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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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    1. Matthias Birkner & Niklas Scheuer & Klaus Wälde, 2023. "The dynamics of Pareto distributed wealth in a small open economy," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(2), pages 607-644, August.
    2. Khieu, Hoang & Wälde, Klaus, 2023. "Capital income risk and the dynamics of the wealth distribution," Economic Modelling, Elsevier, vol. 122(C).
    3. Yves Achdou & Jiequn Han & Jean-Michel Lasry & Pierre-Louis Lionse & Benjamin Moll, 2022. "Income and Wealth Distribution in Macroeconomics: A Continuous-Time Approach," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 89(1), pages 45-86.
    4. Donsimoni Jean Roch & Glawion René & Plachter Bodo & Wälde Klaus, 2020. "Projecting the spread of COVID-19 for Germany," German Economic Review, De Gruyter, vol. 21(2), pages 181-216, June.
    5. Nguyen, Hien Phuc & Khieu, Hoang, 2021. "Progressive wealth tax: An inquiry into Biden’s tax policy," Economic Analysis and Policy, Elsevier, vol. 72(C), pages 735-742.
    6. Achdou, Yves & Han, Jiequn & Lasry, Jean Michel & Lions, Pierre Louis & Moll, Ben, 2022. "Income and wealth distribution in macroeconomics: a continuous-time approach," LSE Research Online Documents on Economics 107422, London School of Economics and Political Science, LSE Library.
    7. Andrea Modena & Luca Regis, 2024. "Capital risk, fiscal policy, and the distribution of wealth," Mathematics and Financial Economics, Springer, volume 18, number 8, October.
    8. Hoang Khieu, 2024. "On the distribution of lifetime wealth accumulation," Journal of Economics, Springer, vol. 143(1), pages 87-100, September.

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    More about this item

    Keywords

    uncertainty in continuous time; counting process; existence; uniqueness; stability;
    All these keywords.

    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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