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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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    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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