Issues and models in empirical research on aggregate consumer expenditure

VWterDolde* Ciamegte4kietttm University

per an~yzes recent major developments in empi&al research 631 te consumer spending, Five leading ‘models of’ consumer spending provide the vehicle for this -analysis, The investigation of each model includes 81reytiew of the SSU~S it seeks to address, reestimation on a common, data set, and execution of out-of-sample forecasting exercises. The empirical successes and failures of the models in combination, in turn%shed light on the issues of impWtWX* The five models investigated are: (1) the life cycle model as embodied irr the Federal eserve-MIT-Penn (FMP) model; (2) Darby’s version of the permanent income model; (3) a composite model typical of the consumer expenditure sectors of large forecasting models; (4) the consumer expenditure sector of Fair’s r?l;npiricai macro model; and (5) a model w,bich disaggregates plbrnlanent and $ImsGory income by source. AU of these models are estimated o:tl the data from the FMP model for the sample periods 195i4:1 - 1972: 2 and 195&l - 1975:4. All were estimated with an instrumental variable technique and with the agIumption of firs&order autocorrelation of the .errors. The re suiting estimates are used to compute out+f*ample foreca,sts for the periods 1972:3 - 197314 and 1976: 1 - 1977:2. All of tile models have root mean squared errors 1CR.M.S.E.)which are rtbout one poj:cent of aggregate personal consumer expenditures for at least one of the two forecasting periods.(Only tlhe Fair model achieves this performance for both forfzasting periods. The remaining R.MS.E.s for the other models rangs up to about two petcent of total .expenditure. All of the models do as well +r better than a naive model which uses a constant and the log of lagged par apita expenWWures to explain the log of current per capita expenditdres. A numbgijrof issues are discussed in light of the empirical results. First, it ig concluded hat incom.e variables are appropriate arguments of aggregate ex,pcnditure equa,tions, even though only paicesand state variabks might appear

Ca~11B?gie~RochestE!rConEerence Series on I?uMic Policy E2 (1980) 161-205

Nwth4Ialland PvbliahingCompany

in micro IeveI expenditure equations where involuntary unemployment is

ruled out. More ,gene=liy, aggregatedata are not SC& multiples of the data pertaining to individual households. Thus, some variables in aggrzgate equations necessarily reflect these aggregation effects. A second issue relates to the timing of expenditure responses to fluctuations in aggregate income. In part because a portion of an into for other reasons, the is saved in the foim of durables p~dmse~, and h in income is about contemporaneous expenditure effect of a dollar xpenditure by about 40 cents. After five quarters, an income c:hange ra 60 cents on the dollar. Virtually all of the ultimate response, which is roughIy 80 cents on the dohar, is achieved within nine quarters. A third issue is the neutrality of aggregate consumer expenditure with respect to government fiscal variables. The empiriti results here cause us to reject such neutrality. The high degree of sensitivity of expenditure to current and ne2.r term income variables implies households behave as if they discount the future at rates much higher than that at which the government borrows in financirg changes in current fiscal variables. Some of the models include tax liability or tax rate variables which provide a direct test of the neutrahty proposition. A fourth issue discussed, although the current models do not address it, is the relationship among housing expenditures, services, and other consumption and consumer expenditure. Finally, aggregation difficulties, mcluding the Lucas econometric inference problem, are discussed. It is observed that all of the models examined, except the naive moc!el, forecast remarkably well out-ofampie in the turbulent 1970s. Further, the Fair model is successively reestimated and made to forecast outof-sample year-by-year. In four of five forecasting periods, the R.M.S.E.s are 1.3 percent or less of aggregate personal consumer expenclitures. Only for the period 1975: 1 - 1976: 2 does the R.M.S.E.jump up, and then only to about 2 percen:. Section II of this paper describes the data end estimation technique. Section III discusses each I-Ilode in turn and prwnts the estimated equations. Section 1V describes the out-ofsample forecastin exercises and pre results. A discussion of issues in empirical research ased on the current findin comprises Section V. II. Dtita and Estimation Procedure All of the major madels of consumer expenditure have been estimated on aggregate U.S. time series data. Major differences exist, however, among the 162

jeriods and estimation techniques used, To provide for a fairer coInpa+ son mhcbngthe theaies of consumer expenditure, the leading models have all been recstimat*d hens using the same data set, the same sample period, and the same eshation technique. This approach may not display all tlaf the n-iod& a~ favonkbb- 8s they xwe appeared in other places in the literature, Robustness with respect to sam;?le period is clearly a desirable property. Similarly, the Wimath technique seeks to avoid overstatement of the models’ consistency with the data due to simuttaneity and autocorrelation, Literally hundreds of decisions must be made in preparing empirical rkcluding estimation of and forecasting with 12 stochas$tic equations from fiw different models of consumer expencliture. Consequently, it has not been possible to follow up every promising lead. Indeed, it has been necessary to adopt quite the opposite strategy. Almost without exception, no experimentation has been undertaken; rather, only a single method of proceeding has been UWXI at each sta,se. For example, in the selection of explanatory variables for each model, no variables have been added or excluded on the basis of tstatistics. Rather, t-he lists of exprRnarory variables are the same as those appearing:in some recent published versio:ls of the models used. In the published versions, it is clear that the original authors have, themselves, Idone some experimenting on %e inclusion and exclusion of variables. ‘The data for this work are from the Fecleral Reserve-MIT-Penn(FMP) model. ‘key incorporate the July 1977 revisions of the national income accounts. The FMP data do not include a disaggregation of consumer durables between expenditures on automobiles and other durables. Neither do they include a disaggregation of consumption of nondurables between nondurable goods anti services. The July 1977 revisions of these variables and their implicit deflators have been &ken from the Survey of Current Business for use here. ‘Variablesused here are referred to by their symbols in the directory to the FMP data bank. All current dollar variables end in a dollar sign. Thus, MI $ is tl e money supply, demand deposits plus currency, in current dollars, Dollar amount variables not ending in a dollar sign are in constant lW2 dollar:.:. Thus, EP12fi is personal consumption expenditures in constant 15172dollarsn I fnless noted otherwise, dollar amount variables are in billions of dollars, el.cept for we&h variables, which are in ‘trillions,Population variables are in mil ions. These knit conventions are not alwarysthe same as those adopted in earlier work on the% models. Thus, in making comparisons between these results an 1 those that appear elsewhere, care must be exercised to I&W for units differences, Ill some cases, the variables from the FMP model do not correspond

163

exactly to those specified ty o&id &~OXS. These differences are not major, and any minimally robust model should not be affected by them. The estimation procedure used here incorporates both instrumental variables and the estimation of a first-order auton:gressive scheme in the residuals. Fair (1970) has shown that the resulting estimates are con&tent if the list of instrume;nts inclutdcs the predetermined v~~bl~~ the predete&nd variables lagged once, the lagged dependent variable, and ments. In this paper, these othet instruments were lappmp of the lagged Federal Reserve discount rate (ZLMA,l), unborrowed tesewes at member banks plus currency outside of banks lagged once and twice {ZIW$,l, zIwS!§_2),exports of goods and services lagged once (EEX_l), and Federal government expenditures lagged once and twice (EGF$+ EGS’!S_2). All contemporaneous economic variables and transformations of them were treated as endogenous. This includes, for example, the money supply (M1%). An example of a contemporaneous variable treated as exogenous is the population (N). -AI1 lagged variables were treated as predetermined. In the Fair method for instrumental estimation with autocorrelated em>rs, the relevant !betof predetermined variables changes with each estimate of p, the autocorrelakion coefficient of the errors. Values of p from 0.0 to 1.O were investigated in increments of 0.05. ;9nsome cases, the likelihood function had two local maxima. Estimates were colmputed for two sample periods: 1954: 1 - 1972:2 ;I.nd9954: 1 - 19754,. In Tables 1 - 3 and 5 - 6, the coefficient estimates for the Il;lngersample period appear directly in front of the corresponding explanatory variable. Thz estimate’s t-statistic appears below it in parentheses. Above the variable, in square brackets, is the estimate for the shorter. sample period and its t&atistic. Two sample periods were used in order to permit two otltafsample forecasting experiments with the various models. The estimated eqilations for 1954:l - 1972:2 were made to forecast 1972:3 - 1973:4. Similarly, the estimated equations for 1954: 1 - 19X:4 vuere made to forecast 1976: 1 - 197712. Appearing below each regression equation ate summary statistics. Ve:ry little is known about the distribution of estimafors in instrumental estimation performed with iin autocorrelation correction. While formal hypothesis testing based on these statistics would be inappropriate, the statistics do ptovide a convenient reference for characterizing the empirical results. The: statistic M,L)Vis the sample rt-,ean of the dependent variable. For each statistic, the louver number in each pair is for the sample period 1954: 1 - 1975:4, The upper number, in square brack.ets, is for the sample period 1954: 1 - 1972:2.

