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

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  • Hellwig, Martin F.
  • Schmidt, Klaus M.

Abstract

This paper studies the relation between discrete-time and continuoustime principal-agent models. We derive the continuous-time model as a limit of discretetime models with ever shorter periods and show that optimal incentive schemes in the discrete-time models approximate the optimal incentive scheme in the continuous model, which is linear in accounts. Under the additional assumption that the principal observes only cumulative total profits at the end and the agent can destroy profits unnoticed, an incentive scheme that is linear in total profits is shown to be approximately optimal in the discrete-time model when the length of the period is small.

Suggested Citation

  • Hellwig, Martin F. & Schmidt, Klaus M., 2001. "Discrete-Time Approximations of the Holmström-Milgrom Brownian-Motion Model of Intertemporal Incentive Provision," Discussion Papers in Economics 22, University of Munich, Department of Economics.
  • Handle: RePEc:lmu:muenec:22
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    File URL: https://epub.ub.uni-muenchen.de/22/1/0111_hellwig.pdf
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    References listed on IDEAS

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    1. Itoh, Hideshi, 1992. "Cooperation in Hierarchical Organizations: An Incentive Perspective," 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," Review of Economic Studies, Oxford University Press, vol. 66(1), pages 3-21.
    4. Grossman, Sanford J & Hart, Oliver D, 1983. "An Analysis of the Principal-Agent Problem," Econometrica, Econometric Society, vol. 51(1), pages 7-45, January.
    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.
    7. Hellwig, Martin F., 1996. "Sequential decisions under uncertainty and the maximum theorem," Journal of Mathematical Economics, Elsevier, vol. 25(4), pages 443-464.
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    Citations

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    Cited by:

    1. Giat, Yahel & Subramanian, Ajay, 2013. "Dynamic contracting under imperfect public information and asymmetric beliefs," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2833-2861.
    2. Ernst Fehr & Klaus M. Schmidt, 2004. "Fairness and Incentives in a Multi-task Principal-Agent Model," Scandinavian Journal of Economics, Wiley Blackwell, vol. 106(3), pages 453-474, October.
    3. Romuald Elie & Dylan Possamai, 2016. "Contracting theory with competitive interacting agents," Papers 1605.08099, arXiv.org.
    4. 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.
    5. Dietl, Helmut M. & Grossmann, Martin & Lang, Markus & Wey, Simon, 2013. "Incentive effects of bonus taxes in a principal-agent model," Journal of Economic Behavior & Organization, Elsevier, vol. 89(C), pages 93-104.
    6. Jaeyoung Sung, 2005. "Optimal Contracts Under Adverse Selection and Moral Hazard: A Continuous-Time Approach," Review of Financial Studies, Society for Financial Studies, vol. 18(3), pages 1021-1073.
    7. Barlo, Mehmet & Ayca, Ozdogan, 2012. "Team beats collusion," MPRA Paper 37449, University Library of Munich, Germany.
    8. Coles, Jeffrey L. & Lemmon, Michael L. & Felix Meschke, J., 2012. "Structural models and endogeneity in corporate finance: The link between managerial ownership and corporate performance," Journal of Financial Economics, Elsevier, vol. 103(1), pages 149-168.
    9. Thibaut Mastrolia & Dylan Possamai, 2015. "Moral hazard under ambiguity," Papers 1511.03616, arXiv.org, revised Oct 2016.
    10. James Mirrlees & Roberto Raimondo, 2013. "Strategies in the principal-agent model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 53(3), pages 605-656, August.
    11. Drew Fudenberg & David K. Levine, 2009. "Repeated Games with Frequent Signals," The Quarterly Journal of Economics, Oxford University Press, vol. 124(1), pages 233-265.
    12. Guo, Ming & Ou-Yang, Hui, 2006. "Incentives and performance in the presence of wealth effects and endogenous risk," Journal of Economic Theory, Elsevier, vol. 129(1), pages 150-191, July.
    13. Hellwig, Martin F., 2007. "The role of boundary solutions in principal-agent problems of the Holmstrom-Milgrom type," Journal of Economic Theory, Elsevier, vol. 136(1), pages 446-475, September.
    14. Armstrong, Christopher S. & Guay, Wayne R. & Weber, Joseph P., 2010. "The role of information and financial reporting in corporate governance and debt contracting," Journal of Accounting and Economics, Elsevier, vol. 50(2-3), pages 179-234, December.
    15. repec:spr:finsto:v:22:y:2018:i:1:d:10.1007_s00780-017-0344-4 is not listed on IDEAS
    16. Drew Fudenberg & David Levine, 2007. "Continuous Time Limits of Repeated Games with Imperfect Public Monitoring," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 10(2), pages 173-192, April.
    17. Jakv{s}a Cvitani'c & Dylan Possamai & Nizar Touzi, 2015. "Dynamic programming approach to principal-agent problems," Papers 1510.07111, arXiv.org, revised Jan 2017.
    18. Thibaut Mastrolia & Zhenjie Ren, 2017. "Principal-Agent Problem with Common Agency without Communication," Papers 1706.02936, arXiv.org, revised Jan 2018.
    19. Thibaut Mastrolia & Zhenjie Ren, 2018. "Principal-Agent Problem with Common Agency without Communication," Working Papers hal-01534611, HAL.

    More about this item

    Keywords

    Principal-agent problems ; linear incentive schemes ; intertemporal incentive provision ; Brownian motion;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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