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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.

Suggested Citation

  • Zhang, Yuzhe, 2009. "Dynamic contracting with persistent shocks," Journal of Economic Theory, Elsevier, vol. 144(2), pages 635-675, March.
  • Handle: RePEc:eee:jetheo:v:144:y:2009:i:2:p:635-675
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    Cited by:

    1. LiCalzi, Marco & Pavan, Alessandro, 2005. "Tilting the supply schedule to enhance competition in uniform-price auctions," European Economic Review, Elsevier, vol. 49(1), pages 227-250, January.
    2. Noah Williams, 2011. "Persistent Private Information," Econometrica, Econometric Society, vol. 79(4), pages 1233-1275, July.
    3. Zhiguo He & Bin Wei & Jianfeng Yu & Feng Gao, 2017. "Optimal Long-Term Contracting with Learning," Review of Financial Studies, Society for Financial Studies, vol. 30(6), pages 2006-2065.
    4. 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.
    5. Daniel Garrett & Alessandro Pavan, 2009. "Dynamic Managerial Compensation: A Mechanism Design Approach," 2009 Meeting Papers 375, Society for Economic Dynamics.
    6. Malin Arve & David Martimort, 2016. "Dynamic Procurement under Uncertainty: Optimal Design and Implications for Incomplete Contracts," American Economic Review, American Economic Association, vol. 106(11), pages 3238-3274, November.
    7. Thibaut Mastrolia & Dylan Possamai, 2015. "Moral hazard under ambiguity," Papers 1511.03616, arXiv.org, revised Oct 2016.
    8. Golosov, M. & Tsyvinski, A. & Werquin, N., 2016. "Recursive Contracts and Endogenously Incomplete Markets," Handbook of Macroeconomics, Elsevier.
    9. Garrett, Daniel F. & Pavan, Alessandro, 2015. "Dynamic managerial compensation: A variational approach," Journal of Economic Theory, Elsevier, vol. 159(PB), pages 775-818.
    10. David L. Fuller & B. Ravikumar & Yuzhe Zhang, 2015. "Unemployment Insurance Fraud and Optimal Monitoring," American Economic Journal: Macroeconomics, American Economic Association, vol. 7(2), pages 249-290, April.
    11. Brett Green & Curtis R. Taylor, 2016. "Breakthroughs, Deadlines, and Self-Reported Progress: Contracting for Multistage Projects," American Economic Review, American Economic Association, vol. 106(12), pages 3660-3699, December.
    12. Jianjun Miao & Alejandro Rivera, 2016. "Robust Contracts in Continuous Time," Econometrica, Econometric Society, vol. 84, pages 1405-1440, July.
    13. 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.
    14. Marco Battaglini & Rohit Lamba, 2012. "Optimal Dynamic Contracting," Working Papers 1431, Princeton University, Department of Economics, Econometric Research Program..
    15. Ravikumar, B. & Zhang, Yuzhe, 2010. "Optimal Auditing in a Dynamic Model of Tax Compliance," MPRA Paper 23218, University Library of Munich, Germany.
    16. Daniel F. Garrett & Alessandro Pavan, 2012. "Managerial Turnover in a Changing World," Journal of Political Economy, University of Chicago Press, vol. 120(5), pages 879-925.
    17. Grochulski, Borys & Zhang, Yuzhe, 2009. "Borrowing Constraint as an Optimal Contract," MPRA Paper 23216, University Library of Munich, Germany.
    18. Ravikumar, B. & Zhang, Yuzhe, 2012. "Optimal auditing and insurance in a dynamic model of tax compliance," Theoretical Economics, Econometric Society, vol. 7(2), May.
    19. Battaglini, Marco & Lamba, Rohit, 2015. "Optimal Dynamic Contracting: the First-Order Approach and Beyond," CEPR Discussion Papers 10956, C.E.P.R. Discussion Papers.
    20. Piskorski, Tomasz & Westerfield, Mark M., 2016. "Optimal dynamic contracts with moral hazard and costly monitoring," Journal of Economic Theory, Elsevier, vol. 166(C), pages 242-281.
    21. Xi Chen & Yu Chen & Xuhu Wan, 2018. "Delegated Project Search," Graz Economics Papers 2018-11, University of Graz, Department of Economics.
    22. Daniel Garrett & Alessandro Pavan, 2014. "Dynamic Managerial Compensation: On the Optimality of Seniority-based Schemes," Discussion Papers 1579, Northwestern University, Center for Mathematical Studies in Economics and Management Science.

    More about this item

    Keywords

    Persistence Principal-agent problem Stochastic control problem Efficiency lines;

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • E61 - Macroeconomics and Monetary Economics - - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook - - - Policy Objectives; Policy Designs and Consistency; Policy Coordination

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