ALAN S. BLINDER Brookings Institution and Princeton University ANGUS DEATON Princeton University The Time Series Consumption Function Revisited THERELATIONSHIP between consumer spending and income is one of the oldest statistical regularitiesof macroeconomics-and one of the stur- diest. Like the aging movie star, it needs a little touching up now and again, but always seems to come bouncingback. A dozen yearsago, boththe theoreticalderivation and the econometric form of the aggregateconsumption function were considered settled. Most economists adheredto one of two ways of puttingFisher's theory of intertemporaloptimization into operation: Milton Friedman's per- manent income hypothesis (henceforth, PIH) or Franco Modigliani's life-cycle hypothesis (henceforth,LCH). ' Since each variantseemed to have sound theoretical underpinnings,and since the two had similar econometricforms that explainedthe data well and had similarimplica- tions for policy, there was not a greatdeal to quarrelabout. Perhapsthe most contentious empirical issue was the apparently large marginal This paperhas benefitedfrom the commentsand suggestionsof AlbertAndo, Whitney Newey, and members of the Brookings Panel and from seminar presentationsat the Universityof Warwick,Princeton University, and Johns Hopkins University.We thank Peter Rathjensand Lori Gruninfor researchassistance and the National Science Foun- dationfor financialsupport. 1. Milton Friedman, A Theory of the Consumption Function (Princeton University Press, 1957); Franco Modigliani and Richard Brumberg, "Utility Analysis and the ConsumptionFunction: An Interpretationof Cross-SectionData," in KennethK. Kuri- hara, ed., Post-KeynesianEconomics (Rutgers University Press, 1954), pp. 388-436; AlbertAndo and FrancoModigliani, "The 'Life-Cycle'Hypothesis of Saving:Aggregate Implications and Tests," American Economic Review, vol. 53 (May 1963), pp. 55-84. 465 466 BrookingsPapers on EconomicActivity, 2:1985 propensityto consume out of transitoryincome, which was variously explained by a "short horizon" (that is, a high discount rate) or by liquidityconstraints. Thingsare quite differentnow. Developmentsin economic research, as well as actual events, have raised fundamentalquestions about the consumptionfunction. At the same time, the rangeof experience of the last dozen years has been great enough to hold out the hope of getting some answersfrom aggregate data. This seems, therefore,an auspicious time to take a fresh, and unabashedlyempirical, look at the time series consumptionfunction. Questions Raised by Modern Research The Lucas Critique. Reasons aboundfor questioningthe traditional consumption function and its implicationsfor how tax policy affects consumer spending. Robert Lucas has pointed out that, under rational expectations, the PIH does not lead to a "structural" relationship between consumptionand income, but ratherto a statisticalrelationship that should change whenever the stochastic process generatingincome changes. The Lucas critique calls for estimation methods that treat consumptionand incomejointly.2 The "Random Walk" Hypothesis. Robert Hall sharpened the impli- cations of the PIH by showingthat the rationalexpectations hypothesis impliesthat only "surprises"in permanentincome shouldaffect current consumption,once lagged consumptionis controlledfor.3 The work of Hall and Lucas added a new dichotomy-that between anticipated and unanticipatedchanges in income-to the traditional permanent-transitorydichotomy. It is this new dichotomy, ratherthan the old one, thathas absorbedthe attentionof contemporaryresearchers. Hall's work in particularhas spawned an infant industry estimating Euler equations linkingcurrent and lagged consumptionin the manner 2. RobertE. Lucas,Jr., "EconometricPolicy Evaluation: A Critique,"in KarlBrunner and Allan H. Meltzer, eds., The Phillips Curve and Labor Markets, Carnegie-Rochester Conference Series on Public Policy, vol. 1 (Amsterdam:North-Holland, 1976), pp. 19-46. 3. Robert E. Hall, "Stochastic Implicationsof the Life Cycle-PermanentIncome Hypothesis:Theory and Evidence," Journal of Political Economy, vol. 86 (December 1978), pp. 971-87. Alan S. Blinder and Angus Deaton 467 impliedby the first-orderconditions of a Fisherianintertemporal opti- mizationproblem. We have our doubts about the wisdom of modeling aggregateconsumption as the interior solution to a single individual's optimizationproblem in adjacentperiods,4 but in any case thinkit fairto say that the research done to date has not supportedthe econometric restrictions implied by the Euler equation approach. Nor has further investigationvalidated the hypothesisthat the response of consumption to income (henceforth, Y) reflects only the usefulness of current Y in predictingfuture