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

Hector Chade () and Jeroen M. Swinkels ()
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Hector Chade: Department of Economics, Arizona State University
Jeroen M. Swinkels: Kellogg School of Management, Northwestern University

Theoretical Economics, 2020, vol. 15, issue 2

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.

Keywords: Log-supermodularity; quasi-concavity; moral hazard; first-order approach (search for similar items in EconPapers)
JEL-codes: D81 D86 (search for similar items in EconPapers)
Date: 2020-05-01
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Citations: View citations in EconPapers (3)

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