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-.
--Mark
Prof. Mark Schaffer
Director, CERT
Department of Economics
School of Management & Languages
Heriot-Watt University, Edinburgh EH14 4AS
tel +44-131-451-3494 / fax +44-131-451-3296
email: [email protected]
web: http://www.sml.hw.ac.uk/ecomes
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