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Dynamic contracting with persistent shocks

  • Zhang, Yuzhe

In this paper, we develop continuous-time methods for solving dynamic principal-agent problems in which the agent's privately observed productivity shocks are persistent over time. We characterize the optimal contract as the solution to a system of ordinary differential equations and show that, under this contract, the agent's utility converges to its lower bound--immiserization occurs. Unlike under risk-neutrality, the wedge between the marginal rate of transformation and a low-productivity agent's marginal rate of substitution between consumption and leisure will not vanish permanently at her first high-productivity report; also, the wedge increases with the duration of a low-productivity report. We apply the methods to numerically solve the Mirrleesian dynamic taxation model, and find that the wedge is significantly larger than that in the independently and identically distributed (i.i.d.) shock case.

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Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 144 (2009)
Issue (Month): 2 (March)
Pages: 635-675

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Handle: RePEc:eee:jetheo:v:144:y:2009:i:2:p:635-675
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  1. Noah Williams, 2008. "Persistent Private Information," NBER Working Papers 13894, National Bureau of Economic Research, Inc.
  2. Yuzhe Zhang, 2005. "Dynamic contracting, persistent shocks and optimal taxation," Working Papers 640, Federal Reserve Bank of Minneapolis.
  3. V. V. Chari & Patrick J. Kehoe & Ellen R. McGrattan, 1996. "Sticky Price Models of the Business Cycle: Can the Contract Multiplier Solve the Persistence Problem?," NBER Working Papers 5809, National Bureau of Economic Research, Inc.
  4. Mikhail Golosov & Narayana Kocherlakota & Aleh Tsyvinski, 2002. "Optimal Indirect and Capital Taxation," Levine's Working Paper Archive 391749000000000449, David K. Levine.
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  6. Marek Kapicka, 2013. "Efficient Allocations in Dynamic Private Information Economies with Persistent Shocks: A First-Order Approach," Review of Economic Studies, Oxford University Press, vol. 80(3), pages 1027-1054.
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  9. Narayana R. Kocherlakota, 2003. "Zero Expected Wealth Taxes: A Mirrlees Approach to Dynamic Optimal Taxation," Levine's Bibliography 666156000000000426, UCLA Department of Economics.
  10. Mikhail Golosov & Aleh Tsyvinski, 2006. "Optimal Taxation with Endogenous Insurance Markets," Levine's Bibliography 784828000000000445, UCLA Department of Economics.
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  12. Werning, Ivan & Farhi, Emmanuel, 2007. "Inequality and Social Discounting," Scholarly Articles 3451391, Harvard University Department of Economics.
  13. Stefania Albanesi, 2006. "Optimal Taxation of Entrepreneurial Capital with Private Information," NBER Working Papers 12419, National Bureau of Economic Research, Inc.
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  15. Noah Williams, 2004. "On Dynamic Principal-Agent Problems in Continuous Time," Levine's Bibliography 122247000000000426, UCLA Department of Economics.
  16. Ana Fernandes & Christopher Phelan, 1999. "A recursive formulation for repeated agency with history dependence," Staff Report 259, Federal Reserve Bank of Minneapolis.
  17. Cvitanic Jaksa & Wan Xuhu & Zhang Jianfeng, 2008. "Principal-Agent Problems with Exit Options," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 8(1), pages 1-43, October.
  18. Marek Kapicka, 2006. "Optimal Income Taxation with Human Capital Accumulation and Limited Record Keeping," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 9(4), pages 612-639, October.
  19. Klaus Walde, 2008. "Applied Intertemporal Optimization," Books, Business School - Economics, University of Glasgow, number econ1.
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