164

III. Estimationof the Models This section bri&ly describes, in turn, each of the five models and its estimation. We present 2nd discuss each model in terms of the variat%s and s from the FMP data set. In some cases thievariables are not identical to those used by the original authors. The differences are not major. For a mom complete discussion of the motivation of each model and the speci&:ation of the included variables, however, the reader should consult the references cited for eacl~model. The FMP Model

The consumption sector of the FMP model represents the culm.ination of research O:I the We cycle theory (LCT) by Modigliani and his collabcrators. 2 The specific axsion of the FMP consumption sector reestimated here appears in Board of Governors of the Federal Reserve System (1977). Alone among the models discussed here, the FMP model con&ucts a series and estimates an equation for consumption (CON)3 rather than for expenditures. The appeal of treating consumption, of course, is that it t.:onstitutes the argutnent of consumers’ utility functions. In this FMP model, ho*wever, all sources 01’ consumption (housing, services, nondurable goods, etc.) are perfect substi:lJtes for each other. A separate equation for expenditures on durables (ECD) is also estimated. Since the consumption of the servit:cs of durables is included in CON, the expenditures equation has a motivation r#elated to transactions costs, price speculation, and other dynamic considerations. Specifically, the durables ecluation does not result from the services of durables being treated a3 a separate argument in a utility function. CON is related to personal consumption expenditures (EPCE) by subtracting out ECD and adding in depreciation (WCD) and net income WD) from the stock of durables:

CC1N=EPCE4CD+WCD+ YCD.

(1)

The cr:knsumptiont:quation begins with the elements of the liftstime budget constra nt, property net worth, and a proxy folr the present value of nonproperty in8:ome. Let wli and h, represent these, respectively, for the household indexed by a for its a*ge.For the class of utility functions with constant elasticities of r marginalutili:y , each household’s consumption is proportional to wa and ha:

co 165

The: LCT emphasizes that Q, We, and Iia all vary for households at different stqes, a, of their life cycles. Aggregatingover a, we have C=aW+W,

(3)

wa

a=Cy a cI%i+

(4)

and C, W, and H represent the respective aggregates of CapWo) and ha. Thus, the LCT implies different responses to dollar ch s in the present values of aggregate property and nonproperty net worth, because they are distributed diffizently over households of different ages in the population. This is true of the aggregates even though an individual household’s expenditures woukl respend to a one-dollar present value increase in lifetime resources with a propensity ?a) independently of whether the increase was in Wa or ha. In earlier work, potential variation of u and I? over time was ignored as 21secondorder problem, but in the current FMP consumption function, a and /3are functions of the age distribution of the popul$ation. The empirical proxy for the present value of current and future nonproperty income is a distributed lag of current and past income. As with the perrranent income hypothesis discussed below, the motivation here relates to the formation of expectations about future nonproperty life cycle resources. The income variable is disposable income rather than nonproperty income. One justification involves revising equation (3) to include: interest rate effects: C = (a+cl r)W+ pH.If the distributed lag for the rW effect is assumed to be approximately the same as that for proxying H by nonproperty income, a distributed lag in disposable income results. The property component of the life cycle resources budget constraint already occurs in stock form. Nevertheless, the stock market component is separated, and the current value is replaced by a distributed lag. Households realize that the current market value of corporate equities represents their consumption value if consumed today. Since the bulk of these resources will be consumed in the future, however, a distributed lag i:r;used to recognize the evanc?scenceof stock market capital gains and losses. In the FMP model the lags for income and for stock market wealth are second-degree polynomials. The more complicated estimation procedure used here made it impractical to estimate these Almon lags. Instead the following 166

prclwiure was used. X, jlvhere the tfvJ’ .

i.

‘This

XLAG=

t

Eb F”‘ki

of are the RW

rLet

represent a distributed lag In the variaB3le

estimates of a secondkiegrele polynomial lag it;;mplaced by two variables in the current paper: 2: a& b$ *)t where b; = $3’ / t pp. Observe thalt C b; = 1. Separate

Itsm estimated for x m-dXLAG. This procedure) preserves the shape

FMP di&ibNhh from the f’itst lag onwards. The values of bi(and pp VM be eq~laf only if *theestimated coefficient of XLAC is unity. The zero lag term is treated sepuately since .it is an endogenous variab1.ein the instrumental estimation technique,+vhile XLACT is a predetermined v&able. Estimation ret&s for the FMP model appear in Table 1. The demographic variables POP and POP? are both scaled to average unity over the longer sample period and forecastllngperiod 1954: 1 to 1977% Thus, the impact effect of a change in disposable income on consumption is about 0.261 at an unemploymentempioyrnent ratio cf 0.05 (0.249 + 0.233 (O.olS) = 0.261). This response is consid;:rably larger than the inverse of the life expectancy of the typical household, 3s would be the case in the simplest life cycle models. Three reasons likely account for this responsiveness: positive rather than neutlral time preference; severe limits on borrowing against future nonproperty income; and induced expectations of further ircome changes. Even if it does ztot persist for more than one quarter, an income change should cause perceptible changes in consumption for a number of quarters as its effects are spread ovt:r the life cycle. An income change which lasts longer than a quarter increases the consumption response over time: there is a greater quantity of income increase to spread over the life cycle, and there are further induced expectations of future income increases. The peak and total responses to a sustained change in YD occur a:fter another eight quarters and measure 0.690. Household net worth excluding stock market wealth (KU) has a consumption impact of 0.06 per doharP Stock market wealth (VST$) has only about half that effect (0.0303) and orll’)rover the current and six succeeding quartad The coefficient of VI is in the middle of the range of estimates typically found in this Mcdigliani-type consumption function. The coefficierat of VS1”$is at the lower end of the range. In fact, the coefficients of the KS?% terms are not significant& different frora zero at the five-percent level, though the t-stat&tic on the laggec! term suggests that it should be retained for forecasting purposes. Finfly, we observe the high estimate on the lagged error term, which is 0.80 to the nearest 0.05. The equation for durables expenditures (KD) Indicates a much higher 167

(0.915)

W8)

[O.?Si%69) a80 u-l mm

0.220

08172

0.130

o&93

o&61

ao3s

sots

Looo

0382

01207

0.072

a023

d07f

do92

do66

Loo0

0.234

0.192

0.147

OJOl

[0.l01/1.06) - 0.0666 (-0.940)

(Oe273/4.94 J

1.000

&OS1

[a2rSlam]

[-tk276/&3S]

US6

+ ON362 (7.23)

(*=D

(*a30

-. (oAsoj4*9q 0.30 #*l 1293) S BI

0.200

0.240

0.240

0.2

0.120

6

ECD YCD WCD N YD PtWl N20 N25 N45 tKt+A us4

N65 V.

