2SLS Appropriate with a Binary Endogenous Regressor and a Continuous Dependent Variable

[hussein bataineh]

HI,

I would appreciate some advice regarding the suitability of conventional fixed-effects 2SLS for my panel data analysis.

My dependent variable (y) is continuous, while my potentially endogenous explanatory variable (w) is a dummy variable (0/1). My baseline regression includes firm and year fixed effects, with standard errors clustered at the firm level.

I am considering the following conventional fixed-effects 2SLS specification:
ivreghdfe y x1 x2 ... xK (w = z), /// absorb(id year) cluster(id) first endog(w)
where z is the excluded instrumental variable and x1 to xK are the control variables.

My question is whether conventional fixed-effects 2SLS is appropriate when the endogenous explanatory variable is binary (0/1), given that the first stage is linear rather than probit.

Would this specification be econometrically appropriate, with firm and year fixed effects incorporated in both stages, or would a nonlinear first-stage approach be preferable?

Thank you very much for your time and guidance.

Best regards,
Hussein Bataineh

[Joao Santos Silva]

Dear hussein bataineh,

In the context of 2SLS estimation, the first step is just a linear projection; not necessarily an economic model. So, having an endogenous dummy is not a reason to avoid 2SLS. In contrast, using a nonlinear first step can lead to a so-called forbidden regression, and that would be invalid.

Best wishes,

Joao

[hussein bataineh]

Thank Professor João very much for your helpful clarification.

I would appreciate your confirmation of my understanding. Given that my dependent variable is continuous and the potentially endogenous explanatory variable is binary (0/1), I understand that conventional fixed-effects 2SLS with a linear first stage is econometrically appropriate, provided the standard IV assumptions hold.

I intend to estimate the following specification:

ivreghdfe y x1 x2 (w = z), absorb(id year) cluster(id) first endog(w)

Would you consider this specification appropriate, particularly regarding the inclusion of firm and year fixed effects in both stages?

Thank you again for your time and valuable guidance.

Best regards,
Hussein Bataineh

[Manh Hoang Ba]

I think #3 in this post is a helpful answer. Correct Stata procedure/code for binary endogenous regressor with FE: probit first stage + OLS second stage? - Statalist

[hussein bataineh]

Thank you very much for your helpful suggestion.

I have carefully reviewed Professor Wooldridge's response in post #3. My understanding is that conventional fixed-effects 2SLS with a linear first stage is appropriate even when the endogenous explanatory variable is binary. Professor Wooldridge also suggests that, if the linear 2SLS estimates are sufficiently precise, this approach can be retained as the main specification, while the Mundlak-adjusted probit approach may be used as a robustness check.

Therefore, I am inclined to use conventional fixed-effects 2SLS as my main IV estimation approach, subject to satisfactory instrument validity and estimation precision.

I would appreciate your thoughts on whether this interpretation is correct.

Thank you again for your time and guidance.

Best regards,

[Manh Hoang Ba]

I share your interpretation of Professor Wooldridge's comment. I would also follow that approach in my own applications.