2sls with binary endogenous variable

[Stephen GZ Chen]

Dear all,

I would like to perform 2SLS,

First stage: Y1 (Dummy variable) = IV1, IV2, X1, X2, X3
Second stage: Y2 (Continuous variable) = Y1, X1, X2, X3

I conduct Probit regression in the first stage and OLS in the second stage.
IV1 and IV2 are instrumental variables. Y1 are endogenous variable. X1, X2, and X3 are exogenous variables.

How do I test instrument relevance and instrumental exogeneity by using STATA?

Thanks for your help.

Chen

[Maxence Morlet]

Accomplished econometricians will correct me if I'm wrong, but in the meantime I can try to help:

Instrument relevance: the instrument must have a strong correlation with the endogenous variable for which it is instrumenting. A classical example in the literature is proximity to a two year community college to instrument for educational attainment. You could argue that your instrument is relevant if the coefficient on the instrument in the first stage regression (endogenous variable regressed on instrument) is significant and has a large magnitude.

You cannot really test for exogeneity per se, i.e. there is no consensus in the literature, to the best of my knowledge (please correct me if I'm wrong), on how to test for instrument exogeneity. Instrument exogeneity should be argued.

[Joao Santos Silva]

Dear Stephen GZ Chen,

Maxence Morlet is right about about relevance and exogeneity.

I would like to add that it is not a good idea to estimate the model as you describe (actually, your description is not very clear). You should just use 2SLS and Stata offers different commands to do that. One thing you may want to do is to start by estimating the probit model and then using the predicted probabilities and IV1 and IV2 as instruments.

Best wishes,

Joao

[Jeff Wooldridge]

Here's a link to a paper by my former student, Ruonan Xu, who studies the weak IV problem in this case:

IV with probit fitted values.

I would also recommend trying the control function approach to allow for unobserved heterogeneity in the effect of Y1. This is the Heckman switching regression approach. If you look at Chapter 21 of my book "Econometric Analysis of Cross Section and Panel Data" or my 2015 Journal of Human Resources paper you can see the pros and cons of IV vs CF.

[Ibai Ostolozaga Falcon]

Here's a link to a paper by my former student, Ruonan Xu, who studies the weak IV problem in this case:

IV with probit fitted values.

I would also recommend trying the control function approach to allow for unobserved heterogeneity in the effect of Y1. This is the Heckman switching regression approach. If you look at Chapter 21 of my book "Econometric Analysis of Cross Section and Panel Data" or my 2015 Journal of Human Resources paper you can see the pros and cons of IV vs CF.

Hello Professor Jeff.

I read the paper that you cited and the chapter of the book cited. However, I am a little bit confused when trying to estimate a model by using instrumental variable when my endogenous regressor is a binary one and furthermore when it is interacted with another exogenous variable. Here an example using fertil2 database:

ivregress 2sls children (i.educ7 i.educ7#c.age=i.frsthalf i.frsthalf#c.age) age evermarr i.urban i.electric i.tv, first

The first stages are estimated by using OLS, but in the first stage estimations, educ7 is a binary variable. As a consequence I do not if this approach is correct.

Thank you and best!