VCN1S KM1 PEH PCON VSTS JWD PCD

11 CCD

= 0389+0.01RCB-Q

ph$cD~

&s4:1-66:4 Q

?i! = 4~oc1161:lmd n

RCB SK!

dommy

fat

awl 1970 &t&a

170

impact effect of YD than does itself (0.362 verrus 0.261). Y st the ratio of &CD to CON was only 123 peree_ntin the sample pe od 19,5&l to f975:4, ThiS It affis the idea that a convenient way to “Sal a*substamial porticn of an income dhange ig by adjusting durables purchases. ifn the tongl:r run, the income elasticiQ~ qf l~cn in lower, since growth of KC’; depresses Et% with a f capital terms (CCD) are of the -expected sigr but not nt, Note. from the key to Table 3 that an inflation term Tltrcer auto strike dummy (JK’) and the housing starts variable are both statistically &gnifican~:and quantitatively important? The PermanentIncome Hypothesis The pemmt:nt income hypothesis (PIH) is inseperable from the name

of Milton Friedman (1957,1963). Numerous other researchers have contributed to the theoretical development and extensive testing of the PIH. Thz most comprehensive recent treatment appears in a series of papers by Darby (1972, 1974, 1975, 1978). Pt is the Darby formulation of the PIH that we examine here. Darby shifts the emphasis somewhat away from testing the PIlI and toward explaining aggregate consumer expenditures. In doing so, he is obligated to provide an explanation for durables expenditures. He does trris, and htr also includes a model of the allocation of transitory income among acqtiisition of durables, money balances, and other uses. Let d* and d represer.t the desired and actual stocks of consumer . durables. Similarly, let V* and m equal desired and actual money holdings. Then expenditures on durables, say edur, depend on (d*-d), (m&n), transitory income, and other variable:s. The desired stocks d* and 1%” are themse.!,ves functions of permanent inco:me,relative prices, and interest rates. Consumption of nondurable goods and services, say cnon, depends on many of the same variables, Le., permanent ‘income, relative prices, and inter&: rates. Darby does not estimate separate equations’ for @dtuand cnon. Rathc!r, he sums the two and estimates a single equation for personal consumpW1 expenditures (EN’,‘,). What would be the structural parameters of the individu II equations are, for the most part, not identified, This approach does resul:t, however, in an equation for explaining and forecasting expenditures.’ Derby experiments with alternative definitions of the appropriatt? income variable, The one used here and indicated in Darby (1975) is privhltei income (YPRW’), the sum of disposable income, corporate Mained profits, and net mmrne from the stock of consumer durables. YPWV is divided into its

K0)f

EPCE

consumption expundituro6

YP

pwmulent comment

YT

cnndtary component of YPRW

YPRf V

=

of YIRI V*

YD + YCR$/PPCE(OaOl) + YCD

YD

dispombls pemoml incame, accrud b

YCRS

corpowe rained

PPCE

implicit deflator foa EK’E

YCD

net imputed income from coasumtr du

Ml

=

profita

MlS/PPCE(O.O1)

MlS

mamy

PCD

imp!icit defhtor for ax

PPCND

implicit Wlator

RGB

rata on fedsnl

KCD

stock of conbumur durablee

t~pp1y,

demand dgpodol ph& curfwq dltums an

mwdun

for expencliture8on nondu WMMht

bon&

* See text for construction of’ YPRI V.

172

1-d-d

permanent and transitory components as follows. First, She average growth te of YPRW over the sample period is estimated from the ordinary leas!

In YPNV = 4.855 + 0.009305TT~8

(6)

Then p~~~n~nt income (YP) is YP”cp YPRIv+(l

-@)(l tg) YP+

where g is related to the coeffkient of time n equation (6) by g = exp 0.009305 - 1 = 0.009 (8) I 1 The necessary benchmark for YP is the fitted value of equation (6) for 19~0: I y The adjustment parameter is to be estimated with the behavioral parameters. This results in an iterative grid search over p. Maximum likelihood comprises the estimation technique used here. The estimates for the PIH appear in Table 2. The adjustment parameters, not indicated there, are 8 = 0.082 per quartet for the sample period 1954: l19’?2:2 and # = 0.052 per quarter for 1954: 1 - 1975:4. The lower estimate of fi implies that a continuing onedollar change ;n YPRIV causes YAPto change by 19.5 cents by the fourth quarter &d by 35.8 cents by the eighth quarter of the income change. The higher estimate implies fourth and kghth quarter adjustments of YP of 29.4 cents and $1 .O c!nts on the dollar. These estimates correspondclosely to Friedman’s own judgments (1957,1973) on the response of permanent income to current income. These estimates Jndicate considerably more permanent income revision than those determined by Darby

.’

The estimated coefficient for YP in Table 2 is 1.07, which is not significantly different from unity. It is, however significantly different from the average propensity to expend from YP, which is approximately 0.85. Thui, the relative constancy of the personal saving rate in the long run has a mart: complex explanation than that the marginal and average propensities to expend. from permanent income are identical. The marginal propensity to expend from transitory income YT is both statistically and numerically significant. This finding need not be found in conflict with the PIH, since we are dealing with an expenditure function. The expenditure component in Darby’s theory comprises one of the main applications of *tn&tory income. At the same time, the sizable coefficient of 173

YT offers little support for the view that Keynesian multipliem are n Y small because of HH considerations. Note also that YPRIY is more sensitive to fluctuations in income and spending than is the more convent disposable income. Fluctuations in corporate retained pmfits, one shock absorbersdamping exogenous spending and income fluctusltrionsbefore zh\eyaffect disposable income, are fully re ected in YP!%r, The impact effect on expend in Y~~~~is03 with 0.358 x 0.948 from YT and 1.07 x 0.052 The effect of WI income change by the fourth quarter is a sizable 0.548, while the eighth quarter effect is 0.722. Estimates for the shorter sample period are somewhat higher. The coefificient of the money stock is quite unstable. It is trivial and insignificant for the sample period 1954: 1 - 1972:2, but it incre~~ to 0.743 with a t-statistic of 4.34 when the additional 14 quarters are added to the peri,od. The positive sign is the anticipated sign: part of an increase of actual money balances relative to desired ones is allocated to purchases of durables. The government bond rate enters with the anticipated negative sign but declines by an !order of magnitude with the extension of the sample period. This change in absolute size is just the reverseof that for the money coefficient and may not be unzelated. In Darby’s work, the relative price term enters from the equation for durables expenditures. As sue h, it is expecte to have a negative sign, Here the sign is positive. Since WC% aggregates nondurable goods and services with durables, one might not be surprisedby either sign on the relative price term. In lny ewent,the coefficient is st;atistizally insignificant. The stock of durables has the hypothesized negative sign. As with the monegr stock and government bond rate, the coefficients change dramatically with the extension of the sample period. We note also iri As connection that the autocorrelation c~~efficic:ntof the error term differs considerably between the two sample periods. Estimation of a Composite Forecssting Model Thits section desctibes the construction and estimation of a consumer expendfture sector which is typical of those of large forecasting models such as Wharton, Michigan, Chase, or DRI. The model presented here draws particular motivation from Acklt:y (1978, pp. 6OO-3), Evans (1969, pp. 43342 ), and Eckstein, Green, and Sinai (1974, p. 602). It is something more than the intersection of those models and something less than the union, Four equations are presented: auto (,BZX+M) and other (ECDU)durables expenditures; consumpl;ion of nondurable goods (CN); and consumption of sewices (C’S). In comparison with the models already discussed, the forecasting 174

12!is!&, t iv

[d).602/-2.011 - a970

t-3.17)

[10.79O/dL797] +0&809 (YDmt)

___- - -__[-1.04/-1.75) [-O.l3S/a43] - a145 LULU * 0.0708 DTAX

(l.OQ N

(-06293)

(Q.585)N "

pao&14/w30]

[ao336/wl7) fMM!i98/&84) [W97jdM4,3) (YD.l-TR.1) KcDA*l QWD~RTB)+O.lOS 'I0.00514 JIG - ,0*924

* O-73

mm

(1.98)

p&819/2m]

[1.82/1&S]

+oJo8rDg=]I (2.72)

MI.822 Nl?4

N

[a367la.l9]

ECDO

r;-3.s9) N

f 1.28/2.70]

1;0.75/9.69]

+ 158 N2s64

+ c.75 u-l (JxO.6)

SJf&m t~Oo6801 O.OQ848

,,fDy = [OJ631 0.174

F1(IO.62)=130

[O&tsrl2As]

[-0.187/-1.78]

[-QW46/4.QQb]

N

+0.0954 +

-=.a447 N

(-6)

c;.lO, N

@57B

R2 ,ioe964] 0.964 2

N-l

- o.Os17 rjfjy

t-7Jw

c1*W

[0,0198~35]

[-0.113/*1.90]

FtJtO,76)=156

-

0.00301 (I&%#- R TB)

(-0.685)

(-3AO1,

,,,Dy p Ial"] 0.210

F(7#5)=3,059 F(7,79)=4,682

(-0.188)’

[M/4.76]

[0.0444/5.49] +O.OH6 MA.1

+a766 qi

(3.00) N

(SW ,‘J

.

