Testing Sign Agreement

Abstract: This article considers the problem of testing sign agreement of a finite number of means. This problem naturally emerges in numerous empirical contexts including detecting sign-opposing average treatment effects across subgroups in randomized controlled trials, testing homogeneity of local average treatment effects (LATE) across subpopulations, and examining the testable implication of the assumptions for LATE. For the null hypothesis that the means are all non-negative or all non-positive, I propose two novel bootstrap tests: the Least Favorable and the Hybrid tests. Unlike existing tests, both tests accommodate arbitrary dependence among estimators for any finite number of means. I show that both tests control their asymptotic sizes uniformly over a large class of nonparametric distributions. Results from simulation studies in finite samples, indicate that rejection probabilities of both tests reach the nominal level under the null hypothesis. The Hybrid test exhibits higher power than the Least Favorable test in a broad class of data generating processes. 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.