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An Equilibrium Theory of Declining Reservation Wages and Learning

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Author Info
Francisco M. Gonzalez
Shouyong Shi

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Abstract

In this paper we consider learning from search as a mechanism to understand the relationship between unemployment duration and search outcomes as a labor market equilibrium. We rely on the assumption that workers do not have precise knowledge of their job finding probabilities and therefore, learn about them from their search histories. Embedding this assumption in a model of the labor market with directed search, we provide an equilibrium theory of declining reservation wages over unemployment spells. After each period of search, unemployed workers update their beliefs about the market matching efficiency. We characterize situations where reservation wages decline with unemployment duration. Consequently, the wage distribution is non-degenerate, despite the facts that matches are homogeneous and search is directed. Moreover, aggregate matching probability decreases with unemployment duration, in contrast to individual workers' matching probability, which increases over individual unemployment spells. The difficulty in establishing these results is that learning generates non-differentiable value functions and multiple solutions to a worker's optimization problem. We overcome this difficulty by exploiting a connection between convexity of a worker's value function and the property of supermodularity.

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Paper provided by University of Toronto, Department of Economics in its series Working Papers with number tecipa-292.

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Length: 38 pages
Date of creation: 25 Jun 2007
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Handle: RePEc:tor:tecipa:tecipa-292

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Related research
Keywords: Reservation wages Learning Directed search Supermodularity

Other versions of this item:

Find related papers by JEL classification:
E24 - Macroeconomics and Monetary Economics - - Macroeconomics: Consumption, Saving, Production, Employment, and Investment - - - Employment; Unemployment; Wages; Intergenerational Income Distribution
D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search, Learning, and Information
J64 - Labor and Demographic Economics - - Mobility, Unemployment, and Vacancies - - - Unemployment: Models, Duration, Incidence, and Job Search

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  1. Kenneth Burdett & Shouyong Shi & Randall Wright, 2001. "Pricing and Matching with Frictions," Journal of Political Economy, University of Chicago Press, vol. 109(5), pages 1060-1085, October. [Downloadable!] (restricted)
  2. Burdett, Kenneth & Judd, Kenneth L, 1983. "Equilibrium Price Dispersion," Econometrica, Econometric Society, vol. 51(4), pages 955-69, July. [Downloadable!] (restricted)
  3. Burdett, Kenneth & Vishwanath, Tara, 1988. "Declining Reservation Wages and Learning," Review of Economic Studies, Blackwell Publishing, vol. 55(4), pages 655-65, October. [Downloadable!] (restricted)
  4. Lazear, Edward P, 1976. "Age, Experience, and Wage Growth," American Economic Review, American Economic Association, vol. 66(4), pages 548-58, September. [Downloadable!] (restricted)
    Other versions:
  5. Darity, William A, Jr & Goldsmith, Arthur H, 1996. "Social Psychology, Unemployment and Macroeconomics," Journal of Economic Perspectives, American Economic Association, vol. 10(1), pages 121-40, Winter. [Downloadable!] (restricted)
  6. Shouyong Shi, 2006. "Directed Search for Equilibrium Wage-Tenure Contracts," Working Papers tecipa-260, University of Toronto, Department of Economics. [Downloadable!]
  7. Blanchard, Olivier Jean & Diamond, Peter A, 1994. "Ranking, Unemployment Duration, and Wages," Review of Economic Studies, Blackwell Publishing, vol. 61(3), pages 417-34, July. [Downloadable!] (restricted)
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  8. Daron Acemoglu & Robert Shimer, 1999. "Efficient Unemployment Insurance," Journal of Political Economy, University of Chicago Press, vol. 107(5), pages 893-928, October. [Downloadable!] (restricted)
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  9. Peters, Michael, 1984. "Bertrand Equilibrium with Capacity Constraints and Restricted Mobility," Econometrica, Econometric Society, vol. 52(5), pages 1117-27, September. [Downloadable!] (restricted)
  10. Peters, Michael, 1991. "Ex Ante Price Offers in Matching Games Non-steady States," Econometrica, Econometric Society, vol. 59(5), pages 1425-54, September. [Downloadable!] (restricted)
  11. Moen, Espen R, 1997. "Competitive Search Equilibrium," Journal of Political Economy, University of Chicago Press, vol. 105(2), pages 385-411, April.
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  12. Santos, Manuel S, 1991. "Smoothness of the Policy Function in Discrete Time Economic Models," Econometrica, Econometric Society, vol. 59(5), pages 1365-82, September. [Downloadable!] (restricted)
  13. Amir, Rabah & Mirman, Leonard J & Perkins, William R, 1991. "One-Sector Nonclassical Optimal Growth: Optimality Conditions and Comparative Dynamics," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 32(3), pages 625-44, August. [Downloadable!] (restricted)
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  16. Amir, Rabah, 1996. "Sensitivity analysis of multisector optimal economic dynamics," Journal of Mathematical Economics, Elsevier, vol. 25(1), pages 123-141. [Downloadable!] (restricted)
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  17. Shi, Shouyong, 2001. "Frictional Assignment. I. Efficiency," Journal of Economic Theory, Elsevier, vol. 98(2), pages 232-260, June. [Downloadable!] (restricted)
  18. Ham, John C & LaLonde, Robert J, 1996. "The Effect of Sample Selection and Initial Conditions in Duration Models: Evidence from Experimental Data on Training," Econometrica, Econometric Society, vol. 64(1), pages 175-205, January. [Downloadable!] (restricted)
  19. Milgrom, P. & Shannon, C., 1991. "Monotone Comparative Statics," Papers 11, Stanford - Institute for Thoretical Economics.
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  20. Butters, Gerard R, 1977. "Equilibrium Distributions of Sales and Advertising Prices," Review of Economic Studies, Blackwell Publishing, vol. 44(3), pages 465-91, October. [Downloadable!] (restricted)
  21. 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.
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