The Life - Cycle Precautionary Motive with Asset Return and Labour Income Uncertainty

When marginal utility is convex and there is pure labour income uncertainty, certain results are well-known: there is an upward tilt to the expected consumption time pro le; the slope of the time pro le will be independent of the current level of cash-in-hand; and the marginal propensity to consume is a nonlinear, decreasing function of current assets. Asset return uncertainty is often assumed to have qualitatively similar e ects. We show that this assumption is not correct. Asset return uncertainty gives rise to an additional term in the Euler equation, which by introducing a role for current cash-in-hand, may work in the opposite direction to the precautionary motive, leading to ambiguity in the slope of the expected consumption time pro le. It also quali es conclusions about the properties of the marginal propensity to consume. We present a linearised version of the Euler equation, and an associated closed form solution, in order to provide intuition for these results. Numerical analysis indicates that the approximation is reasonable for empirically plausible estimates of the variances of the underlying disturbances. Address for correspondence: Stephen Wright, Faculty of Economics and Politics, Austin Robinson Building, Sidgwick Avenue, Cambridge CB3 9DD, U.K.. Tel.: +44 1223 335234; fax.: +44 1223 335475; e-mail: [email protected]. Filename: PRECMOT5.tex. We are grateful to Donald Robertson for useful comments. Drafts of this paper can be found at http://www.soton.ac.uk/ ram2/papers.html.