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CONVOLUTION AND COMPOSTION OF TOTALLY POSITIVE RANDOM VARIABLES IN ECONOMICS
(Click above to download a pdf copy of the paper)
- 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.
- Publication: Journal of Mathematical Economics, 47 (4-5), 479-490, August/October, 2011.
- JEL: C00, D42, D82.
- First version: June 2010.
- Current version: May 2011.
- Funding: None.
- Seminars: University of Pennsylvania, University of Valencia.
- Conferences: 2001 North-American Summer Meeting of the Econometric Society in Maryland.
- Presentations: PDF.
- Media Citations: None so far.
- Noteworthy: An early version circulated as CARESS Working Paper #01-01.
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