st: Re: reg3 command and first-stage estimations

[Kit Baum <baum@bc.edu>]

Please provide the exact command you are using. What you describe  
below doesn't make a lot of sense---if y = f (e,k) and both of those  
regressors are endogenous, then you have a three-equation system. E.g.

y = b0 + b1 e + b2 k + err  (requires two instruments by order  
condition)

e = c0 + c1 w + err (for instance)

k = d0 + d1 d + err (for instance)

The FSRs will be the regression of each of the endog on all of the  
exog. E.g.

. webuse klein

. reg3 (consump profits wagepriv) ( profits invest) ( wagepriv  
capital1), first

The only difference between the point and interval estimates of this  
consump equation and those of

ivreg2 consump (profits wagepriv=invest capital1)

is that the reg3 estimates apply the exclusion restrictions that  
capital1 does not appear in the 2d eqn and invest does not appear in  
the 3d eqn. Those are testable hypotheses (as you can see by using  
the first option on ivreg2) and in this case the exclusion  
restrictions are rejected by the data (and the equations are  
misspecified, leading to misspecification error in the equation of  
interest as well).

If the equations for e and k in your context are not truly  
simultaneous---i.e. if they do not contain y--then there is no need  
to use 3SLS to estimate the system. If you fear that e and k are  
correlated with the error in the y eqn, use 2SLS (IV). You will find  
that 2SLS and 3SLS yield the same point and interval estimates if you  
relax the exclusion restrictions in the 2d and 3d eqns.

Kit

Kit Baum, Boston College Economics and DIW Berlin
http://ideas.repec.org/e/pba1.html
An Introduction to Modern Econometrics Using Stata:
http://www.stata-press.com/books/imeus.html


On Sep 5, 2007, at 2:33 AM, statalist-digest wrote:


> I'm using the -reg3- command because I want to simultaneously  
> estimate some equations, since I expect the error term across these  
> equations to be correlated. I'm also using instruments for the  
> regressors, because I have an endogeneity problem. I use the option  
> exog(varlist) and endog(varlist) to specify which are the  
> endogenous regressors and which are the instruments. The dependent  
> variable is y, the regressors are e and k and the instruments are w  
> and d. Stata provides the first-stage estimation for the  
> endongenous regressors (e,k). But, what I don't understand is why  
> it also provides this first-stage estimation for the dependent  
> variable (y). I had never seen that before. Is it something  
> particular to seemlingly unrelated regressions? Or is something  
> that I'm doing wrong in Stata?
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