Hi Statalist

In the help files for -hausman- we see an example (eg1 on p.894, Stata 16) in which all the regressors vary with time.

My question is whether the Hausman test is still valid when there are time-invariant regressors that the FE model subsequently remove?

In the simulated data below, the unobserved time-invariant component is correlated with regressor x1. As such, it would suggest that we should apply an FE model instead of an RE model.

However, x1 is time-invariant and the resultant Hausman test supports the use of RE. Does this mean that in order for the Hausman test to be valid (ignoring homoskedasticity for the time being), both sets of RE and FE equations must contain the same set of regressors?

Thanks.

In the help files for -hausman- we see an example (eg1 on p.894, Stata 16) in which all the regressors vary with time.

My question is whether the Hausman test is still valid when there are time-invariant regressors that the FE model subsequently remove?

In the simulated data below, the unobserved time-invariant component is correlated with regressor x1. As such, it would suggest that we should apply an FE model instead of an RE model.

However, x1 is time-invariant and the resultant Hausman test supports the use of RE. Does this mean that in order for the Hausman test to be valid (ignoring homoskedasticity for the time being), both sets of RE and FE equations must contain the same set of regressors?

Thanks.

Code:

***************** clear set seed 111 set obs 1000 ***************** generate id = _n generate year = 2000 generate x1 = runiform()> .5 generate nu = rnormal() generate alpha = x1 + nu ***************** expand 5 bysort id: replace year = year + _n ***************** generate x2 = rbeta(2,3) generate u = rnormal() ***************** generate y = (3) + (1) * x1 + (1) * x2 + alpha + u // the unobserved time-invariant component alpha is correlated with regressor x1, // so FE would be more appropriate xtset id year xtsum // to check that x1 is time-invariant whereas x2 varies with time quietly xtreg y x1 x2, re estimates store RE quietly xtreg y x1 x2, fe estimates store FE hausman FE RE, sigmamore ---- Coefficients ---- | (b) (B) (b-B) sqrt(diag(V_b-V_B)) | FE RE Difference S.E. -------------+---------------------------------------------------------------- x2 | .9144598 .9098057 .0046541 .016269 ------------------------------------------------------------------------------ b = consistent under Ho and Ha; obtained from xtreg B = inconsistent under Ha, efficient under Ho; obtained from xtreg Test: Ho: difference in coefficients not systematic chi2(1) = (b-B)'[(V_b-V_B)^(-1)](b-B) = 0.08 Prob>chi2 = 0.7748

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