Economics Job Talk

Abstract: This article considers the problem of testing sign agreement of a finite number of means. Examples of this problem include detecting heterogeneous treatment effects with opposite signs, testing casual interpretation of two-stage least-squares estimand, and testing political affiliation alignment across multiple groups. For the null hypothesis that the means are all non-negative or all non-positive, I propose two novel statistical tests: the Least Favorable and the Hybrid tests. Both tests control their asymptotic sizes uniformly over a large class of distributions for the observed data. They can be implemented with either bootstrap-based critical values or simulation-based critical values. In the literature of sign agreement tests, both tests are the first to accommodate arbitrary dependence among estimators for any finite number of means. Results from simulation studies indicate that, with finite samples, the rejection probabilities of both tests reach the nominal level under the null hypothesis. The Hybrid test exhibits higher power than the Least Favorable test when there are more than three means; this relationship reverses when considering only two means. I demonstrate the utility of both tests in an application inspired by Angelucci et al. (2015), in which I study the impacts of microloans on various groups and outcomes.