0.7 0.1 0.2 0.7 0.1III 1.3 1.5 2.5 0.6 0.3 Ci 0.9 0.1IV 0.9 2.1 2.2 04 02 05 1.2 02

1964 I 0.9 1.7 2.7 1.4 03 Co 14 02II 1.1 0.1 2.3 3.2 -0.3 06 14 02

1.5 1.7 4.0 --2.7 0.5 0.8 16 02IV 0 --1.7 2.2 68 0.4 09 12 0.2

Average Error 0.11 076 1.55 1 88 0.28 049 1.16 0.16Root Mean

Squared Error 200 1.49 2.92 309 0.33 0.60 1.28 021

$:sr.,plr. ps.,4

E~,no-rs..u. car silOs\\ lssu:., It’ It-I :1.. WI: rn’,,Si. I . l:c..—:~’b.’ st. I ‘rn.

:!C,.l..., of b-liar-u.

Unns;rutr.d fr.,m the eel of impl,est -rice rId an5Per cent.

Srmrrru M. K. K’r1rst and L. B. KleNs. 7k. 11 he,!.,,. irp,.o.,,tr.r ct .u...W,4s, 2r.rI Er:iar,’rri

Edition Phila,l,’l:,hia:t.ricersr..y ‘‘I Pr nn—vh~::in, ]9~c . mi Er—an’ R,.e—,e i:rmnk otSt I.,siie.


Page 17

FEDERAL RESERVE BANK OF ST. LOUIS

The comparison is not meant to imply that the St. Louis model issuperior. Rather, the suggestion is offered that a small model con-structed within a monetarist framework may yield as much informa-tion about the key aggregates as a large structural model. In summary,small monetarist models may be useful as a guide in the formulationof stabilization policy.

i%nte ~An cx ante dynamic simulation is like an cx post dynamic simula-

tion, except that it extends beyond the sample period. To conductsuch a simulation for this model, it was necessary to re-estimate themodel for a subpeniod within the full sample period. All equationsof the model were re-estimated with data through 1967. The periodof the cx ante dynamic simulation is 1968 and 1969. The results aresummarized in Chart II and in Tables VIII and IX.

The success of the cx ante dynamic simulation can be assessed bycomparing it with the tracking record of the cx post simulation forthe same period. A comparison of the errors associated with the cxante simulation with those of the cx post simulation (where the errorsin both cases are computed with reference to actual values) suggeststhat any structural shifts that occurred in the 1968-69 period werenot of such a magnitude that the cx ante tracking ability of themodel was significantly different from that of cx post simulation.

Any conclusions about the tracking ability of the model are neces-sarily tentative, because they are based on only one cx ante dynamicsimulation experiment. Nevertheless, these results provide a tentativebasis for confidence in the tracking ability of the model in es-

Table VIIIMODEL SIMULATIONS

1968 1969I II Ill IV I II Ill IV

GM? t veI (Balboa of dollars)Acluat 835 3 858 7 8764 892.5 908.7 924 8 942 8 952 2ExAntet

8341 8567 8789 8999 9176 9323 9459 9572Ex Post2 8346 854.7 *77.7 897.8 9149 929.4 9434 9551

Annual Rate at Change in VAtuol 97 11.7 85 76 75 73 8.0 40ExActs 9.1 11,3 10.8 9.9 81 66 60 43E,rPast 94 11,0 102 9.5 7.8 65 6.1 51

Annual Rote of Change in XActual 5 9 7.4 40 3.2 2.6 2.0 2.2 0.4ExAnte 5.7 7-6 70 59 40 24 17 07ExPot 5.4 6.7 57 4.8 3.0 16 11 0.0

Annual Rate af Change in PActual 37 40 40 43 49 52 54 4.7Es Ante 3.3 3,4 3.6 3.8 4,0 4.1 4.2 42EAPost 38 40 4.3 44 47 4.9 5,0 50

Unemployment Rate (per cent)Actual 3.7 3.6 3 6 3.4 3.4 3.5 3 4 3 6ExAnte 39 3.8 35 33 32 32 33 3.5Es Post 3.9 37 35 3.4 34 3.5 3.7 39

Corparate Aoa Rate (per cent)Actual 61 6.3 61 6,2 67 69 7.1 75ExAtte 58 5.9 60 6.4 6.5 67 7,0 71E Post 59 60 61 65 6.7 6.9 72 7.4

