Liquidity Constraints and Intertemporal Consumer Optimization: Theory and Evidence from
Durable Goods
Author(s): Eun Young Chah, Valerie A. Ramey, Ross M. Starr
Source: Journal of Money, Credit and Banking, Vol. 27, No. 1 (Feb., 1995), pp. 272-287
Published by: Ohio State University Press
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EUN YOUNG CHAH
VALERIE A. RAMEY
ROSS M. STARR
LiquidityConstraintsandIntertemporal
ConsumerOptimization:
TheoryandEvidence
fromDurableGoods
THE PROPOSITION
that individuals arrangetheir saving and
spendingbased on intertemporaloptimizationhas both theoreticaland intuitive appeal. Unfortunately,most tests of the strongest form of this proposition the life
cycle-permanent-income hypothesis with rationalexpectations reject the theory.
Researchersfrequentlyappealto liquidityconstraintsto explain the discrepancybetween theoreticaland actual behavior.l ESorts to formalize the notion of liquidityconstrainedconsumershave not to date producedtestableimplicationsas strikingas
those derived for the permanent-incomehypothesis (for example, Robert Hall
1978). The difficulty in deriving testable implications stems from the unobservability of the key variable in the model the shadow price of borrowing.Most investigators have dealt with this difficulty by using some proxy for liquidity
constraints,either splitting the sample by some indicatorof the likelihood of binding liquidity constraints(for example, Zeldes 1989; Jappelli 1990; Runkle 1991;
Flavin 1994) or controllingdirectly for the likelihood of facing liquidity contraints
in a regression context (for example, Flavin 1985). Flavin (1985), Zeldes (1989),
and Jappelli (1990) find some evidence for borrowing constraints, while Runkle
(1991) and Flavin (1994) find no evidence for borrowingconstraints.
This paperdevelops a theory of optimal consumptionbehaviorin the presence of
The authors are grateful to Olivier Blanchard, John Conlisk, Robert Engle, Clive Granger,Emily
Lawrence, and participantsat the 1991 Asian EconometricSociety meetings for helpful comments. Valerie Ramey gratefullyacknowledgessupportfrom the NationalScience foundation.
1. See, for example, Flavin (1981), Hall and Mishkin (1987), Hayashi (1987), and Wilcox (1989).
EUNYOUNGCHAHis an assistantprofessorat Ewha Woman'sUniversityin Seoul, Korea.
VALERIE
RAMEY
is associate professor of economics at the Universityof California, San Diego, and afaculty researchfellow of the National Bureauof EconomicResearch. ROSSSTARR
is professor of economics at the Universityof California, San Diego.
Journal of Money, Credit, andBanking, Vol. 27, No. 1 (February1995)
Copyright 1995 by The Ohio State University Press
EUN YOUNGCHAH, VALERIEA. RAMEY,AND ROSS M. STARR : 273
borrowing constraints, and tests that theory using aggregate data on the stock of
durable goods and purchases of nondurablegoods. We assume households are
forward-lookingand maximize expected lifetime utility, subject to currentassets,
currentincome, and expected futureincome. Householdsare assumedto be unable,
however, to borrowthe necessaryamountsto smoothall consumptionover time. We
show that liquidity constraintsinduce a distinctiverelationshipbetween household
stocks of durablegoods and consumptionof nondurablegoods. Durablegoods provide services over an extended time period, so capital marketimperfectionsaffect
the timing of durablegoods expendituresdifferentlyfrom nondurablegoods expenditures. Our test focuses on the relationshipbetween the marginalutility of houseconsumption.If
hold durablegood holdings and the marginalutility of nondurable
capital marketsare perfect, then these two variableswill always be in an equilibrium relationshiprelative to one another.In the presenceof capitalmarketimperfections, however, the lagged value of the discrepancybetweenthese two variableswill
have predictivepower for the currentchange in nondurablegoods consumption.
If durable goods expenditures cannot be debt-financed, then forecastable increases in income are precededby reductionsin expenditureson durables.Consumers temporarilyrundown theirdurablesstocks andreallocateexpendituresto current
nondurableconsumption;they anticipatea subsequentincrease in sustainableexpenditurelevels and they plan a future augmentationin durablegoods stocks and
expenditures.Alternatively,if durablegoods expenditures,but not nondurableconsumption, can be debt-financed,then forecastableincreasesin income are preceded
by a rise in durablesexpendituresanticipatingthe increasein debt-servicecapacity.
In either case, the theory implies thatthe level of durablegoods holdingsrelativeto
the level of nondurablegoods purchasesshould have predictivepower for changes
in nondurableconsumptionexpenditure.
