The asymptotic distribution of the F‐test statistic for individual effects

Abstract

This paper employs first-order asymptotic theory in order to establish the asymptotic distribution of the F-test statistic for fixed effects, under non-normality of the errors, when N→∞ (the number of cross-sections) and T is fixed (the number of time periods). Three theoretical results emerge: (i) the standard F-test procedure will still deliver asymptotically valid inferences; (ii) under (pure) local random effects, the F-test and random effects test procedures have identical asymptotic power; (iii) under local fixed, or random effects which are correlated with the regressors, the F-test will have higher asymptotic power than the random effects test.