Information Shocks and Precautionary Saving

Skinner’s (1988) second-order approximation to the consumption function under CRRA utility is generalized to accomodate any structure of uninsurable income risk. To second order` the expected rate of consumption growth depends on higher moments only through the currently perceived variance of the expected present value of future income. This approximation reveals that precautionary saving is a decreasing function of both the time preceding an income shock and the time remaining in the consumer’s lifespan after information shocks about this income shock. Since these effects oppose each other` the timing of shocks has an ambiguous effect on precautionary saving. 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.