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Dynamic costs and moral hazard: A duality-based approach

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  • Arie, Guy

Abstract

The marginal cost of effort often increases as effort is exerted. In a dynamic moral hazard setting, dynamically increasing costs create information asymmetry. This paper characterizes the optimal contract and helps explain the popular yet thus far puzzling use of non-linear incentives, for example, in sales-force compensation. The result is obtained by complementing the standard dynamic program with a novel dynamic dual formulation. The dual program is monotonic and sub-modular, providing stronger results, including a proof for the sufficiency of one-shot deviations.

Suggested Citation

  • Arie, Guy, 2016. "Dynamic costs and moral hazard: A duality-based approach," Journal of Economic Theory, Elsevier, vol. 166(C), pages 1-50.
    • Handle: RePEc:eee:jetheo:v:166:y:2016:i:c:p:1-50
    DOI: 10.1016/j.jet.2016.08.002
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    1. Fudenberg, Drew & Holmstrom, Bengt & Milgrom, Paul, 1990. "Short-term contracts and long-term agency relationships," Journal of Economic Theory, Elsevier, vol. 51(1), pages 1-31, June.
    2. Zhao, Rui R., 2006. "Renegotiation-proof contract in repeated agency," Journal of Economic Theory, Elsevier, vol. 131(1), pages 263-281, November.
    3. Stephen E. Spear & Sanjay Srivastava, 1987. "On Repeated Moral Hazard with Discounting," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 54(4), pages 599-617.
    4. Alex Edmans & Xavier Gabaix & Tomasz Sadzik & Yuliy Sannikov, 2012. "Dynamic CEO Compensation," Journal of Finance, American Finance Association, vol. 67(5), pages 1603-1647, October.
    5. Ábrahám, Árpád & Koehne, Sebastian & Pavoni, Nicola, 2011. "On the first-order approach in principal-agent models with hidden borrowing and lending," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1331-1361, July.
    6. Matthias Messner & Nicola Pavoni & Christopher Sleet, 2012. "Recursive Methods for Incentive Problems," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 15(4), pages 501-525, October.
    7. Paul Oyer, 1998. "Fiscal Year Ends and Nonlinear Incentive Contracts: The Effect on Business Seasonality," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 113(1), pages 149-185.
    8. J. Gabriel & Raquiel López-Martínez & Onésimo Hernández-Lerma, 2001. "The lagrange approach to infinite linear programs," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 9(2), pages 293-314, December.
    9. Cheng Wang, 2000. "Renegotiation-Proof Dynamic Contracts with Private Information," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 3(3), pages 396-422, July.
    10. Sanjog Misra & Harikesh Nair, 2011. "A structural model of sales-force compensation dynamics: Estimation and field implementation," Quantitative Marketing and Economics (QME), Springer, vol. 9(3), pages 211-257, September.
    11. Albert Marcet & Ramon Marimon, 2019. "Recursive Contracts," Econometrica, Econometric Society, vol. 87(5), pages 1589-1631, September.
    12. Canice Prendergast, 1999. "The Provision of Incentives in Firms," Journal of Economic Literature, American Economic Association, vol. 37(1), pages 7-63, March.
    13. Ramon Marimon, 2011. "New Results in Recursive Contract Theory," 2011 Meeting Papers 752, Society for Economic Dynamics.
    14. Toshihiko Mukoyama & Ayşegül Şahin, 2005. "Repeated moral hazard with persistence," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 25(4), pages 831-854, June.
    15. Noah Williams, 2011. "Persistent Private Information," Econometrica, Econometric Society, vol. 79(4), pages 1233-1275, July.
    16. Dirk Bergemann & Ulrigh Hege, 2005. "The Financing of Innovation: Learning and Stopping," RAND Journal of Economics, The RAND Corporation, vol. 36(4), pages 719-752, Winter.
