A Robust Permutation Test for Subvector Inference in Linear Regressions

TL;DR

This paper introduces a new permutation test for subvector inference in linear models that is exact under independence and asymptotically valid under relaxed conditions, with good practical power.

Contribution

The paper presents a novel permutation test for subvector inference that remains valid under weaker assumptions and provides theoretical guarantees and empirical evidence of effectiveness.

Findings

Test is exact under independence of regressors and errors.

Test is asymptotically correct and consistent under relaxed conditions.

Simulation results show good power when the number of strata is small.

Abstract

We develop a new permutation test for inference on a subvector of coefficients in linear models. The test is exact when the regressors and the error terms are independent. Then, we show that the test is asymptotically of correct level, consistent and has power against local alternatives when the independence condition is relaxed, under two main conditions. The first is a slight reinforcement of the usual absence of correlation between the regressors and the error term. The second is that the number of strata, defined by values of the regressors not involved in the subvector test, is small compared to the sample size. The latter implies that the vector of nuisance regressors is discrete. Simulations and empirical illustrations suggest that the test has good power in practice if, indeed, the number of strata is small compared to the sample size.