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

A Robust Permutation Test for Subvector Inference in Linear Regressions