Stochastic Growth with Short-run Prediction of Shocks

We study a one sector stochastic growth model with independent and identically dis- tributed shocks where agents acquire information that enables them to accurately predict next period's productivity shock (but not shocks in later periods). Optimal policy de- pends on the forthcoming shock. We derive conditions under which a more productive realization of the forthcoming shock increases or decreases current investment; relative risk aversion and the elasticity of marginal product play important roles in these condi- tions. A better shock always increases next period's optimal output if it increases both marginal and total product. We derive explicit solutions to the optimal policy function for three well known families of production and utility functions. Volatility of output, sensitivity of output to shocks and expected total investment may be higher or lower than in the standard stochastic growth model where no new information is acquired over time. Under restrictions similar to that used in the standard model, optimal outputs converge in distribution to a unique invariant distribution whose support is bounded away from zero; the limiting distribution may differ from that obtained in the standard model.