The predictionsof the theory are sharpenough to distinguishbetween a liquidity
constraintmodel and a "Keynesian"rule-of-thumbmodel, where consumptionvaries directly with currentincome. Hall (1978), Hayashi (1987), and Campbell and
Mankiw (1989) have suggestedthatthe excess sensitivityof consumptionto predictable changes in income might be attributableto a fractionof the populationfollowing a Keynesian nonoptimizing rule of thumb. Borrowing constraintsdo not, in
general, imply Keynesian rule-of-thumbbehavior. Liquidity constrainedforwardlooking consumers smooth consumptionwithinstages of their lives, these stages
being defined endogenously by the level of consumptionsustainablewithout debt
(Heller and Starr1979; Zeldes 1989). The typical optimalprogramis characterized
by several relatively smoothly changingsegmentsof consumptionwith abrupttransitions between them. Along the smooth segments, the usual marginalequivalences
are fulfilled. If the consumersanticipaterelaxationof liquidity constraintsat date t
(presumablywith an increase in currentincome), they arrangetheirexpendituresin
priorperiods to run assets down to their lower bound at t - 1. Upon relaxationof
the constraint,consumptionlevels rise, formingthe abrupttransition.If consumers
face liquidity constraints, but are forward-lookingoptimizers, then predictable
changes in income should not be statisticallysignificantpredictorsof consumption,
274
: MONEY, CREDIT,AND BANKING
once the effects of liquidityconstraintshave been accountedfor throughlagged values of the marginal utility of durables and nondurablesas explanatoryvariables.
Alternatively,if some consumersare Keynesian,then predictablechanges in income
should remain significant. The model and empiricalresultsbelow suggest that consumers behave as rational forward-lookingoptimizers in a liquidity constrained
environment.
1. THEORY
OptimalConsumptionPaths with LiquidityConstraints:Simple Case
We first develop intuitionin the context of a simple model (Chah 1990). To highlight the effect of liquidity constraints, we assume that interest rates and relative
prices are constant, and that the interestrate equals the rate of time preference.The
next section will relax these assumptions.
Consider a consumer who faces a stochastic income stream and chooses consumptionand asset holdings to maximizeexpectedlifetime utility subjectto the constraintthat assets must be nonnegative. The problemto be solved is
00
Max Eo E (1 +
C,K,A t=O
p)-t
At
+
=
(1
+
r)At_l
At + e4PdSt< O,
U(Ct, Kt)
Yt-Ct-Pd(Kt-(1
subjectto
-a)Kt-l)
whereA_ 1, K_ 1 given,
t = 0, 1, 2, .
whereAt is financialwealth at the end of periodt, Ct is consumptionof nondurables
duringperiod t, Kt is the stock of durablesat the end of period t, Ytis labor income
during period t, Pd is the (constant)relative price of durablesin terms of nondurables, r is the (constant)real interestrate, p is the subjectiverateof time preference,
8 is the physical depreciationrate of durables,e4is the fractionof durablesthat can
be financed, U is increasingand concave in C andK with Uc(O,K) = Uk(C, 0) = oo,
and Eo is the expectationbased on period Oinformation.
The only nonstandardfeature of our model is the second constraint, which restrictsa particulardefinitionof the consumer'snet assets to be nonnegativein every
period. The parametere4in the constraintrepresentsthe fractionof durablesthat the
consumer is allowed to finance. If e4is zero, the consumer cannot borrow against
futureincome to financecurrentexpendituresfor durableconsumption;the consumer is constrainedto have nonnegativefinancialassets. At the other extreme, if e4is
unity, durablespurchases are fully financeable, and only total assets the sum of
financial assets and the value of the durablestock need be nonnegative. The purchase of a durablein this case does not adversely affect currentliquidity since the
increase in financialliabilities is offset by the increasein physical assets. In such an
environment,the consumeris constrainedonly to have positive total net worth. Fi-
EUN YOUNGCHAH, VALERIEA. RAMEY, AND ROSS M. STARR : 275
nally, if e4 is between zero and unity, then durablesare partiallyfinanceable. We
expect e4to be close to unity since financing is available for most durablegoods.
Note that in no case is spendingon nondurablegoods financeable.
Solving the asset evolution equationfor Ct and substituting,the Lagrangeanand
first-orderconditions for the problemare
00
L = Eo
E
(1 +p)-t{U[(1 +r)At_l+Yt-Pd(Kt-(1-8)Kt-l)-AtaKt]
t=0
+ At[At + PdKt]}
EtUC(t+ 1) =
Uk(t,
Ft
=
Pd
UC(t)-At
L Uc(t) -
S
(l)
1 + r E,UC(t + 1) 1
(pPdFt,
' °,
(2)
(3)
(At + PdKt)At
= °
Uc denotes the derivative of the utility function with respect to C, and Uk denotes
the derivativewith respectto K. Ft iS the shadowprice at date t of the nonnegativity
constrainton the household asset position. Ft assumes positive values only in those
periods t where the asset position fulfills the constraintwith equality.Typically,the
nonnegativityconstraintwill be binding at some dates in the program,and this affects the optimal path throughoutthe program,even at dates where Ft = O and the
constraintis not currentlybinding. In the absence of a liquidity constraint,that is,
with Ft = Ofor all t, equation(1) would be the usual relationshipbetween marginal
utilities across periods. With a perfect capital market,the expected marginalutility
of consumptionis constantover time since p = r and Ft iS always zero. In contrast,
the expected marginalutility will not be constantin the presence of liquidity constraints binding at some dates of the program. In conjunctionwith equation (3),
equation (1) implies that in the presence of liquidity constraintsthe expected marginal utility of nondurableconsumptioncannotbe rising over time (Heller and Starr
1979). If the liquidityconstraintis bindingin periodt, so that Ft iS strictlypositive,
then the expected marginalutility of nondurableconsumptiondeclines from period
t to period t + 1.
