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st: Re: reg3 command and first stage estimations

From   Kit Baum <[email protected]>
To   [email protected]
Subject   st: Re: reg3 command and first stage estimations
Date   Thu, 6 Sep 2007 06:39:18 -0400

You have specified a model with 27 endogenous variables and 18 exogenous variables (none of which are included in the specification). That in itself is a peculiar specification for a simultaneous equations system as in such a system the exogenous variables are meant to appear somewhere; it is their exclusion from various equations that provides identification, but the exog() list in reg3 should indicate that those variables appear in at least one equation as regressors. In your case the exclusion restrictions exclude all exogenous variables from all equations.

You should have 27 FSRs as you have 27 endogenous variables.

I suspect that as you are specifying the identical set of exogenous variables in each of those FSRs that there is no gain from 3SLS, and you would be just as well off specifying each individual equation in 2SLS terms. That would also reduce the possibility that misspecification or failure of orthogonality conditions in one equation would pollute the entire system. If you estimate each equation with IV/2SLS (or IV-GMM, if you want to allow for robust, cluster, etc.) you will avoid that problem.

Kit Baum, Boston College Economics and DIW Berlin
An Introduction to Modern Econometrics Using Stata:

On Sep 6, 2007, at 2:33 AM, Marta wrote:

This is my model.

lny1 = b0 + b1 lnye1 + b2 lnk1 + err

lny2 = c0 + c1 lnye2 + c2 lnk2 + err

lny3 = d0 + d1 lnye3 + d2 lnk3 + err

lny4 = q0 + q1 lnye4 + q2 lnk4 + err

lny5 = g0 + g1 lnye5 + g2 lnk5 + err

lny6 = h0 + h1 lnye6 + h2 lnk6 + err

lny7 = m0 + m1 lnye7 + m2 lnk7 + err

lny8 = n0 + n1 lnye8 + n2 lnk8 + err

lny9 = p0 + p1 lnye9+ p2 lnk9 + err

And the additional equations instrumenting each of the regressors with the instruments (lnw1, ..., lnw9, lnd1, ..., lnd9).

The command I'm using in Stata is the following:

. reg3 (lny1 = lne1 lnk1)(lny2 = lne2 lnk2)(lny3 = lne3 lnk3)(lny4 = lne4 lnk4)(lny5 = lne5 lnk5)(lny6 = lne6 lnk6)(lny7 = lne7 lnk7) (lny8 = lne8 lnk8)(lny9 = lne9 lnk9), endog (lne1 lne2 lne3 lne4 lne5 lne6 lne7 lne8 lne9 lnk1 lnk2 lnk3 lnk4 lnk5 lnk6 lnk7 lnk8 lnk9) exog (lnw1 lnw2 lnw3 lnw4 lnw5 lnw6 lnw7 lnw8 lnw9 lnd1 lnd2 lnd3 lnd4 lnd5 lnd6 lnd7 lnd8 lnd9) first

With reference to the exclusion restrictions, every first stage estimation has 18 regressors, and some of them are significant and some others are not. Additionally, I thought of using -reg3- command because of the fact that the especification is the same for all nine sectors.

I've run in Stata the example you suggested in your answer, and I still don't understand why in the first-stage regressions when using -reg3- command, the instruments (capital1 and invest) are used to estimate the dependent variable (consump). When using - ivreg2- command, the first-stage estimations correspond to the regressors and the instruments, but no estimation of the dependent variable on the instruments is provided.
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