Almost sure convergence to zero in stochastic growth models

Abstract

This paper considers the resource constraint commonly used in stochastic one-sector growth models. Shocks are not required to be i.i.d. It is shown that any feasible path converges to zero exponentially fast almost surely under a certain condition. In the case of multiplicative shocks, the condition means that the shocks are sufficiently volatile. Convergence is faster the larger their volatility, and the smaller the maximum average product of capital.