The informationcontainedin equation(2) is much more apparentif equation(2)
is combined with equation(1). This combinationyields
Uc(t) = 1 +
^
pl Uk(t) + i4(1
r)+ ^(1
b)
Ft
.
(5)
When Ft iS zero in equation(5), we obtainthe usual equalitybetween the marginal
rate of substitutionbetween nondurableand durablegoods and their relative price,
276
: MONEY, CREDIT,AND BANKING
(1 + r)/(r + b)Pd-l. Nonzero values of Ft affect the intratemporalrelationshipbetween the two goods in period t because they alter the shadow price of durables
relative to the shadow price of nondurables.How that shadow price is altered depends on the degree to which durablescan be financed.If epis zero the coefficienton
Ft iS negative. Hence, duringa periodwhen the consumerrunshis financialassets to
zero, the marginalutility of nondurableswill be low relative to the marginalutility
of durables;equivalently nondurableconsumptionwill be high relative to durable
consumption.This resultreflectsthe natureof durables(thatthey yield theirservices
slowly) and the assumptionthatthey are not countedas assets. With borrowingconstraints,durablegoods must be paid for "up front,"even thoughthe utility yield of
durablesextends over many periods. When the borrowingconstraintis binding, the
currentuser cost of durablesis very high because durablesemploy liquid assets that
could be used to increase consumptionof nondurables.Thus, durablegood consumptionfalls temporarilyin anticipationof a rise in income.
The natureof the optimal path changes dramaticallyfor e4equal to unity. When
durablesare fully financeable,the coefficienton Ft in equation(S) is equal to one. In
this case, the consumerincreases his ownershipof durablesin the periodbefore the
increasein income. The consumerfinds it optimalto do this because he can begin to
enjoy the benefits of the durablesone period before he begins to pay the rentalcost
(consisting of interestand depreciation).
Equations(1) and (5) can be combinedto producean expressionfor the change in
marginalutility from the consumptionof nondurablesin terms of the discrepancy
between marginalutility from durablesand nondurables:
UC(t
+
1)-
UC(t)
=
-Ft
= _
+
et+l
r+ 8
i4(1 + r)-(1-b)
[ Uc(t)
r
+
8
p
Uk(t)
]
+
et+l
S
(6)
where et+ 1 iS an expectationalerrorand is uncorrelatedwith informationavailableat
time t. If liquidity constraintsare never binding, so that Ft iS always equal to zero
and the term in brackets in equation (6) is always equal to zero, no information
availablein period t can predictthe change in the marginalutility between periods t
and t + 1 (Hall 1978). If, however, liquidity constraintsare binding in some periods, then the deviations from the lagged linear combinationof Uc(t) and Uk(t)will
have predictivepower for IvUc(t+ 1); these deviations, in fact, are proportionalto
the value of the Lagrangemultiplieron the borrowingconstraint.Equation(6) is the
key theoreticalresult and testable implicationof this paper.
Generalizationof the Theory
We now discuss how changes in the model affect the implicationsderived in the
last section. We begin by briefly discussing the relevanceof the results in a general
EUN YOUNGCHAH, VALERIEA. RAMEY,AND ROSS M. STARR : 277
equilibriumsetting. We then analyze how generalizationsof the model change the
results.
The implicationsof perfect capital marketsversus liquidityconstraintsalso hold
in a general equilibriumcontext. Underthe purepermanent-incomehypothesis, the
lagged behaviorof durablegoods shouldnot predictthe change in the marginalutility of the consumptionof nondurablegoods, even in a general equilibriummodel.
Any lagged informationthataffects expectedincome shouldalreadybe incorporated
in consumptionbehavior.Using an example from Baxter's(1992) generalequilibrium model, if there is a shock to consumers'desiredholdings of durablegoods, and
if that shock is known to affect futureincome and wealth, then the consumptionof
nondurablegoods should respondimmediately.Thus, the finding that lagged information about the marginalutility of durablegoods predictsthe change in the marginal utility of nondurablegoods is contraryto the assumptionof perfect capital
markets.
