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Discrete-Time Approximations of the Holmström-Milgrom Brownian-Motion, Model of Intertemporal Incentive Provision

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  • Hellwig, Martin

    (Sonderforschungsbereich 504)

  • Schmidt, Klaus M.

    (Universität München)

Abstract

This paper studies the relation between multi-period discrete-time and continuous-time principal-agent models. We explicitly derive the continuous-time model as a limit of discrete-time models with ever shorter periods and show that the optimal incentive scheme in the continuous model, which is linear in accounts, can be approximated by a sequence of optimal incentive schemes in the discrete models. For a variant of the discrete-time model in which the principal observes only total profits at the end of the last period and where the agent can destroy profits unnoticed we show, that if the length of each period is sufficiently small, then an incentive scheme that is linear in total profits is approximately optimal.

Suggested Citation

  • Hellwig, Martin & Schmidt, Klaus M., 1998. "Discrete-Time Approximations of the Holmström-Milgrom Brownian-Motion, Model of Intertemporal Incentive Provision," Sonderforschungsbereich 504 Publications 98-06, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
    • Handle: RePEc:xrs:sfbmaa:98-06
    Note: For helpful comments and discussions we are grateful to Darell Duffie, Oliver Hart, Bengt Holmström, Nobuhiro Kiyotaki, John Moore, Holger Müller, Sven Rady, and Jae Sung. We are also grateful for research support from the Schweizerischer Nationalfonds, the Deutsche Forschungsgemeinschaft, and the Taussig Chair at Harvard University.
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    References listed on IDEAS

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    1. Itoh, Hideshi, 1992. "Cooperation in Hierarchical Organizations: An Incentive Perspective," The Journal of Law, Economics, and Organization, Oxford University Press, vol. 8(2), pages 321-345, April.
    2. Martin F. Hellwig & Klaus M. Schmidt, 2002. "Discrete-Time Approximations of the Holmstrom-Milgrom Brownian-Motion Model of Intertemporal Incentive Provision," Econometrica, Econometric Society, vol. 70(6), pages 2225-2264, November.
    3. J. A. Mirrlees, 1999. "The Theory of Moral Hazard and Unobservable Behaviour: Part I," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(1), pages 3-21.
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    5. Holmstrom, Bengt & Milgrom, Paul, 1987. "Aggregation and Linearity in the Provision of Intertemporal Incentives," Econometrica, Econometric Society, vol. 55(2), pages 303-328, March.
    6. Jaeyoung Sung, 1995. "Linearity with Project Selection and Controllable Diffusion Rate in Continuous-Time Principal-Agent Problems," RAND Journal of Economics, The RAND Corporation, vol. 26(4), pages 720-743, Winter.
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    More about this item

    JEL classification:

    • J33 - Labor and Demographic Economics - - Wages, Compensation, and Labor Costs - - - Compensation Packages; Payment Methods
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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