Almost Sure Convergence to Zero in Stochastic Growth Models

This paper shows that in stochastic one-sector growth models, if the production function does not satisfy the Inada condition at zero, any feasible path converges to zero with probability one provided that the shocks are sufficiently volatile. This result seems significant since, as we argue, the Inada condition at zero is difficult to justify on economic grounds. Our convergence result is extended to the case of a nonconcave production function. The generalized result applies to a wide range of stochastic growth models, including stochastic endogenous growth models, overlapping generations models, and models with nonconcave production functions.