  In longitudinal panels and other regression models with unobserved effects,
fixed effects estimation is often paired with cluster-robust variance
estimation (CRVE) in order to account for heteroskedasticity and un-modeled
dependence among the errors. CRVE is asymptotically consistent as the number of
independent clusters 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 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, we find that conventional cluster-robust Wald tests can severely
under-reject while the proposed small-sample test maintains Type I error very
close to nominal levels.
