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- Title
PRESERVING LOG-CONCAVITY UNDER CONVOLUTION: COMMENT.
- Authors
Miravete, Eugene J.
- Abstract
The article presents a comment on preserving log-concavity under convolution. It informs that in a recent work, B. Biais, D. Martimort, and J.C. Rochet, (BMR) develop a common agency model in which agents' types have two dimensions that lie on the real line and define a single dimensional aggregate. Thus, BMR face two alternative models of screening: either accounting for each source of asymmetry of information separately. In arguing that their results are broadly applicable BMR claim that log-concavity of the convolution is not a very restrictive condition, since it is implied by the log-concavity of either the density. Nevertheless, to ensure the existence of a separating equilibrium in nonlinear strategies, BMR only need the weaker assumption that F0 is increasing hazard rate (IHR). But this approach reduces the set of distributions that can be used to model the screening of agents with stochastic demands because it excludes those IHR distributions whose density functions are not log-concave.
- Subjects
CONCAVE functions; MARTIMORT, D.; ACCOUNTING; MATHEMATICAL convolutions; DISTRIBUTION (Probability theory); MATHEMATICAL functions
- Publication
Econometrica, 2002, Vol 70, Issue 3, p1253
- ISSN
0012-9682
- Publication type
Article
- DOI
10.1111/1468-0262.00327