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.
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I would like to thank Santanu Roy, John Stachurski, Lars J. Olson, and an anonymous referee for helpful comments and suggestions. The general result in section 2 owes much to the referee’s comments on an earlier version of this paper. Financial support from the 21 Century COE Program at GSE and RIEB, Kobe University is gratefully acknowledged.
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Kamihigashi, T. Almost sure convergence to zero in stochastic growth models. Economic Theory 29, 231–237 (2006). https://doi.org/10.1007/s00199-005-0006-1
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DOI: https://doi.org/10.1007/s00199-005-0006-1