Stochastic Implications of the Life Cycle-Permanent Income Hypothesis: Theory and Evidence

This paper shows that if consumers maximize expected lifetime utility subject to an intertemporal budget constraint under uncertain future earnings – the standard life cycle-permanent income model – then the marginal utility of consumption must satisfy a stochastic Euler equation implying that no variable observed at time t, including past income or wealth, has any predictive power for future consumption beyond current consumption itself: apart from a deterministic trend, marginal utility – and, for reasonable utility functions and the small quarter-to-quarter innovations actually observed, consumption itself – evolves as a random walk. This result yields a test of the hypothesis that does not require assuming income is econometrically exogenous, unlike traditional consumption-function regressions on current or lagged income, which Hall argues are undermined by the two-way dependence between consumption and income (citing Haavelmo 1943 and Friedman and Becker 1957); instead the theory is tested by regressing consumption on its own lagged value plus other lagged variables and checking whether those other variables retain any additional predictive power. Using quarterly postwar U.S. data on consumption of nondurables and services, Hall finds that lagged consumption alone explains current consumption extremely well, that additional lags of consumption beyond the first add essentially nothing, and that lagged disposable income – whether a single lag or an extended distributed lag – has no statistically or economically meaningful additional predictive power, consistent with the pure hypothesis and inconsistent with both an excess-sensitivity-to-current-income account and with ad hoc, nonoptimal distributed-lag models of permanent income. However, lagged changes in an index of common stock prices do have statistically significant, if numerically modest, predictive power for consumption, formally rejecting the strictest version of the random-walk hypothesis; Hall reconciles this with a modified version of the hypothesis in which permanent income still evolves unpredictably but consumption adjusts to it with a brief lag, since stock prices are themselves close to a random walk and so a plausible proxy for genuinely new information about permanent income. The paper concludes that, under the (modified) hypothesis, forecasting future consumption from anything beyond its own recent trend is of little value, and that stabilization policy affects consumption only to the extent, and with the timing, that it changes households’ assessment of their permanent income.

Robert E. Hall | Macro Paper Warehouse

Stochastic Implications of the Life Cycle-Permanent Income Hypothesis: Theory and Evidence