Commercial Paper Rate (per cent)Actual 5 6 6.1 &0 60 6J 74 8 5 848 Ante 51 6.1 Si 56 57 60 66 67Es Post 58 58 5.8 6.5 66 70 78 80

IC to bbreviationsV Nominal ON?N Real ON?P ON? Iiitee deftato

Sunulatton based a equation est,n-sated h ough Tv/ba?.i5 ulatson based on squat o a estimated tbmugh mV/igsa

rage is

APRIL, 1970

Results ofEx Ante Dynamic Simulation

i toni

Percent Per Cent12 2

ii 11

10

9 9

8 8

7 7

6 6

5 5

4 4

3 3

2 2

0 0

Real ONP 8

7 7

6 6

5 5

$ 4

3 3

2 2

0

2 -2

Implicit Price_Deflator6 --______ --— - -~ 6

5 -~— ‘. 5Ac Is a I

___- -__

1967 1968 1969- me,,

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). z o -I j~ -I - 6 C ~ > t ~ r (0 ~


No-change case — A course of no change in themoney stock from the first quarter of 1970 would leadto further reduction in the rate of increase of totalspending in 1970 and 1971 (Table X). A slowing oftotal spending along with up\vard pressures on pricesfrom the past inflation (anticipated price effect)would lead to continued declines in output through1971. Such a restrictive course of monetary actionswould slow the rate of price increase to a four percent rate by late 1970 and to a two per cent rate bylate 1971. The decline in output would be accom-panied by a rise in the unemployment rate to overseven per cent by late 1971.

The effects of such restrictive monetary actions oninterest rates would be to keep the long-term interestrate at recent levels through 1970, mainly becauseof the effects of past inflation. By early 1971, theslower advance of prices in 1970 and the slowing ofoutput growth would lead to declines in the long-term rate. The short-term interest rate, on the otherhand, would hold at recent levels only temporarily,partly because of continued restrictive monetary ac-tions. Short-term rates would drop sharply by thesecond half of 1970, reflecting primarily the slowingof output growth. Since the price lags are shorter forthe short-term rate, the effects of past inflation are notso pervasive as for the long-term rate.

Three per cent case — Growth of the money stockat a three per cent annual rate is presented to illus-trate the effects of a moderate expansion of money.This rate corresponds to the trend rate of increase inmoney from 1961 to 1965. In the current economicsituation, a three per cent rate of expansion in moneywould represent a moderate easing of monetary policyfrom its restrictive influence of late 1969 and early1970.

The effect of such expansion would be to maintaingrowth in total spending at a rate about the same asin the fourth quarter of 1969. Given the influence ofpast inflation on prices, output would decline slightlythrough 1970, but would resume its increase by 1971.The effect on prices in 1970 would be little differentfrom the no-change case, but by late 1971 the differ-ence would be marked. In the three per cent caseprices would still be rising at a three per cent rate bylate 1971 compared with a two per cent rate for theno-change case. Moderate expansion of the moneystock leads to a rise in the unemployment rate through1970 and 1971. In general, for this model, the unem-ployment rate rises as long as output grows at lessthan a four per cent rate.

Page 20

The long-term interest rate would remain at recentlevels throughout 1970, and not until early 1971would the effect of slower price increases and outputgrowth be enough to offset the effects of past infla-tion. The short-term interest rate would fall morequickly than the long-term rate but would not fall asmuch by late 1971 as in the no-change case. Such apattern for the short-term rate illustrates the short-and longer-run influence of quickened monetaryexpansion.

Six per cent case — A six per cent annual rate ofincrease in money is shown to illustrate the effectsof a sudden shift to a very rapid rate of Inonetaryexpansion in the second quarter of 1970. Such in-crease in money would be about the same as during1967 and 1968.

A major effect of shifting to rapid monetary ex-pansion would be to advance the rate of total spend-ing growth. By late 1971, total spending would beincreasing at an eight per cent rate with such mone-tal-y actions. The rate of price increase would fallsomewhat, however, because of past restrictive mone-tary actions. But the gain in price performance wouldbe small, because by late 1971 prices would still beincreasing at a four per cent rate. The effectl of pastmonetary and fiscal actions, along with past inflation,would lead to a decline in output through mid-1970.From then through 1971, output growth wouldincrease.

