Testing inference in heteroskedastic fixed effects models

• We wrote the test statistics as ratios of Gaussian quadratic forms.
• We used numerical integration to compute their exact null distributions.
• We compare the limiting null distribution with the exact null distributions.
• Most accurate asymptotic approximations are obtained with CHC4 and CHCR0 tests.
• We recommend that inference in FE models be based such quasi-t test statistics.

This paper considers the issue of performing testing inference in fixed effects panel data models under heteroskedasticity of unknown form. We use numerical integration to compute the exact null distributions of different quasi-t test statistics and compare them to their limiting counterpart. The test statistics use different heteroskedasticity-consistent standard errors. Our results reveal that the asymptotic approximation is usually poor in small samples when the test statistic is based on the covariance matrix estimator proposed by Arellano (1987). The quality of the approximation is greatly increased when the standard error is obtained using other heteroskedasticity-consistent estimators, most notably the CHC4 estimator. Our results also reveal that the performance of Arellano’s test improves considerably when standard errors are computed using restricted residuals.