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- Title
Stochastic growth, conservation of capital and convergence to a positive steady state.
- Authors
Mitra, Tapan; Roy, Santanu
- Abstract
In a general one-sector model of optimal stochastic growth where the productivity of capital is bounded but may vary widely due to technology shocks, we derive a tight estimate of the slope of the optimal policy function near zero. We use this to derive a readily verifiable condition that ensures almost sure global conservation of capital (i.e., avoidance of extinction) under the optimal policy, as well as global convergence to a positive stochastic steady state for bounded growth technology; this condition is significantly weaker than existing conditions and explicitly depends on risk aversion. For a specific class of utility and production functions, a strict violation of this condition implies that almost sure long run extinction of capital is globally optimal. Conservation is non-monotonic in risk aversion; conservation is likely to be optimal when the degree of risk aversion (near zero) is either high or low, while extinction may be optimal at intermediate levels of risk aversion.
- Subjects
CAPITAL productivity; RISK aversion; STOCHASTIC convergence; UTILITY functions; STOCHASTIC models; ECONOMIC convergence
- Publication
Economic Theory, 2023, Vol 76, Issue 1, p311
- ISSN
0938-2259
- Publication type
Article
- DOI
10.1007/s00199-022-01461-1