re: st: hausman test xtivreg(re) vs ivreg

[Kit Baum <baum@bc.edu>]

<>
Sergio wrote

> Let me clarify the context. I am evaluating certain treatment that is
> available only at some hospitals, but my data is at the patient level.
> There are unobservables in the selection process, therefore the need for
> an IV strategy. I am concerned about whether to adjust SE by this
> clustering issue. Fixed effects at the hospital level is not possible, but
> "xtivreg, re" is possible with "xtset hospital". So I am exploring whether
> a hausman test is possible in this context, as a way to test whether a RE
> model is a better specification than my IV estimation.
> I just read in the xtivreg documentation that "If the nosa option is
> specified, the consistent estimators described in Baltagi and Chang (2000)
> are used." (Page 213, xtivreg, re). Does that mean that a hausman test is
> possible?

No. The discussion in the manual is only speaking of consistent estimation of the variance components, that for the
unit-specific error and that for the idiosyncratic error. But the RE estimator will not yield consistent estimates of anything if
you violate the maintained hypothesis that the random effect is orthogonal to the regressors. 

As I said before, a Hausman test contrasts the estimates from two models under two states of the world:
i) name-consistent: consistent estimates under both states
ii) name-efficient: consistent and relatively efficient in state A, but inconsistent in state B

For OLS vs IV, IV is name-consistent, OLS is name-efficient, with state A: E(u|X)=0, state B, not so.
For RE vs FE, FE is name-consistent, RE is name-efficient, with state A: E(v|X)=0, state B, not so, with v the random component.

In a panel setting, FE is consistent in the presence of unobserved heterogeneity, and OLS is inconsistent in that case. But there is no Hausman test in this regard; you just do the F-test for all fixed effect coefficients = 0. To apply a RE model, you have to be able to establish that E(v|X)=0. We usually do that via the above Hausman test, which you say can't be implemented because your variable of interest is subsumed in the individual (hospital) fixed effect.

If there are unobservables in the selection of patients into hospitals, then why aren't you doing something like a selection model?

This is not a 'clustering issue'. Ignoring clustering might mess up your VCE, but it would not make the estimates inconsistent. Ignoring the unobservables, or ignoring unobserved heterogeneity, would make the estimates inconsistent.

Kit Baum   |   Boston College Economics & DIW Berlin   |   http://ideas.repec.org/e/pba1.html
                              An Introduction to Stata Programming  |   http://www.stata-press.com/books/isp.html
   An Introduction to Modern Econometrics Using Stata  |   http://www.stata-press.com/books/imeus.html


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