IDEAS home Printed from https://ideas.repec.org/p/jgu/wpaper/1110.html
   My bibliography  Save this paper

Describing the Dynamics of Distributions in Search and Matching Models by Fokker-Planck Equations

Author

Listed:
  • Christian Bayer

    (Department of Mathematics, University of Vienna, Austria)

  • Klaus Waelde

    (Department of Economics, Johannes Gutenberg-Universitaet Mainz, Germany)

Abstract

The analysis of distributions is central to search and matching models. Wage distributions are a central concern but distributions of productivities, fi?rm types, human capital, entitlement to unemployment benefi?ts and wealth become increasingly important. We present a method - the Fokker-Planck equations - which allows to describe and analyse the dynamics of distributions in a very general way. We illustrate this approach by analysing optimal saving of risk-averse households in a frictional labour market. Our Fokker-Planck equations describe the evolution of the joint distribution of labour market status and wealth. A very intuitive interpretation is provided.

Suggested Citation

  • Christian Bayer & Klaus Waelde, 2011. "Describing the Dynamics of Distributions in Search and Matching Models by Fokker-Planck Equations," Working Papers 1110, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz, revised 21 Jul 2011.
    • Handle: RePEc:jgu:wpaper:1110
    as

    Download full text from publisher

    File URL: https://download.uni-mainz.de/RePEc/pdf/Discussion_Paper_1110.pdf
    File Function: First version, 2011
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Andrey Launov & Klaus Wälde, 2013. "Estimating Incentive And Welfare Effects Of Nonstationary Unemployment Benefits," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 54(4), pages 1159-1198, November.
    2. Giuseppe Bertola & Luigi Guiso & Luigi Pistaferri, 2005. "Uncertainty and Consumer Durables Adjustment," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(4), pages 973-1007.
    3. Rasmus Lentz & Torben Tranas, 2005. "Job Search and Savings: Wealth Effects and Duration Dependence," Journal of Labor Economics, University of Chicago Press, vol. 23(3), pages 467-490, July.
    4. Jeremy Lise, 2006. "On-the-Job Search and Precautionary Savings: Theory and Empirics of Earnings and Wealth Inequality," 2006 Meeting Papers 137, Society for Economic Dynamics.
    5. Rasmus Lentz, 2009. "Optimal Unemployment Insurance in an Estimated Job Search Model with Savings," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 12(1), pages 37-57, January.
    6. Pierre Cahuc & Fabien Postel-Vinay & Jean-Marc Robin, 2006. "Wage Bargaining with On-the-Job Search: Theory and Evidence," Econometrica, Econometric Society, vol. 74(2), pages 323-364, March.
    7. Samuel Bentolila & Giuseppe Bertola, 1990. "Firing Costs and Labour Demand: How Bad is Eurosclerosis?," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 57(3), pages 381-402.
    8. Yuliy Sannikov, 2007. "Games with Imperfectly Observable Actions in Continuous Time," Econometrica, Econometric Society, vol. 75(5), pages 1285-1329, September.
    9. Christopher J. Flinn, 2006. "Minimum Wage Effects on Labor Market Outcomes under Search, Matching, and Endogenous Contact Rates," Econometrica, Econometric Society, vol. 74(4), pages 1013-1062, July.
    10. Winfried Koeniger & Julien Prat, 2007. "Employment Protection, Product Market Regulation and Firm Selection," Economic Journal, Royal Economic Society, vol. 117(521), pages 302-332, June.
    11. Yuan, Chenggui & Mao, Xuerong, 2003. "Asymptotic stability in distribution of stochastic differential equations with Markovian switching," Stochastic Processes and their Applications, Elsevier, vol. 103(2), pages 277-291, February.
    12. Gerard J. van den Berg, 1990. "Nonstationarity in Job Search Theory," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 57(2), pages 255-277.
    13. Lo, Andrew W., 1988. "Maximum Likelihood Estimation of Generalized Itô Processes with Discretely Sampled Data," Econometric Theory, Cambridge University Press, vol. 4(2), pages 231-247, August.
    14. Nicolas Jacquemet & Jean-Marc Robin, 2011. "Marriage with Labor Supply," Post-Print halshs-00639313, HAL.
    15. Shouyong Shi, 2009. "Directed Search for Equilibrium Wage-Tenure Contracts," Econometrica, Econometric Society, vol. 77(2), pages 561-584, March.
    16. Leo Kaas & Philipp Kircher, 2015. "Efficient Firm Dynamics in a Frictional Labor Market," American Economic Review, American Economic Association, vol. 105(10), pages 3030-3060, October.
