Sargan Test

The Sargan test is a test of the validity of instrumental variables. It is a test of the overidentifying restrictions. The hypothesis being tested with the Sargan test is that the instrumental variables are uncorrelated to some set of residuals, and therefore they are acceptable, healthy, instruments.

If the null hypothesis is confirmed statistically (that is, not rejected), the instruments pass the test; they are valid by this criterion.

In the Shi and Svensson working paper (which shows that elected national governments in 1975-1995 had larger fiscal deficits in election years, especially in developing countries), the Sargan statistic was asymptotically distributed chi-squared if the null hypothesis were true

Hausman Test

Given a model and data in which fixed effects estimation would be appropriate, a Hausman test tests whether random effects estimation would be almost as good. In a fixed-effects kind of case, the Hausman test is a test of H₀: that random effects would be consistent and efficient, versus H₁: that random effects would be inconsistent. (Note that fixed effects would certainly be consistent.) The result of the test is a vector of dimension k (dim(b)) which will be distributed chi-square(k). So if the Hausman test statistic is large, one must use FE. If the statistic is small, one may get away with RE.