A second issue of interestis the effect of adjustmentcosts. Bernanke(1985) and
Startz(1989) both study the joint behaviorof the consumptionof durablegoods and
nondurablegoods in a frameworkwith a nonseparableutility functionand with adjustment costs for durable goods. Bernanke uses this frameworkto determine
whether these changes can explain rejections of the permanent-incomehypothesis
for nondurablegoods. Among his findingsare that(1) separabilityis a good approximation, and (2) nondurableconsumptionis still excessively sensitive to changes in
income. Startz, on the other hand, uses the frameworkto determinewhether the
changes can explain the rejectionsof the permanent-incomehypothesisfor durable
goods. He finds that the exercise is generally successful, but the lack of rejection
may be due to low power of the tests.
Their results raise the questionof whetheradjustmentcosts may be mistakenfor
liquidityconstraints.If utility is separablein durables,nondurables,and adjustment
costs, which is consistent with Bernanke'sfindings, then adjustmentcosts do not
have the same implicationsas liquidityconstraints.To see this, simply augmentthe
utility function with an adjustmentcost, so that it is written U(Ct, Kt, Kt-Kt_l).
Without borrowing constraints, the first-ordercondition for nondurableconsumption is EtUC(t+ 1) = Uc(t). Since adjustmentcosts on durablegoods do not affect
the marginalutility of nondurablegoods, the model still has the implicationthat all
relevant informationavailable in period t is incorporatedin U^(t).The presence of
adjustmentcosts in the borrowingconstraintmodel will make it more difficult to
detect borrowingconstraints,but will not lead to false acceptanceof the liquidity
constrainthypothesis.
We now derive implicationsof liquidity constraintsunderthe more general conditions of nonconstantrelative prices and variableinterestrates, which will be useful for our empiricaltest. The Lagrangianfor the more generalmodel is
00
L = Eo
E
(1 + p)-t{U[(1 + rt)At_l + Yt
t=0
-Pdt(Kt-(1
-b)Kt_l)-At,
Kt]
+
At[At
+
PdtKt]}
.
278
: MONEY, CREDIT,AND BANKING
The variablert is the real interestrate on financialassets held between periods t-1
and t. In the generalproblem, the necessaryconditionsare
Et
1 +t+1
Pdr
Ukft)
Uc(t
+
1) =
L Uc(t)
UC(t)-Ft
(lt)
S
1 + p Et((1 +
st+l)
UC(t +
1)) ]
9Pd,>t,
(2
)
where 1 + st+l equals Pdt+llPdt, the gross inflation rate of the relative price of
durables.
The slackness conditionsare identicalto the ones in the precedingsection. Eqllations (1 ') and (2') are similar to those presentedearlier. The key difference is that
the relationshipsbetween the marginalutilities of consumptionhave variablecoeflicients that depend on relativeprices and interestrates.
In order to derive implicationswithout specifying a general equilibriummodel,
we assume that both rt+1 and Pdt+ 1 are known at time t.2 With these assumptions,
equations(S) and (6) from the simple case presentedabove become
+ rt+ 1
Rt+l
Uc(t + 1)-
1 Uk(t)
dt
1+ r
k
Rt+
+ 9
Uc(t) = 1 + rP
=
_
1 +
At + et+l
Rtk+l
P
1 + rt+ 1 9(1
* [ Uc(t)
-
Rk
+ rt+ 1)-(1-8)(1
p
Uk(t)
+ st+ 1)
1 + et+ 1
(6 )
+ st+l). These equationsyield the same basic
where Rtk+l = 1 + rt+l-(1-b)(1
are
binding, the lagged relationshipbetween duconstraints
liquidity
when
insight:
rable stocks and nondurableflows has predictivepower for the futurechange in the
marginalutility of nondurables.The relationshipis the termin squarebrackets,now
statedto include variableprices. When e4is unity,the relationshipshould enterwith
a time-varyingcoeicient of negative (1 + p)/(1 + rt+l), since the expression involving e4is equal to Rtk+ 1; when e4is zero, the relationshipshould enterwith a timevarying positive coefficient.
2. EMPIRICALTEST
The theoretical section above suggests a simple empirical exercise: determine
whether the deviations from the long-runrelationshipbetween durablestocks and
2. Withoutthis assumption, we would have to specify the conditionalcovariancesbetween r and Pd
on one hand, and the marginalutility of nondurableson the other.
EUN YOUNG CHAH, VALERIEA. RAMEY, AND ROSS M. STARR : 279
nondurableflows have predictivepower for futurechanges in nondurableconsumption. Although this test is simple in principle, complicationsarise in the empirical
implementation.We will discuss these complicationsin the following sections.
