xtabond2: question on multiple lagged indepedent variable and gmm() with eq(diff)

[Leon Schmidt]

Dear all,

At the moment I am learning to use xtabond2. After reading through many discussions here, I still have two questions. Thank you very much for your help!

1) Is it OK to include multiple lags of the independent variable in order to get a p-value larger than 0.05 for the AR(2) test (securing the absence of autocorrelation)? And when doing so, can I still include instruments starting at lag 2 in the gmm option? So basically is it OK to run something like

xtabond2 y l.y l2.y x i.t, gmm(y x, collapse lag(2 .)) iv(i.t, eq(level)) cluster(id) twostep small

2) What happens intuitively when specifying the eq(diff) option in gmm()? I get very similar point estimates when running the following model with eq(diff) compared to the one above

xtabond2 y l.y l2.y x i.t, gmm(y x, collapse lag(2 .) eq(diff)) iv(i.t, eq(level)) cluster(id) twostep small

The only difference is that the Hansen test is insignificant in the second model, which is what I want (if I understand correctly. The Sargan test is significant though, I don´t know if that´s problematic). I´ve read that the eq(diff) reduces the number of instruments and that this might be better to pass the Hansen test, but I am not sure if I understood that correctly.

Thanks a lot!

All the best
Leon

[Sebastian Kripfganz]

1. Yes and yes. (Note that you are including multiple lags of the dependent variable, not the independent variable.)

2. In your first specification, xtabond2 creates GMM-style instruments for both the first-differenced and the level model. In your second specification, those instruments are only created for the first-differenced model. To ensure that the command is really doing what you intend it to do, I recommend to always explicitly specify the eq() suboption. In other words: Do not rely on the default settings. Make sure you understand the underlying theory and then specify all the instruments explicitly. With a two-step system GMM estimator, the Sargan test is not really useful because it does not use an optimal weighting matrix. Just focus on the Hansen test. Instruments for the level model rely on an additional mean-stationarity assumption that might be violated, and thus the Hansen test could turn significant as a consequence.

For more details on dynamic panel data GMM estimation, you might find my 2019 London Stata Conference presentation useful:

• Kripfganz, S. (2019). Generalized method of moments estimation of linear dynamic panel data models. Proceedings of the 2019 London Stata Conference.

[Leon Schmidt]

Thank you very much Sebastian Kripfganz for your answer, they´re always very helpful!

Regarding 1) It was a typo on my side, you´re correct, I meant dependent variable.

Regarding 2) So you say that if I include the level model in the gmm (not iv) option, I am making this additional mean-stationarity assumption? I think your comment is spot on because the Hansen test is suddenly significant when including the level model in gmm (otherwise nothing much changes).

Also, which statistic is relevant from the "Difference in Hansen test", the p-value next to "Hansen test excluding group" or the one next to "Difference (null H = exogeneous)" (or both)?

Thank you again very much!

[Sebastian Kripfganz]

2. Whether you do this with the gmm() or the iv() option does not make much of a difference. The latter is just a collapsed version of the former; see slide 22 of my presentation.

Also, which statistic is relevant from the "Difference in Hansen test", the p-value next to "Hansen test excluding group" or the one next to "Difference (null H = exogeneous)" (or both)?

Both. While you are primarily interested in not rejecting the difference-in-Hansen test, this test is only meaningful if the Hansen test excluding that particular group of instruments was not rejected. Otherwise, you would compare two misspecified models with each other; see slide 48 of my presentation.

[Leon Schmidt]

Thanks again Sebastian Kripfganz ! What I meant to ask was basically if it is ok to have gmm( ... , eq(diff)) while at the same time having iv(... , (level))? And if I change this to include the level option in gmm, whether I am then making the assumption of mean stationarity?

[Sebastian Kripfganz]

Yes and yes.

[Leon Schmidt]

Great, thanks a lot!