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Optimal Incentive Contracts with Job Destruction Risk

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Abstract

We study the implications of job destruction risk for optimal incentives in a long-term contract with moral hazard. We extend the dynamic principal-agent model of Sannikov (2008) by adding an exogenous Poisson shock that makes the match between the firm and the agent permanently unproductive. In modeling job destruction as an exogenous Poisson shock, we follow the Diamond-Mortensen-Pissarides search-and-matching literature. The optimal contract shows how job destruction risk is shared between the rm and the agent. Arrival of the job-destruction shock is always bad news for the rm but can be good news for the agent. In particular, under weak conditions, the optimal contract has exactly two regions. If the agent's continuation value is below a threshold, the agent's continuation value experiences a negative jump upon arrival of the job-destruction shock. If the agent's value is above this threshold, however, the jump in the agent's continuation value is positive, i.e., the agent gets rewarded when the match becomes unproductive. This pattern of adjustment of the agent's value at job destruction allows the firm to reduce the costs of effort incentives while the match is productive. In particular, it allows the firm to adjust the drift of the agent's continuation value process so as to decrease the risk of reaching either of the two inefficient agent retirement points. Further, we study the sensitivity of the optimal contract to the arrival rate of job destruction.

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  • Grochulski, Borys & Wong, Russell & Zhang, Yuzhe, 2017. "Optimal Incentive Contracts with Job Destruction Risk," Working Paper 17-11, Federal Reserve Bank of Richmond.
  • Handle: RePEc:fip:fedrwp:17-11
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    File URL: https://www.richmondfed.org/-/media/richmondfedorg/publications/research/working_papers/2017/pdf/wp17-11.pdf
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    References listed on IDEAS

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    1. Mortensen, Dale & Pissarides, Christopher, 2011. "Job Creation and Job Destruction in the Theory of Unemployment," Economic Policy, Russian Presidential Academy of National Economy and Public Administration, vol. 1, pages 1-19.
    2. DeMarzo, Peter M. & Livdan, Dmitry & Tchistyi, Alexei, 2014. "Risking Other People's Money: Gambling, Limited Liability, and Optimal Incentives," Research Papers 3149, Stanford University, Graduate School of Business.
    3. 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.
    4. Florian Hoffmann & Sebastian Pfeil, 2010. "Reward for Luck in a Dynamic Agency Model," Review of Financial Studies, Society for Financial Studies, vol. 23(9), pages 3329-3345.
    5. Tomasz Piskorski & Alexei Tchistyi, 2010. "Optimal Mortgage Design," Review of Financial Studies, Society for Financial Studies, vol. 23(8), pages 3098-3140, August.
    6. 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.
    7. repec:eee:mateco:v:71:y:2017:i:c:p:74-91 is not listed on IDEAS
    8. Pissarides, Christopher A, 1985. "Short-run Equilibrium Dynamics of Unemployment Vacancies, and Real Wages," American Economic Review, American Economic Association, vol. 75(4), pages 676-690, September.
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    More about this item

    Keywords

    dynamic moral hazard; job destruction; jump risk;

    JEL classification:

    • D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law

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