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 ind...

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Bibliographic Details
Published inQuantitative economics Vol. 15; no. 1; pp. 27 - 87
Main Authors D'Haultfœuille, Xavier, Tuvaandorj, Purevdorj
Format Journal Article
LanguageEnglish
Published New Haven, CT The Econometric Society 2024
John Wiley & Sons, Inc
Subjects
asymptotic validity
C12
C15
C21
Central limit theorem
Confidence intervals
Econometrics
exact tests
heteroskedasticity
Linear analysis
Linear regressions
permutation tests
Power
Reinforcement
Simulation
Tests
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Summary: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.
ISSN:1759-7331
1759-7323
1759-7331
DOI:10.3982/QE2269