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Heteroskedasticity-Robust Inference in Linear Regression Models

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  • Jochmans, K.

Abstract

This paper considers inference in heteroskedastic linear regression models with many control variables. The slope coefficients on these variables are nuisance parameters. Our setting allows their number to grow with the sample size, possibly at the same rate, in which case they are not consistently estimable. A prime example of this setting are models with many (possibly multi-way) fixed effects. The presence of many nuisance parameters introduces an incidental-parameter problem in the usual heteroskedasticity-robust estimators of the covariance matrix, rendering them biased and inconsistent. Hence, tests based on these estimators are size distorted even in large samples. An alternative covariance-matrix estimator that is conditionally unbiased and remains consistent is presented and supporting simulation results are provided.

Suggested Citation

  • Jochmans, K., 2019. "Heteroskedasticity-Robust Inference in Linear Regression Models," Cambridge Working Papers in Economics 1957, Faculty of Economics, University of Cambridge.
    • Handle: RePEc:cam:camdae:1957
    Note: kj345
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    References listed on IDEAS

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    1. James H. Stock & Mark W. Watson, 2008. "Heteroskedasticity-Robust Standard Errors for Fixed Effects Panel Data Regression," Econometrica, Econometric Society, vol. 76(1), pages 155-174, January.
    2. John M. Abowd & Francis Kramarz & David N. Margolis, 1999. "High Wage Workers and High Wage Firms," Econometrica, Econometric Society, vol. 67(2), pages 251-334, March.
    3. Raj Chetty & John N. Friedman & Jonah E. Rockoff, 2014. "Measuring the Impacts of Teachers I: Evaluating Bias in Teacher Value-Added Estimates," American Economic Review, American Economic Association, vol. 104(9), pages 2593-2632, September.
    4. Matias D. Cattaneo & Michael Jansson & Whitney K. Newey, 2018. "Inference in Linear Regression Models with Many Covariates and Heteroscedasticity," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(523), pages 1350-1361, July.
    5. Jonah E. Rockoff, 2004. "The Impact of Individual Teachers on Student Achievement: Evidence from Panel Data," American Economic Review, American Economic Association, vol. 94(2), pages 247-252, May.
    6. 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.
    7. Chesher, Andrew & Jewitt, Ian, 1987. "The Bias of a Heteroskedasticity Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 55(5), pages 1217-1222, September.
    8. Joshua Angrist & Jinyong Hahn, 2004. "When to Control for Covariates? Panel Asymptotics for Estimates of Treatment Effects," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 58-72, February.
    9. MacKinnon, James G. & White, Halbert, 1985. "Some heteroskedasticity-consistent covariance matrix estimators with improved finite sample properties," Journal of Econometrics, Elsevier, vol. 29(3), pages 305-325, September.
    10. Koen Jochmans & Martin Weidner, 2019. "Fixed‐Effect Regressions on Network Data," Econometrica, Econometric Society, vol. 87(5), pages 1543-1560, September.
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    Cited by:

    1. Anatolyev, Stanislav & Sølvsten, Mikkel, 2023. "Testing many restrictions under heteroskedasticity," Journal of Econometrics, Elsevier, vol. 236(1).

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