Despite a shift to a very rapid rate of monetarygrowth, unemployment would rise until mid-1971.This increase in unemployment ‘would follow becauseof the continued influence of past monetary and fiscalactions. By late 1971, the recovery in output growthwould he pushing the unemployment rate back down.

A shift to rapid monetary expansion has a pro-nounced effect on market interest rates. The long-term rate would stay at recent levels through 1971,because the influence of past prices (anticipatedprice effect) would not be offset by a sustained re-duction in output growth. The short-term rate wouldfall, in response to the temporary reduction in outputgrowth, but the decline by late 1971 would be lessthan for either the no-change or three per cent case.

iin.ptrcatzons Of the /11ode! forth.e.1 ong Rim

Short-run prospects for economic variables tend

to dominate policymakers’ decisions. However, thelonger-run consequences of alternative monetary poli-cies should also be given consideration. This model


is incomplete for long-run analysis; nevertheless, ityields results that are of interest and may not be toofar removed from results that might evolve from amore complete specification.31

When simulations are conducted for long periodsinto the future (thirty years), the model demonstratesproperties consistent with those expounded by theclassical economists. Over the long run, monetaryactions have no effect on real magnitudes; the rateof growth of output, the unemployment rate, andthe real rate of interest all tend to move towardsome equilibrium rate, regardless of which rate ofmoney growth is maintained. The effects of alterna-tive rates of monetary expansion are on nominalmagnitudes, namely, total spending, prices, and mar-ket interest rates.

Based on the assumptions of the model, a six percent rate of growth in money along with a six per centgrowth rate in Federal expenditures, for example,would lead ultimately to about a six per cent rate ofgrowth in total spending, a four per cent rate ofgrowth in output, a two per cent rate of increase inprices, and market interest rates about two percent-age points in excess of the real rate. Alternatively, atwo per cent growth rate in money would result ap-proximately in a two per cent growth in total spend-ing, a four per cent rate of growth in output, a twoper cent rate of decline in prices, and market interestrates about two percentage points below the realrate, Over the long run, the model indicates thathigh employment and price stability are compatible.

Summary

The main purpose of this study has been toquantify the effects of monetary and fiscal actions

3tThe shortcomings of the model for the long-run analysisare quite evident. There are no assumptions specified as tolabor force growth and productivity. Furthermore, there isno investment function and, therefore, the capital stock isnot an endogenous variable. All long-run assumptions areembodied in assumptions about the growth rate ot potentialoutput. With these assumptions, policy actions cannot affectthe economy’s long-run growth rate.

within a small-model framework and thereby offeran alternative to existing large-scale econometricmodels. Such a model has been formulated and theeffects of monetary and fiscal actions on spending,output, prices, employment, and interest rates havebeen estimated.

The model developed in this article is primarily“monetarist” in character, The estimated equationsindicate that monetary actions, as measured bychanges in the money stock, play a strategic role.Fiscal actions, as measured by high-employmentFederal expenditures, have some short-run effects,but for periods of a year or more the net effect onspending, output, and prices is near zero. Simula-tions of alternative rates of monetary expansion pro-duce short-run and long-mn responses which areconsistent with the general monetarist view of theeconomy.

One of the chief advantages of this model is thatit depends primarily on information about only twovariables — the money stock and high-employmentexpenditures.32 Considerable insight can be gainedabout the pattern of expected movements of certainstrategic economic variables by considering alterna-tive courses of monetary and fiscal actions. How-ever, since the model is limited to only monetaryand fiscal influences, to the exclusion of other inde-pendent forces, it is not suitable for exact forecast-ing.33 Its primary purpose is to measure the generalpattern of influence of monetary and fiscal actions onseveral strategic economic variables. Since the econ-omy is viewed as being basically stable, other factorsinfluencing total spending, output, and prices are notconsidered to be of great importance in estimatingthe response to monetary and fiscal actions.

i2This feature has led John Deaver to conjecture that thestandard error of forecast in the Andersen-Jordan modelmay he far lower than that of the FEB-MIT model. Seehis “Monetary Model Building,” Business Economics, (Sep-tember 1969), p. 30.

33See Andersen and Jordan, pp. 15, 23, 24, and Leonall C.Andersen, “Money in Economic Forecasting,” BusinessEconomics, (September 1969), p. 17.

This article is available as Reprint No. 55.

The Appendices to this article begin on the next page.

