A Robust Permutation Test for Subvector Inference in Linear Regressions

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. Simulations and an empirical illustration suggest that the test has good power in practice.