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Dynamic contracting with persistent shocks

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  • Zhang, Yuzhe

Abstract

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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Bibliographic Info

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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Web page: http://www.elsevier.com/locate/inca/622869

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Keywords: Persistence Principal-agent problem Stochastic control problem Efficiency lines;

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References

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  1. 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.
  2. Mikhail Golosov & Narayana Kocherlakota & Aleh Tsyvinski, 2002. "Optimal Indirect and Capital Taxation," Levine's Working Paper Archive 391749000000000449, David K. Levine.
  3. Narayana Kocherlakota, 2004. "Zero Expected Wealth Taxes: A Mirrlees Approach to Dynamic Optimal Taxation," Levine's Bibliography 122247000000000729, UCLA Department of Economics.
  4. Mikhail Golosov & Aleh Tsyvinski, 2006. "Optimal Taxation with Endogenous Insurance Markets," Levine's Bibliography 784828000000000445, UCLA Department of Economics.
  5. 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.
  6. Stefania Albanesi, 2006. "optimal taxation of entrepreneurial capital with private information," 2006 Meeting Papers 310, Society for Economic Dynamics.
  7. Klaus Walde, 2008. "Applied Intertemporal Optimization," Books, Business School - Economics, University of Glasgow, number econ1, December.
  8. 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.
  9. Yuzhe Zhang, 2005. "Dynamic contracting, persistent shocks and optimal taxation," Working Papers 640, Federal Reserve Bank of Minneapolis.
  10. 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.
  11. 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.
  12. 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.
  13. Emmanuel Farhi & Iván Werning, 2007. "Inequality and Social Discounting," Journal of Political Economy, University of Chicago Press, vol. 115, pages 365-402.
  14. Stefania Albanesi & Christopher Sleet, 2006. "Dynamic Optimal Taxation with Private Information," Review of Economic Studies, Oxford University Press, vol. 73(1), pages 1-30.
  15. Ana Fernandes & Christopher Phelan, 1999. "A recursive formulation for repeated agency with history dependence," Staff Report 259, Federal Reserve Bank of Minneapolis.
  16. 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.
  17. Yuliy Sannikov, 2007. "Games with Imperfectly Observable Actions in Continuous Time," Econometrica, Econometric Society, vol. 75(5), pages 1285-1329, 09.
  18. Noah Williams, 2007. "Persistent Private Information," 2007 Meeting Papers 158, Society for Economic Dynamics.
  19. Noah Williams, 2004. "On Dynamic Principal-Agent Problems in Continuous Time," Levine's Bibliography 122247000000000426, UCLA Department of Economics.
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Citations

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Cited by:
  1. Noah Williams, 2008. "Persistent Private Information," NBER Working Papers 13894, National Bureau of Economic Research, Inc.
  2. Daniel Garrett & Alessandro Pavan, 2009. "Dynamic Managerial Compensation: a Mechanism Design Approach," Discussion Papers 1491, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  3. George-Marios Angeletos & Alessandro Pavan, 2006. "Socially Optimal Coordination: Characterization and Policy Implications," Discussion Papers 1496, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  4. B. Ravikumar & Yuzhe Zhang, 2011. "Optimal auditing and insurance in a dynamic model of tax compliance," Working Papers 2011-020, Federal Reserve Bank of St. Louis.
  5. Marco LiCalz & Alessandro Pavan, 2002. "Tilting the Supply Schedule to Enhance Competition on Uniform-Price Auctions," Discussion Papers 1495, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  6. Jianfeng Yu & Bin Wei & Zhiguo He, 2012. "Optimal Long-term Contracting with Learning," 2012 Meeting Papers 221, Society for Economic Dynamics.
  7. Grochulskiy, Borys & Zhang, Yuzhe, 2011. "Optimal risk sharing and borrowing constraints in a continuous-time model with limited commitment," MPRA Paper 36539, University Library of Munich, Germany.
  8. Ravikumar, B & Zhang, Yuzhe, 2010. "Optimal auditing in a dynamic model of tax compliance," MPRA Paper 22924, University Library of Munich, Germany.
  9. David L. Fuller & B. Ravikumar & Yuzhe Zhang, 2012. "Unemployment insurance fraud and optimal monitoring," Working Papers 2012-024, Federal Reserve Bank of St. Louis.
  10. Grochulski, Borys & Zhang, Yuzhe, 2009. "Borrowing Constraint as an Optimal Contract," MPRA Paper 23216, University Library of Munich, Germany.

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