Inspecting the Mechanism Exactly: A Closed-form Solution to a Stochastic Growth Model

Abstract

This paper considers the canonical stochastic growth model with CRRA utility and Cobb-Douglas technology. It obtains a closed-form solution for the case where capital's share is equal to the reciprocal of the intertemporal elasticity of substitution. This provides a useful benchmark that illuminates the transmission mechanism under uncertainty. In particular, it highlights the complicated ways in which risk and nonlinearities interact, via Jensen's inequality, to affect the steady state capital stock.