    17. Alessandro Bonatti & Johannes Horner, 2011. "Collaborating," American Economic Review, American Economic Association, vol. 101(2), pages 632-663, April.
    18. Chow, Gregory C., 1997. "Dynamic Economics: Optimization by the Lagrange Method," OUP Catalogue, Oxford University Press, number 9780195101928.
    19. Dirk Bergemann & Ulrigh Hege, 2005. "The Financing of Innovation: Learning and Stopping," RAND Journal of Economics, The RAND Corporation, vol. 36(4), pages 719-752, Winter.
    20. Ian Larkin, 2014. "The Cost of High-Powered Incentives: Employee Gaming in Enterprise Software Sales," Journal of Labor Economics, University of Chicago Press, vol. 32(2), pages 199-227.
    21. Fernandes, Ana & Phelan, Christopher, 2000. "A Recursive Formulation for Repeated Agency with History Dependence," Journal of Economic Theory, Elsevier, vol. 91(2), pages 223-247, April.
    22. Martin L. Weitzman, 1973. "Duality Theory for Infinite Horizon Convex Models," Management Science, INFORMS, vol. 19(7), pages 783-789, March.
    23. Daniel F. Garrett & Alessandro Pavan, 2012. "Managerial Turnover in a Changing World," Journal of Political Economy, University of Chicago Press, vol. 120(5), pages 879-925.
    24. Peter M. DeMarzo & Michael J. Fishman, 2007. "Optimal Long-Term Financial Contracting," The Review of Financial Studies, Society for Financial Studies, vol. 20(6), pages 2079-2128, November.
    25. Abreu, Dilip & Milgrom, Paul & Pearce, David, 1991. "Information and Timing in Repeated Partnerships," Econometrica, Econometric Society, vol. 59(6), pages 1713-1733, November.
    26. Bhaskar, Venkataraman, 2014. "The Ratchet Effect Re-examined: A Learning Perspective," CEPR Discussion Papers 9956, C.E.P.R. Discussion Papers.
    27. Gian Luca Clementi & Hugo A. Hopenhayn, 2006. "A Theory of Financing Constraints and Firm Dynamics," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 121(1), pages 229-265.
    28. Bruce Shearer, 2004. "Piece Rates, Fixed Wages and Incentives: Evidence from a Field Experiment," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 71(2), pages 513-534.
    29. Rogerson, William P, 1985. "Repeated Moral Hazard," Econometrica, Econometric Society, vol. 53(1), pages 69-76, January.
    30. repec:oup:restud:v:84:y::i:1:p:182-236. is not listed on IDEAS
    31. Bester, Helmut & Strausz, Roland, 2001. "Contracting with Imperfect Commitment and the Revelation Principle: The Single Agent Case," Econometrica, Econometric Society, vol. 69(4), pages 1077-1098, July.
    32. Mele, Antonio, 2014. "Repeated moral hazard and recursive Lagrangeans," Journal of Economic Dynamics and Control, Elsevier, vol. 42(C), pages 69-85.
    33. Marina Halac & Navin Kartik & Qingmin Liu, 2016. "Optimal Contracts for Experimentation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 83(3), pages 1040-1091.
    34. Son Ku Kim, 1997. "Limited Liability and Bonus Contracts," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 6(4), pages 899-913, December.
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    Cited by:

    1. Cheng Wang, 2000. "Renegotiation-Proof Dynamic Contracts with Private Information," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 3(3), pages 396-422, July.
    2. Xun Liu & Sen Lin & Lixing Liu & Fei Qian & Kun Zhang, 2020. "Exploring the Factors Triggering Occupational Ethics Risk of Technology Transaction in Chinese Construction Industry," IJERPH, MDPI, vol. 17(4), pages 1-18, February.
    3. Bhaskar, V & Roketskiy, Nikita, 2023. "The ratchet effect: A learning perspective," Journal of Economic Theory, Elsevier, vol. 214(C).

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    More about this item

    Keywords

    Dynamic moral hazard; Nonlinear incentives; Private information; Dynamic mechanism design; Duality;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law

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