3SLS equation

[Biswanath Behera]

Suppose I have two equations
Y1= Y2+X1+X2+Z+eit
Y2= X1+X2+X3+M+uit

Suppose equation 1 have 6 variables and equation 2 have 5 variables. I want to use 3SLS to solve the above two equations simultaneously. Since, Y2 appears in both the equations it leads to a simultaneity. Can I use the 3SLS here?

[George Ford]

help reg3. in the 3rd set of examples, the first one is IV.

I think it goes something like this.

clear all
sysuse auto, clear
reg3 (eq1: price = mpg foreign displacement) (eq2: mpg = weight foreign length) , endog(mpg) exog(foreign displacement weight length) ireg3
reg3 (eq1: price = mpg foreign displacement) (eq2: mpg = weight foreign length) , inst(foreign displacement weight length) ireg3

[Biswanath Behera]

Yes sir, thank you for your clarification and for the reference.

[Biswanath Behera]

George Ford Sir, how do we check for the identification and the reliability of instruments used in 3SLS? Is there any post estimation techniques? For example in system GMM there is Sargan and Hansen test for instrumental validity. So, what are the post estimation techniques (codes) to be used after 3SLS in STATA for the same?

[George Ford]

I don't think so. Use ivreg2 for the main equation and use those results.

ivreg2 price (mpg = length weight) foreign displacement, r endo(mpg)

or you could try to code them yourself from the reg3 results.

eregress will give you the same results as ivreg2. ivreg2 also incoporates the residual correlation (LIML). Yet, the results between reg3 and ivreg2/eregress are not identical. But, if you are using reg3 to address residual correlation, then I'd use ivreg2 or eregress (the former giving you more diagnostics). Since both equations do not include an endogenous variable, I think these alternatives are sensible.

[Biswanath Behera]

Okay Sir George Ford ,
Thank you for the insights. I will look into it.