Optimal Long-Term Contracting with Learning

Zhiguo He, Bin Wei, Jianfeng Yu, and Feng Gao

Working Paper 2016-10
November 2016

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We introduce uncertainty into Holmstrom and Milgrom (1987) to study optimal long-term contracting with learning. In a dynamic relationship, the agent's shirking not only reduces current performance but also increases the agent's information rent due to the persistent belief manipulation effect. We characterize the optimal contract using the dynamic programming technique in which information rent is the unique state variable. In the optimal contract, the optimal effort is front-loaded and decreases stochastically over time. Furthermore, the optimal contract exhibits an option-like feature in that incentives increase after good performance. Implications about managerial incentives and asset management compensations are discussed.

JEL classification: D8, D86, M12

Key words: executive compensation, moral hazard, Bayesian learning, hidden information, belief manipulation, private savings, continuous time, stock options


The authors thank Francesca Cornelli, Philip Dybvig, Johannes Horner, Navin Kartik, Mark Loewenstein, Andrey Malenko, Hui Ou Yang, Julien Prat, Yuliy Sannikov, Lars Stole, Noah Williams, and participants at the Federal Reserve Board, Cheung Kong Graduate School of Business, the 2014 American Finance Association annual meeting in Philadelphia, the 2013 Econometric Society winter meeting in San Diego, the 2012 Society of Economic Dynamics meeting, and the 2012 China International Conference in Finance for helpful comments. Zhiguo He gratefully acknowledges financial support from the Center for Research in Security Price at the University of Chicago Booth School of Business. Jianfeng Yu gratefully acknowledges financial support from the Dean's Small Grant from the Carlson School of Management at the University of Minnesota. The views expressed here are the authors' and not necessarily those of the Federal Reserve Bank of Atlanta or the Federal Reserve System. Any remaining errors are the authors' responsibility.
Please address questions regarding content to Zhiguo He, University of Chicago, Booth School of Business, and NBER, 5807 South Woodlawn Avenue, Chicago, IL 60637, 773-834-3769, zhiguo.he@chicagobooth.edu; Bin Wei, Federal Reserve Bank of Atlanta, 1000 Peachtree Street NE, Atlanta, GA 30309, 404-498-8913, bin.wei@atl.frb.org; Jianfeng Yu, University of Minnesota, Carlson School of Management, CSOM 3-122, 321 19th Avenue South, Minneapolis, MN 55455, and PBC School of Finance, Tsinghua University, Beijing, China, 612-625-5498, jianfeng@umn.edu; or Feng Gao, Tsinghua University, School of Economics and Management, Beijing, China, gaof@sem.tsinghua.edu.cn.
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