2 Question about endogeneity and two step system GMM

[Nataley valencia]

Hello everyone,
i hope all of you are doing well.

im new here and i have some questions if any of you kindly help me out.

Im trying to study the relationship between economic volatility, economic growth and political stability. however, im having problems on how to estimate the relationship. i wanna use the two-step system GMM (N=30 and T=10).
From the literature I've understand that endogeneity is a problem that need to be consider. To do so, i selected 4 IV.
my questions:

1) can i use IV2SLS and IVGMM to prove the existence of endogeneity and that the IV ive used are good, and then go on to use the two step system GMM to estimate the relationship ?
2) my data shows the presence of heteroscedasticity, do i need to add the rebust (vce(r)) option in IV2SLS and IVGMM ? or should i use the option only for two step system GMM.

Thank u in advance.

[Sebastian Kripfganz]

1) It is unclear to me what estimator you have in mind when you talk about IV2SLS and IVGMM. The 2SLS estimator is a special case of a GMM estimator with a particular weighting matrix. "system GMM" usually refers to a GMM estimator with a particular set of instruments, and "two-step" just means that a GMM estimator with optimal weighting matrix is used (which is not special to "system GMM"). To what extent are you using different instruments in what you are calling IV2SLS/IVGMM? Specific Stata code would be helpful. And why do you think you need to first use one estimator to "prove" (how?) endogeneity, and then another estimator to estimate your model? If the first estimator is a good one (with valid and relevant instruments), then there is no need to use a different one afterwards. If the first one is not a good estimator, then you should not use it in the first place.
2) Yes, use vce(robust) throughout, assuming you are using panel data (xt) commands; otherwise, use vce(cluster id), where id is the panel identifier.

I do not want to appear dismissive. We just need more information to understand what you are doing, and why you are doing it this way (or why you think you should potentially be doing it this way).

[Nataley valencia]

1) i see your point and it make sense. i was thinking wrong, ive though that to know if endogeneity exists in a model (and to test the validity of IVs used) i need to go through IV2SLS as a pre estimation (kinda like a first step) before running two-step GMM. but from your explanation i've understand that the IV2SLS estimator is in itself can be used to estimate the relationship. My bad. can i use one as base (IV2SLS) and the second as robust ?
2) can you please give me an exemple of what "using (xt) command and id" means ?

thank you sooo much

[Sebastian Kripfganz]

1) Yes, you could use one as a robustness check for the other. The 2SLS estimator is generally inefficient under heteroskedasticity.
2) You initially declare your data to be panel data with the xtset command. The variable that defines your groups is often called the id-variable. Commands that make use of the panel data structure typically start with the letters xt in the command name. For those commands, vce(robust) is equivalent to vce(cluster id). For other commands, say ivregress, you explicitly need to specify vce(cluster id) to allow for potential correlation of the errors over time (e.g. due to group-specific effects).

[Nataley valencia]

1) thats mean i cant use 2SLS, ive test for heteroskedasticity whit the Breusch-Pagan test and i got p=0.0009. what do you recommend as an alternative estimator ? or maybe i should just use 2 different dependent variables, one for the main tests and the other for robustness check.
2) i was reading about the two step system GMM and i've come across an interesting presentation for a new command. the xtdpdgmm command, what do you think about it ? even tho it look kinda complicated for someone of my level but the advantages make it better than xtabond2, well from what i've read .

you made my day, thank youuuuu so much. i think im starting to get an idea of what i should do.

[Sebastian Kripfganz]

1) 2SLS is still a consistent estimator when there is heteroskedasticity. It is just not efficient. Two-step GMM would be the efficient estimator. (2SLS is a special case of GMM with a particular type of weighting matrix.

2) "System GMM" is an advanced estimator primarily used for dynamic panel data models. Both xtabond2 and xtdpdgmm have a quite complicated syntax. They essentially require you to have a good understanding of the underlying econometric theory, so that you know what you are doing. In the latest version, the xtdpdgmm package comes with the xtdpdgmmfe command, which has a somewhat simpler syntax, but still requires you to make a couple of choices regarding the model assumptions (first and foremost the exogeneity/endogeneity of your variables). The starting point for you is to decide about your model: Does it need to be dynamic (with a lagged dependent variable)? Are some of the regressor likely to be endogenous? Initially, you mentioned that your data set has N=30 and T=10. "System GMM" and related estimators usually require larger N for reliable estimates. So, before you get lost in all of the details about system GMM, a conventional 2SLS estimator with robust standard errors might just do the job, provided you have good instruments.

[Nataley valencia]

Really, i didnt know that. So if i understand correctly to know if the optimal choice of estimatoire i have to run them both and see which results make more sense.
i've got an idea : can i use 2SLS and two step system GMM, and make an argument that the first estimator is more likely to not give efficient results under heteroskedasticity assomption thats why the second estimator is used, and that the second estimator (two-step GMM) is more efficient in large panel and thats why 2SLS will be use also. Meaning that they complet each other
to answer your questions : Yes im adding the lag dependent variable in the model. Both of may main regresses are likely to be endogenous (if i add the lagdv, thats that mean he will also be consider as endogenous?)

thank you so much i really learned lot from you

[Sebastian Kripfganz]

i've got an idea : can i use 2SLS and two step system GMM, and make an argument that the first estimator is more likely to not give efficient results under heteroskedasticity assomption thats why the second estimator is used, and that the second estimator (two-step GMM) is more efficient in large panel and thats why 2SLS will be use also.

That's about right.

When T is small, as it is in your case, the lagged dependent variable cannot be treated as exogenous. You also need to find instruments for it. That is the main idea behind the "system GMM" and related estimators. A simple approach, which does not require xtabond2 or xtdpdgmm, would be to simply use the lagged first-difference of the dependent variable as an instrument for the lagged dependent variable. (This idea is similar to the one used by the "system GMM" estimator.) If you want to go further, I recommend reading some articles about GMM estimation of dynamic panels to understand the intuition behind the instruments used in these models.

[Nataley valencia]

Thank you so much, i will start by reading some articles about GMM as you recommended to understand more about it.