adding regional fixed effect to system GMM

[Giorgio Carlini]

Hello,
I'm estimating a dynamic panel model using GMM system xtabond2. I've a general question.
I might recall a post saying that regional fixed effect cannot be added within a GMM system estimation method. Is it this correct?
Thanks a lot.

[Jeff Wooldridge]

There's a way to do this, and Sebastian Kripfganz is the best person to show you how.

[Giorgio Carlini]

Thanks a lot Prof. Wooldridge. Should I post again for a comment from Prof. Kripfganz?
thanks a lot

[Jeff Wooldridge]

I can find a do file that contains an example using xtabond2. I use it in short courses I teach.

[Jeff Wooldridge]

Here is what I used for a dynamic fare equation. The two distance variables do not change over time. They get eliminated using the usual Arellano-Bond approach. But the system approach allows for coefficients on the time constant variables. Importantly, the coefficients on all time-varying variables are still the A-B estimates.Those are given in the first command. The second command brings in the two time-constant variables.

xtabond2 lfare L.lfare concen y99 y00, gmmstyle(L.lfare)  ivstyle(concen y99 y00) nolevel robust
xtabond2 lfare L.lfare concen y99 y00 ldist ldistsq, gmmstyle(L.lfare, equation(diff)) ivstyle(concen y99 y00, equation(diff))  ///
ivstyle(ldist ldistsq, equation(level)) robust

[Sebastian Kripfganz]

Thank you Jeff for stepping in.

Giorgio: In Jeff's example, an implicit assumption is that the observed time-invariant variables ldist ldistsq are uncorrelated with any unobserved time-invariant characteristics. If you are not happy with this assumption, you have to look for appropriate instruments. As Jeff correctly notes, the coefficients of the time-varying regressors remain unchanged in his example whether you add the time-invariant regressors or not. This only holds because the initial estimator was the "difference GMM" estimator. It is no longer the case if you use a traditional "system GMM" estimator with first differences of these time-varying variables as instruments in the level equation. In the latter case, you need to exert more caution on the identifiying assumptions for your time-invariant regressors because they will also affect the coefficients of the time-varying regressors.

You can find some more information on slides 82 to 86 of my recent presentation at the 2019 London Stata Conference.

[Giorgio Carlini]

Thanks a lot Prof. Kripfganz, and also thanks to Prof. Wooldridge for useful comments and suggestions
giorgio