3SLS with Instrument Variables

[Garima Dhir]

Is it possible to run a 3SLS specification using instrument variables in Stata?

I have the following system of equations that I'm trying to estimate using 3SLS. The variables in orange are endogenous.

Y₁= C₁ + b₁X₁ + b₂X₂ + b₃X₃ + e₁
Y₂ = C₂ + b₄Y₁ + b₅X₄ + b₆X₅ + e₂
Y₃ = C₂ + b₇Y₂ + b₈X₆ + b₉X₇ + e2

A simple 3 SLS on this system of equations would look like:

reg3 (Y₁ X₁ X₂ X₃) (Y₂ Y₁ X₄ X₅) (Y₃ Y₂ X₆ X₇)

However, I would like to instrument X₁ to deal with the engogeneity problem. Is there a way to do so while using 3SLS? I understand that we can use ivregress using 2SLS, but can a similar command be run using 3SLS?

Thanks!

[Joro Kolev]

-reg3- is a full information system estimator. The easiest way to do what you want is to spell out the system explicitly.

reg3 (Y₁ X₁ X₂ X₃) (Y₂ Y₁ X₄ X₅) (Y₃ Y₂ X₆ X₇) (X₁ X₂ X₃ X₄ X₅ X₆ X₇)

[Garima Dhir]

Thanks Joro, this was quite useful.

If this is the case, I wanted to check 2 more things

Question 1: If I have an instrument for X1, say Z1, then is the following command same as above?
reg3 (1: Y₁ X₁ X₂ X₃) (2: Y₂ Y₁ X₄ X₅) (3: Y₃ Y₂ X₆ X₇), enog(X₁) exog(Z₁)

Question 2: Since this is a recursive or triangular model (that is Y₂ is not appearing in the estimation equation of Y₁ or Y₃ in the estimation equation of Y₁ and Y₂), as a robustness check, can I run the 1^st equation as simple IV (since Z₁ is an instrument for X₁) and the remaining two equations using a simple Fixed effects model.

PS: The data is a panel dataset with 112 cross-sectional units and 13 time periods.

Thanks!
Garima

[Joro Kolev]

Probably I should start by clarifying that 3SLS uses all instruments/exogenous variables appearing anywhere in the system in the reduced form.

It seems to me that you are thinking incorrectly that you have Z1 for X1--in 3SLS there is no such thing as Z1 for X1, in the reduced form all the exogenous/instruments will appear in the equation for X1.

1. Yes, the syntax you show in Question 1 is equivalent to the syntax I showed.

2. Recursive or non recursive model, you can always estimate a full system equation by equation, the procedure is consistent and more robust, but not as efficient as the full information system estimator. Note that when you estimate the first equation by IV, you can try only Z1 as an instrument for X1, or all exogenous/instruments appearing anywhere in the system as instruments for X1.

Thanks Joro, this was quite useful.

If this is the case, I wanted to check 2 more things

Question 1: If I have an instrument for X1, say Z1, then is the following command same as above?
reg3 (1: Y₁ X₁ X₂ X₃) (2: Y₂ Y₁ X₄ X₅) (3: Y₃ Y₂ X₆ X₇), enog(X₁) exog(Z₁)

Question 2: Since this is a recursive or triangular model (that is Y₂ is not appearing in the estimation equation of Y₁ or Y₃ in the estimation equation of Y₁ and Y₂), as a robustness check, can I run the 1^st equation as simple IV (since Z₁ is an instrument for X₁) and the remaining two equations using a simple Fixed effects model.

PS: The data is a panel dataset with 112 cross-sectional units and 13 time periods.

Thanks!
Garima

[Garima Dhir]

Thanks Joro, this was very useful!

Best
Garima