Information shocks and precautionary saving

Skinner's [1988. Risky income, life cycle consumption, and precautionary savings. Journal of Monetary Economics 22, 237-255] second-order approximation to the consumption function under CRRA utility is generalized to accommodate any structure of uninsurable income risk. To second order, a future income shock will induce precautionary saving in the present that depends on the variance of the expectation of the income shock at each intervening period. However, the expected rate of consumption growth depends only on the currently perceived variance of the expected present value of future income. In a finite-horizon model, precautionary saving produces a hump-shaped lifecycle profile of mean consumption primarily because the variance of future income decreases with age, but the lifecycle dynamics of total wealth also affect the shape of the profile. For a Markov income process with autocorrelations on the order of 0.9 or less, the second-order approximation performs surprisingly well for common parameter choices from the literature, but it does poorly as the autocorrelation approaches 1.