EmpiricalSpecification
We assumethatthe utilityfunctiontakesthe CES form U = ntCtl- l/ + vtStl- l/,
where (x and t are parameters,andn and v arepossible randomshocks to the utility
function, observable to households but unobservableto the econometrician.If we
substitutethis functionalform into the key equationsfrom the last section, we obtain
1 +
Rtk+
-
rt+l
1
1
1
Pdt
(1
-
l/t)vtSt
1/
(1
-
l/(x)tCt
1/
-9(1
+
rt+l)-(1
-8)(1
-
+
flt+l)
Ft
Rk
1 + r+t
nt+l
nt(l
-
_
l/a)Ct
(5tt)
,
1/
At
{C+I}-l/t
(6")
For convenience, we take logarithmsof the equationsabove and use the approximation ln(1 + x)-x for small x. The model thus becomes
ln Ct = constant + (x/ ln Kt + (x ln Pdt + °z ln Rtk+1-(x
Aln Ct+l = 00
+
(x
rt+
1
+
02t+
1 Zt
+
(xAlnnt+
1-tet+
rt+ 1 +
Zt
.
(7)
(8)
1
where
Rk
02t+
Zt
=
1 =
(xlnnt-aln
-
9(
1
+
vt-a
rt+
l )-(
9(1
1
+
-8)(
rt+l)-(1-8)(1
1
+
st+
Rtk+l
l)
+
st+l)
Ft
nttl - l/a)Ct-l/t
This system has the form of an errorcorrectionmodel. Many studies, such as Engle
and Granger's(1987), have shown thatconsumptionis well-describedas a unit root
process, so that the growth rate of consumptionis stationary.This empirical fact
implies that the terms on the right-handside of equation(8), includingZ, should be
stationary.3Since Z is the errorterm in equation (7), equation (7) is essentially a
cointegratingrelationshipbetween durablestocks and nondurableflows andZ is an
errorcorrectionterm. Z, which is a functionof the Lagrangemultiplier>, predicts
future changes in nondurableconsumption, as is seen in equation (8). The coeffi3. Of course, it is possible that each of the componentsis nonstationary,but cointegratedwith each
280
: MONEY, CREDIT,AND BANKING
cient on Z, denoted 02t+1, is a functionof e4.If e4is unity,then 02 will be a constant,
equal to minus one. For other values of e4,the coefficientwill be a functionof time
as interest rates and rental costs vary. If e4is near unity, the average value of the
coefficient will be negative, whereas if e4is close to
the averagevalue of the
coefficient will be positive. Testingfor statisticalsignificanceof 02 in equation(8) is
equivalent to testing for the presence of binding liquidity constraints affecting
consumption.
The formulationis precise enough to distinguish the predictionsof alternative
models. For example, the pure permanent-incomemodel with no unobservable
shocks predictsthat variablesdated t or earliershould have no predictivepower for
ACt+
1- A Keynesianrule-of-thumbmodel, on the otherhand, predictsthatforecastable variationin disposable income should have predictivepower for /Ct+ l .
The unobservablesin the utility function, nt and vt, complicatethe analysis. The
cointegratingrelationshipbetween durablesand nondurablesstill holds, as long as
the unobservedelements are stationary,but the errortermof the cointegratingequation will be a function not only of Ft but also of nt and vt. The presence of the
additionalelements will not affect the consistencypropertiesof the estimatesof the
cointegratingvector, but will affect the inferencesderivedfrom the errorcorrection
equation. To be specific, even in the absence of binding liquidity constraints,the
errorcorrectionterm may have predictivepower for the change in the consumption
of nondurables,because the errorcorrectionterm, which containslnnt, may be correlatedwith the errorterm in equation(8), which contains lvlnnt+l . If lnnt is white
noise, the correlationbetween lnnt and lvlnnt+1 will be-0.5 . Thus, if we allow for
the presence of unobservablesin the utility function, we must estimate the error
correctionequation (8) using instrumentsfor the errorcorrectionterm that are not
correlatedwith Ant+l or st+ l
In the estimation, we will use a general errorcorrectionmodel, augmentedby
lagged differencesin the consumptionand durablestock variables.The inclusion of
these lags can account for any additionaldynamicsresultingfrom adjustmentlags.
The estimatingequationis specified as follows:
ZtA0,
lvln Ct+l = constant + Olrt+l + 02t+1Zt+ 0351nCt
+ 0451nKt + Tt+l,
(9)
where Tt+1 is the errortermcontainingst+ 1 and lvln nt+ l . We estimatetwo versions
of equation (9): first, underthe assumptionthat 02 is a eonstant, and then assuming
02 is significantly differentfrom zero, using a nonlinearestimator,treatinge4as a
parameter.The reasonfor estimatingthe linearrelationshipfirstto determinewhether the coefficient is nonzero is that there exists no value of e4for which 02 is zero.
Data Description
We use monthly data from 1959:1 to 1989:12 for real per capita personal consumption expendituresand disposable income, as well as the real per capita net
EUN YOUNG CHAH, VALERIEA. RAMEY, AND ROSS M. STARR : 281
TABLE 1
UNIT ROOTTESTS (p-values)
ADF test on levels
ADF test on dlfferences
Varlable
(in logs)
no trend
Services
Nondurables
Income
Durable Stock
Motor Vehicles
Other Durables
0.26
0.86
0.82
0.98
0.96
0.99
trend
0.96
0.78
0.92
0.09
0.46
0.00
no trend
0.00
0.00
0.00
0.17
0.03
0.37
trend
0.71
0.05
0.17
0.04
0.16
0.01
Four lags were included In each test.
stock of durables, split into motor vehicles and parts and all other. Motor vehicles
and motor vehicle parts are combined into a single aggregatedenoted cars. Nonauto durablesconstitutethe aggregateotherdurables.See the data appendixfor details on the constructionof the data. We treatexpenditureson nondurablesand services separately.We use monthly data because the monthly frequencycorresponds
to the frequencyat which debt service on consumerdebt is paid. The effect of variation in the immediacyof the liquidityconstraintshouldbe evidentat this frequency.