Page 21


APPENDIX A

EXPLANATION OF THE PRICE EQUATION

The and lags) isprice equation (omitting timescripts= f (D, ~pA)

where D, demand pressure, is defined asD = — (X

5— X).

AY is the change in total spending, (X” — X) is theG~~Pgap, that is, the difference between potential andactual output, and ~p~’ is anticipated price change. Thisspecification of the price equation is based on standardtheory of macroeconomic equilibrium.

Macroeconomic equilibrium can be depicted graph-ically as in Figure I. The solid downward-sloping line,

is the total spending line, which represents the

combinations of prices and output consistent with aparticular level of total spending, Y. This total spendingline can he interpreted as total demand for output.

P

Figure I

Macroeconomic Equilibrium(Determination of Output and Prices)

The upward-sloping line, labeled X5, is the total supplyline. This line corresponds to that combination of pricesand output which maximizes profits of firms, given theprices of factors of production, the degree of competitionamong firms and the stock of human and physical capital(defined to embody the state of technology).

The intersection of total supply and total demanddetennines the levels of output and prices. The equilib-rium price level is that level which equates the amountof output supplied \vith the amount demanded.

The focus of the model is on the change in pricesand the change in output. In terms of Figure I,changes in prices and output are brought about by shiftsin demand and/or supply. Since X~is drawn for a level

of total spending, a shift of that line upward and to theright to ~ represents an increase in total spending.If the total supply line remains fixed, the effect of AYon prices depends on (1) the magnitude of AY, and on(2) the slope of the total supply line, X5

The purpose of the model is to estimate the responseof spending, output, and prices to monetary and fiscalactions, not to test a hypothesized structure. Conse-quently, rather than attempt to determine the shapeof the total supply line empirically, its variable slope isproxied by the difference between potential output andactual output. As drawn in Figure I, there is a one-to-onerelationship between X’~ X5 and the slope of X5. As-suming that this relationship is approximately linearwithin the range of experience since 1955, and that theobserved values fall on the supply line, the effect ofa variable slope for X~can be approximated by X5

— X.

In this way the term [AY — (XF — X)l brings to-gether both the magnitude of demand shift and theslope of the supply line.

The other term in the price equation, anticipated pricechange, APA, is considered as a separate influence onprices. In terms of Figure I, the anticipated price termis a shift parameter for the total supply line (an increasein APA shifts X5 upward and to the left). Including it inthis way allows for the influence of past prices on currentpricing policies of firms and factors of production.

‘

N

x

Page 22


APPENDIX B

GRAPHICAL ILLUSTRATION OF THE MODEL

The workings of the model can be demonstrated withgraphical techniques. Figure II is a representation of thecore 0f the model, showing the determination of changesin spending, output, and prices.

Panel A of Figure II is a graphical representation of thetotal spending equation with AM on the horizontal axisand AY on the vertical axis. Changes in AE shift the totalspending line.

Panel B shows prices (AP) as a function of A?. Ashort-run price line (APs) is drawn consistent with empir-ical results showing that AP is not very sensitive to AY inthe short run. Important determinants of the position ofthe short-mn price line are the size of the CNP gap andanticipated price changes. The long-run price line(AT’ (LE)) is drawn to show the relationship betweenAP and AY when the CNP gap is zero and anticipatedprices are equal to actual prices. Its slope (45 degrees

ày

St2

ÀY1

ax

(A)

Figure

Model in Graphical Form

from its origin on the AY axis) is based on the monetaristview that in the long run, AM influences only AP.

Panel C expresses the total spending identity in graph-ical terms. Total spending is divided between output andprices; to reflect this, the line in panel C is drawn as a45 degree line with its position determined by the magni-tude of total spending (AY). There is a family of 45degree lines, one for each possible AX’. Also included inpanel C is a horizontal line representing the long-mngrowth rate of output. It is shown as a horizontal line toindicate that long-run output growth is exogenously de-termined by resource growth and technology.

In panel D, the AX1 line shows the relationship betweenmoney (AM) and output (AX) as derived from the otherthree panels. The equation for this line is not shown inExhibit I in the text, but it can be derived from the otherequations of the model.

