Regression with two endogenous variables (one is interaction) and possible exclusion restriction violation?

[Krista Lane]

I am trying to estimate the naive regression:

d = b + s + s*b, where s is endogenous. I'm instrumenting for s with iv.

I've seen other posters run something similar to the following regression

ivreg2 d = b (s s_b = iv iv_b)

where s_b and iv_b are interaction terms.

However, I would really like to do something like this instead:

ivreg2 d = b (s = iv) (s_b = iv_b)

because I'm don't think s should be predicted with iv_b since I worry that b might influence s.

My questions are:
(1) is there a way to run my second regression?
(2) if my concern is correct, would that constitute a violation of the exclusion restriction?
(3) is my second regression correct?

[Jeff Wooldridge]

Krista: The command will not let you do what you want, and you should not do what you want to do. You should instead use the first command, or ivregress 2sls. Any time you have two or more endogenous explanatory variables, it is important to include everything treated as exogenous -- whether it's in the equation or not -- in every reduced form. This is what ivreg2 and ivregress do. This is Stata's way of protecting you from yourself. Who's to say that iv_b won't have some predictive power for s, or that iv has some predictive power for s_b? If they do, they need to be in the first stages, and the first command does that.

Now, it's true that, if you look at the first stages, the hope is that iv "mostly" predicts s and iv_b "mostly" predicts the s_b, but there's no restriction as long as you let IV work they way it's supposed to. The only thing I would add is to use the "robust" option if you have cross-sectional data.

JW

[Krista Lane]

Thank you! That makes sense.

[Thon Hoang]

Krista: The command will not let you do what you want, and you should not do what you want to do. You should instead use the first command, or ivregress 2sls. Any time you have two or more endogenous explanatory variables, it is important to include everything treated as exogenous -- whether it's in the equation or not -- in every reduced form. This is what ivreg2 and ivregress do. This is Stata's way of protecting you from yourself. Who's to say that iv_b won't have some predictive power for s, or that iv has some predictive power for s_b? If they do, they need to be in the first stages, and the first command does that.

Now, it's true that, if you look at the first stages, the hope is that iv "mostly" predicts s and iv_b "mostly" predicts the s_b, but there's no restriction as long as you let IV work they way it's supposed to. The only thing I would add is to use the "robust" option if you have cross-sectional data.

JW

Dear Mr. Jeff Wooldridge,

I use the xtivreg2 like below:
xtivreg2 d b (s s_b = iv iv_b), fe cluster(id)

However, variable s in my model is positive variable.
If just using xtivreg2, in the first stage, the s_hat (prediction of s in the first stage) can be non-positive.
And is there any bias in the results in the second stage compared to the case we get all positive values of s_hat in the first stage? If yes, do you any suggestion for to fix this problem?

Thank you in advance!

Yours Sincerely,
Thon Hoang