,,,

=.

[‘-I

(0.997/2A8] 0.130

(Oe882)

$v*B

s

1.90

IO*002391 O&l318

[0.095~/233] +0.133F (5.33) [0*0063§/5.24] +0,00#02 TT (S.05)

[0.328/2.89] [1.42/~2.81] - 0.325 j$g +0.166 F (3Al) .[0.0946/0.653] + 0.210,cs,l,

(IlS41 [0.65/X31) + 0.55u-ll

(1.72) N-l

(6.14)

MDy o b18] 1.25

F(S,67~10$39 F(5,81)a6,185

[0.269~1.06] 4.

CN y-

R2

= OS31

&W = I1*951 206

= NW 0.997

CBS

unemploymenthunnce hofib

PPCE

implicitdeflrtoafor conalmet atpcmdliftuc#r

LULU

unemploymantWe of tot& laborlow hdudhg 8tmed

DTZaX

t8x sl#

RGB

nte on Federalgwemment bon&

RTB

Traasuy bill rate

JIG

dummyvariablefor 1964 and 1976

KCDA

0.232 f?CDA + 0.928 KCDQ

IHA

@fSLS + MMSS f M

MSL$

total da

tp4 to the Qmpwuy ffecdrof the 1968 and 1975 tax text)

ts at

MMS$ A4TCSS iWCDA$ Mits

ns?y

me

to

populaticm aver 16

177

mlodelhas a largernumber of explanatory voui3blcsbut iioes not include the long dktributed lags as proxies for Iife’cycle ar pwnanent income or wealth, Tk forecasting model is not without its own dynamics, however, as the durable stocks (KCDA and KCDO) erlter their corresponding expenditure equations, and lagged consumption enters the equations for consumption of nondurable goods and services. Many of the large number not variables that would appear equations bwed on utility maximization. At the sane time, they more justification than that they wo well empiriczlly. Except in the unlikely situation that some very strong aggregation conditions obtain, aggregate time series data will not be sc e multiples of the data pertaining to individual households. The additional v ables in aggregate equa then, capture cyclical and secular aggregation effects which influence a gate flata but are not present in individual household data. Estimation results for the fbrecasting m&ei appear in Table 3. Of particular interest in the auto equatiolil is the dummy variable for the temporary Vdum of the Temporary Tax Dummy Mlkw of 1972 ddlua)

68:3 68:4

7.2 8.3

69: 1 69:2 69:3 69:4

12.1 12.3 8.0 8.2

70: 1 70:2 70:3

SA

ble @TAX)

7Si2 7s:3 7S:J

-36.7 - 9.8 - 9.4

76: 1 76:2 76:3

-125 -129 *loa

’

SA

,_

OA

,/

taxes of 1968:3 - 1970:3 and 1975:2 - 1976:3. In the quarte~dicateJ,DTAX takes on values equai to the effect of the temporary tax changes on disposable income. lo The nun&Cal values appear in Table 4. In all other quarters, the value of DTAX is zero. If the coefficient of DTAI were zero, then the temporary taxes would be judged to have about as much effect on auto expenditures as any other chang+ lin disposable income. A positive coefficient on the order otf 0.186, the sum of the coefficients on current and la would indicate tha: the temporary taxes had no effect here is actually nelgtative,but not signifil: ntly different frow zk Apparently, the temporary tax:s had about the same effect on auto expenditures as other disposable income t:han 178

Many

a CJUUempiricist has noted, especially in the financial

press,

expenditures continued to rise, and personal savings rates deciin@dduring the surcharge of 1968-70. As Okun ( 1971) has noted, however, automobile purchasesexperienced an apparently autonomous increase, which, bY i&If, more than offset even the most optimistic predic$ed effect of the tempo e on 41 forms of con#sumerspending. The current work indicates that the autonomous increase was not a perverse reaction to the tax that c~~~mr

The spread between the government bond rate (RGB) and the Treasury bill rate (RTB) in the durables equations attempts to capture the effects of credit tightness. We would hypothesize a positive coefficient: tight credit conditions’ in which consumer credit restrains durables purchases are associated with short rates relatively high compared to long rates. While a positive coefficient is anticipated, the estimates are negative, significantly so in the EC.0 equation. The lagged stocks of money-like assets have sizable and significant effects on both ECDA and ECDO. Some commentators would view this result as annother facet of the credit tightness effect which the interest rate spread attempts to capture. An alternative view turns the explanation on its head: consumers transfer wealth into liquid assets in anticipation of the portion of durables purchases made in cash. Under both views, lagged liquid assets might prove useful for forecasting consumer durable purchases. The demographic variables have the anticipated positive signs. Those for the proportion of the working-age population are statistically significant. These coefficients are numerically significant as well, for they have the units “billions of 1972 dollars per million population.” It is tempting to link this observation with the observed sharp increase in automobile purchases in the late 1960s noted above. The relative price terms are troublesome. In the ECDO equation, the sign is negative but insignificant. The sign in the auto equation was positive (and significant), even with. the use of instrumental variable estimation. Here I made the single exception to the rule of not experimenting with functional form and omitted the relative price term from the ECDA equation. Finally, it is interesting to note the instability of the coefficients of the income terms in the durables equations. All increase dramatically with the addition of 19723 - 1975% to the sample period. Of course, these 14 quarters include the lalgestswing in disposable income in the sample period. Not only do these quarters get consitlemble weight in determining the coefficientes+ mates, but they improve the precision of the estimates. The estimated standard emon (not shown) of all the income coefficients are smaller for the SalnPle Pedod with the greater income variation. 179

The nandurable consumption equations are considerably simpler. Transfer payments (TR) appear in addition to disposable income (YD) itself. The marginal propensities to consume services and nondurable goods are 0.301 from YD (0.133 + 0.168) and 0.103 from TR (0.166 - 0.0635). Together with the coefficients of YD from the durables equations, these imply an impact effect of YD (UZ held constant) on to&I consumer expenditure of 0.477. This is broadly consistent with the findin@ of the LCT and PIH ~models, es peciaIIy irr light of the differences in the income variables used, The relative price terms have the expected n ey are significant or nearly so for the longer sample period. The coefficients on the lagged dependent variables are lowlzr than one might hayre expected. The long-run effec of changes in other t:-slplanatory variables (are only 27 percent higher than the impact effect for S.rvices. For nondurable goods the &mate effect is 58 percent higher than the impact effect, One shoulld note that the CS equation, with the lower coefficient en the 1 dependent variable, has a higher autocorrelation coefficient for the errors. Estimation of the Fair Model T:he Fair model differs considerably from the others both in form and in derivation. Fair (1974,1976) analyzed the results of numerical siml,Wions of dynamic programming problems for households before deciding upon fucctional forms. Thq: households’ decision variables included housing and labor supply as well as expenditure decisions. In the spirit of this maximizing framewo ) many of the variables entering the aggregate expenditure equation!; are either price or state variables: the wage rate; interest rates; the prices of the various expenditure categories; net worth; the stocks of durables and housing. Fair allows for the posGbility that labor and credit markets are not continuously in equilibrium so that ~OUIWholds may face nonprice rationin of employment and credit, As a result, his aggregate expenditure equations also include disequilibrium variables which, in fact, turn out to be statistically significant.l-* Fair’s estimating equations differ from the other models in two other respects, First, the dependent variables are the rosturu2!ogs of per capita expenditures, rather than per capita expenditures, per se, or absolute expenditures. This probably reduces the heteroscedasticity of the errors. Second, the depend* ent variable in Fair’s durables equation is the stock of durables (KCD), rather than the flow of expenditures (EC’). Presumably, Fair’s forecast for flC&anti the one adopted below--is

