Testing the validity of the assumption, that the errors in a regression model are normally distributed, is a standard pastime in econometrics. We use this assumption when we construct standard confidence intervals for, or test hypotheses about, the parameters of our models. In

More recently,

**a post some time ago**I pointed out that this assumption is actually is sufficient,*but not necessary*, for the validity of these inferences.More recently,

**here**and**here**, I discussed some aspects of the normality test that most econometricians use - the asymptotically valid test of Jarque and Bera (1987). Let's refer to this as the JB test. In the first of those posts I made brief mention of the finite-sample properties of the JB test, and I concluded:"However, more recent evidence suggests that the power of the J-B test can be quite low in small samples, for a number of important alternative hypotheses -The main results obtained by Thadewald and Buning are summed up in the abstract to their paper .............e.g., see Thadewald and Buning (2004). I'll address this aspect of the J-B test more fully in a later post."