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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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File URL: https://mpra.ub.uni-muenchen.de/23108/1/MPRA_paper_23108.pdf
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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 23108.

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Date of creation: 2009
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Publication status: Published in Journal of Economic Theory 2.144(2009): pp. 635-675
Handle: RePEc:pra:mprapa:23108
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Web page: https://mpra.ub.uni-muenchen.de

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  1. Schattler Heinz & Sung Jaeyoung, 1993. "The First-Order Approach to the Continuous-Time Principal-Agent Problem with Exponential Utility," Journal of Economic Theory, Elsevier, vol. 61(2), pages 331-371, December.
  2. V. V. Chari & Patrick J. Kehoe & Ellen R. McGrattan, 1998. "Sticky price models of the business cycle: can the contract multiplier solve the persistence problem?," Staff Report 217, Federal Reserve Bank of Minneapolis.
  3. Mikhail Golosov & Narayana Kocherlakota & Aleh Tsyvinski, 2003. "Optimal Indirect and Capital Taxation," Review of Economic Studies, Wiley Blackwell, vol. 70(3), pages 569-587, 07.
  4. Tsyvinski, A. & Golosov, M., 2004. "Optimal Taxation with Endogenous Insurance Markets," 2004 Meeting Papers 124, Society for Economic Dynamics.
  5. Yuliy Sannikov, 2007. "Games with Imperfectly Observable Actions in Continuous Time," Econometrica, Econometric Society, vol. 75(5), pages 1285-1329, 09.
  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.
  7. Emmanuel Farhi & Iván Werning, 2007. "Inequality and Social Discounting," Journal of Political Economy, University of Chicago Press, vol. 115, pages 365-402.
  8. Narayana Kocherlakota, 2004. "Zero Expected Wealth Taxes: A Mirrlees Approach to Dynamic Optimal Taxation," Levine's Bibliography 122247000000000729, UCLA Department of Economics.
  9. Stefania Albanesi & Christopher Sleet, 2004. "Dynamic optimal taxation with private information," Discussion Paper / Institute for Empirical Macroeconomics 140, Federal Reserve Bank of Minneapolis.
  10. Yuzhe Zhang, 2005. "Dynamic contracting, persistent shocks and optimal taxation," Working Papers 640, Federal Reserve Bank of Minneapolis.
  11. Klaus Walde, 2008. "Applied Intertemporal Optimization," Books, Business School - Economics, University of Glasgow, number econ1, December.
  12. Stefania Albanesi, 2006. "Optimal Taxation of Entrepreneurial Capital with Private Information," NBER Working Papers 12419, National Bureau of Economic Research, Inc.
  13. Drew Fudenberg & Bengt Holmstrom & Paul Milgrom, 1987. "Short-Term Contracts and Long-Term Agency Relationships," Working papers 468, Massachusetts Institute of Technology (MIT), Department of Economics.
  14. Mikhail Golosov & Aleh Tsyvinski, 2006. "Designing Optimal Disability Insurance: A Case for Asset Testing," Journal of Political Economy, University of Chicago Press, vol. 114(2), pages 257-279, April.
  15. Noah Williams, 2011. "Persistent Private Information," Econometrica, Econometric Society, vol. 79(4), pages 1233-1275, 07.
  16. 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.
  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. Noah Williams, 2004. "On Dynamic Principal-Agent Problems in Continuous Time," Levine's Bibliography 122247000000000426, UCLA Department of Economics.
  19. Ana Fernandes & Christopher Phelan, 1999. "A recursive formulation for repeated agency with history dependence," Staff Report 259, Federal Reserve Bank of Minneapolis.
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