The other variables used are the commercialpaperrate, the implicit price deflators for nondurablesexpenditures,services expenditures,new car expenditures,and
durablegoods expenditures,and the real price of refinedpetroleum. All variables
were taken from Citibase. All variables except the interestrate are in logarithms.
As a preliminarystep, we establishedthe time series propertiesof the variables.
This step is importantfor determiningthe order of integrationof the variables, as
well as the natureof the unobservableshocks. We first ran standardtests for unit
roots, which are shown in Table 1. The resultsof the augmentedDickey-Fullertests
suggest that nondurableconsumption,services, income, and the stock of "cars"all
have one unit root. On the other hand, the stock of durablesotherthancars seem to
have only a deterministictrend or two unit roots. Because non-cardurableshave
differenttypes of trends, we exclude them from furtheranalysis.
We then tested (separately)whether the nondurablesand services were cointegratedwith the stock of motor vehicles and parts. In the basic specification,we regressed services or nondurableson a constant,a deterministiclineartrend,the stock
of cars, and the price of cars relative to the price of nondurablesor services. The
results were as follows:4
logt services)= 2. 8 1 + 0. 0015 trend+ 0 .362 log( cars)
(14.7) (12.5)
(14.7)
-0.424 log(relativeprice).
(-9.2)
R2 = 0.998; Test statisticfor null of no cointegration:-4.46; p-value
(10)
= 0.02
4. t-statistics were calculated using a heteroskedastic autocorrelation consistent estimator of the standard errors. A Parzen kernel with twelve lags was used. The cointegration tests included four lags.
282 : MONEY, CREDIT,AND BANKING
log(nondur) = 2.46-0.0002
trend + 0.4411Og(cars)
(13.8) (- 1.6)
(1 1.2)
-0.3 12 log(relativeprice) .
(-8.0)
R2 = 0.985; Test statisticfor null of no cointegration:-3.06; p-value
( 11)
= 0.46
All the coefficients in the regressionshave the predictedsigns, with nondurablesor
services moving positively with the stock of cars, and negatively with the relative
price of nondurablesor services to cars. According to the test statistics, one can
reject noncointegrationin favor of cointegrationin the case of services. Thus, except for a deterministictrend, the marginalrateof substitutionbetween services and
cars is equal to the relative price in the long run. On the other hand, one cannot
reject noncointegrationat the usual significancelevels for nondurables.This result
might be attributableto a nonstationaryunobservableshock to the marginalutility
of nondurables,or to the notoriouslow power of cointegrationtests.S
EmpiricalResults
Testsfor Liquidity Constraints. We now test the permanent-incomehypothesis
againstthe liquidityconstraintalternativeby estimatingequation(9). The errorcorrection terms are the residualsfrom the estimatedequations(10) and (1 1).
As discussed in the previous section, we must extractonly that part of the error
correctionterm thatis correlatedwith Ft and uncorrelatedwith the shocks to utility.
If we assumedthat the shock was not serially correlated,then any variableslagged
one period or more would be valid as instruments.We are not, however, willing to
make such a strong assumption.Instead, we proceed underthe following assumption: the current shocks to nondurable(or service) utility are uncorrelatedwith
lagged shocks to durablegood utility and financialvariables. The instrumentsused
are lags one throughfive of (1) the log change in real disposable income; (2) the
commercialpaperrate;(3) the real interestrate, measuredas the differencebetween
the commercial paper rate and the inflationrate of either nondurablesor services;
and (4) the log change in the stock of cars. Note thatwe do not use lagged values of
the change in nondurables,services, or the errorcorrectionterm as instruments.
Table 2 presents both the linear and nonlinearestimates of equation (9) for services and for nondurables.Considerfirstthe resultsof the linearestimationreported
in Part A. In both equations, the errorcorrectionterm enters significantlywith a
negative coefficient, the coefficient on the lagged dependentvariable is negative,
5. When other variables such as real oil prices, interestrates, and inflationrates are entered, the results are virtuallyunchanged.
EUN YOUNG CHAH, VALERIEA. RAMEY, AND ROSS M. STARR :
283
2
TABLE
TESTS
FOR LIQUIDITY
CONSTRAINTS;
INSTRUMENTAL
VARIABLES
ESTIMATION
Dependent Varlables
A log services (t + 1)
A.