180

ECD=KCD-KCD,,I +WCD,

(9

where WCD is depreciation on consumer durables, i2 TabIe 5 presents the estimates of the equations for consumption of _ services (Cs), consumption of nondurable goods (CN), and the stock of $urables (KCD)- By md large the price, wage, and interest rate variables have the exs and are significant. These coefficiemkrcan be interpreted as elasticities. They imply very little impact sensitivity to prices, wages, and interest mtes, being on the order of 0.05 to 0.4 in absolute value. For C’Sand KCD, tb Hun elasticities are considerably higher. These two equations contain ’ Qhftit respective lagged dependent variables -with respective coefficients of 0,734 (lonwun elasticities higher by a factor of 3.76) and 0.917 (long-run factor, 12.6 The CN equation has a coefficient of the wrong sign on CN_I, although it is not significantly different from zero. As with the composite forecasting model, we observe that in the C’Sand CN equations, lower coefficients on the lagged dependent variable are associated with higher autocorrelation coefficients and vice versa. What sign should be hypothesized for the wage term (PL) in equations for current expenditure is not unambiguous. Leisure and goods might be either substitutes or complements. No constraints were imposed on the estimated price elasticities (including interest rates and wage rates as prices) to enforce homogeneity of degree zero in prices or to enforce consistency with a budget constraint. In all three equations, however, the price coefficients very nearly sum to zero, the condition necessary for price homogeneity. As with the other :models of consumer expenditure, the budget constraint is me”. implicitly by assigning saving only a residual claim on resources, rather than giving it an independent role. Thus, S any price change which affects expenditure also changes saving by an equal and opposite amount. In addition to the price and state variables, nonlabor income (I’NU) also is t&en as given by households in Fair’s view and, thusI,enters expenditure equations even in the absence of disequilibrium effects. YN.$ comprises property and transfer income, One might question the latter, since both unemployment and other transfer payments are countercylical to employment. In any event, the estimated coefficients are not significantly nonzero in any of the expenditure equations, Wealth is a state variable and appears in the equations for nondurable goods and for services. The coefficients are of the anticipated positive sign and, with a single exception, statistically significant. The implied dollar responses of expenditure to dollar changes in wealth are within the range 0.02 181

aw

ww

(~01,

m-3)

[ 2Alj2A8) +

(asosm7f .

4.02lq ZJ

VcIvo.1 + ar03 wPX&!! N14 (Oe233) -I -I

(443) [4.0106/4.137] +

0#0208 (0.326)

(d363j4.889)

-0.m

[4.0369/W 92)

(arowq

2OlajgPcD + O&733

’

@!f 16)

(4.16 1)

(1.21j

(aw

[4SM73/3.62]

1%

[Om914119,0]

[

+ 0,912

- 0. t-2.78)

(4.12)

ma8s oMlldnu8d) 1 IQ* 51 (lM;lii)

Q&6)

+lMm284 0704 (Od!M)

[0.50/4.93 J

+ 0*00149 0711 + oso”-1 (iLs1Q) (5"39)

cs N16

FL

employa

compmmtionmte ln noMum

private domwic

budncs

R&f

RTB

w JSTAR

3

codllcisat

of

Tl3fE

in

QLS rslpsrdon of log J on a wmtmt

0mo14S6 ZWE

1947:1= 1,1947:2 = 2,rtc.

J

@MYEI LMHS+ 2.08 (&A+ LEF + LESDjN16

LRfHG

lllmhourm of omploy88& nonf8rm bu8llleMrector

LMns LA

LEF U’S A

VCNS PXB YNLS YDVS

Yn) YART%

.

md

TIM..: g =

YPAGS

GSPS CBS

UTPF KCD

rtoclm of-

dun

PCD

D644 D651 D704 0711

dummy ruhbzsr otha qMar8

384

- 0.05, similar to the lower end of the range typically found1in estimation of the F rates are also in the category of variables that would appear in expenditure -equations not subject to disequilibrium effects. In Fair’s own estimation of his model, a tax rate variable was retained orlly in the CN We do not find the coefficient of the UTPF term statistically signifiat equation either, ZJ is the labor market disequilibrium term. To understand Z”, first consider the variable J, which is the ratio of total annual hours of employment to the total population. Let JISTAR represent J after an exponential time trend has been removed. Then W, the labor market disequilibrium variable, is near zero when JSTAR is near its sample period peak. As JSTAR moves further fern its sample period peak, ZJ declines as the square of the difference. The closer ZJ is to zero, its maximum possible value, the less involuntary unt:mployment curtails expenditure plans. If disequilibrium effects are important, the coefficlient of ZJ should?.be large and positive. In fact, the coefficient of 21 is positive in all three equations, is significantly nonzero in the CN and KCD equations, and is nearly so in the CS equation. Estimation of the Income Source Model There are a number of reasons why fluctuations in different income sources m t affect consumer expenditure differently. The relative variances of the permanent and transitory components of income may differ for different income sources. If SO,the presumption about the permanence of a change in income, and, thus, the expenditure response, depends on the source of that income. Further, as the life cycle model emphasizes, altenlative iwome types are distributed across populations with different remaining lifetimes and different propensities to consume and save. Third, changes in prop&y ind+nrl)a: due to changes in rates of return may have intertemporal substitu%on effects on consumption which changes in nonproperty income lack. Finally, we have Kaldor’s (1960) hypothesis about class dlfferettces between capitalists and laborers resulting in different savings propen C’’ I A. In an earlier paper I (Dolde, 1976), investigated differences in WCs and tran&ory-permanent splits from different income sources and from tax liabilities. In that study, I found that tax changes had a quicker and larger effect on consumption of nondurable goods and services than did other changes in &po&le income, Modigliani ( 1975) investigates differential consum@ion effects between labor and property income. He emphasizes that the substitution effects of property income make it inappropriate to regard regression coeffi-

185

MPCs. He also addresses and rejects ( 1978) separates “special” incomie-namely , the temporary

cienb

a

liabilities of 1968-70 and 1975-76-from “regular” expenditure effects of special income are about a quarter to a half those of regular income. current model allows for four source income (YL); property i income: tax rates (TILL, TXR). Chaqgesin each and transitory components. The definitb e 6. Note that TXL, the &x festive tax rate on personal income plus half r’.xR for property income is the average effective ta rate on personal income. I assume transfer income is untaxed. e components: permanent afterAfter-tax income of any type h &x income source; and bansitax income; transitory income due ts tie tory income due to tax changes. After-t iabor income, for example, ie YL (l- TX&l. Both YL and TXL are composed of permanent and transitory compane+ YL = YLP+ YLT

(10)

TXL = TXLP + TXLT.

(11)

Thus, after-tax labor income can be rewritten as YL(l-TXL) = YLP(l-TXLP) + YLT(l-TXLP) -YL .TXLT.

(12)

The first term OIIthe right-hand side of equation (12) is permanent. The second is transitory due to transitory before-tax income, The last is transitory due to transitory tax rate changes. Property income is treated analogously. SPnce it is assumed untaxed, transfer income has only the usual permanent and transitory components. The pemlsanent (XP) and transitory (XT) components for a variable X were derived as follows. We begin with MI, an eightquarter moving average of the: series X: 7 (13)

X8 =r, X.. 8. t A quarterly growth rate quarters:

g

is estimated from experience over the last eight

186

gt= (X8-1 /X8+) 118-1.

(14)

The estimate of XP is then formed from X8-1 and g, allowing for the growth r&e g if*bthe previous eight quarters and assuming it will obtain into thcr next

quarter:

iy

income isthen XT=X-XP.

