Testing Sign Agreement

This article considers the problem of testing sign agreement among a finite number of parameters. This problem arises in empirical settings such as detecting treatment effects with opposite signs across subgroups, outcomes, or time periods, and testing instrument validity for local average treatment effects. For the null hypothesis that the parameters are either all non-negative or all non-positive, I propose two novel tests: a least favorable test and a conditional test. The least favorable test uses a worst-case null critical value, while the conditional test first screens components with large positive or negative estimates and then tests the remaining sign-ambiguous components conditional on the screening event. Unlike existing tests, both procedures accommodate arbitrary dependence among estimators; in the special case of independent estimators, the critical values depend only on the dimension and testing levels. I show that both tests control asymptotic size uniformly over a large class of nonparametric distributions. Local asymptotic power analysis reveals a tradeoff: the least favorable test is more powerful near boundary configurations where sign restrictions bind, whereas the conditional test is more powerful when some components are well separated from zero. Simulation evidence supports these theoretical predictions in finite samples. An application to Wolfers’s (2006) study of unilateral divorce laws detects a sign reversal in dynamic treatment effects, with positive short-run effects on divorce rates and negative longer-run effects.