Economists are often interested in identifying effective policies or treatments together with subpopulations of individuals who respond positively (or with a sign that is expected) to these treatment interventions. This paper proposes an optimal false discovery rate controlling method that is especially useful for one-sided testing problems of such kind. The proposed procedure is optimal in the sense of minimizing the false nondiscovery rate while controlling the false discovery rate at a pre-specified level and uses a nonparametric MLE-based deconvolution method that allows for a broader class of treatment effect distributions than existing methods do. The proposed test demonstrates good small sample performance in Monte Carlo simulations and is applied to study the effect of attending a more selective high school in Romania following Pop-Eleches and Urquiola (2013). The application reveals strong evidence of treatment effect heterogeneity in that students who marginally gain access to higher-ranked schools are more likely to benefit if the higher-ranked school has a relatively high admission score cut-off, or, in other words, is more selective.
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