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


From   Jordana Rodrigues Cunha <jordana.rodrigues@unibo.it>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   st: 2nd Step GMM estimation with nonlinear endogenous regressors is biased?
Date   Tue, 14 Dec 2010 15:24:26 +0000

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