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

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  • Klaus Reiner Schenk-Hopp�

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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  • Klaus Reiner Schenk-Hopp�, "undated". "Is There a Golden Rule for the Stochastic Solow Growth Model ?," IEW - Working Papers 033, Institute for Empirical Research in Economics - University of Zurich.
    • Handle: RePEc:zur:iewwpx:033
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    1. Robert J. Barro, 2013. "Inflation and Economic Growth," Annals of Economics and Finance, Society for AEF, vol. 14(1), pages 121-144, May.
    2. Robert M. Solow, 1956. "A Contribution to the Theory of Economic Growth," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 70(1), pages 65-94.
    3. 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 101-116, February.
    4. 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.
    5. 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 271-286, June.
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    Cited by:

    1. Cuong Van & John Stachurski, 2007. "Parametric continuity of stationary distributions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 33(2), pages 333-348, November.
    2. Darong Dai, 2014. "A Golden Formula in Neoclassical-Growth Models with Brownian-Motion Shocks," Scottish Journal of Political Economy, Scottish Economic Society, vol. 61(2), pages 211-228, May.
    3. Schenk-Hoppe, Klaus Reiner, 2005. "Poverty traps and business cycles in a stochastic overlapping generations economy with S-shaped law of motion," Journal of Macroeconomics, Elsevier, vol. 27(2), pages 275-288, June.

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    More about this item

    Keywords

    Stochastic Solow model; golden rule; random fixed points; random dynamical systems;
    All these keywords.

    JEL classification:

    • E13 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Neoclassical
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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