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Federal Reserve Bank of Richmond
Working Paper
Optimal Incentive Contracts with Job Destruction Risk
Borys Grochulski
Russell Wong
Yuzhe Zhang
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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Borys Grochulski & Russell Wong & Yuzhe Zhang, Optimal Incentive Contracts with Job Destruction Risk, Federal Reserve Bank of Richmond, Working Paper 17-11, 06 Oct 2017.
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Keywords: dynamic moral hazard; job destruction; jump risk
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