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The No-Upward-Crossing Condition, Comparative Statics, and the Moral Hazard Problem, Theoretical Economics

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.

Type

Article

Author(s)

Jeroen Swinkels, Hector Chade

Date Published

2019

Citations

Swinkels, Jeroen, and Hector Chade. 2019. The No-Upward-Crossing Condition, Comparative Statics, and the Moral Hazard Problem. Theoretical Economics.

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