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Ergodic chaos and aggregate stability: A deterministic discrete-choice model of wealth distribution dynamics

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  • Takashi Kamihigashi

Abstract

This paper studies wealth distribution dynamics in a small open economy with a continuum of consumers indexed by initial wealth. Each of them solves a discrete-choice problem whose optimal policy function exhibits ergodic chaos. We show that for any initial distribu- tion of wealth given by a density, the wealth distribution converges to a unique invariant distribution, and aggregate wealth converges to the corresponding value. Thus ergodic chaos leads to aggregate stability rather than instability. These results are illustrated with various nu- merical examples.
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  • Takashi Kamihigashi, 2013. "Ergodic chaos and aggregate stability: A deterministic discrete-choice model of wealth distribution dynamics," International Journal of Economic Theory, The International Society for Economic Theory, vol. 9(1), pages 45-56, March.
    • Handle: RePEc:bla:ijethy:v:9:y:2013:i:1:p:45-56
    DOI: 10.1111/j.1742-7363.2013.12007.x
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    1. Kamihigashi, Takashi, 2012. "Discrete Choice And Complex Dynamics In Deterministic Optimization Problems," Macroeconomic Dynamics, Cambridge University Press, vol. 16(S1), pages 52-69, April.
    2. Rose-Anne Dana & Cuong Le Van & Tapan Mitra & Kazuo Nishimura, 2006. "Handbook on optimal growth (volume 1)," Post-Print halshs-00101345, HAL.
    3. Takashi Kamihigashi, 2008. "On the principle of optimality for nonstationary deterministic dynamic programming," International Journal of Economic Theory, The International Society for Economic Theory, vol. 4(4), pages 519-525, December.
    4. Eric W. Bond & Kazumichi Iwasa & Kazuo Nishimura, 2012. "The dynamic Heckscher–Ohlin model: A diagrammatic analysis," International Journal of Economic Theory, The International Society for Economic Theory, vol. 8(2), pages 197-211, June.
    5. Takashi Kamihigashi, 2000. "The Policy Function of a Discrete-Choice Problem is a Random Number Generator," The Japanese Economic Review, Japanese Economic Association, vol. 51(1), pages 51-71, March.
    6. Takashi Kamihigashi, 2000. "Indivisible labor implies chaos," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 15(3), pages 585-598.
    7. Nishimura, Kazuo & Sorger, Gerhard & Yano, Makoto, 1994. "Ergodic Chaos in Optimal Growth Models with Low Discount Rates," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(5), pages 705-717, August.
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    More about this item

    JEL classification:

    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution

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