Stochastic growth, conservation of capital and convergence to a positive steady state

Tapan Mitra and Santanu Roy

Economic Theory, 2023, vol. 76, issue 1, No 9, 351 pages

Abstract: 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.

Keywords: Stochastic growth; Conservation; Extinction; Positive steady state; Global stability; Risk aversion (search for similar items in EconPapers)
JEL-codes: C6 D9 O41 (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s00199-022-01461-1

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