Linear
0.0022
(3.25)
0.338
(3.23)
0.03
-0.0017
(- 1.58)
-0.
196
( - 2.21)
0.350
(1.84)
- 0.175
(-0.92)
0.666
(2.89)
0.07
0.0022
(3.18)
1.18
(12.1)
-0.336
(-1.97)
-0.267
(- 1. 17)
0.346
(3.30)
0.04
- 0.0016
(- 1.57)
1.14
(14.5)
0.343
(1.82)
-0.186
(-0.98)
0.645
(2.88)
°.°S
Constant
Error
correction
term
Real
-0.
(t)
rate
1)
Dependent
variable
(t)
Alog
(cars
p-value
(t)
for
test
overident.
B.
of
Nonlinear
Estimation
error
rection
cor-
term
Real interest
(t + 1)
Dependent
(t)]
rate
variable
(t)
Alog
p-value
cars
(t)
for
overident.
1 .04)
restrict.
Constant
9 [from
159
2.11)
- 0.334
(-1.96)
- 0.238
(-
interest
(t +
A log nondurables (t + 1)
Estimation
test
of
restrict.
t-statistlcs are In parentheses. The error correction term is from the relevant cointegrating equation reported in the text. The Instruments used
are lags one through five Of: the log change in real dlSposable Income, the commerclal paper rate, the real Interest rate (described in the text),
and the log change in the stock Of cars.
but not significantlydifferentfrom zero, and the coefficienton the lagged change in
cars is positive and very significant. The implicationsof these results are twofold.
First, even afterextractingthe effects of unobservableshocks to the utility function,
the lagged behaviorof cars and nondurableshave predictivepower for the change in
nondurableconsumption. Thus, we can reject the permanent-incomehypothesis in
favorof the liquidityconstraintalternative.Second, the sign of the coefficients suggests that the stock of cars rises in anticipationof an increase in nondurableand
service consumption. As discussed earlier,this patternof behaviorsuggests a high
value of ep.
PartB of Table2 presentsthe resultsof the nonlinearestimation.The estimateof
epis almost identical in both cases, with a value of 1.18 for services and a value of
1.14 for nondurables.The point values are greaterthan one, the presumedmaximum value of ep, but both are within two standarddeviations of one. A possible
technical explanationfor the high estimated value of epis the mannerin which ep
enters the time-varyingcoefficient. The absolutevalue of the coefficientis decreasing in epand is very steep near the point where epequals (1-b)(1 + s)/(1 + r),
since the denominatorvanishes at thatpoint. Thus, any misspecificationthatbiases
284 : MONEY,CREDIT,
ANDBANKING
the coefficienttowardzero will bias the estimateof epupward.Alternatively,a value
of epgreaterthan one may be consistent with the credit arrangementsfor financing
new cars. Carsdepreciatefasterthanthe loans financingthem are amortized,resulting in more than 100 percent financingof the outstandingstock of cars and a value
of epgreaterthan unity.
In sum, when we test the permanentincome null hypothesis against a precisely
specified alternativehypothesis of liquidity constraints,we can reject the null hypothesis. Furthermore,the values of the coefficients are generally consistent with
the alternativetheory, and suggest that a large fractionof durablesis financeable.
Testsfor Rule-of-ThumbBehavior. The next step is to determinewhetherthe liquidity constrainthypothesis or the Keynesianhypothesis is a betterdescriptionof
the data. Hall (1978), Hayashi (1987), and Campbelland Mankiw (1989) suggest a
model in which a certainpercentof the consumersfollow permanent-incomebehavior, while the rest follow Keynesianbehavior.According to their model, when the
change in consumptionis regressedon the predictablechange in income, the coefficient gives the percentof the consumerswho are Keynesian.
We first reproducethe results obtainedby Campbelland Mankiw using our data
definitionsand instruments.We estimatethe effect of the currentgrowthrate of real
disposable income on the growthrateof services and nondurables,separately,using
the instrumentsemployed above. The results are given in columns 1 and 3 of Table
3. In the case of services, the coefficientestimateis 0.203 with a t-statisticof 2.67;
in the case of nondurables,the coefficientestimateis 0.288 with a t-statisticof 1.85.
These estimates are somewhatlower thanthose obtainedby Campbelland Mankiw,
most likely because our data are higher frequency.The estimates we obtain, however, supportthe hypothesisthatconsumptionis excessively sensitive to predictable
c :anges ln lncome.
.
TABLE
.
