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Re: Re: st: st. Simultaneous Equations Model & GMM Estimation

From   Bond Tiger <>
Subject   Re: Re: st: st. Simultaneous Equations Model & GMM Estimation
Date   Mon, 19 Jul 2010 22:49:14 -0700 (PDT)

I have few more questions: 

(1) Can I use IV-GMM with dummy regressors (endogenous and exogenous)?

(2) Also if instruments are defined as dichotomous (with 1 & 0 values) then can 
IV-GMM estimation or CUE give consistent & efficient estimates?

My instruments are satisfying overidentifying restriction tests, however, they 
are appearing to be weak instruments. I have tested for weak instruments using 
Kleibergen-Paap rk Wald F statistics and Stock-Yogo weak IV test critical 

(3) Do you think, since my instruments are dichotomous variables (and also the 
frequencies of 0s are more than 1s for these instruments) therefore this weak 
instrument problem is arising (even if the instruments are passing the 
overidentifying restriction tests)?

Also I have tested for weak instrument robust inference (using Anderson-Rubin 
Wald test and Stock-Wright LM test statistics, to test significance of the 
endogenous regressors in the structural equation) and it also fails to reject 
null. What does this imply?  

Please help.



----- Original Message ----
From: Bond Tiger <>
Sent: Mon, July 19, 2010 9:16:41 AM
Subject: Re: Re:  st: st. Simultaneous Equations Model & GMM Estimation

Thank you so much. Your advice are really helpful and greatly appreciated.



----- Original Message ----
From: Christopher Baum <>
To: "" <>
Sent: Mon, July 19, 2010 5:57:09 AM
Subject: Re: Re:  st: st. Simultaneous Equations Model & GMM Estimation 

On Jul 19, 2010, at 2:33 AM, Bond wrote:

> Thank you very much Dr. Baum for your response. This is what I have understood
> from your response, please correct me if I am wrong......
> (1) It would not matter if I use system estimation technique but test my
> instruments in a single equation setup.
> (2) I may not have to test for endogeneity of the regressors (Y1 and Y2) in 
> single equation setup as by model specification itself I have considered the
> regressors to be endogenous.
> I may consider estimating the equations simultaneously, otherwise if single
> equation estimation is considered efficiency may be lost. Also I may have the
> following situations:
> (A) I may consider Seemingly Unrelated Regression (SUR) equations, in which 
> I may have different sets of explanatory variables in both the equations but 
> disturbance terms in both the equations may be correlated (may be some
> unconsidered factors influence the disturbance terms in both the equations) 
> then estimating all the equations simultaneously taking the covariance 
> of the residuals into account would lead to efficient estimates of parameters.
> Otherwise, single equation estimation would lead to inefficient estimates.
> (B) If I consider cross-equation parameter restrictions (in case both the
> equations have common explanatory variables), then also the only way to test 
> impose these restrictions is in a simultaneous equations setup.
> Therefore, not ruling out (A) and (B), I may finally estimate both the 
> simultaneously.
> (3) So is there any code in STATA for SYSTEM ESTIMATION?

Re point (1) above: not quite so, but if your instruments reject the 
overidentifying restrictions in single-equation estimation, stop there.

Re point (2): in specifying (in any estimator) which variables you consider 
endogenous, you invoke the appropriate estimator.

Re point (A): the discussion of SUR is irrelevant. SUR does not handle equations 

with endogenous regressors. It is OLS applied to each equation, taking account 
of the error correlations across equations. If any of the regressors are 
endogenous, SUR is inconsistent.

Re point (B): just because the equations contain the same regressors, there is 
no implication that there are cross-equation restrictions unless theory suggests 


Re point (3): the only 'canned' code is that of reg3, which is a very old and 
severely limited implementation of three-stage least squares (it does not, for 
instance, allow for anything beyond iid errors: no robust, cluster, HAC, IV-GMM, 

etc.)  Unless you can conclusively argue that your errors are iid, I would not 
use it. I would use single equation estimation with IV-GMM.


Kit Baum   |   Boston College Economics & DIW Berlin   |
                              An Introduction to Stata Programming  |
   An Introduction to Modern Econometrics Using Stata  |

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