Dynamic Contracting with Persistent Shocks

44 Pages Posted: 3 Jun 2010

Date Written: September 30, 2008

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.

Keywords: Persistence, Principal-agent Problem, Stochastic Control Problem, Efficiency Lines

JEL Classification: D80, D82, E61

Suggested Citation

Zhang, Yuzhe, Dynamic Contracting with Persistent Shocks (September 30, 2008). Journal of Economic Theory, Vol. 144, 2009, Available at SSRN: https://ssrn.com/abstract=1619998

Yuzhe Zhang (Contact Author)

Texas A&M University ( email )

Langford Building A
798 Ross St.
College Station, TX 77843-3137
United States

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