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Faculty of Economics

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Jochmans, K.

Heteroskedasticity-Robust Inference in Linear Regression Models


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.

Keywords: bias, fixed effects, heteroskedasticity, inference, leave-one-out estimator, many regressors, unbalanced regressor design, robust covariance matrix, size control, statistical leverage

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