A Nonparametric Test for the Value of Sample Selection

I develop a nonparametric test of whether selecting the highest realizations of a random sample makes it more or less informative about an underlying state. The test builds on the results of Di Tillio, Ottaviani, and Sørensen [Econometrica, 89: 911–953, 2021], who show that such maximal sample selection benefits any decision maker with interval-dominance-ordered preferences if and only if the reverse hazard rate of the data distribution is log-supermodular. I show that this condition can be tested from the empirical cumulative distribution function alone, without smoothing the density. I propose a test statistic and smoothed bootstrap for computing p -values. Monte Carlo simulations demonstrate reasonable finite-sample properties across various data generating processes. I illustrate the test on whether major stock market indices are more informative about the US economy than random portfolios. Using a large sample of individual U.S. stocks from 1976 to 2023, I find that market indices are suboptimal relative to random portfolios precisely when the future state of the economy is adverse.