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

• 成果类型: Article
• 署名作者: Chade, Hector; Swinkels, Jeroen
• 署名单位: Arizona State University; Arizona State University-Tempe; Northwestern University
• 刊物名称: THEORETICAL ECONOMICS
• ISSN/ISSBN: 1933-6837
• DOI: 10.3982/TE2937
• 发表日期: 2020-05-01
• 页码: 445-476
• 关键词: Log-supermodularity; quasi-concavity; moral hazard; first-order approach; D81; D86

摘要

We define and explore 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.