3
TEST OF RULE-OF-THUMB
VARIABLES ESTIMATION
BEHAVIOR VERSUS LIQUIDITY CONSTRAINTS INSTRUMENTAL
DependentVariables
Explanatory
Variables
Constant
log dispos.
income (t + 1)
Real interest
rate (t + 1)
Errorcorrection
term (t)
Dependent
variable (t)
lvlog cars (t)
A
a
log services (t + 1)
a
log nondurables(t + 1)
4
1
2
3
0.002
(7.50)
0.203
(2.67)
0.0021
(3.14)
0.092
(1.06)
-0.292
(- 1.74)
-0.130
(-1.71)
-0.219
(- 1.00)
0.292
(2.69)
0.0005
(1.06)
0.288
(1-85)
-0.0015
(- 1.32)
0.062
(0.305
0.328
(1.64)
-0.172
(-1.45)
-0.189
(-0.978
0.601
(1.94)
t-statistics are in parentheses.The errorcorrectiontermis from the relevantcointegratingequationreportedin the text. The instrumentsused
are lags one throughfive of: the log change in real disposableincome, the commercialpaperrate, the real interestrate(describedin the text),
and the log change in the stock of cars.
EUN YOUNGCHAH, VALERIEA. RAMEY, AND ROSS M. STARR :
285
Are predictablechanges in income still significantwhen we include them in the
liquidity constraintmodel? The Campbell-Mankiwmodel would suggest a positive
answer, but in a rational forward-lookingliquidity constraintmodel, predictable
changes in disposable income should not be significantafter the effects of liquidity
constraintshave been taken into account fully. Columns 2 and 4 of Table3 present
estimates of the linearmodel estimatedin Table2, with the log change in disposable
income added. In each case the coefficienton income dropsprecipitouslycompared
to columns 1 and 3, and is no longer significant.On the otherhand, the coefficients
on the liquidity constraintterms fall only slightly in absolute value, and generally
remain significantly different from zero. Hence we reject the Keynesian rule-ofthumb model in favor of a liquidity constraintmodel. It is neither necessary nor
useful to characterizehousehold behavioras rule of thumbto accountfor the data.
We should add thatthese results are entirelyconsistentwith Wilcox's (1989) tests
using increases in Social Security benefits. In all of his specifications, he includes
lagged changes in durablesand nondurableswhen he tests for the significance of
predictablechanges in benefits. Accordingto his Table2, durablegood expenditures
(but not nondurablegoods) are sensitive to predictablechanges in benefits Furthermore, his estimates show that lagged changes in durablesexpenditurespredict the
change in nondurables
3. CONCLUSIONS
We have developed and tested the stochastic implicationsof a forward-looking
model of rationaloptimizing consumerssubjectto liquidityconstraints.This paper
should be viewed as a contributionto the body of evidence includingFlavin (1985),
Zeldes (1989), and Jappelli (1990) that argues that liquidity constraintsdominate
myopia as an explanationfor the excess sensitivity of consumptionto predictable
changes in income The theory and the results provide the following descriptionof
the behaviorof consumers. Most consumersare forwardlooking in their behavior:
they smooth consumption as much as capital marketspermit. When they receive
news of a future increase in income, they increase their durablegoods holdings in
anticipation. They cannot, however, increase their nondurablesor services consumptionbecause they cannot finance the increase. The anticipatorymovement of
durablescontains more informationabout the futurechange in the marginalutility
of nondurablesand services than does the predictedchange in income.
On the other hand, the results provide evidence againstKeynesianrule-of-thumb
behaviorin favor of forward-lookingbehaviorwith liquidityconstraints.The addition of predictablechanges in income to the model show them to have no significant
additionalpredictive value. Consumersare forwardlooking, but the horizon over
which they can smooth their consumption is limited by capital market imperfections. The excess sensitivity of consumptionto predictablechanges in income is
attributableto liquidityconstraint.
286 : MONEY,CREDIT,
ANDBANKING
DATA APPENDIX
In this appendixwe describeconstructionof the durablesstock. For both the case
of total durables and motor vehicles and parts, we used the Bureau of Economic
Analysis estimates of the end of the year stock. We consider the BEA estimates to
be superiorto those obtainedusing investmentseries and assumingconstantexponential depreciation.In the case of motorvehicles and parts, the BEA dataare quite
accuratebecause they use the Polk data on the numberand age of autos registered.
For all types of durables, straight-linedepreciationschedules are used.
We estimated monthly stocks of durables as follows. In all cases, we used
straight-linedepreciation. The within-yearrate of depreciationof new purchases
was assumed constant for all years. We chose the monthly rate of 0.003 for both
total durablesand motor vehicles and partsbecause this was the only value that did
not generatespuriousseasonality.We allowed the rate of depreciationof carry-over
stock from the year before to vary year to year The value was chosen so that the
estimatedvalue of the stock by year end was equal to the BEA value. The estimated
monthly straightlinedepreciationranged from .0170 to .0191 for all durables, and
from .0214 to .0280 for motor vehicles and parts. The stock of durablesother than
motor vehicle and parts was set equal to the differenceof total durablesand motor
vehicles and parts.
In the theoreticalmodel, we assume exponentialdepreciationfor simplicity. The
only case when we must have a value for this depreciationrate, o, is when we perform the nonlinearestimation. For cars, we choose a value of o of .028 per month,
which is the exponential rate that is the closest approximationto the straight-line
rates for within and across years that we estimatefrom the BEA data
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