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The Invariant Distribution of Wealth and Employment Status in a Small Open Economy with Precautionary Savings

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  • Christian Bayer
  • Alan D. Rendall
  • Klaus Wälde

Abstract

We study optimal savings in continuous time with exogenous transitions between employment and unemployment as the only source of uncertainty in a small open economy. We prove the existence of an optimal consumption path. We exploit that the dynamics of consumption and wealth between jumps can be expressed as a Fuchsian system. We derive conditions under which an invariant joint distribution for the state variables, i.e., wealth and labour market status, exists and is unique. We also provide conditions under which the distribution of these variables converges to the invariant distribution. Our analysis relies on the notion of T-processes and applies results on the stability of Markovian processes from Meyn and Tweedie (1993a, b,c).

Suggested Citation

  • Christian Bayer & Alan D. Rendall & Klaus Wälde, 2018. "The Invariant Distribution of Wealth and Employment Status in a Small Open Economy with Precautionary Savings," CESifo Working Paper Series 7397, CESifo.
    • Handle: RePEc:ces:ceswps:_7397
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    References listed on IDEAS

    as
    1. Yves Achdou & Jiequn Han & Jean-Michel Lasry & Pierre-Louis Lions & Benjamin Moll, 2017. "Income and Wealth Distribution in Macroeconomics: A Continuous-Time Approach," NBER Working Papers 23732, National Bureau of Economic Research, Inc.
    2. Shuhei Aoki & Makoto Nirei, 2016. "Pareto Distribution of Income in Neoclassical Growth Models," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 20, pages 25-42, April.
    3. Robert M. Anderson & Roberto C. Raimondo, 2008. "Equilibrium in Continuous-Time Financial Markets: Endogenously Dynamically Complete Markets," Econometrica, Econometric Society, vol. 76(4), pages 841-907, July.
    4. SeHyoun Ahn & Greg Kaplan & Benjamin Moll & Thomas Winberry & Christian Wolf, 2018. "When Inequality Matters for Macro and Macro Matters for Inequality," NBER Macroeconomics Annual, University of Chicago Press, vol. 32(1), pages 1-75.
    5. S. Rao Aiyagari, 1994. "Uninsured Idiosyncratic Risk and Aggregate Saving," The Quarterly Journal of Economics, Oxford University Press, vol. 109(3), pages 659-684.
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    More about this item

    Keywords

    uncertainty in continuous time; counting process; existence; uniqueness; stability;

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D91 - Microeconomics - - Micro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making
    • J63 - Labor and Demographic Economics - - Mobility, Unemployment, Vacancies, and Immigrant Workers - - - Turnover; Vacancies; Layoffs

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