Re: st: RE: ivreg2 and xtoverid error

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

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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