Why STATA represents a shift in my PPF
From the STATA-list digest:
New version of -xtoverid- that tests fixed vs random effects available from SSC
Thanks to Kit Baum, a new version of -xtoverid- is available from SSC.
The main change is that, after a standard random effects estimation using -xtreg,re-, -xtoverid- will report an artificial regression based test of fixed vs random effects. In the special case of homoskedastic errors, the test reported by -xtoverid- is equivalent to the standard Hausman-type test of fixed vs random effects. The advantages of the -xtoverid- test over the test statistic generated using the -hausman- command are that (a) it extends straightforwardly to the cases of heteroskedastic or clustered errors, and (b) it will always generate a nonnegative test statistic.
For those who are wondering why a test of fixed vs random effects is supported by a module for testing "overidentifying restrictions", the reason is that the extra orthogonality conditions that make random effects more efficient than fixed effects can be seen as overidentifying restrictions. In GMM-speak, the fixed effects estimator uses the orthogonality conditions that the regressors are uncorrelated with the idiosyncratic error e_it, i.e., E(X_it*e_it)=0. The random effects estimator uses the additional orthogonality conditions that the regressors are uncorrelated with the group-specific error u_i (the "random effect"), i.e., E(X_it*u_i)=0. These additional orthogonality conditions are overidentifying restrictions. See the -xtoverid- help file for further discussion, references, and an example where the test statistic reported by -xtoverid- is numerically equal to the test statistic reported by -hausman-.
How long would you have to wait for SAS to implement such a test? As far as I can tell, this change in STATA came within a couple of weeks of the topic first being mentioned on the STATA listserv.
This is one reason why my vitae has almost 200% larger than when I applied for tenure five years ago.