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Dynamic Incentive Contracts under Parameter Uncertainty

  • Jovanovic, Boyan
  • Prat, Julien

We analyze a long-term contracting problem involving common uncertainty about a parameter capturing the productivity of the relationship, and featuring a hidden action for the agent. We develop an approach that works for any utility function when the parameter and noise are normally distributed and when the effort and noise affect output additively. We then analytically solve for the optimal contract when the agent has exponential utility. We find that the Pareto frontier shifts out as information about the agent's quality improves. In the standard spot-market setup, by contrast, when the parameter measures the agent's 'quality', the Pareto frontier shifts inwards with better information. Commitment is therefore more valuable when quality is known more precisely. Incentives then are easier to provide because the agent has less room to manipulate the beliefs of the principal. Moreover, in contrast to results under one-period commitment, wage volatility declines as experience accumulates.

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Paper provided by C.E.P.R. Discussion Papers in its series CEPR Discussion Papers with number 8136.

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Date of creation: Dec 2010
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Handle: RePEc:cpr:ceprdp:8136
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  1. Marek Kapicka, 2013. "Efficient Allocations in Dynamic Private Information Economies with Persistent Shocks: A First-Order Approach," Review of Economic Studies, Oxford University Press, vol. 80(3), pages 1027-1054.
  2. Leena Rudanko, 2006. "Labor Market Dynamics under Long Term Wage Contracting," 2006 Meeting Papers 314, Society for Economic Dynamics.
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  4. Bengt Holmstrom & Paul R. Milgrom, 1985. "Aggregation and Linearity in the Provision of Intertemporal Incentives," Cowles Foundation Discussion Papers 742, Cowles Foundation for Research in Economics, Yale University.
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  7. Robert Gibbons & Kevin J. Murphy, 1991. "Optimal Incentive Contracts in the Presence of Career Concerns: Theory and Evidence," NBER Working Papers 3792, National Bureau of Economic Research, Inc.
  8. Jovanovic, Boyan, 1979. "Job Matching and the Theory of Turnover," Journal of Political Economy, University of Chicago Press, vol. 87(5), pages 972-90, October.
  9. Ana Fernandes & Christopher Phelan, 1999. "A recursive formulation for repeated agency with history dependence," Staff Report 259, Federal Reserve Bank of Minneapolis.
  10. Yahel Giat & Steve T. Hackman & Ajay Subramanian, 2010. "Investment under Uncertainty, Heterogeneous Beliefs, and Agency Conflicts," Review of Financial Studies, Society for Financial Studies, vol. 23(4), pages 1360-1404, April.
  11. Tobias Adrian & Mark M. Westerfield, 2009. "Disagreement and Learning in a Dynamic Contracting Model," Review of Financial Studies, Society for Financial Studies, vol. 22(10), pages 3873-3906, October.
  12. Jarque, Arantxa, 2010. "Repeated moral hazard with effort persistence," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2412-2423, November.
  13. 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.
  14. Hugo Hopenhayn & Arantxa Jarque, 2007. "Moral hazard and persistence," Working Paper 07-07, Federal Reserve Bank of Richmond.
  15. Rogerson, William P, 1985. "The First-Order Approach to Principal-Agent Problems," Econometrica, Econometric Society, vol. 53(6), pages 1357-67, November.
  16. Noah Williams, 2004. "On Dynamic Principal-Agent Problems in Continuous Time," Levine's Bibliography 122247000000000426, UCLA Department of Economics.
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