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Dynamic Contracting with Persistent Shocks

  • Zhang, Yuzhe

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.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 23108.

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Date of creation: 2009
Date of revision:
Publication status: Published in Journal of Economic Theory 2.144(2009): pp. 635-675
Handle: RePEc:pra:mprapa:23108
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  2. Mikhail Golosov & Aleh Tsyvinski, 2006. "Designing Optimal Disability Insurance: A Case for Asset Testing," Journal of Political Economy, University of Chicago Press, vol. 114(2), pages 257-279, April.
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  7. Yuzhe Zhang, 2005. "Dynamic contracting, persistent shocks and optimal taxation," Working Papers 640, Federal Reserve Bank of Minneapolis.
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  12. Stefania Albanesi, 2006. "optimal taxation of entrepreneurial capital with private information," 2006 Meeting Papers 310, Society for Economic Dynamics.
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  18. Yuliy Sannikov, 2007. "Games with Imperfectly Observable Actions in Continuous Time," Econometrica, Econometric Society, vol. 75(5), pages 1285-1329, 09.
  19. Marek Kapicka, 2006. "Optimal Income Taxation with Human Capital Accumulation and Limited Record Keeping," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 9(4), pages 612-639, October.
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