Re: st: RE: Hausman test (via a Wald test)

[John Antonakis <John.Antonakis@unil.ch>]

Right, Eric.

But some estimators are more efficient; take the case where you compare 
IV estimates (consistent) versus OLS estimates (efficient).  The Hausman 
test will suggest that an efficient estimator is not consistent in the 
case where, for example, a regressor is endogenous, because the 
consistent vs efficient estimates will be significantly different, as 
tested by the usual  Hausman test:

(d_IV - d_OLS)/(SE_d^2_IV - SE_d^2_OLS)^-1.

Thus, I am suggesting that one uses the Wald postestimation test 
following the OLS model to determine whether the estimate/s of the OLS 
model is/are significantly different from the estimate/s of the IV 
model.  My question has to do with the fact that the Wald test, in this 
case, tests the OLS coefficient/s against a specific value/s (that of 
the IV estimator) and ignores the variance in the IV estimate/s--so I 
was wondering whether this was econometrically sound to do.

Best,
J.

__________________________________________

Prof. John Antonakis
Faculty of Business and Economics
Department of Organizational Behavior
University of Lausanne
Internef #618
CH-1015 Lausanne-Dorigny
Switzerland
Tel ++41 (0)21 692-3438
Fax ++41 (0)21 692-3305
http://www.hec.unil.ch/people/jantonakis

Associate Editor
The Leadership Quarterly
__________________________________________


On 01.05.2011 17:03, DE SOUZA Eric wrote:
> John,
>
> I don't get your point. Consistency refers to the parameter estimate, efficiency refers to the variance of the estimate.
>
> The Hausman principle compares two estimators, both of which are consistent under the null but only one under the alternative.
>
> This is quite general.
>
>
> Eric de Souza
> College of Europe
> Brugge (Bruges), Belgium
> http://www.coleurope.eu
>
>
> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of John Antonakis
> Sent: 01 May 2011 16:51
> To: statalist@hsphsun2.harvard.edu
> Subject: st: Hausman test (via a Wald test)
>
> Hi:
>
> Given that sometimes Stata cannot compute the Hausman test (because it is undefined or because the estimation procedure does not allow it), I have been thinking about ways to go around this limitation (and find SUEST to be particularly useful in this regard).
>
> I was wondering, though, if anyone is aware of literature showing that a Wald test could do too (which would be particularly useful in the case of models where the Hausman test can't be used in Stata); more specifically, the Wald test I am suggesting is to test whether the parameters (of interest) from the efficient estimator are significantly different from those of the consistent estimator.  It would be very simply to do and could accommodate a large class of estimators.
> However, this test is only a constraint on the coefficient estimate/s from the efficient estimator and ignores the variance of estimates from the consistent estimator (thus I don't know to what extent this test would be useful).
>
> Any thoughts?
>
> Best,
> John.
>
> --
> __________________________________________
>
> Prof. John Antonakis
> Faculty of Business and Economics
> Department of Organizational Behavior
> University of Lausanne
> Internef #618
> CH-1015 Lausanne-Dorigny
> Switzerland
> Tel ++41 (0)21 692-3438
> Fax ++41 (0)21 692-3305
> http://www.hec.unil.ch/people/jantonakis
>
> Associate Editor
> The Leadership Quarterly
> __________________________________________
>
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