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Matching and Saving in Continuous Time: Theory

Author

Listed:
  • Christian Bayer

    (Institute of Mathematics, Technische Universität Berlin, Germany)

  • Klaus Wälde

    (Chair in Macroeconomics, Johannes Gutenberg-Universität Mainz, Germany)

Abstract

We analyse optimal saving of risk-averse households when labour income stochastically jumps between two states. The generalized Keynes-Ramsey rule includes a precautionary savings term. A phase diagram analysis il- lustrates consumption and wealth dynamics within and between states. There is an endogenous lower and upper limit for wealth. We derive the Fokker-Planck equations for the densities of individual wealth and em- ployment status. These equations also characterize the aggregate distrib- ution of wealth and allow us to describe general equilibrium. An optimal consumption path exists and distributions converge to a unique limiting distribution.

Suggested Citation

  • Christian Bayer & Klaus Wälde, 2010. "Matching and Saving in Continuous Time: Theory," Working Papers 1004, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz, revised 13 Jan 2010.
    • Handle: RePEc:jgu:wpaper:1004
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    File URL: https://download.uni-mainz.de/RePEc/pdf/Discussion_Paper_1004.pdf
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    Citations

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    Cited by:

    1. Flórez, Luz A., 2017. "Informal sector under saving: A positive analysis of labour market policies," Labour Economics, Elsevier, vol. 44(C), pages 13-26.
    2. 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.
    3. Khieu, Hoang & Wälde, Klaus, 2023. "Capital income risk and the dynamics of the wealth distribution," Economic Modelling, Elsevier, vol. 122(C).
    4. Carlos Miguel Silva & Ana Paula Ribeiro, 2011. "The Impacts of Structural Changes in the Labor Market: a Comparative Statics Analysis Using Heterogeneous-agent Framework," CEF.UP Working Papers 1104, Universidade do Porto, Faculdade de Economia do Porto.
    5. Bayer, Christian & Rendall, Alan D. & Wälde, Klaus, 2019. "The invariant distribution of wealth and employment status in a small open economy with precautionary savings," Journal of Mathematical Economics, Elsevier, vol. 85(C), pages 17-37.
    6. Jeremy Lise, 2013. "On-the-Job Search and Precautionary Savings," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 80(3), pages 1086-1113.

    More about this item

    Keywords

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    JEL classification:

    • D91 - Microeconomics - - Micro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making
    • E24 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Employment; Unemployment; Wages; Intergenerational Income Distribution; Aggregate Human Capital; Aggregate Labor Productivity
    • J63 - Labor and Demographic Economics - - Mobility, Unemployment, Vacancies, and Immigrant Workers - - - Turnover; Vacancies; Layoffs
    • J64 - Labor and Demographic Economics - - Mobility, Unemployment, Vacancies, and Immigrant Workers - - - Unemployment: Models, Duration, Incidence, and Job Search

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