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Optimal Contracts with Reflection

Author

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  • Yuzhe Zhang

    (Texas A&M University)

  • Borys Grochulski

    (Federal Reserve Bank of Richmond)

Abstract

In this paper, we show that whenever the agent's outside option is nonzero, the optimal contract in the continuous-time principal-agent model of Sannikov (2008) is reflective at the lower bound. This means the agent is never terminated or retired after poor performance. Instead, the agent is asked to suspend effort temporarily, as in Zhu (2013), which brings the agent's continuation value up. The agent is then asked to resume effort, and the contract continues. We show that a nonzero agent's outside option arises endogenously if the agent is allowed to quit and find a new rm. In addition, we find new dynamics of the reflection at the lower bound. In the baseline model, the reflection is slow, as in Zhu (2013), i.e., effort is suspended often. However, if the agent's disutility from the first unit of effort is zero, which is a standard Inada condition, or if his utility of consumption is unbounded below, the reflection becomes fast, i.e., effort is suspended seldom.

Suggested Citation

  • Yuzhe Zhang & Borys Grochulski, 2017. "Optimal Contracts with Reflection," 2017 Meeting Papers 544, Society for Economic Dynamics.
  • Handle: RePEc:red:sed017:544
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    References listed on IDEAS

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    1. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
    2. Markus K. Brunnermeier & Yuliy Sannikov, 2014. "A Macroeconomic Model with a Financial Sector," American Economic Review, American Economic Association, vol. 104(2), pages 379-421, February.
    3. Borys Grochulski & Yuzhe Zhang, 2017. "Marketā€Based Incentives," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 58, pages 331-382, May.
    4. Spear, Stephen E. & Wang, Cheng, 2005. "When to fire a CEO: optimal termination in dynamic contracts," Journal of Economic Theory, Elsevier, vol. 120(2), pages 239-256, February.
    5. PETER M. DeMARZO & YULIY SANNIKOV, 2006. "Optimal Security Design and Dynamic Capital Structure in a Continuous-Time Agency Model," Journal of Finance, American Finance Association, vol. 61(6), pages 2681-2724, December.
    6. Wang, Cheng & Yang, Youzhi, 2015. "Equilibrium matching and termination," Journal of Monetary Economics, Elsevier, vol. 76(C), pages 208-229.
    7. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters,in: Theory Of Valuation, chapter 5, pages 129-164 World Scientific Publishing Co. Pte. Ltd..
    8. Atkeson Andrew & Lucas Jr. , Robert E., 1995. "Efficiency and Equality in a Simple Model of Efficient Unemployment Insurance," Journal of Economic Theory, Elsevier, vol. 66(1), pages 64-88, June.
    9. Thomas, Jonathan & Worrall, Tim, 1990. "Income fluctuation and asymmetric information: An example of a repeated principal-agent problem," Journal of Economic Theory, Elsevier, vol. 51(2), pages 367-390, August.
    10. John Y. Zhu, 2013. "Optimal Contracts with Shirking," Review of Economic Studies, Oxford University Press, vol. 80(2), pages 812-839.
    11. Yuliy Sannikov, 2008. "A Continuous-Time Version of the Principal-Agent Problem," Review of Economic Studies, Oxford University Press, vol. 75(3), pages 957-984.
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    More about this item

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law
    • M52 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Personnel Economics - - - Compensation and Compensation Methods and Their Effects

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