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st: R: 2nd Step GMM estimation with nonlinear endogenous regressors is biased?


From   Jordana Rodrigues Cunha <jordana.rodrigues@unibo.it>
To   "Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>, "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   st: R: 2nd Step GMM estimation with nonlinear endogenous regressors is biased?
Date   Fri, 17 Dec 2010 09:51:00 +0000

Dear professor, thank you very much for such 'amazing' answer! Now I can be sure about my conclusions and seems that the work is done ;))
 
I am very curious about one last thing, please if you could, let me know what you think.
If I need to estimate all the variables simultaneously in a "full information" system, as you said all the functional forms of my equations will be need to be correctly specified.
 
I thought about a 3sls regression, because it accepts non-recursive models. But as each dependent equation of my system would have different functional forms (1 dependent is continuous , other dichotomous and another ordinal ranked), with a 3sls I would not be able to inform the different functional forms once it takes for grant that the system is linear, right?
 
I tried to write the model as a recursive mixed process to use _cmp procedure, in order to specify correctly the functional form of each equation and after 870 interactions trying to fit the full model I gave up;I thought about to treat the model using _treatreg but one of my treatment equations was a ordered probit instead a probit and I couldn't treat the 2 endogenous regressors at the same time, I gave up too;

So, I would like to ask you if STATA has some implemented procedure that lead with full information systems that allows endogeneity among equations with different functional forms without the need to program ;(
I thank you very much for  your time and for clarify this point, whenever you could answer me,

I wish you a merry Christmas!
Jordana
________________________________________
Inizio: Schaffer, Mark E [M.E.Schaffer@hw.ac.uk]
Inviato: giovedì 16 dicembre 2010 18.35
Fine: statalist@hsphsun2.harvard.edu
Cc: Jordana Rodrigues Cunha
Oggetto: RE: 2nd Step GMM estimation with nonlinear endogenous regressors is biased?

Jordana,

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of
> Jordana Rodrigues Cunha
> Sent: 14 December 2010 15:24
> To: statalist@hsphsun2.harvard.edu
> Subject: st: 2nd Step GMM estimation with nonlinear
> endogenous regressors is biased?
>
> Dear all,
> I need to test the endogeneity of two regressors (a
> dichotomous and an ordinal ranked in five levels ) in a
> single equation model with a continuous dependent variable. I
> would like to confirm if I could do this using the amazing
> GMM option of ivreg2.

Thanks for the kind words.  Or did you mean a new kind of GMM estimator?
2-step efficient GMM, continuously updated GMM, amazing GMM....

> As I am not interested in estimating
> the full system of equations (fitting in the first stage, in
> this case a probit and an ordinal probit and in the 2nd stage
> an OLS), I don't need to give the correct functional form of
> my regressors in the first stage, do I?

Correct.  ivreg2 estimates single-equation ("limited information")
models only.  Adding functional form assumptions for the first stage is
akin to estimation a system of two equations (a "full information"
setup) where you have to specify both equations correctly.

> I explain:
>
> All the tests for underidentification (I am using clustered
> robust errors) and the J Hansen shows that if I need to
> instrumentalize my regressors I would be able to do it, even
> if my endog results confirms that my regressors are not
> endogenous and in this way, seems that my OLS results are
> more efficient.

I had to read this a couple of times but I think I understand: the
equation isn't underidentified; the overidentifying restrictions are
apparently valid; and an endogeneity test fails to reject the hypothesis
that your endogeneous regressors are actually exogenous.

> My point, than, is:
>
> The parameters estimated in the 2nd stage GMM are not
> significative for the tested regressors, but those in the OLS
> are...

This is quite possible.  OLS is more efficient than 2-step GMM, so the
standard errors are smaller and the estimates are more precise.

> While the assumption of a linear relationship between
> the dependents and independents variables in my 2 first stage
> models is violated,

Not true.  There is no such linearity assumption.  You're using a
single-equation, limited-information setup precisely so that you don't
have to make such assumptions.  The tradeoff is that your results are
more robust but not as efficient vs. using a system estimator.  This is
basically what you yourself say above.

> they recover correct standard errors that
> will be applied in the second stage, when I need to good
> estimates. Am I right? The parameters estimated with the 2nd
> step GMM could be biased after the assumption of linear form
> in my first stage

"Bias" is the wrong word - you mean "inconsistent".

And no, your second-stage estimates are consistent, because there is no
linear functional form assumption for the first stage - see above.

Best wishes,
Mark

> and I can believe in the results in my OLS,
> or the parameters estimated with ivreg2 GMM are better?
> Any help will be appreciate, thank you very much,
>
> jordana
>
>
> Jordana Rodrigues Cunha
> PhD. Candidate
> University of Bologna
> Department of Management
> Via Capo di Lucca, 34, 1st floor
> 40126 - Bologna, ITALY
> Fixed line:  0039 (051) 20 98 073
> Fax: 0039 (051) 20 98 074
> jordana.rodrigues@unibo.it
> www.sa.unibo.it
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>


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