Convolution and Composition of Totally Positive Random Variables in Economics

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 singlepeakedness 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.