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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

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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Keywords: Persistent Information; Principal-agent Problem; Private Information; Optimal Taxation;

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References

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  1. Narayana R. Kocherlakota, 2005. "Zero Expected Wealth Taxes: A Mirrlees Approach to Dynamic Optimal Taxation," Econometrica, Econometric Society, vol. 73(5), pages 1587-1621, 09.
  2. 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.
  3. 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.
  4. 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.
  5. Fernandes, Ana & Phelan, Christopher, 2000. "A Recursive Formulation for Repeated Agency with History Dependence," Journal of Economic Theory, Elsevier, vol. 91(2), pages 223-247, April.
  6. Noah Williams, 2008. "Persistent Private Information," NBER Working Papers 13894, National Bureau of Economic Research, Inc.
  7. Stefania Albanesi, 2006. "Optimal Taxation of Entrepreneurial Capital with Private Information," NBER Working Papers 12419, National Bureau of Economic Research, Inc.
  8. Tsyvinski, A. & Golosov, M., 2004. "Optimal Taxation with Endogenous Insurance Markets," 2004 Meeting Papers 124, Society for Economic Dynamics.
  9. Werning, Ivan & Farhi, Emmanuel, 2007. "Inequality and Social Discounting," Scholarly Articles 3451391, Harvard University Department of Economics.
  10. Noah Williams, 2004. "On Dynamic Principal-Agent Problems in Continuous Time," Levine's Bibliography 122247000000000426, UCLA Department of Economics.
  11. 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.
  12. Albanesi, Stefania & Sleet, Christopher, 2003. "Dynamic Optimal Taxation with Private Information," CEPR Discussion Papers 4006, C.E.P.R. Discussion Papers.
  13. Klaus Walde, 2008. "Applied Intertemporal Optimization," Books, Business School - Economics, University of Glasgow, number econ1, December.
  14. 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.
  15. 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.
  16. Yuliy Sannikov, 2007. "Games with Imperfectly Observable Actions in Continuous Time," Econometrica, Econometric Society, vol. 75(5), pages 1285-1329, 09.
  17. Fudenberg, Drew & Holmstrom, Bengt & Milgrom, Paul, 1990. "Short-term contracts and long-term agency relationships," Journal of Economic Theory, Elsevier, vol. 51(1), pages 1-31, June.
  18. 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.
  19. Yuzhe Zhang, 2005. "Dynamic contracting, persistent shocks and optimal taxation," Working Papers 640, Federal Reserve Bank of Minneapolis.
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Cited by:
  1. Noah Williams, 2008. "Persistent Private Information," NBER Working Papers 13894, National Bureau of Economic Research, Inc.
  2. Grochulski, Borys & Zhang, Yuzhe, 2011. "Optimal risk sharing and borrowing constraints in a continuous-time model with limited commitment," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2356-2388.
  3. 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.
  4. George-Marios Angeletos & Alessandro Pavan, 2007. "Socially Optimal Coordination: Characterization and Policy Implications," Journal of the European Economic Association, MIT Press, vol. 5(2-3), pages 585-593, 04-05.
  5. Jianfeng Yu & Bin Wei & Zhiguo He, 2012. "Optimal Long-term Contracting with Learning," 2012 Meeting Papers 221, Society for Economic Dynamics.
  6. Marco LiCalzi & Alessandro Pavan, 2003. "Tilting the Supply Schedule to Enhance Competition in Uniform-Price Auctions," Working Papers 2003.22, Fondazione Eni Enrico Mattei.
  7. 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.
  8. Ravikumar, B. & Zhang, Yuzhe, 2010. "Optimal Auditing in a Dynamic Model of Tax Compliance," MPRA Paper 23218, 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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