Testing Sign Agreement

2026-08-10

AI Summary

This study addresses the problem of testing finite-dimensional parameter sign consistency—i.e., whether all components are nonnegative or all are nonpositive—with applications to heterogeneous treatment effect identification and instrumental variable validity. The authors propose two novel approaches: a least favorable test that employs critical values derived from the least favorable null distribution, and a conditional test that first screens out components with unambiguous signs and then conducts inference on the remaining parameters conditionally. For the first time, these methods achieve valid inference under arbitrary dependence structures among estimators, and in the independent case, their critical values depend only on the dimension and significance level. Theoretical results establish asymptotic size control uniformly over broad nonparametric classes of distributions. Simulations demonstrate that the least favorable test performs better near the boundary of the null hypothesis, whereas the conditional test exhibits higher power when some parameters are substantially away from zero.

Abstract

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-unresolved components conditional on the screening event. Unlike existing sign agreement 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. We 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.

Problem

• sign agreement
• treatment effects
• instrument validity
• hypothesis testing
• parameter signs

Innovation

• sign agreement test
• least favorable test
• conditional test
• arbitrary dependence
• asymptotic size control