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Re: st: RE: ivreg2 and xtoverid error


From   John Antonakis <john.antonakis@unil.ch>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: RE: ivreg2 and xtoverid error
Date   Sat, 03 Apr 2010 22:46:31 +0200

Thank Kit.

One small bit of evidence for the fact that the fixed effects don't correlate with the error might come from the -xtoverid- test for random vs fixed effects. The classic interpretation of the test is that if it is significant, it suggests that the endogenous regressors correlate with y when the fixed-effects are not included. However, and equally so, if the test is significant, it means too that the fixed-effects correlate with y when controlling for the endogenous regressors (the fixed-effects correlate with the residual variance of y when controlling for the endogenous regressors). This test is akin to a mediation test as follows, where x is the endogenous regressor and z is exogenous:

1. regress y on x (obtain significant coefficient)
2. regress y on z (obtain significant coefficient)
3. regress y on x and z (obtain significant coefficient only for x)

If in step 3 the coefficient of z becomes non-significant (when it was significant before), then we have evidence of mediation--that is, that the correlation of x with y is stronger than that of z with y while controlling for the relation of x and z. The -xtoverid- test does an analogous thing: if it is non-significant we know that the endogenous regressors account for all the variance in y and that instruments don't correlate with y when controlling for the regressors; thus as an exogenous instrument, it should not correlate with the residual. I got the Sargan-Hansen statistic from the -xtoverid- 12.979 Chi-sq(13) P-value = 0.4494.

Also, I estimated the following fixed-effects model, a direct analog of the above mediation effect model :

reg y x1-x13 i.lead_num, cluster(lead_num)
est store fe
reg y x1-x13, cluster(lead_num)
hausman fe, force

This test is non-significant too (though I should not be using the Hausman test with a robust estimator). Thus controlling for the endogenous variable, the fixed-effects do not correlate with y. I hope that what I have said makes sense.

Also, concerning the power issue, on one hand, with more instruments the model has more ways to go wrong so ceteris paribus, power to detect misspecification goes up with more degrees of freedom, correct? On the other hand, with weak instruments the power of the test is reduced. I guess a simulation would be needed to settle this.

Anyway, you are right in that it is possible that my instruments are weak and thus introduce bias. I have taken note of this limitation. I actually have direct measures of the leader's ability, personality, and other things, though I am saving them for another publication. I will check though to see what they give too in comparison to the fixed-effects instruments.

Best regards,
John.

____________________________________________________

Prof. John Antonakis, Associate Dean 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

Faculty page:
http://www.hec.unil.ch/people/jantonakis

Personal page:
http://www.hec.unil.ch/jantonakis
____________________________________________________



On 03.04.2010 17:14, Kit Baum wrote:
<>
John said

I get exactly the same estimates and standard errors with -ivreg- and -ivregress-, with the cluster robust variance estimator. When using -ivreg2- with the -noid- option it works and I get the same estimates; more importantly, I also get the Hansen J-test, which is what interests me most (the -ivregress- estimator does not report an overid for cluster-robust vce's):

Hansen J statistic (overidentification test of all instruments): 402.476, Chi-sq(404) P-val = 0.5121

The one thing to worry about here is that which arises with Sargan-Hansen tests after xtabond or user-written xtabond2: the overid test may not have much power when confronted with hundreds of instruments.
You also mention the test provided by 'estat endogenous', which could be done in ivreg2 via the endog() option. This Durbin-Wu-Hausman test is merely telling you that you shouldn't use OLS on this model. But you're probably convinced of that in any event. Rejecting OLS as inconsistent does not imply that IV is consistent; that depends on the overid test of the excluded instruments (which you pass, but as mentioned may have low power to detect a problem) and the proper specification of the model. You might want to use ivreg2's orthog() option to consider just the non-dummy instruments as a group, and check to see that that Hansen "GMM distance" test also supports the notion that those excluded instruments are suitably orthogonal to the error.

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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