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A Robust Permutation Test for Subvector Inference in Linear Regressions

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  • Xavier D'Haultf{oe}uille
  • 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'Haultf{oe}uille & Purevdorj Tuvaandorj, 2022. "A Robust Permutation Test for Subvector Inference in Linear Regressions," Papers 2205.06713, arXiv.org, revised Sep 2023.
    • Handle: RePEc:arx:papers:2205.06713
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    References listed on IDEAS

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    2. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    3. Purevdorj Tuvaandorj, 2021. "Robust Permutation Tests in Linear Instrumental Variables Regression," Papers 2111.13774, arXiv.org, revised Jun 2023.
    4. Hansen, Bruce E. & Lee, Seojeong, 2019. "Asymptotic theory for clustered samples," Journal of Econometrics, Elsevier, vol. 210(2), pages 268-290.
    5. Wooldridge, Jeffrey M., 2001. "Asymptotic Properties Of Weighted M-Estimators For Standard Stratified Samples," Econometric Theory, Cambridge University Press, vol. 17(2), pages 451-470, April.
    6. Guido W. Imbens & Paul R. Rosenbaum, 2005. "Robust, accurate confidence intervals with a weak instrument: quarter of birth and education," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 168(1), pages 109-126, January.
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    1. de Chaisemartin, Clément & D’Haultfœuille, Xavier, 2023. "Two-way fixed effects and differences-in-differences estimators with several treatments," Journal of Econometrics, Elsevier, vol. 236(2).

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