    17. S. Rao Aiyagari, 1994. "Uninsured Idiosyncratic Risk and Aggregate Saving," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 109(3), pages 659-684.
    18. Julien Prat, 2007. "The Impact of Disembodied Technological Progress on Unemployment," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 10(1), pages 106-125, January.
    19. Fabien Postel-Vinay & Jean-Marc Robin, 2002. "Equilibrium Wage Dispersion with Worker and Employer Heterogeneity," Econometrica, Econometric Society, vol. 70(6), pages 2295-2350, November.
    20. Robert Shimer & Iván Werning, 2007. "Reservation Wages and Unemployment Insurance," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 122(3), pages 1145-1185.
    21. Walde, Klaus, 1999. "Optimal Saving under Poisson Uncertainty," Journal of Economic Theory, Elsevier, vol. 87(1), pages 194-217, July.
    22. Per Krusell & Toshihiko Mukoyama & Ayşegül Şahin, 2010. "Labour-Market Matching with Precautionary Savings and Aggregate Fluctuations," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 77(4), pages 1477-1507.
    23. Bontemps, Christian & Robin, Jean-Marc & Van den Berg, Gerard J, 1999. "An Empirical Equilibrium Job Search Model with Search on the Job and Heterogeneous Workers and Firms," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(4), pages 1039-1074, November.
    24. Pissarides, Christopher A, 1985. "Short-run Equilibrium Dynamics of Unemployment Vacancies, and Real Wages," American Economic Review, American Economic Association, vol. 75(4), pages 676-690, September.
    25. Tor Jakob Klette & Samuel Kortum, 2004. "Innovating Firms and Aggregate Innovation," Journal of Political Economy, University of Chicago Press, vol. 112(5), pages 986-1018, October.
    26. Giuseppe Moscarini & Fabien Postel-Vinay, 2009. "The Timing of Labor Market Expansions: New Facts and a New Hypothesis," NBER Chapters, in: NBER Macroeconomics Annual 2008, Volume 23, pages 1-51, National Bureau of Economic Research, Inc.
    27. Moen, Espen R, 1997. "Competitive Search Equilibrium," Journal of Political Economy, University of Chicago Press, vol. 105(2), pages 385-411, April.
    28. Giuseppe Moscarini, 2005. "Job Matching and the Wage Distribution," Econometrica, Econometric Society, vol. 73(2), pages 481-516, March.
    29. Huggett, Mark, 1993. "The risk-free rate in heterogeneous-agent incomplete-insurance economies," Journal of Economic Dynamics and Control, Elsevier, vol. 17(5-6), pages 953-969.
    30. Jovanovic, Boyan, 1984. "Matching, Turnover, and Unemployment," Journal of Political Economy, University of Chicago Press, vol. 92(1), pages 108-122, February.
    31. Mortensen, Dale & Pissarides, Christopher, 2011. "Job Creation and Job Destruction in the Theory of Unemployment," Ekonomicheskaya Politika / Economic Policy, Russian Presidential Academy of National Economy and Public Administration, vol. 1, pages 1-19.
    32. repec:hal:spmain:info:hdl:2441/c8dmi8nm4pdjkuc9g8grh35j2 is not listed on IDEAS
    33. Toche, Patrick, 2005. "A tractable model of precautionary saving in continuous time," Economics Letters, Elsevier, vol. 87(2), pages 267-272, May.
    34. Fabien Postel-Vinay & Jean-Marc Robin, 2002. "Equilibrium Wage Dispersion with Worker and Employer Heterogeneity," Post-Print hal-03458567, HAL.
    35. Stephen J. Turnovsky, 2000. "Methods of Macroeconomic Dynamics, 2nd Edition," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262201232, December.
    36. Yuliy Sannikov & Andrzej Skrzypacz, 2010. "The Role of Information in Repeated Games With Frequent Actions," Econometrica, Econometric Society, vol. 78(3), pages 847-882, May.
    37. Acemoglu, Daron & Shimer, Robert, 1999. "Holdups and Efficiency with Search Frictions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(4), pages 827-849, November.
    38. repec:hal:spmain:info:hdl:2441/eu4vqp9ompqllr09j00420pk7 is not listed on IDEAS
    39. Fabien Postel-Vinay & Jean-Marc Robin, 2002. "Equilibrium wage dispersion with worker and employer heterogeneity," Post-Print hal-03587660, HAL.
    40. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    41. Lucas, Robert Jr. & Prescott, Edward C., 1974. "Equilibrium search and unemployment," Journal of Economic Theory, Elsevier, vol. 7(2), pages 188-209, February.
    42. repec:hal:spmain:info:hdl:2441/dc0ckec3fcb29ms985085gkbp is not listed on IDEAS
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Dinopoulos, Elias & Grieben, Wolf-Heimo & Şener, Fuat, 2023. "A Policy Conundrum: Schumpeterian Growth or Job Creation?," Economic Modelling, Elsevier, vol. 126(C).
    2. Bolle Friedel & Otto Philipp E., 2016. "Matching as a Stochastic Process," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 236(3), pages 323-348, May.
