IDEAS home Printed from https://ideas.repec.org/p/xrs/sfbmaa/98-06.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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.
    as

    Download full text from publisher

    File URL: http://www.sfb504.uni-mannheim.de/publications/dp98-06.pdf
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. Holmstrom, Bengt & Milgrom, Paul, 1987. "Aggregation and Linearity in the Provision of Intertemporal Incentives," Econometrica, Econometric Society, vol. 55(2), pages 303-328, March.
    3. Hellwig, Martin F., 1996. "Sequential decisions under uncertainty and the maximum theorem," Journal of Mathematical Economics, Elsevier, vol. 25(4), pages 443-464.
    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. 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.
    6. 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.
    7. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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.
    4. 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.
    5. repec:spr:finsto:v:22:y:2018:i:1:d:10.1007_s00780-017-0344-4 is not listed on IDEAS
    6. Romuald Elie & Dylan Possamai, 2016. "Contracting theory with competitive interacting agents," Papers 1605.08099, arXiv.org.
    7. 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.
    8. 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, pages 93-104.
    9. 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.
    10. Barlo, Mehmet & Ayca, Ozdogan, 2012. "Team beats collusion," MPRA Paper 37449, University Library of Munich, Germany.
    11. 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.
    12. Thibaut Mastrolia & Dylan Possamai, 2015. "Moral hazard under ambiguity," Papers 1511.03616, arXiv.org, revised Oct 2016.
    13. 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.
    14. 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.
    15. Thibaut Mastrolia & Zhenjie Ren, 2017. "Principal-Agent Problem with Common Agency without Communication," Papers 1706.02936, arXiv.org, revised Jan 2018.
    16. Thibaut Mastrolia & Zhenjie Ren, 2018. "Principal-Agent Problem with Common Agency without Communication," Working Papers hal-01534611, HAL.
    17. 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.
    18. 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.
    19. 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.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:xrs:sfbmaa:98-06. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Carsten Schmidt). General contact details of provider: http://edirc.repec.org/data/sfmande.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.