Y. Instead, research typically finds "excess sensitivity" to currentincome.' But the case is by no means closed. So a central question of this study is whether informationknown at time t - 1, such as anticipatedincome, has any predictive power for changes in con- sumption between times t - 1 and t. The Barro Equivalence Hypothesis. A rather different objection to standardconsumption functions, based on the idea that private and government accounts should be consolidated, was raised by Robert Barro.6The income (that is, disposable income) and wealth (that is, household net worth, including government debt) variables normally used in consumptionfunctions imply that intertemporalshifts in the 4. Cornersolutions stemmingfrom liquidity constraints pose one problem.Aggregation poses others. For example, with mortal consumers, a constant age distributionof the population,and neithersurprises nor changesin interestrates, the ratioC,+ IC,(where C denotes consumption)would be 1 plus the growthrate of per capita income. The Euler equationapproach models the growthrate of consumptionas a functionof the interestrate andthe timediscount rate, and uses the observedgrowth rate to estimatethe intertemporal elasticityof substitution.Background growth of per capitaincome seems to be ignored. 5. MarjorieFlavin, "The Adjustment of Consumptionto ChangingExpectations about Future Income," Journal of Political Economy, vol. 89 (October 1981), pp. 974-1009; RobertE. Hall and FredericS. Mishkin,"The Sensitivityof Consumptionto Transitory Income:Estimates from Panel Data on Households,"Econometrica, vol.50 (March1982), pp. 461-81; Ben S. Bernanke,"Adjustment Costs, Durables,and AggregateConsump- tion,"Journal ofMonetaryEconomics, vol. 15(January 1985), pp. 41-68; Ben S. Bernanke, "PermanentIncome, Liquidity,and Expenditureon Automobiles:Evidence from Panel Data," QuarterlyJournal of Economics, vol. 99 (August 1984),pp. 587-614;N. Gregory Mankiw,Julio J. Rotemberg,and LawrenceH. Summers,"Intertemporal Substitution in Macroeconomics,"Quarterly Journal of Economics, vol. 100(February 1985), pp. 225- 51;Martin Browning, Angus Deaton, and Margaret Irish, "A ProfitableApproach to Labor Supply and CommodityDemands over the Life Cycle," Econometrica,vol. 53 (May 1985), pp. 503-43; Charles R. Bean, "The Estimation of 'Surprise' Models and the 'Surprise'Consumption Function," Discussion Paper 54 (Centerfor Economic Policy Research,February 1985). 6. Robert J. Barro, "Are GovernmentBonds Net Wealth?" Journal of Political Economy,vol. 82 (November-December1974), pp. 1095-1117. 468 BrookingsPapers on EconomicActivity, 2:1985 patternof taxes, with no change in their presentvalue, produce shifts in the time patternof consumption.This should not be so, Barroargued, if people can freely transferincome across generations. The Barro equivalence hypothesis is not theoreticallyunobjection- able. In addition to the usual perfect capital markets assumption, it requires that bequests be motivated by intergenerationalaltruism and thatpeople have extremelylong time horizons. It also has troubledealing with childless people or with the possibility of "corner solutions" in which the unconstrainedoptimal bequest cannot be enforcedbecause it is negative. Because of these and other problems,many economists find the equivalencehypothesis implausibleon a priorigrounds. But a priori reasoningis not the way to settle the issue, and empiricalstudies have foundit surprisinglydifficult to rejectthe equivalencehypothesis.7 More evidence would be welcome, and we try to obtain some below. Intertemporal Substitution. Modern macroeconomic analysis has reemphasized intertemporalsubstitution. Yet standard consumption functionsoften omit the rate of interestas an argument-not on theoret- ical grounds, but on empiricalgrounds. The consensus conclusion that consumption,and hence saving, is insensitive to the rate of returnhas been questioned by Michael Boskin and, more recently, by Lawrence Summers.8What do recent data say about this issue? 7. For some theoreticalarguments, see MartinS. Feldstein, "Perceived Wealth in Bonds and Social Security:A Comment,"Journal of Political Economy, vol. 84 (April 1976), pp. 331-36; Robert J. Barro, "Reply to Feldstein and Buchanan,"Journal of Political Economy, vol. 84 (April 1976), pp. 343-49; and Willem H. Buiter and James Tobin, "Debt Neutrality:A Brief Review of Doctrineand Evidence," in GeorgeM. von Furstenberg, ed., Social Security vs. Private Saving (Ballinger, 1979), pp. 39-64. The conclusionthat the empiricalevidence is mixedis reachedby KarlBrunner after a thorough review of the literature.See Brunner,"Fiscal Policy in Macro Theory: A Survey and Evaluation" (Federal Reserve Bank of St. Louis, January 1985). But both Roger C. Kormendi,in "GovernmentDebt,