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A test of fixed vs. random effects can also be seen as a test of overidentifying
restrictions. 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. The test is implemented by xtoverid
using the artificial regression approach described by Arellano (1993) and
Wooldridge (2002, pp. 290-91), in which a random effects equation is reestimated
augmented with additional variables consisting of the original regressors
transformed into deviations-from-mean form. The test statistic is a Wald test of
the significance of these additional regressors. A large-sample chi-squared test
statistic is reported with no degrees-of-freedom corrections. Under conditional
homoskedasticity, this test statistic is asymptotically equivalent to the usual
Hausman fixed-vs-random effects test; with a balanced panel, the artificial
regression and Hausman test statistics are numerically equal. See Arellano
(1993) for an exact statement and the example below for a demonstration. Unlike
the Hausman version, the test reported by xtoverid extends straightforwardly to
heteroskedastic- and cluster-robust versions, and is guaranteed always to
generate a nonnegative test statistic.
原假设是 随机效应
拒绝原假设是 选择固定效应
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