Hi,

I am dealing with an econometric modeling issue which is new to me. While I have used 2SLS and dealt with the difficulty of instrumental variables, the simultaneity of equations in 3SLS is confusing me.

I have a model like the following:

X1=a1+b2*X2+b3*X3+b4*X4+ Z*CV+e (equation 1)
X2=a1+b1*X1+b3*X3+b4*X4+ Z*CV+e (equation 2)
X3=a1+b1*X1+b2*X2+b4*X4+ Z*CV+e (equation 3)
X4=a1+b1*X1+b2*X2+b3*X4+ Z*CV+e (equation 4)

CV represents the vector of control variables that are the same across the four equations.

As every independent variable in one equation is indicated to be produced in another equation (as a DV), X1, X2, X3, and X4 are endogenous.

In
HTML Code:
-reg3-
command, the inst() option is for instrumental variables. Since all instrumental variables are to be specified inside this option's function, I presume that Stata uses the same set of instruments for all four equations. Let's say I have five instruments: IV1, IV2, IV3, IV4, IV5. If this is used in equation 1, and if these are good instruments, they are supposed to be correlated with X2, X3, and X4 and uncorrelated with X1 (or, e in theory).

Then, if the same set of instruments is used for the second equation, they will be supposed to be correlated with X1, X3, X4 while in equation 1 we explicitly assumed that the instruments are not correlated with X1.

--How should I handle this issue when Stata uses the same set of instruments for every equation?
--Do I need 3SLS?

Thanks,
Navid