Almost sure convergence to zero in stochastic growth models


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 is, and the smaller the maximum average product of capital is.

Keywords and Phrases: Stochastic growth; Inada condition; Convergence to zero; Extinction

JEL Classifcation Numbers: C61, C62, E30, O41

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