Dealing with endogeneity of a dummy variable as a treatment effect

[Anuththari Bandara]

I am currently studying the Public Wage Premium in Sri Lanka. I have been looking at the literature on the switching regression and using a endogenous dummy variable model (1=public, 0=private) for wage employees. I then came across a paper by Wooldridge (2008) "Instrumental Variables Estimation of the Average Treatment Effect in the Correlated Random Coefficient Model" and was keen to apply it in my analysis. From this paper, I have a vague idea in my head but I am not sure if I am on the right track and whether it is a feasible approach. I am hoping I could get some advice on modelling it.

Here is my approach, which I'm sure is very flawed at present so I apologize for that:

1. Estimate probit (1=public, 0=private) or two probit regressions (for public and private employees seperately). I am not sure which is more suitable.

probit public age age2 years_in_education gender ethnicity

2. Obtain the predicted probabilities

predict p (say, p_hat)

3. The second stage will use IV to estimate the wage function (where the dummy variable is endogenous)

ivregress 2sls log_wage age age2 years_in_education gender ethnicity (public=father_in_public_sector spouse_in_public_sector p_hat), robust first

If I estimate two probit regressions instead of one, then I would end up with two correction terms for my second step IV (if I understood it correctly).

Does this sound like a sensible approach, or have I completely misunderstood the concepts? Ideally, I wish to employ a switching regression model while controlling for endogeneity of sector choice.

Thank you for the help

Reference:
Woolridge, J. (2008), "Instrumental Variables Estimation of the Average Treatment Effect in the Correlated Random Coefficient Model", Advances in Econometrics, 21, pp. 93 - 116

[Sebastian Scheurle]

I would suggest the following:

ivregress 2sls log_wage age age2 years_in_education gender ethnicity (public=father_in_public_sector spouse_in_public_sector age age2 years_in_education gender ethnicity), robust first

As far as I know you don't need the 2 stages. Also, you should consider leaving out all variables in the selection command that are also part of the main regression, i.e.

ivregress 2sls log_wage age age2 years_in_education gender ethnicity (public=father_in_public_sector spouse_in_public_sector), robust first

[Richard Hofler]

Have you looked at Stata's set of commands for endogenous treatment-effects estimation? Here's an excerpt from the intro:

"Title
eteffects — Endogenous treatment-effects estimation


Description
eteffects estimates the average treatment effect (ATE), the average treatment effect on the treated (ATET), and the potential-outcome means (POMs) from observational data when treatment assignment is correlated with the potential outcomes. It allows for continuous, binary, count, fractional, and nonnegative outcomes and requires a binary treatment. To control for the endogeneity of the treatment assignment, the estimator includes residuals from the treatment model in the models for the potential outcomes, known as a control-function approach."

I hope this helps.
Richard

[Anuththari Bandara]

Thank you Sebastien and Richard! It definitely helps. Hoping to get more feedback in this forum

[Ariel Karlinsky]

Sorry for bumping, but this seems like posting here instead of opening a new thread is preferable.
I'm reading into eteffects models in stata, but what I "fail" to understand is the difference between such models and instrumental variables models. If anyone can explain or provide a resource detailing the similarities and differences, that would be great.