(16)

This procedure was performed individually for X = YL, 13, YF, TXL,, and xr& It has two advantages over Darby’s procedure and others used in Dolde (1976). It assumes no exact knowledge of the future, which is implicit in basing pemanent income estimates on a growth rate estimated from a whole sample perhi. Second it does not require iterative estimation. Darby’s procedure would require a search over a Gvedimensional grid. Equations for the income source model for consumption of nondurable gmds and services (Cfi’D)and expenditures on consumer durables (ECLa)appear in Stable 6. In addition to the income variables, both equations contain relative price variables which are not, however, significant. The ECD equation also includes the lagged stock, for which the signs are wrong but insigniflcant. A strike dummy is significant in the ECLIequation. Turning to the income varia,bles, the labor income variables generalliy havi8 the expected sign, are statistically significant, and have the expected relative magnitudes. Thus, in the nondurables equation, the coefficient on permane+ labor income (0.726) exceeds that on transitory income due to both traa.sitory before-tax labor income (0.645) and transitory tax changes (U.498).13 The absolute sizes of the latter two estimates, however, are somewha,t larger than one might have expected in an equaltion for nondurables. Ungjike &,g&$es, non&u&km are not viewed as a vehicle for saving transitoW income. In the durables equation, the coefficient of transitory before-talc: labor income exceeds that of permanent labor income:.This is consistent with the finding&of other models that short-run elasticitie:!;for durables are largerthalnllong-run elasticities. Part of transitory income fhctuations is saved in the form of durables. The coefficient on transitory tax-generated iiabor income has lthe wrong sign but is not significantly different from zero.

187

I.

[oars/z.3cq o 726 rLp(l-TXm e N (8wO3)

WD

--yy-=

m N

(5.63)

[-0.222/0.1363) .

[&200~0.395]

YRP(l-TXRP)

.0+392 (-2.06)

[-OA4O~~Z46] I’L “TXLT 0.498 ‘-N (-3.98)

+ ‘0.372

N

YR"TXRT N

(1.85)

[ 11.1 l/2.50] YIP + 1.57iv (7J4) [ 126~OJ64 1 1.28 (0.712) R2 = fO.9991 0.999

MD,/

(2A11 2.52

[O&9/2.75] 0348 YLT(l-TXm N

(OA16/2.25] 0,128 x;v

ECD 2. -5 N

=

F(9,,77)t8QlO

~4.064Slas;ii~) YL'TXLT + 0.0368 N (0.355)

(0.389/1.27] YR'TXAT . oo340 . N (-0.322)

[ 0.12OlO.653) .

YRP(I-TXRP) 0.0191 N

o.171 YRT(bTXRP) N

(AI.193) [ =0.25#0.994] .

0.0262 y

-

(9.130)

+

(d198/&638]

f-0.0799/-0.317]

PCD

0.333j5g

(-1.21)

(1.22)

[0.124/0.0521 J

[=0.00348/-2.82) [o.o374~aO8a6][0.70/8.37]

0.162 y&

AMI

(0.854)

(-3.48)

R.2 = ww

S/-E

0,992

I

JIG

*

~O~~W

0.0102

+ 0.325

0.70u*l

(0.835)

(9.14)

MDv p [0.3S2] F(llbW412 0.383 F(11,7~sp901

--=a---

---I

Key CJVD

personalcomuunption expendibrres on nondunble goods md

N

population, millionr

188

Table6 @on#nued) YP

pemwnentcomponentof income soumctIf+

YjT

transitory componentof incomeaowcej*

ilXjP

permanenttax rate for incomesourcej*

TXjT

trmmky

I%

tax sate for incomeswcej*

= (Y&S+ YLAG$)/PPCE(O.Ol) + EGFL + EGSL

PJ’CE

implicitpricedeflatoafw perwnrl consumptionexpendhures

YAS$

.iaborincome,nonfarmtwine88 sector

YLAGS

compens8tionof eraployeer,agricul~ke

EGFL

conpaWion of Federalempl~ees

EGSL

employeecompenerdonby state and hgP government

TX&

= U?l’F/lOO + UTO/200

effectiverateof pemonatincome tax

UWF

OASI coutdbudoa rate, total

YR

s

(YAan

4 YDV$ + YII$ + YPAGS + YSE$ + YCRSW’WO.01)

YARm

rentalincomeof peX8om

YDVS

cwte

YIIS

intea

YPAGS

agticultunl plcBprietors’prdita

YSES

propdetod profIt

YCRS

corpo!!te retained profits

dividenda income

TXR

= UTPF

YF

= (GBS + GW$4 GSPS + YBrS)/PPCE~O.Ol)

GBS

unemploymentinsurancebenefit8

GIPS

Fedwallgfwmment tranldsirprymen& to pemn8 otherthanunemplcrymenlt insurance benefits fitateundlocaltransferpaymab to peraonr

ECD

expendlitwwon cowumer dumblea

PCD

impWr pplcedeflatorfw ECD

1.89

ofcolltlumoll

KCD

rtvck

JIG

dummy variable f6r 1964and 1970autoatdIms

l

see tat for cofwnlction fkom

dlmblm

Yj.

190

Th43c0MMent Of permanent transfer income (YFP) in the non&r&& equation ext=eed~unity but is not significantly different from u&y. A relatively of the- l'@c@hts of transfer income are at the yoc,gger and life cycle, the periods when less saving or even &saving OCCUR. A c~ffihmt of unity for permanent transfer income is consistent with this ProPe~~s NJ b a %%&cient of approximately aero in the durables equation. bb% fia hdf’ Of“transitorytransfer income is spent on nondurables in the quarter in Which it is aiquired, while another ,quarter is spent on durables, Tkre Co@f’f’i&nts of transitory transfer income do differ, however, for the two -Pks Fbds. The extra 14 quarters in the longer sample period, 19723 197S:$ do include major fluctuations in trarisfer payments. The greater variability in the dependent variable allows more precision in the parameter estimates. Krause; the effects of property incomk on expenditure include sub-. stitution as well as income effects, negative coefficients cannot be ruled out a priori. In fact, ttre coefficients in the nondurables equation all have signs opposite of what would obtain for income effects alone. For the longer sample period, these coefWents are significantly different from zero or nearly so. For the shorter sample period, the signs are the same, but none of the coefficients is significantlynonzero. In the durabes equation, none of the coefficients is significantly different from zero. The coefficients of property income clearly are significantly different from those on labor and transfer income. That they are negative, however, indicates that they cannot be accounted fur by Kaldor’s hypothesis alone, since that would imply coeffrcLsnts smaller than those from other income sources but positive. Under a simple Kaldorian hypothesis the coefficients in expenditure equations sum to unity less the savings propensities. ‘me final observation about the estiimates of the income source model is the hi& estimate of the autocorrelation coefficient for the errors This occurs despite the facts that income is d&aggregated by type, that the permanent iname proxy depejjds only on the most recent eight quarters of clata, and that relative prices and a ca ital stock variable also appear in the equations. IV. A Comparisonof Out<,f*ample Forecast

me five models discussed in Section 111were compared in their ability to foremt outside &he sample period on IJrrhichthey were estimated. TWO Such comparisons were made, The fmt took the estimates for the sample period 1954:l - 1972:2 l4 and forecast the quarters 1972:3 I 197334. The second

took the estimates for 1954: 1 - 19754 ‘* and forecast the quarters 1976: 1 1977:2. Both static.and dynamic forecasts were computed. In the static the forecasts were generated using the actual values for all of the right&and&l variables, including the lagged dependent variable in eases where it is used as an explan&ury variable. In the dynamic case, the forecast value was used where lagged dependent variables occurred. Dynamic forecasts were not computed for those dulrPtblesequations which include the stock of d tory variable. Implicit in a forec;rst of current expenditu endof-period stock. Since the stock variables enter the expenditures equations with negative signs, dynamic fc~recastsare less likely to blo up &m $&& forecasts. Thus, no dynamic forecasts were necessary to keep these models honest. The autocorrelation coefficients estimated for t,le five models were almost universally significantly nonzero. I have not, however, computed forecasts which include an autocorrelation correction b d on the last error in the estimation period. 1 did exarmine the effects for the models with the worst outof-sample Iforecasts and concluded that the autocorrelation correction would have affected the root mean squared errors (RMAE.) only trivially. The five models differ in their degrees of disaggregation of personal consumption expenditures (EPCE). Consequently, the variablesfor which outof-sample forec:rstsare available differ as well. In all cases, the forksts of the components were summed to form a forecast for EPCE itself. The dnglecquation Darby model required no aggregation of forecasts, since its dependent variable is EPCE. The dependent variables in the FMP model are consumption (COW and expenditures on consumer durables (ECD). The Fh@ fimxast of EPCE then depends on the use of the identity in equation (17) CO!t’= EPCE - ECD + WCD+ YCD

