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st: Re: reg3 command and first-stage estimations


From   Kit Baum <baum@bc.edu>
To   statalist@hsphsun2.harvard.edu
Subject   st: Re: reg3 command and first-stage estimations
Date   Wed, 5 Sep 2007 06:47:09 -0400

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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