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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 discrete-time and continuous-time principal-agent models. We derive the continuous-time model as a limit of discrete-time 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.

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Bibliographic Info

Paper provided by Sonderforschungsbereich 504, Universität Mannheim & Sonderforschungsbereich 504, University of Mannheim in its series Sonderforschungsbereich 504 Publications with number 01-52.

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Length: 85 pages
Date of creation: 29 Nov 2001
Date of revision:
Handle: RePEc:xrs:sfbmaa:01-52

Note: For helpful comments and discussions we are grateful to Darell Duffie, Oliver Hart, Florian Herold, Bengt Holmström, Nobuhiro Kiyotaki, Paul Milgrom, John Moore, Holger Müller, Sven Rady, Jae Sung, three anonymous referees and the editor, Drew Fudenberg. The first author gratefully acknowledges research support from the Schweizerischer Nationalfonds, the Deutsche Forschungsgemeinschaft, and the Taussig Chair at Harvard University. The second author is grateful for research support from the Deutsche Forschungsgemeinschaft through grants SCHM1196/2-1 and /4-1 and for the hospitality enjoyed at the economics department of Stanford University.Financial support from the Deutsche Forschungsgemeinschaft, SFB 504, at the University of Mannheim, is gratefully acknowledged.
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References

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  1. 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.
  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. 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. Mirrlees, J A, 1999. "The Theory of Moral Hazard and Unobservable Behaviour: Part I," Review of Economic Studies, Wiley Blackwell, vol. 66(1), pages 3-21, January.
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Citations

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Cited by:
  1. Helmut Dietl & Martin Grossmann & Markus Lang & Simon Wey, 2010. "Incentive Effects of Bonus Taxes in a Principal-Agent Model," Working Papers 0140, University of Zurich, Institute for Strategy and Business Economics (ISU), revised Feb 2012.
  2. Ernst Fehr & Klaus M. Schmidt, . "Fairness and Incentives in a Multi-Task Principal-Agent Model," IEW - Working Papers 191, Institute for Empirical Research in Economics - University of Zurich.
  3. 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.
  4. Coles, Jeffrey & Lemmon, Michael & Meschke, Felix, 2007. "Structural Models and Endogeneity in Corporate Finance: the Link Between Managerial Ownership and Corporate Performance," MPRA Paper 4374, University Library of Munich, Germany, revised 15 Feb 2007.
  5. Hellwig, Martin F. & Schmidt, Klaus M., 2002. "Discrete-time approximations of the Holmström-Milgrom brownian-motion model of intertemporal incentive provision," Munich Reprints in Economics 19425, University of Munich, Department of Economics.
  6. 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.
  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. Drew Fudenberg & David K Levine, 2007. "Repeated Games with Frequent Signals," Levine's Working Paper Archive 814577000000000009, David K. Levine.
  9. James Mirrlees & Roberto Raimondo, 2013. "Strategies in the principal-agent model," Economic Theory, Springer, vol. 53(3), pages 605-656, August.
  10. 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.
  11. Barlo, Mehmet & Ayca, Ozdogan, 2012. "Team beats collusion," MPRA Paper 37449, University Library of Munich, Germany.

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