W)

and on the accuracy of the imputed depreciation (WCD) and net iname (YCD) from durables. For comparison purposes, I have comput d out-of-sample forecasts for a naivlzmodel. The equations of the naive model are ln(CA”D/N)= &+ jQn(CND/N),l

(18)

ln(ECD/N) = ci& + /3ln(ECD/N),l

(19)

EPCE = CND + ECD.

m

192

Hem, WD h ~n~mption tures on du~bles,.ERX

of nondurable gooddsand services, ECD is expendiis personal consumption expenditures, and M is, the

population. Table 7 presents the R.M.S.E.s in bitilions of 1972 dollars for the forecasting exercise. Six observations are immediately apparent. First, ai1 five mdels forecast remarkablywell. Half,of the percentage R.M.S.&s for total expenditures (EpicE) are about one percent or less, and the der a& within about two percent. (The average levels of actual EpcE I for the two foECasting periods we $760.2 bililion atlld $831.7 billion.) This is e&ecidi encouraging; gkn the k&e and novel ‘changesin the variables &fluencini households’expenditure decisions in the i97Os. Second, taking the two forecastinge:Kercisest(Jgether, the Fair model wins hands down over the other models. Its R.MS.E.s for EPCE are $6.5 i>iUion ad $6.9 billion for the two forecasting periods. These are each less than one percent of the respective average actual levels of EPCE. Only the FMP model comes close in both forecast periods, and then only if we compare its forecasts fat CVA! ($6.3 billion and $10.3 billion) rather than EPCE ($7.5 billion and $14.9 billion). Third, we observe the importance of having done two forecasting exercises. All of the models do very well on at least one of the forecasting periods. All save the Fair model do considerablyworse on one of the forecasting periods. A related fourth obsexrationis that the second period, 1976: 1 - 1977~2, was more difficult to forecast than the earlier period, 1972:3 - 1973:4. Five of the models, including here the naive model, had R.M.S.E.s of $10 billion or less in the eartier period. Only three did better than that in the later period in the static forecasts, and or@ two in the dynajmic forecasts. Fifth, we observe that forecasting d.urables provides a greater challenge than forecasting consumption of nondurable goads and services. The R.M.S.E.s for the durables equations are generally two to three times as large as those for the nondurables equations, despite the fact that durables comprise only about an eighth of total consumer expenditure. Ike czomposite forecasting ,model is an err;wpaon, doing rehtively better on forecasting durables than on nondurables, This suggests that its freer use of proxies for aggregation effects and nonlinearities has some effect other than merely improving in*amPle fit~bay, we observe that the differences between the static and dYnmic forgcab Me only trivial except for the naive mod$el.Of the models contaming lagged depend& v&&les, only the naive model exhibited a tendency to blow up dthout wta) expenditures replacing forecast expenditures- 16

193

2a s

cu

3A 283

27 13

es

x7

7s

4.1.

0s

Ewe

**u ‘, _e 17a 7a

13s 4.1

6.3

Id1 6B9 3A 9.9

lb 2a

l&9 1st

4a

3.9

h3cE

ECD

Mm3

CON

1976:1-1977~2

9s 6s

7s 5.2

7.0

3s

7e3 4e4

CB

2.8 1A

4b 22

CN

3.10 7.2

123

CND

Je3

ECM

7.5

3.9

Arm

6.1

7.0

196

83

18s

A!ms

9.9

1OB 7.5

This section reviews a number of important issues in applied macroeconomics related to the,.empirical results presented here. None of the models all of these issues, of course, the quantity of evidence iffer &o in the division of their respective motivations esesi’aiiiing in the understanding of the historical sample,,’ lI%m@ again, they are not all equ suitable for d&u&on of any given iseue. Still, the five models-toigether pres a large body of information, exhibit considerable agreement on some issues, and indicate where further work is most needed, The remainder of this section discusses a number of issues in turn. The order ranges roughly from those on which considerable evidence is available to those of a more speculative nature. Incomein AggregateExpenditureFunctiions Income does not appear in expenditure functions resulting from a microeconomic utility maximization framework with labor supply as a decision variable unconstrained except by the number of hours in a day, Rather, microeconomic expenditure functions with labor supply unconstrained would include &kive prices and state variables kch as nonhumazi we&h and sto&s of housing &id durables. Yet, ’ income is generally the k&t-and sometimes thk only-variable used in aggregate expenditure functions. The Fair mode! explicitly separates the wage rate from a quantity of labor variable representirrg nonwage constraints on the availability of employment opportunities. In three equations estimated for each of two sample periods, the labor market constraint variable

obtains t-statistics of 1.59 to 4.43, all of the appropriate sign. In all of the other models, income represents both a quantitatively and statistically significant explanatory variable, even controlling for relative prices, state variables and other variables that might appear in microqevel expenditure equations, and demographic and other variables which capture aggregatica effects.. The Timfns of E XF,B ltulre Responses to Income Fhwtwtions The life cycle theory (I,CT]r and the permanent income hypothesis (BIH) raise the possib%ty that households plan to ssm0or.hthe effects of income fluctuations over long horizons, responding only trivially in the current period. This possibility, if true, would imply that consumer expenditure (actually, consumption) would not greatly majgnify the effects of such fluctuations on egate demand. It would also make consumer expenditure (or at least consumption) an unlikely target fo shortrun stab%ation efforts* 195

The possible :3hort-run imemitivity* of consumer expenditure is 8311 empirical question, however, and t&e empiricaI evidence Iines up soIidIy against insensitivity. This is especially true for expenditures on consumer durables, where the short-run income elasti&ies generally exceed the longrun elasticities. But consumption of n.ondurablegoods and services also contributes to the short-run responsiveness of total personal consumption expenditures (EKE). In the four models w income variables b.npacteffect of a dolhrrchange come on EKE is represents half or more:of the ultimate mponse. Ab ultimate response OCCUIS within the first fnre quarters, and virtually all of it, within nine quarters.The relatively high impact effect followed by de&grating growth in the effect on total expenditure is explained by the differing time profiles of durables expenditures and other consumption. Durables expenditures start high, and later fall off as the stock of consumer durables grows and has an increasingly strong retarding effect. Consumption of nondurables grows over time as the inferred permanence of an income change increases. Neutrality of Fiscal Policy Variables A theoretical result which relies on consumers formulating consumption plans in accordance with the LCT or the PIH denies that changes in foal policy variables have any influence on consumption. This result obtains only under very strong assumptions about intertemporal preferences and access to capital markets. The empirical results above make it clear that consumption is far too sensitive to contemporaneous and near-term income fluctuations for the neutrality proposition to be seriously entertained as characteristic of the real world. 1 7 In other work, I (Dolde, 1976, 1978, 1979) have reported similar results and analyzed the possible explanations. In particular, differentisls between borrowing and lending rates and quantitative limits on borrowingopportunities, together with the rising ihape of the typical life cycle income profile, cause wtili;y-maximizing households to act, at some ages, as if they discount the future at rates of 30 percG:ntand more per year. This implicit discount rate far exceeds the interest rate at which the ernment can borrow, Cone sequently, these households vieIN the present value of future tax changes for interest ana; principal ali far less than the corresponding current change in fiscal variables. 14s a result, their expfntiituses do not exhibit neutrality with respect to fiscal variables. A related con!;ideration is the:,relative effectiveness of permanent and temporary tax changes. We noted above that after five quarters, a change in income has about three-fourths o the effect it would ultirnate~y haye if it were 196

