CPANEL Procedure
Hausman Specification Tests
For models that include random effects, the CPANEL procedure outputs the results of the Hausman (1978) specification test. This test was also proposed by Wu (1973) and further extended in Hausman and Taylor (1982).
Consider two estimators, 
and 
, which under the null hypothesis are both consistent but only is asymptotically efficient. Under the alternative hypothesis, only is consistent. The m statistic is
where 
and 
are estimates of the asymptotic covariance matrices of and . The statistic 
follows a 
distribution with 
degrees of freedom, where is the rank of 
. This rank is normally equal to the dimension of 
, but is reduced when regressors that are constant within cross sections are dropped from the fixed-effects model.
The null hypothesis is that the effects are independent of the regressors. Under the null hypothesis, the fixed-effects estimator is consistent yet inefficient, whereas the random-effects estimator is both consistent and efficient. Failure to reject the null hypothesis favors the random-effects specification.