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The no-upward-crossing condition, comparative statics, and the moral-hazard problem

Author

Listed:
  • Chade, Hector

    (Department of Economics, Arizona State University)

  • Swinkels, Jeroen M.

    (Kellogg School of Management, Northwestern University)

Abstract

We define and explore the No-Upward-Crossing NUC, a condition satisfied by every parameterized family of distributions commonly used in economic applications. Under smoothness assumptions, NUC is equivalent to log-supermodularity of the negative of the derivative of the distribution with respect to the parameter. It is characterized by a natural monotone comparative static, and is central in establishing quasi-concavity in a family of decision problems. As an application, we revisit the first-order approach to the moral hazard problem. NUC simplifies the relevant conditions for the validity of the first-order approach and gives them an economic interpretation. We provide extensive analysis of sufficient conditions for the first-order approach for exponential families.

Suggested Citation

  • Chade, Hector & Swinkels, Jeroen M., 2020. "The no-upward-crossing condition, comparative statics, and the moral-hazard problem," Theoretical Economics, Econometric Society, vol. 15(2), May.
    • Handle: RePEc:the:publsh:2937
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    References listed on IDEAS

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    3. Philipp Renner, 2020. "An augmented first-order approach for incentive problems," Working Papers 297498586, Lancaster University Management School, Economics Department.

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    More about this item

    Keywords

    Log-supermodularity; quasi-concavity; moral hazard; first-order approach;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law

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