to Jpersistindeftitely* Should the same ratio be expected to apply to temporary taX danges? llJhe answer depends on the speed and accuracy with which the public makes inferences about the permanence of tax changes,,As I have noted elsewhere (Dolde, 1979), there have beeAl13 major tax revisi0n.sin the postwar period. Of these, only two were advertised as explicitly temporary, and these were subject to extension. Thus, the relative durations of temporary and “permanent” tax changes may not differ greatly*?. iinder (1978) finds temporary b be about a quarter10 8 h4f as effective as ordinary income ch su sts that households do not distinguishthem from other income fluctuations. Modigliani and Steindet (1977) find the temporary taxes-including the rebate portion of the 1975 tax cut-to have been about half as effestive as permanent tax changes. Two of the r;nodels estimated here shed some light on this question. The income source model finds that the effects of transitory taxes on labor income reduce consumption of nondurable goods and services by $0.498 per dollar of tax liability- change. This is a little more than two-thirds of the effect of a change in permanent after-tax labor income, which is $0.726 per dollar. A durables equation in the same model has a coeffkient for transitory taxes which differs only insignificantly from zero. The automobile equation in the composite forecasting model includes the variable DTAX. The only nonzero values of DTAX represent the tax liabiiities corresponding to the temporary portions of the 1968-70 and 1975-76 tax changes. Disposable income for these p<#riodsalready reflects the t~~orary tax changes, ‘Ihe estimated coefficient on DTAX is not significantly different from zero, consistent with the notion that consumers responded to the temporary taxes as they would have responded to any other income change. Housing and Consumption

Most macroeconomic models afford housing variablesa rather schizophrenic treatment. Expenditures are modeled separately-and not merely because the national income accountantclassifiesthem with investmentrather than with personat consumer expenditures, At the same time, most models do not separate the imputed consumption of housing wrvices from the consumption of other se&es, implying a ‘relatively high degree of substitutability between the con-’ sumption of housiag and other services, Such an assumption hardly seems justified, especially in a comparative scnsc. C!oj,rsumptionof durables services are not aggregated with consumption of other seATices,even where a stock of durables is computed from the history of expenditures on durables. A second reaso,c:for disaggregating housing services from other services relates to relatively high adjustment costs. These are acknovledged in the 397

’

presentation of an t:xptMitunr:equation. Ytt despitt must be an importaM determinant o the StrVictstG+t con of this relationship is not exploited. t sttms Hktly th3t accrue from treating the housing stock as a state vtible and txplaining the consumption of se3ices separal,ely. Aggregation lIsffi.l

The 1970s been years of much economic variables than cxcwrtd in the of many of the variables infllltncing I greater variability reflects changes in tl tory variables, then. the parameters oft change in response. These idseashave been lucidly expressed by Lucrr~(1976) in the context of lbolicy tvairaatirsn.They apply mart gentrally, however, to the generation of all explanatory vaflo8blts,not just policy variables, It is unproductive tcjIdebate the literal truth of the assumptions un lying empirical work such a~ tiat reviewed here. ‘tie entirety of economic!1is devoid of results if we require its assumptions to be literally true. Tht imporbmt: consideration is to determine: those circumstances in which paramtter instabil.ity is a l;‘ust-orderproblem, those in which it is secondorder, and so on. In most cases, this determination is an empirical issue. Aggregation difficulties have always confronted empirical macroeconomics. Theory prowide:svery littl~ehelp in assessing or rtmtdying them. Even at the level of the individual consumer, empirW analy&s rtquirts approximation of utilitymslximizirrgdtcision rules. Tht problem the consumer actually solves is far too complex to be analytically tractable withou: such approximation. Empirical analysis at tihe aggrtgate level makes its approAnations al that po.intratherthan at the ltvtl of the individual.Tht appropriateness her type of arpproximrttion can ont:ybt an tmpirical question. The models discussed in Section III err.hib1.tvarying degrerte of parameter stability. The parameters of tht Fair model, wMch I
endingin"the fourth qu

p8 of each year from 1971 to 1975, Then vti‘ were computed r the six quarters immediately succeeding each estknrition period. Table 8 presents the results of this exercise, AN of the R.M.SJ3.s for total consumer expenditure are within the l-to 2-percent range. ‘The novel events of 1974.75 apparently made forecasting that period somewhat more dWicult.-After the data from these periods became incorporate 41 the dimatide sample,the R,M,S,E. for the ensuing 1976-77 f&cast a@n retuked td a lower level, *I3

199

s4:1- 7k4 s4:1- T&4 !w:1 ‘*734 !54:1-74:4 54:i - 759

72tl- 7322 73:1- 7422 74~1 L 75:2 7&l’, 76:2 7&l- 77r2

LO 1.2 13 I.6 t7

$8

&O

7*7 3.8 &1 2J

$4 794 711 3.9

t t x6& 69

1,

‘)

truamtal

t&e 2.

vmuhbier In d&u

t8nm

w8m

dividedby the population in cas8s

in per carpirr twms. M

a fhorctu~ and indljhtful int8ll8ctusl histoq of the development d Rebdei (19775 hav8app&d the FMPmode’lto the effectiveness

of

ti

ba ti

mOdd

a8

d41tlnedm&8 fUliy in a k8y rlppsruingh

the

table

mCMM. in thb p8per and in the FMPdats.am measuredin trillionsof

6.

AiC hrr v&ma (2plpl) for 1964:4-1965:2, (692,-2) for 1970:4-197132, and 28X0 elsewhene. b d-ted squation foQcuon and edur a8w8ll as a single integrat8d t&is&H8 fi&drthe d#b&wpatiOn appmdi prefeaabie.&je Purvis(1978) for a rtock qurtm8nt m0del thrrtin&d88 expenditure cledaions with portfolio

a 9. wtion

?‘TiB101 ill 1947:1,1’02 h 1947:2,8tC. ti n for the diff@ence8betw8en Dacbyb e&mater and oth8rsis that Darbymakesno lot uumtmd &dTub, deapidbgenerallylow Ducbin-Wa@on ncpttistic&

109 ~bfxeat ddhr t8tim@8 Of the88 t8mpomcytax effects on fliqm%aMe income appearin Okun (1971) and Mnder (1978), N8d aa the worlt of Chufe8 A. Wtite and Joseph C. Wak8field of the Commcaoar Dsputmmt. Some appear In W&e and Wak8fleld(1976). 11. &au@ the aebit muket dimqui@#iumocouraonly in the housingequation in Fair’swork, itisnotrhckr?here.

12. hn tit, lome mbror odjuutmenb wer8 m8d8 brtthe &pmcirtion series to accommodate I&# dU’fese@zes in uauuptions about hhg betweenthe Fairmodel and the FMPdata.

&&nate8 for th8 umple p&d l9S4:1 - 1972:2 ~$8 the upper numbers in the equate 14. ba&ets haT1#ar Id mb Sb. Ths m&mate8me fallowedby their ri&atlstic& 15.

The@e#&n8bsr8~

&8&y in hOnt of the c+o#rerpondingvrtirMes InTables 19 and 56.

l6.

k Mica&l lar&Mm v, th8 n&e mod8Spsrlarnnr8ven worm8for th8 perbd 1974:l of itr dynamk fwmob far that pmiodis $323 billiom1972 dollars.

197S:Z The BUHS~,

In a m@n:lpiper, Hsll(I1978) feporlr tits whtih mightrppearto be !n conflict with tholre 17. mported he#et Isr frrct,thef!l i8 no conf!ict. Fir& HalI8%pnrirnsr only csnsumptiou of nondurable8and rdnicsk w&UeIt Irr defrt t&t iiwW4 mount fol muchof the $r0ft7un dl~ctuationin conlruiner 8XpendippOtt“...fhe Vi8W that policy dly, t!xm ia a mnmtlc diff8mnc8, Hall rtaterthat his fts , To a@sountfor the f&tuaafrem unuump@m &y M much u itMf8ct@psan~t,lncoIn~~ i~mme path that evolves daa wfth pefmtmmt Looms &me msirslywquirer a permurcsnt lidlieamoo&ly throb& w&y inferred.

201

Ackley,

G.

(1978)

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(1974)

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A Model of Macmeconomfc Activity, vol. 1: The Theoretical Model. Cambridge: Ballin r Publishing Company.

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( 1978)

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Survey of Current Busifiess,