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Moral hazard and the spanning condition without the first-order approach

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  • Kirkegaard, René

Abstract

The “spanning condition” describes a situation where the agent's effort determines the weights placed on two distinct technologies. Sufficient conditions are known under which the first-order approach (FOA) is valid when the spanning condition holds. In this paper, a complete solution to the problem is provided. Thus, the problem is solved even when the FOA is not valid. The solution has two main steps. The first step fully characterizes the set of implementable actions. The second step establishes that the optimal contract can be found by applying the FOA to the newly identified set of feasible actions. This procedure correctly solves a famous counterexample due to Mirrlees in which the standard FOA is not valid. A much simpler and economically more compelling counterexample is provided. Moreover, the model provides a tractable environment in which it is possible to study comparative statics even when the FOA is not justified.

Suggested Citation

  • Kirkegaard, René, 2017. "Moral hazard and the spanning condition without the first-order approach," Games and Economic Behavior, Elsevier, vol. 102(C), pages 373-387.
    • Handle: RePEc:eee:gamebe:v:102:y:2017:i:c:p:373-387
    DOI: 10.1016/j.geb.2017.01.001
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    References listed on IDEAS

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    1. Patrick Bolton & Mathias Dewatripont, 2005. "Contract Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262025760, December.
    2. Jung, Jin Yong & Kim, Son Ku, 2015. "Information space conditions for the first-order approach in agency problems," Journal of Economic Theory, Elsevier, vol. 160(C), pages 243-279.
    3. Rogerson, William P, 1985. "The First-Order Approach to Principal-Agent Problems," Econometrica, Econometric Society, vol. 53(6), pages 1357-1367, November.
    4. Hermalin, Benjamin E & Katz, Michael L, 1991. "Moral Hazard and Verifiability: The Effects of Renegotiation in Agency," Econometrica, Econometric Society, vol. 59(6), pages 1735-1753, November.
    5. Philipp Renner & Karl Schmedders, 2015. "A Polynomial Optimization Approach to Principal–Agent Problems," Econometrica, Econometric Society, vol. 83, pages 729-769, March.
    6. Jewitt, Ian, 1988. "Justifying the First-Order Approach to Principal-Agent Problems," Econometrica, Econometric Society, vol. 56(5), pages 1177-1190, September.
    7. Araujo, Aloisio & Moreira, Humberto, 2001. "A general Lagrangian approach for non-concave moral hazard problems," Journal of Mathematical Economics, Elsevier, vol. 35(1), pages 17-39, February.
    8. Kirkegaard, René, 2017. "A unifying approach to incentive compatibility in moral hazard problems," Theoretical Economics, Econometric Society, vol. 12(1), January.
    9. Jewitt, Ian & Kadan, Ohad & Swinkels, Jeroen M., 2008. "Moral hazard with bounded payments," Journal of Economic Theory, Elsevier, vol. 143(1), pages 59-82, November.
    10. Bernard Sinclair-Desgagné, 2009. "Ancillary Statistics in Principal-Agent Models," Econometrica, Econometric Society, vol. 77(1), pages 279-281, January.
    11. 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.
    12. Sinclair-Desgagne, Bernard, 1994. "The First-Order Approach to Multi-signal Principal-Agent Problems," Econometrica, Econometric Society, vol. 62(2), pages 459-466, March.
    13. Grossman, Sanford J & Hart, Oliver D, 1983. "An Analysis of the Principal-Agent Problem," Econometrica, Econometric Society, vol. 51(1), pages 7-45, January.
    14. Kadan, Ohad & Swinkels, Jeroen M., 2013. "On the moral hazard problem without the first-order approach," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2313-2343.
    15. Marco LiCalzi & Sandrine Spaeter, 2003. "Distributions for the first-order approach to principal-agent problems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 21(1), pages 167-173, January.
    16. John R. Conlon, 2009. "Two New Conditions Supporting the First-Order Approach to Multisignal Principal-Agent Problems," Econometrica, Econometric Society, vol. 77(1), pages 249-278, January.
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    Cited by:

    1. Wang, Wenbin & Hu, Shanshan, 2021. "Moral hazard with limited liability: Random-variable formulation and optimal contract structures," Games and Economic Behavior, Elsevier, vol. 126(C), pages 374-386.

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    More about this item

    Keywords

    First-order approach; Moral hazard; Principal-agent models; Spanning condition;
    All these keywords.

    JEL classification:

    • 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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