Simultaneous Equations and Instruments

[Mustafa Abd]

I’m working on a simultaneous equation model and I appreciate your help in that regard.

Original OLS equations are as follows:

Y = X + Controls
Z = X + Controls

We probably have 2 issues here:

1) Y & Z are jointly determined
2) X is a governance variable and it is probably an endogenous variable too in both equations. The governance structure of the firm may be jointly determining all 3 variables.

I’m not sure what’s the best solution to tackle the above mentioned issues. Please note that the literature has already identified an instrument for X. I’ll call it XIV. I’m thinking of one of the following 2 options:

Option 1: Run the following 3 equation simultaneous equation model:
Y = X + Z + Exogenous Variables (Eq. 1)
Z = X + Y + Exogenous Variables (Eq. 2)
X = Y + Z + Exogenous Variables (Eq. 3)

One of the issues here for me is how to specify XIV as an instrument for X while running the models through STATA’s reg3 command. Do I add XIV through the endog(XIV) command? But in that case I’m not specifying XIV as an instrument for X specifically but rather for all 3 endogenous variables!! I’m leaning towards adding XIV to the list of exogenous variables in Eq. 3 above. Accordingly, and to the best of my knowledge, the model uses XIV to estimate X in the equations 1 & 2. Am I right?

Option 2: Run the following 2 equation simultaneous equation model:

Y = X + Exogenous Variables (Eq. 1)
Z = X + Exogenous Variables (Eq. 2)

In addition, I specify X as an endogenous variable and XIV as an additional exogenous variable through endog(X) exog(XIV) in the Stata’s reg3 3SLS regression.

I appreciate your advice in that regard. Thank you.

[Joro Kolev]

You probably want to do something like this:

reg3 (Y X controls) (Z X controls) (X XIV controls)

[Mustafa Abd]

So you agree that the instrument should enter Eq. 3 and not be added using the exog() command?