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Re: st: RE: ivreg2 and xtoverid error
From
John Antonakis <[email protected]>
To
[email protected]
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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