Stochastic growth with short-run prediction of shocks

Abstract

We study a variation of the one-sector stochastic optimal growth model with independent and identically distributed shocks where agents acquire information that enables them to accurately predict the next period’s productivity shock (but not shocks in later periods). Optimal policy depends on the forthcoming shock. A “better” predicted realization of the shock that increases both marginal and total product always increases next period’s optimal output. We derive conditions on the degree of relative risk aversion and the elasticity of marginal product under which optimal investment increases or decreases with a better shock. Under fairly regular restrictions, optimal outputs converge in distribution to a unique invariant distribution whose support is bounded away from zero. We derive explicit solutions to the optimal policy for three well-known families of production and utility functions and use these to show that volatility of output, sensitivity of output to shocks, and expected total investment may be higher or lower than in the standard model where no new information is acquired over time; the limiting steady state may also differ significantly from that in the standard model.