endogenous treatment effects for panel data

[MariaCamila Jimenez]

Hi everyone, I'm trying to use eteffects with panel data, when I establish panel data with xtset and then I do eteffects I obtain results, but it is possible? some foros says eteffects it's only for cross-sectional data and other says it's possible. The manual isn't specific about that. Thank you for your help.

[Jeff Wooldridge]

Yes, etregress can be used with panel data. You need to use the vce(cluster id) option for standard errors and inference. This is justified if you have reasonably large N and not-so-large T.

A general rule is that if a method applies to cross-sectional data, it can be used with panel data (and even time series data). The issue is always with computing standard errors. The large-N, small-T case with independence across the cross-section units is fairly easy with vce(cluster id). Stata does the hard work and accounts for the two-step estimation.

My concern in moving to panel data is the nature of the exogeneity of the instrument. A straight application of etregress means you're assuming your IVs (and any explanatory variables assumed exogenous) are exogenous with respect to not only idiosyncratic errors, but also the unobserved heterogeneity. Assuming the IV is exogenous with respect to heterogeneity is pretty strong. If your IV is time-varying (hopefully), you can relax this. But a bit of work is needed.

There is nothing wrong with applying xtivreg, fe as a starting point. While it doesn't allow for unobserved heterogeneity to interact with treatment, it's fine in every other way. And you can do a weak IV analysis. It doesn't matter that your endogenous explanatory variable is binary. And you can interact the binary EEV with exogenous explanatory variables without difficulty.

If you say more about your application, I can say more. There's a Mundlak-type version of etregress in Murtuzashvili and Wooldridge (2016, Journal of Econometrics). It's easy to implement in Stata, but standard errors must be computed using GMM or bootstrapping to account for the multi-step estimation. By using the Mundlak correlated random effects approach along with a control function approach, you allow the IV to be correlated with heterogeneity.

[MariaCamila Jimenez]

Thank you, Mr. Wooldridge.
My application is about a treatment effect, applying this code:

ettefects (resultado programanumero promediosemestre, probit) (treated facultadnumero estrato)

where resultado and treated are binary variables.
I have my panel with N= 3500 T=3

First I did an xtlogit with DV (result) and IV (treated) to evaluate endogeneity, and at the same time, I did an xtlogit with DV (treated) and IV (covariables) to evaluate bias selection.

estat endogenous rejected null hypothesis, suggesting endogeneity

Under the assumptions of endogenous treatment effects and the behavior of my data, I decided to estimate my causal inference with this model with robust standard errors.
How do you tell me about my process? Maybe I'm omitting steps or forgetting some assumptions.