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Abstract:
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In longitudinal panel models with unobserved effects, fixed effects estimation is often paired with cluster-robust variance estimation (CRVE) in order to account for un-modeled dependence among the errors for each unit. CRVE is asymptotically consistent as the number of cross-sectional units increases, but can be biased downward for sample sizes often found in applied work, leading to hypothesis tests with overly liberal rejection rates. One solution is to use bias-reduced linearization (BRL), which corrects the CRVE so that it is unbiased under a working model, and t-tests with Satterthwaite degrees of freedom. We propose a generalization of BRL that can be applied in panel models with arbitrary sets of fixed effects, where the original BRL method is undefined, and describe how to apply the method when the regression is estimated after absorbing the fixed effects. We also propose a small-sample test for multiple-parameter hypotheses, which generalizes the Satterthwaite approximation for t-tests. In simulations covering a variety of study designs that occur in economic applications, we find that the small-sample test has Type I error very close to nominal levels.
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