Figure II is drawn to represent aninitial equilibrium for a given AM,

which has associated with it the short-run price and output lines, AP1 andAX,. The effect of a change in AM,given AE, is shown as a movementalong the spending line in panel Afrom 0 to ~ Given the initial priceline, AP1, and the changed AY, theeffect on prices and output is shownin panels B, C and D as a movementfrom 0 to 0

This case illustrates the impact of achange in AM in the short run. Forlonger periods, anticipated price changesand the CNP gap will also change;they become endogenous variables ina long-run model. To illustrate the ef-fects for the long run, the long-runprice line, AP(LR), in panel B, is rele-vant. The interpretation of the long-run price line is that changes in AMare reflected only in AP, with AX de-termined by considerations of resourcegrowth and technology. The horizontalline in panels C and D is the long-runrelation between prices and output.

In the short-mn, the solution of themodel need not lie on the long-runprice line in panel B (or the long-mnoutput line in panels C and D). How-ever, a -succession of short-runs (shownas a shift of the AP and AX lines toAP. and AX2) will tend to move equi-librium toward the long-run price andoutput lines, as anticipated prices ad-just to actual prices and the GNP gapgoes to zero.

Spending Equation(B)

Price Equation

Page 23

The model consists, for the mostpart, of equations which havebeen estimated in previous stud-ies. The purpose of this paper isto combine the equations in away which represents the generalmonetarist view.

The primary distinguishing fea-ture of this model, other than thereduced-form total spending equa-tion, is the inclusion of a priceanticipations variable in the priceequation. Two alternative meth-ods of introducing price anticipa-tions were considered. One alter-native bypasses the precise formof the price anticipations functionand uses the long-term market in-terest rate (yield on corporate Aaabonds) as an independent varia-ble in the plice equation. Theother alternative bypasses both price expectations andinterest rates, and introduces changes in money as anindependent variable in the price equation. Such a speci-fication allows monetary actions to serve as a proxy foranticipated prices.

A Market ta.terert Rate in. i/reP rice Eraa.tion.

The first alternative replaces the price anticipationsvariable with the long-term market interest rate.1 Therationale is that the process of price anticipations forma-tion is so complex that it defics measurement. However,there seems to be agreement that the level of marketinterest rates s-cflects anticipated price changes, how-ever foimed. Thus the market interest rate can be usedas a proxy for price anticipations.

Since interest rates reflect factors other than price an-ticipations, including the interest rate does not providea clean measure of price anticipations. Using the marketinterest rate allows those factors influencing the realrate of interest to enter indirectly as an influence onprices. In general, however, it has been argued that thereal rate of interest is very stable.

Following this reasoning, the price equation was esti-mated by including the long-term interest rate. Theresults are shown in Table XI. The coefficient of theinterest rate variable is significant at the five per centlevel for this specification, and the sum of the coeffi-cients for the demand pressure variable is roughly the

‘The suggestion for using the interest rate in the price equa-tion came from the Money and Banking Workshop atthe University of Chicago.

Page 24

same as for the price anticipations version of the equa-tion. However, the length of the lag structure is longer,indicating that the response of prices to changes in de-mand pressure may be sloxver than in the basic equa-tion. But this need not imply that prices are slower torespond to monetary actions, since the magnitude ofthe interest rate contribution to price change is smallerthan with the price anticipations specification.

Several observers have been critical of price equationsthat do not include monetary variables directly. Asshown in the text, excluding monetary variables fromthe price equation does not necessarily imply a non-monetary theory of inflation.2 Such a conclusion can-not be derived by examining the price equation alone,but requires an examination of the whole model, and thelinkages between money and prices in particular.

The second alternative that is considered is based onthe central proposition of the quantity theory — thatchanges in money are ultimately reflected in changes inthe price level. Accordingly, current and past changesin money are used as a proxy to measure anticipatedmovements in prices.3 Though this rationale for includ-ing money is somewhat narrower than that proposed bysome monetary economists, the direct and indirect ef-fects of money are being measured once it is includedin the price equation.

2Sce Fand, “Some Issues in Monetary Economics,” pp. 20-23.‘This suggestion was made by Professors David Fand andAllan Meltzer.


4I’FF:.\DIx C

.4I:FF:H\.-t’lIVF: Ijilicli EQLATI(Y’IS

Table XIALTERNATIVE PRICE EQUATIONS

(Drperioent Var.obl AP.)

