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Convolution and composition of totally positive random variables in economics

Authors
Journal
Journal of Mathematical Economics
0304-4068
Publisher
Elsevier
Volume
47
Identifiers
DOI: 10.1016/j.jmateco.2011.06.008
Keywords
  • Total Positivity
  • Log-Concavity
  • Basic Composition Formula
  • Favorableness
Disciplines
  • Economics
  • Mathematics

Abstract

Abstract This paper studies a class of multidimensional screening models where different type dimensions can be aggregated into a single-dimensional sufficient statistic. The paper applies results of totally positive functions to show that some critical properties of distributions of asymmetric information parameters, such as increasing hazard rate, monotone likelihood ratio, and single-peakedness are preserved under convolution or composition. Under some general conditions, these invariance results also provide a natural ordering of alternative screening mechanisms. I illustrate how these preservation results provide a unifying framework to interpret several contributions in economic models of adverse selection, moral hazard, and voting.

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