IDEAS home Printed from
MyIDEAS: Login to save this paper or follow this series

Matching and Saving in Continuous Time: Theory

  • Christian Bayer
  • Klaus Wälde

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 illustrates 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 employment status. These equations also characterize the aggregate distribution of wealth and allow us to describe general equilibrium. An optimal consumption path exists and distributions converge to a unique limiting distribution.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL:
Download Restriction: no

Paper provided by CESifo Group Munich in its series CESifo Working Paper Series with number 3026.

in new window

Date of creation: 2010
Date of revision:
Handle: RePEc:ces:ceswps:_3026
Contact details of provider: Postal: Poschingerstrasse 5, 81679 Munich
Phone: +49 (89) 9224-0
Fax: +49 (89) 985369
Web page:

More information through EDIRC

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. Guo, Xin & Miao, Jianjun & Morellec, Erwan, 2005. "Irreversible investment with regime shifts," Journal of Economic Theory, Elsevier, vol. 122(1), pages 37-59, May.
  2. Christian BAYER & Klaus WALDE, 2010. "Matching and Saving in Continuous Time: Proofs," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2010014, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
  3. Huggett, Mark & Ospina, Sandra, 2001. "Aggregate precautionary savings: when is the third derivative irrelevant?," Journal of Monetary Economics, Elsevier, vol. 48(2), pages 373-396, October.
  4. Walde, Klaus, 1999. "Optimal Saving under Poisson Uncertainty," Journal of Economic Theory, Elsevier, vol. 87(1), pages 194-217, July.
  5. 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.
  6. Giuseppe Moscarini, 2005. "Job Matching and the Wage Distribution," Econometrica, Econometric Society, vol. 73(2), pages 481-516, 03.
  7. Andrey Launov & Klaus Wälde, 2010. "Estimating Incentive and Welfare Effects of Non-stationary Unemployment Benefits," SOEPpapers on Multidisciplinary Panel Data Research 328, DIW Berlin, The German Socio-Economic Panel (SOEP).
  8. Yongsung Chang & Sun-Bin Kim & Mark Bils, 2007. "Comparative Advantage in Cyclical Unemployment," 2007 Meeting Papers 508, Society for Economic Dynamics.
  9. John Hassler & José V. Rodríguez Mora & Kjetil Storesletten & Fabrizio Zilibotti, 2005. "A Positive Theory Of Geographic Mobility And Social Insurance," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 46(1), pages 263-303, 02.
  10. Dale T. Mortensen & Christopher A. Pissarides, 1993. "Job Creation and Job Destruction in the Theory of Unemployment," CEP Discussion Papers dp0110, Centre for Economic Performance, LSE.
  11. 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.
  12. Stephen Turnovsky & William Smith, 2004. "Equilibrium Consumption and Precautionary Savings in a Stochastically Growing Economy," Working Papers UWEC-2006-01-P, University of Washington, Department of Economics, revised Oct 2004.
  13. Marcet, Albert & Obiols-Homs, Francesc & Weil, Philippe, 2007. "Incomplete markets, labor supply and capital accumulation," Journal of Monetary Economics, Elsevier, vol. 54(8), pages 2621-2635, November.
  14. Per Krusell & Toshihiko Mukoyama & Ayseg ul Sahin, 2007. "Labor-Market Matching with Precautionary Savings and Aggregate Fluctuations," Levine's Bibliography 122247000000001783, UCLA Department of Economics.
  15. Hassler, John & Rodriguez Mora, Jose V., 1999. "Employment turnover and the public allocation of unemployment insurance," Journal of Public Economics, Elsevier, vol. 73(1), pages 55-83, July.
  16. Giuseppe Bertola & Luigi Guiso & Luigi Pistaferri, 2005. "Uncertainty and Consumer Durables Adjustment," Review of Economic Studies, Oxford University Press, vol. 72(4), pages 973-1007.
  17. Hassler, John & Rodríguez Mora, José V., 2008. "Unemployment insurance design: Inducing moving and retraining," European Economic Review, Elsevier, vol. 52(5), pages 757-791, July.
  18. Per Krusell & Toshihiko Mukoyama & Richard Rogerson & Aysegul Sahin, 2008. "Aggregate Implications of Indivisible Labor, Incomplete Markets, and Labor Market Frictions," NBER Working Papers 13871, National Bureau of Economic Research, Inc.
  19. Robert Shimer, 2005. "The Cyclical Behavior of Equilibrium Unemployment and Vacancies," American Economic Review, American Economic Association, vol. 95(1), pages 25-49, March.
  20. Lucas, Robert Jr. & Prescott, Edward C., 1974. "Equilibrium search and unemployment," Journal of Economic Theory, Elsevier, vol. 7(2), pages 188-209, February.
  21. 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, 07.
  22. 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.
  23. Andolfatto, David, 1996. "Business Cycles and Labor-Market Search," American Economic Review, American Economic Association, vol. 86(1), pages 112-32, March.
  24. Robert Shimer & Ivan Werning, 2006. "Reservation Wages and Unemployment Insurance," NBER Working Papers 12618, National Bureau of Economic Research, Inc.
  25. Acemoglu, D. & Shimer, R., 1997. "Efficient Unemployment Insurance," Working papers 97-9, Massachusetts Institute of Technology (MIT), Department of Economics.
  26. 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.
  27. repec:inr:wpaper:155908 is not listed on IDEAS
  28. S. Rao Aiyagari, 1993. "Uninsured idiosyncratic risk and aggregate saving," Working Papers 502, Federal Reserve Bank of Minneapolis.
  29. Mark Bils & Yongsung Chang & Sun-Bin Kim, 2008. "Heterogeneity and Cyclical Unemployment," Discussion Paper Series 0805, Institute of Economic Research, Korea University.
  30. Makoto Nakajima, 2006. "Business Cycles in the Equilibrium Model of Labor Search and Self-Insurance," Computing in Economics and Finance 2006 426, Society for Computational Economics.
  31. Jeremy Lise, 2011. "On-the-Job Search and Precautionary Savings: Theory and Empirics of Earnings and Wealth Inequality," IFS Working Papers W11/16, Institute for Fiscal Studies.
  32. Burdett, Kenneth & Mortensen, Dale T, 1998. "Wage Differentials, Employer Size, and Unemployment," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(2), pages 257-73, May.
  33. Pieter A. Gautier & Coen N. Teulings & Aico Van Vuuren, 2010. "On-the-Job Search, Mismatch and Efficiency ," Review of Economic Studies, Oxford University Press, vol. 77(1), pages 245-272.
  34. van den Berg, Gerard J, 1990. "Nonstationarity in Job Search Theory," Review of Economic Studies, Wiley Blackwell, vol. 57(2), pages 255-77, April.
  35. Toche, Patrick, 2005. "A tractable model of precautionary saving in continuous time," Economics Letters, Elsevier, vol. 87(2), pages 267-272, May.
  36. Merz, Monika, 1995. "Search in the labor market and the real business cycle," Journal of Monetary Economics, Elsevier, vol. 36(2), pages 269-300, November.
  37. Ait-Sahalia, Yacine, 2004. "Disentangling diffusion from jumps," Journal of Financial Economics, Elsevier, vol. 74(3), pages 487-528, December.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:ces:ceswps:_3026. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Julio Saavedra)

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

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

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.