Oracle and adaptive false discovery rate controlling methods for one-sided testing: theory and application in treatment effect evaluation

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. In this paper, we propose an optimal false discovery rate controlling method that is especially useful for such one-sided testing problems. The proposed procedure is optimal in the sense of minimizing the false non-discovery rate while controlling the false discovery rate at a pre-specified level; it uses a deconvolution method based on non-parametric maximum likelihood estimation, which 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 it is applied to study the effect of attending a more selective high school in Romania. 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.