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Is There a Golden Rule for the Stochastic Solow Growth Model ?

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  • Klaus Reiner Schenk-Hoppé

Abstract

This paper analyzes the dependence of average consumption on the saving rate in a one-sector neoclassical Solow growth model with pro-duction shocks and stochastic rates of population growth and depreciation where arbitrary ergodic processes are considered. We show that the long-run behavior of the stochastic capital intensity, and hence average consumption along any sample-path, is uniquely determined by a random fixed point which depends continuously on the saving rate. This result enables us to prove the existence of a golden rule saving rate which maximizes average consumption per capita. We also show that the golden rule path is dynamically efficient. The results are illustrated numerically for Cobb–Douglas and CES production function.

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Paper provided by Institute for Empirical Research in Economics - University of Zurich in its series IEW - Working Papers with number 033.

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Handle: RePEc:zur:iewwpx:033

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Keywords: Stochastic Solow model; golden rule; random fixed points; random dynamical systems;

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  1. Mirman, Leonard J, 1972. "On the Existence of Steady State Measures for One Sector Growth Models with Uncertain Technology," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 13(2), pages 271-86, June.
  2. Mirman, Leonard J., 1973. "The steady state behavior of a class of one sector growth models with uncertain technology," Journal of Economic Theory, Elsevier, vol. 6(3), pages 219-242, June.
  3. Robert J. Barro, 1995. "Inflation and Economic Growth," NBER Working Papers 5326, National Bureau of Economic Research, Inc.
  4. Ambler, Steve & Paquet, Alain, 1994. "Stochastic Depreciation and the Business Cycle," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(1), pages 101-16, February.
  5. Steve Ambler & Alain Paquet, 1992. "Stochastic Depreciation and the Business Cycle Puzzle," Cahiers de recherche CREFE / CREFE Working Papers 8, CREFE, Université du Québec à Montréal.
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