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Optimal Long-term Contracting with Learning

  • Jianfeng Yu

    (University of Minnesota)

  • Bin Wei

    (Federal Reserve Board)

  • Zhiguo He

    (University of Chicago, Booth School of Business)

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This paper introduces profitability uncertainty into an infinite-horizon variation of the classic Holmstrom and Milgrom (1987) model, and studies optimal dynamic contracting with endogenous learning. The agent's potential belief manipulation leads to the hidden information problem, which makes incentive provisions intertemporally linked in the optimal contract. We reduce the contracting problem into a dynamic programming problem with one state variable, and characterize the optimal contract with an ordinary differential equation. In the benchmark case of Holmstrom and Milgrom (1987) without learning, the optimal effort is constant, and the optimal contract is linear. In contrast, in our model with endogenous learning, the optimal effort policy becomes history dependent, and decreases over time on average. Moreover, we show that the optimal contract exhibits an option-like feature in that the incentives rise after good performance shocks.

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Paper provided by Society for Economic Dynamics in its series 2012 Meeting Papers with number 221.

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Date of creation: 2012
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Handle: RePEc:red:sed012:221
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  1. 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.
  2. Julien Prat & Boyan Jovanovic, 2010. "Dynamic Incentive Contracts Under Parameter Uncertainty," NBER Working Papers 16649, National Bureau of Economic Research, Inc.
  3. Harold L Cole & Narayana Kocherlakota, 2010. "Efficient Allocations with Hidden Income and Hidden Storage," Levine's Working Paper Archive 1909, David K. Levine.
  4. Drew Fudenberg & Bengt Holmstrom & Paul Milgrom, 1987. "Short-Term Contracts and Long-Term Agency Relationships," Working papers 468, Massachusetts Institute of Technology (MIT), Department of Economics.
  5. Zhang, Yuzhe, 2009. "Dynamic Contracting with Persistent Shocks," MPRA Paper 23108, University Library of Munich, Germany.
  6. Holmstrom, Bengt & Milgrom, Paul, 1987. "Aggregation and Linearity in the Provision of Intertemporal Incentives," Econometrica, Econometric Society, vol. 55(2), pages 303-28, March.
  7. Tobias Adrian & Mark M. Westerfield, 2008. "Disagreement and learning in a dynamic contracting model," Staff Reports 269, Federal Reserve Bank of New York.
  8. Spear, Stephen E & Srivastava, Sanjay, 1987. "On Repeated Moral Hazard with Discounting," Review of Economic Studies, Wiley Blackwell, vol. 54(4), pages 599-617, October.
  9. Bengt Holmstrom, 1999. "Managerial Incentive Problems: A Dynamic Perspective," NBER Working Papers 6875, National Bureau of Economic Research, Inc.
  10. He, Zhiguo, 2011. "A model of dynamic compensation and capital structure," Journal of Financial Economics, Elsevier, vol. 100(2), pages 351-366, May.
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