2sls regression with interaction between endogenous and exogenous variables

[Sujata Techno]

I am having an endogenous variable X1 and an exogenous variable X2 and instruments Z1 and Z2 for my endogenous variable and having one interaction term between endogenous and exogenous variable X1*X2. So my model goes like this

Y = X1 + X1* X2 + controls

I used instruments Z1 and Z2 in the first stage regression and then use the fitted values of X1 from my first stage to use in the interaction term X1*X2
in the second stage. Have I done this correctly?

[Joro Kolev]

No, you have not done it correctly. Search this board for the terms "forbidden regression" for discussions on the issue.

You can do

ivregress 2sls y x2 (x1 x1*x2 = z1 z2)

or

ivregress 2sls y x2 (x1 x1*x2 = z1 z2 z1*x2 z2*x2)

[Sujata Luiss]

Thank you so very much...is the first code the same as the second one...as it seems that in the second one we are interacting each of the instruments with our exogenous variable as probably x1*x2 is aso considered as an endogenous one

[Joro Kolev]

No, these are different regressions and will give you different results.

And yes, the interaction of an endogenous variable and an exogenous variable is endogenous itself.

Thank you so very much...is the first code the same as the second one...as it seems that in the second one we are interacting each of the instruments with our exogenous variable as probably x1*x2 is aso considered as an endogenous one

[Sujata Luiss]

Thank you so much..it worked for me in the second case as the first code is giving me just identified case

[Joro Kolev]

Very good. I also think the second specification is more appealing on theoretical grounds. It uses what some might call "analogy principle" of constructing the instruments in the same way as the regressors are constructed.

Thank you so much..it worked for me in the second case as the first code is giving me just identified case

[Carlo Lazzaro]

Sujata:
exploting Joro's assist, forbidden regression is touched upon in the wonderful slide presentation on IV regression given by Kit Baum some years ago (from slide 55 onwards):
http://repec.org/usug2007/baumUKSUG2007.pdf.

[Sujata Luiss]

Thank you so much...I am having a look at this presentation now

[Sujata Luiss]

I am sorry...but I am having another doubt cropping up..can beta coefficients of the instruments in first stage 2sls regression have high values?

[Joro Kolev]

I do not understand the question. The coefficients in the first stage are not restricted, they can come up to be whatever they come up to be.

I am sorry...but I am having another doubt cropping up..can beta coefficients of the instruments in first stage 2sls regression have high values?

[Sujata Luiss]

I am having two endogenous regressors...one is X1 (instrument is z1 and z2) and another one is X1*X2 (instrument is z1*x2 z2*x2) .....so in my first stage regression equation, I am having high beta coefficients for z1 (45.69) when my dependent variable is x1. just wanted to confirm whether this is correct or is it possible to have values like this?

[Joro Kolev]

Same comment as before: The coefficients in the first stage are not restricted, they can come up to be whatever they come up to be.

I am having two endogenous regressors...one is X1 (instrument is z1 and z2) and another one is X1*X2 (instrument is z1*x2 z2*x2) .....so in my first stage regression equation, I am having high beta coefficients for z1 (45.69) when my dependent variable is x1. just wanted to confirm whether this is correct or is it possible to have values like this?

[Sujata Luiss]

Thank you so very much

[Sujata Luiss]

Is there any way by means of which I can do weak instruments checking for multiple endogenous regressors...like in my case....as stock-yogo is giving me some values like shown below and not sure how to interpret these results
Stock-Yogo weak ID F test critical values for single endogenous regressor:
5% maximal IV relative bias 16.85
10% maximal IV relative bias 10.27
20% maximal IV relative bias 6.71
30% maximal IV relative bias 5.34
10% maximal IV size 24.58
15% maximal IV size 13.96
20% maximal IV size 10.26
25% maximal IV size 8.31

[Sujata Luiss]

Joro Kolev If you can pls respond Prof