A Nonparametric Test of the Life-Cycle Rational Expections Hypothesis

Abstract

In a world of perfect certainty and perfect capital markets agents allocate expenditure in such a way that the marginal utility of discounted expenditure is the same in each period. In this paper we present a test of whether any particular series of discounted prices and quantities can be exactly reconciled with a utility function and marginal utility of discounted expenditure that do not change from period to period. We find that UK, US and Canadian postwar aggregate data all reject our condition, although it is not rejected for long sub-periods. We show that our results for the UK suggest particular modifications to the strong form of the rational expectations hypothesis that our condition tests. In fact these data are exactly consistent with a number of alternative hypotheses. From this we argue that time series data are ill suited to parametric testing of any of the competing hypotheses on the inter-temporal allocation of expenditure. The pure theory of the inter-temporal allocation of goods and time with perfect capital markets and perfect foresight is identical to the static demand case. There is a single (lifetime) budget constraint and the allocation of expenditure to each period is made so that the marginal utility of discounted expenditure is the same in each period. Bewley (1977) and Hall (1978) have identified the life-cycle/rational expectations hypothesis under uncertainty (REH) with the proposition that expected utility maximising consumers will allocate expenditures and time in such a way as to try and keep the marginal utility of discounted money constant. Given a set of time series on prices, purchases, wages and labor supply we can ask whether these realised plans are consistent with the life-cycle hypothesis. In this paper we propose a test that requires no ad hoc specification of functional forms or error processes but rather gives an answer yes or no based on finite mathematical techniques. The specific hypothesis we test is a strong form of the REH viz that the marginal utility of discounted expenditure is constant over the period of observation. For long time series this seems to be an absurdly strong hypothesis since it is effectively equivalent to assuming perfect capital markets and perfect foresight with regard to all important variables. If, however, we can accept this strong hypothesis for a particular data set then any test of the weaker forms of the life-cycle/rational expectations hypothesis on this data set must be interpreted