Somple Period: I 1955 IV, 1969- - Independent Variable -

con-- Ap’. ~R’, .x .1.01 ZAM, . stonl R

2SE. D-W

Pr ce A’s IkipoYor sSpecification 09 .86 . . 2.70 .87 1 07 1 41

19.151 t~5Sl (707)inc-rest Rot,,Specificolor

3.09 . .11 . 1.93 .88 1.04 1 49

(8.72) (8.73) 14.10)Money Stock

Spec.rcotion:i o~ - . 2.61 2.11 .86 1.11 1.374.61) (7.821 (4.22)

— ~i it iOi~ ‘Sr,tt I .i. ii .iii’!,i

— \‘!,, iii e. .i~iii,ci ~, tI.,It. , ;. - t.i:—.LY:~:... 1.-i.’—.,. _..~. .

ci-. , R—i—tl,.,tci.t . ‘:. in. tl’i.sn..c.I— ~ k..i.rI ., c.,,iii.—.ti-,:qu— . Inst .~,ii,I ‘.51: .1,~ —iii.:....-, i.\1 - ii.t li,ii,;...W;i.. ,.. i,~.. -

FEDERAL RESERVE SANK OF ST. LOUIS APRIL, 1970

The price equation incorporating current and lagged ~values of changes in money is shown in Table XI. Except GNP PRICE DEFLATORfor the current quarter, the coefficients are sigmficant ALTERNATIVE x p05 SIMULATIONSfor nine lagged quarters. The effect of including changes A~UALM P405 PR DIcTEDin money lowers the sum of the coefficients on the de- f~esnpeeded Annual ~nt s * chqrrg Imand pressure variable, however. The overall explana-tory power of the equation is about the same as for the P ice Ant patoni I cc Pals M i, y Sb k- - . Spe ffi ~I on S~ Ot*ttan p n6cationprice anticipations mouei.

96 I tO 43 04-~ - -/~------- - I 0, 02 10

07 10 7IV 02 -04 10

To compare the price equation in the text with the 1 66 1 t 1 0 04two alternatives in this Appendix, the model was sim- t 1.4 15 .0ulated with each of the three different specifications Ga 00 06from 1965 through 1969. The period starting in 1965 1*67 0 03is used because the relative tracking ability of the II 03 Ga 98models during a period of accelerating inflation is es- III 1 if 09pecially relevant in assessing the current economic sitna- V 1 3 1 4 1 1tion. Since the price equation is the only part that varies 968 04 4 0from one model to the next, only the results for the rate 2 0 6of change of prices are reported. (see Table XII). w 6

The price anticipations specification has the smallest 1949 IIaverage absolute error and the smallest root mean ~,s osquared error for the period. During the last two years iv üi 09 9of the period, 1968 and 1969, each of the alternative Av.rn~Abta ftspecifications tends to underestimate price changes.However, for 1968 and 1969, the price anticipations ~ :~ 079specification again has both the smallest average ab- 9fl ~ ~ 44 -04 4 8solute error and root mean squared error. Roal

Squ red Ettc*6569 05* 0* 043

194567 067 076 079- - 196-8 49 27 0.39

An examination of the model reflecting three differentspecifications for the price equation indicates that noneof the specifications is clearly superior as judged by level for alternative growth rates of money. These twoconventional criteiia. A policymaker might well con- alternatives yield the same equilibrium growth rates ofsider the results provided by each of the three. output for alternative growth rates of money, bitt since

- - . - this rate is approached asymptotically, unemploymentWhen simulations are performed for thirty-year pen- stabilizes at a different rate for each alternative growth

ods beginning in 1970, the price anticipations version rate of money.

(as presented in the text) approaches closest a long-run classical solution- For the other two specifications 4Supplementary materials relating primarily to the long-runthe unemployment rate does not stabilize at the same simulations are available on request.

“QUARTEELY EcoNoMic Su~aMAnY,” a new release of thisbank, will replace the quarterly “Triangles of U.S. Eco-noniic Data” next month, and is available to the publicwithout charge. Based on the approach to stabilizationanalysis presented in this article, “Quarterly EconomicSummary” will contain an outlook for Total Spending,Real Prodnct, and Prices. It will include an explanationof the analysis, as well as charts and rates-of-change tablesfor national income accounts data and related series.Persons who have been receiving “Triangles of U.S.Economic Data” will automatically receive the new release.

For subscriptions, write: Research Department, Federal

Reserve Bank of St. Louis, P.O. Box 442, St. Louis, Missouri63166.

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