Comparing the Chosen: Selection Bias When Selection Is Competitive

Thomas Noe

Journal of Political Economy, 2020, vol. 128, issue 1, 342 - 390

Abstract: Consider a decision maker who selects between paired random draws from two unconditional distributions, always selecting the larger draw in the pair. When will the resulting selection-conditioned distributions be ordered by first-order stochastic or monotone likelihood ratio dominance? In various guises, this question arises in many economic contexts—tournaments, contests, auctions, cheap-talk games, announcement returns, qualitative choice models, and treatment effects under self-selection. This paper develops simple, applicable characterizations of the properties of unconditional distributions that result in dominance conditioned on selection and uses these characterizations to analyze a number of economic selection problems.

Date: 2020
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