Binary Endogenous Treatment in Panel Data

[Roel Dom]

Dear all,

I am struggling with the following puzzle. I have an (unbalanced) panel and want to estimate the treatment effect D_i,t (binary) on a continuous outcome variable Y_i,t conditional on a number of controls X_it. I have good reasons to think that treatment is endogenous (selection linked to earlier realisations of Y_i,t ). However, I also believe that I have potential instruments Z_i,t (continuous) for D_i,t . In a cross-sectional setup I would follow Wooldridge (2010) which more or less goes as follows:

1. Probit model: D_i as a function of Z_i and X_i.
2. Obtain fitted values, D_hat_i
3. 2SLS model: Y_i as a function of D_hat_i and X_i

I am wondering if there is a similar procedure that is consistent for panel data, and which would also allow controlling for fixed effects (C_i and T_t )?

Thanks!

--
Reference:

Wooldridge, J. M. (2010). Econometric analysis of cross section and panel data. MIT press.

[Jeff Wooldridge]

A few comments.

1. There is nothing wrong with using the usual fixed effects IV estimator. So use the [CODE]xtivregress[CODE] command in Stata with the FE option, and you should cluster the standard errors. For some reason, people are under the wrong impression that IV cannot be applied when the endogenous explanatory variable is binary. That is not true.

2. You are misunderstanding my recommendation in step (3), or at least it is ambiguous. You are not supposed to use D_hat(i) as a regressor. It is to be used as an instrument for D(i,t), not as a regressor. These are not the same. I state this explicitly in my book.

3. If you want to use probit fitted values as instruments it is easy to modify the cross-sectional procedure. First, I would estimate a probit model using the Chamberlain-Mundlak device. Then, use these fitted values as IVs in the [CODE]xtivregress[CODE] command. And then cluster your standard errors, as usual.

I hope this helps.

[Roel Dom]

Dear Jeff Wooldridge, thank you very much for your help. I highly appreciate it. Could I put a follow-up question out there?


1. Would this hold if the treatment only switches from 0 to 1 (and never back to 0 over the period under consideration)?


Thanks,
Roel

--
(2. My apologies for the ambiguity, I should have taken more care to clarify that the D_i should be included as an instrument not as a regressor.)

[Jeff Wooldridge]

Dear Jeff Wooldridge, thank you very much for your help. I highly appreciate it. Could I put a follow-up question out there?


1. Would this hold if the treatment only switches from 0 to 1 (and never back to 0 over the period under consideration)?


Thanks,
Roel

--
(2. My apologies for the ambiguity, I should have taken more care to clarify that the D_i should be included as an instrument not as a regressor.)

Is it switching from zero to one for every unit in the sample? Or is it always zero for some units? Or, does it switch from zero to one in different time periods across units?

[Roel Dom]

Is it switching from zero to one for every unit in the sample? Or is it always zero for some units? Or, does it switch from zero to one in different time periods across units?

It switches from 0 to 1 for some units and it does so in different time periods. For a number of units it remains 0.

[Jeff Wooldridge]

It switches from 0 to 1 for some units and it does so in different time periods. For a number of units it remains 0.

Then you should be all set. This is the kind of situation you hope for.

[Roel Dom]

Then you should be all set. This is the kind of situation you hope for.

Thank you for your advice.

[Babatunde Abidoye]

Dear Jeff Wooldridge. In second stage with [CODE]xtivregress[CODE] command, do you use D_hat(i) as instrument for D(i,t), or the mills ratio calculated using the D_hat(i)? Thanks.

[Tarjei W. Havneraas]

Dear all,

I am working on a similar challenge. I am awaiting data where the study design is a IV analysis for panel data with binary and count response variables, a binary treatment variable, and a continous instrument.

I have found a lot of literature on IV with continous response variables for cross-sectional and panel data and binary/count response variables for cross-sectional data. However, I have not found much literature on IV analysis with binary/count response variables for panel data. Thus, I am uncertain whether there are important additional considerations compared to the mentioned approaches. Literature tips would be greatly appreciated.

Jeff Wooldridge I am currently working through your excellent Introductory Econometrics and Econometric Analysis for Cross Section and Panel Data. I have not found this topic covered yet, but I might have missed it.