# st: Re: ivreg2 use

 From Christopher F Baum To statalist@hsphsun2.harvard.edu Subject st: Re: ivreg2 use Date Wed, 6 Aug 2003 07:24:46 -0400

```On Wednesday, August 6, 2003, at 02:33 AM, Busakom wrote:

```
```I have two simultaneous equations:

(1)  y1 = a0*y2 + a1*x1 + a2*x2 + a3*x3 + e
(2)  y2 = b0*y1 + b1*z1 + b2*z2 + b3*z3 + u

The variables are first-differences. As I understand,
I can perform 2SLS by using ivreg2:

ivreg2 y1 x1 x2 x3 (y2 = z1 z2 z3)

My problem is slightly more complicated than this.
What if, in each equation, there is a lag dependent
variable:

(3)  y1 = a0*y2 + a1*x1 + a2*x2 + a3*x3 + a4*Ly1 + e
(4)  y2 = b0*y1 + b1*z1 + b2*z2 + b3*z3 + b4*Ly2 + u

Here, Ly1 is correlated with e, and Ly2 is correlated
with u.  I plan to instrument Ly1 with L2y1
(two-period lag of y1) and Ly2 with L2y2 (two-period
lag of y2).

I believe I can still use ivreg2 to deal with this
problem.  My question is whether the following command
syntax is correct?

ivreg2 y1 x1 x2 x3 (y2 Ly1 Ly2 = z1 z2 z3 L2y1 L2y2)

And is -ivreg2, gmm- is the same as -ivgmm0-?
```
Almost correct. You should disabuse yourself of the notion that "this is an instrument for that"; as frequently mentioned on this list and in the cited Stata FAQ, instrumental variables estimators do not work that way. All of the Z variables are instruments for all of the included Y variables. That said, what about your proposed regression?

Your first equation contains regressors y2, x1-x3, and Ly1. It does not contain Ly2, so Ly2 should not be present in the included endogenous list to the left of the equals sign, or it will appear as a regressor in the equation, which presumably it should not. The instrument list is correct, if your assertion that the second lags are orthogonal to e and u is warranted. This can be tested with a diff-Sargan test (ivreg2 orthog option). Note that ivreg2 will report that the instruments include x1, x2, x3 plus those you have specified (and constant) -- and that is correct. The included exogeneous variables are indeed instruments as well.

ivreg2, gmm is essentially the same estimator as the earlier ivgmm0. A version of ivreg2 is currently under development which will provide 'ivgmmN' -- that is, allowing for arbitrary heteroskedasticity and serial correlation in the error process. ivgmm0 (and its implementation within ivreg2) only allows for the former.

Kit
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