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Dynamic contracting with persistent shocks

Author

Listed:
  • 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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    1. Battaglini, Marco & Coate, Stephen, 2008. "Pareto efficient income taxation with stochastic abilities," Journal of Public Economics, Elsevier, vol. 92(3-4), pages 844-868, April.
    2. 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.
    3. V. V. Chari & Patrick J. Kehoe & Ellen R. McGrattan, 2000. "Sticky Price Models of the Business Cycle: Can the Contract Multiplier Solve the Persistence Problem?," Econometrica, Econometric Society, vol. 68(5), pages 1151-1180, September.
    4. Klaus Walde, 2008. "Applied Intertemporal Optimization," Books, Business School - Economics, University of Glasgow, number econ1.
    5. Stefania Albanesi & Christopher Sleet, 2006. "Dynamic Optimal Taxation with Private Information," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 73(1), pages 1-30.
    6. Narayana R. Kocherlakota, 2005. "Zero Expected Wealth Taxes: A Mirrlees Approach to Dynamic Optimal Taxation," Econometrica, Econometric Society, vol. 73(5), pages 1587-1621, September.
    7. Mikhail Golosov & Narayana Kocherlakota & Aleh Tsyvinski, 2003. "Optimal Indirect and Capital Taxation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 70(3), pages 569-587.
    8. 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.
    9. Emmanuel Farhi & Iván Werning, 2007. "Inequality and Social Discounting," Journal of Political Economy, University of Chicago Press, vol. 115(3), pages 365-402.
    10. 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.
    11. Noah Williams, 2004. "On Dynamic Principal-Agent Problems in Continuous Time," Levine's Bibliography 122247000000000426, UCLA Department of Economics.
    12. Noah Williams, 2011. "Persistent Private Information," Econometrica, Econometric Society, vol. 79(4), pages 1233-1275, July.
    13. Holmstrom, Bengt & Milgrom, Paul, 1987. "Aggregation and Linearity in the Provision of Intertemporal Incentives," Econometrica, Econometric Society, vol. 55(2), pages 303-328, March.
    14. Yuzhe Zhang, 2005. "Dynamic contracting, persistent shocks and optimal taxation," Working Papers 640, Federal Reserve Bank of Minneapolis.
    15. Andrew Atkeson & Robert E. Lucas, 1992. "On Efficient Distribution With Private Information," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 59(3), pages 427-453.
    16. Mikhail Golosov & Aleh Tsyvinski, 2007. "Optimal Taxation with Endogenous Insurance Markets," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 122(2), pages 487-534.
    17. Stefania Albanesi, 2006. "optimal taxation of entrepreneurial capital with private information," 2006 Meeting Papers 310, Society for Economic Dynamics.
    18. 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.
    19. Abreu, Dilip & Pearce, David & Stacchetti, Ennio, 1990. "Toward a Theory of Discounted Repeated Games with Imperfect Monitoring," Econometrica, Econometric Society, vol. 58(5), pages 1041-1063, September.
    20. Yuliy Sannikov, 2007. "Games with Imperfectly Observable Actions in Continuous Time," Econometrica, Econometric Society, vol. 75(5), pages 1285-1329, September.
    21. 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.
    22. Marek Kapicka, 2013. "Efficient Allocations in Dynamic Private Information Economies with Persistent Shocks: A First-Order Approach," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 80(3), pages 1027-1054.
    23. 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.
    24. Yuliy Sannikov, 2008. "A Continuous-Time Version of the Principal-Agent Problem," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 75(3), pages 957-984.
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    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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