    3. Juan Carlos Parra‐Alvarez & Olaf Posch & Mu‐Chun Wang, 2023. "Estimation of Heterogeneous Agent Models: A Likelihood Approach," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 85(2), pages 304-330, April.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Christian Bayer & Klaus Wälde, 2010. "Matching and Saving in Continuous Time: Theory," CESifo Working Paper Series 3026, CESifo.
    2. Andrey Launov & Klaus Wälde, 2013. "Estimating Incentive And Welfare Effects Of Nonstationary Unemployment Benefits," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 54(4), pages 1159-1198, November.
    3. Andreas Hornstein & Per Krusell & Giovanni L. Violante, 2011. "Frictional Wage Dispersion in Search Models: A Quantitative Assessment," American Economic Review, American Economic Association, vol. 101(7), pages 2873-2898, December.
    4. Christian Bayer & Klaus Waelde, 2011. "Existence, Uniqueness and Stability of Invariant Distributions in Continuous-Time Stochastic Models," Working Papers 1111, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz, revised 21 Jul 2011.
    5. Andrey Launov & Irene Schumm & Klaus Walde, 2008. "Estimating insurance and incentive effects of labour market reforms," CDMA Conference Paper Series 0813, Centre for Dynamic Macroeconomic Analysis.
    6. Chaumont, Gaston & Shi, Shouyong, 2022. "Wealth accumulation, on-the-job search and inequality," Journal of Monetary Economics, Elsevier, vol. 128(C), pages 51-71.
    7. Burdett, Ken & Coles, Melvyn, 2010. "Wage/tenure contracts with heterogeneous firms," Journal of Economic Theory, Elsevier, vol. 145(4), pages 1408-1435, July.
    8. Violante, Giovanni & Hornstein, Andreas, 2006. "Frictional Wage Dispersion in Search Models: A Quantitative Approach," CEPR Discussion Papers 5935, C.E.P.R. Discussion Papers.
    9. Rogerson, Richard & Shimer, Robert, 2011. "Search in Macroeconomic Models of the Labor Market," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 4, chapter 7, pages Pages: 61, Elsevier.
    10. Elhanan Helpman & Oleg Itskhoki & Stephen Redding, 2010. "Inequality and Unemployment in a Global Economy," Econometrica, Econometric Society, vol. 78(4), pages 1239-1283, July.
    11. Pietro Garibaldi & Espen Moen & Dag-Einar Sommervoll, 2016. "Competitive On-the-job Search," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 19, pages 88-107, January.
    12. Leo Kaas & Philipp Kircher, 2015. "Efficient Firm Dynamics in a Frictional Labor Market," American Economic Review, American Economic Association, vol. 105(10), pages 3030-3060, October.
    13. Axel Gottfries, 2018. "Partial commitment in models of on-the-job search with an application to minimum wage spillovers," 2018 Meeting Papers 567, Society for Economic Dynamics.
    14. Moser, Christian, 2016. "How Could Wage Inequality Within and Across Enterprises be Reduced?," MPRA Paper 95381, University Library of Munich, Germany.
    15. Manning, Alan, 2011. "Imperfect Competition in the Labor Market," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 4, chapter 11, pages 973-1041, Elsevier.
    16. Christopher Flinn & James Mabli & Joseph Mullins, 2017. "Firms' Choices of Wage-Setting Protocols in the Presence of Minimum Wages," Working Papers 2017-070, Human Capital and Economic Opportunity Working Group.
    17. Giuseppe Moscarini & Fabien Postel-Vinay, 2013. "Stochastic Search Equilibrium," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 80(4), pages 1545-1581.
    18. Chéron, Arnaud & Hairault, Jean-Olivier & Langot, François, 2008. "A quantitative evaluation of payroll tax subsidies for low-wage workers: An equilibrium search approach," Journal of Public Economics, Elsevier, vol. 92(3-4), pages 817-843, April.
    19. Morchio, Iacopo & Moser, Christian, 2018. "The Gender Pay Gap: Micro Sources and Macro Consequences," MPRA Paper 99276, University Library of Munich, Germany, revised 24 Mar 2020.
    20. Guido Menzio & Irina Telyukova & Ludo Visschers, 2016. "Directed Search over the Life Cycle," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 19, pages 38-62, January.

    More about this item

    Keywords

    frictional labour markets; optimal saving; incomplete markets; Poisson uncertainty; Fokker-Planck equations; general equilibrium;
    All these keywords.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:jgu:wpaper:1110. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Research Unit IPP (email available below). General contact details of provider: https://edirc.repec.org/data/vlmaide.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.