Note on positive lower bound of capital in the stochastic growth model |
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Authors: | Partha Chatterjee Malik Shukayev |
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Affiliation: | aNUS Business School, National University of Singapore, BIZ 1 Building, 1 Business Link, Singapore 117592, Singapore;bResearch Department, Bank of Canada, 5th Floor, West Tower, 234 Wellington Street, Ottawa, Ont., Canada, K1A0G9 |
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Abstract: | In the context of the classical stochastic growth model, we provide a simple proof that the optimal capital sequence is strictly bounded away from zero whenever the initial capital is strictly positive. We assume that the utility function is bounded below and the shocks affecting output are bounded. However, the proof does not require an interval shock space, thus, admitting both discrete and continuous shocks. Further, we allow for finite marginal product at zero capital. Finally, we use our result to show that any optimal capital sequence converges globally to a unique invariant distribution, which is bounded away from zero. |
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Keywords: | Stochastic growth theory Stochastic dynamic programming Stationary distributions |
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