Mason, Robin and Wright, Stephen
The effects of uncertainty on optimal consumption.
Journal of Economic Dynamics and Control, 25, (1-2), . (doi:10.1016/S0165-1889(99)00073-1).
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When marginal utility is convex and there is pure labour income uncertainty, certain results are well-known. Asset return uncertainty is often assumed to have qualitatively similar effects; see e.g. Skinner (1988. Journal of Monetary Economics 22, 237–255). 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 profile. 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.
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