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A robust permutation test for subvector inference in linear regressions

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  • Xavier D'Haultfœuille
  • Purevdorj Tuvaandorj

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.

Suggested Citation

  • Xavier D'Haultfœuille & Purevdorj Tuvaandorj, 2024. "A robust permutation test for subvector inference in linear regressions," Quantitative Economics, Econometric Society, vol. 15(1), pages 27-87, January.
    • Handle: RePEc:wly:quante:v:15:y:2024:i:1:p:27-87
    DOI: 10.3982/QE2269
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    References listed on IDEAS

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    Cited by:

    1. Alexis Derumigny & Lucas Girard & Yannick Guyonvarch, 2025. "Can we have it all? Non-asymptotically valid and asymptotically exact confidence intervals for expectations and linear regressions," Papers 2507.16776, arXiv.org, revised Jul 2025.
    2. Ian Xu, 2025. "Fast Test Inversion for Resampling Methods," Papers 2512.14024, arXiv.org.

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