Convolution and composition of totally positive random variables in economics

Eugenio J. Miravete

Research output: Contribution to journalArticle

1 Citation (Scopus)

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.
Original languageEnglish
Pages (from-to)479-490
Number of pages12
JournalJournal of Mathematical Economics
Volume47
Issue number4-5
Early online date27 Jul 2011
DOIs
Publication statusPublished - Aug 2011

Keywords

  • Total positivity
  • Log-concavity
  • Basic composition formula
  • Favorableness

Cite this