Dynamic panel with N = 150 and T = 4: alternatives to System GMM?

[Helmi Mansour]

I have a panel of about 150 countries over only 4 years (T = 4) and want to analyze the determinants of inward FDI. Since FDI is dynamic/persistent, I am using System GMM (xtabond2).

The estimates and most diagnostic tests look reasonable, but I consistently fail to even calculate the Arellano-Bond AR(2) test.

Given the very short time dimension, I am concerned that System GMM is not appropriate in my case.

Are there alternative estimators suitable for dynamic FDI models with very small T (T = 4)?

Since Fixed Effects LSDV does not allow for the inclusion of a lagged dependent variable in this context, are there alternative dynamic panel estimators that would be appropriate with such a short T?

I would appreciate any methodological recommendations or Stata implementations.

Thank you,

[Manh Hoang Ba]

Since you only have T=4, while the Arellano–Bond AR(2) test requires at least T=5 (1 for lagged y, 4 for AR2 in Δe_it equation), the AR(2) test cannot be performed because of the data limitation, rather than because of a problem with the method.

One consequence of serial correlation in the error term (e_it) is that some of the lagged instruments may become invalid. I think you could look for evidence of serial correlation indirectly using the Hansen test. If the model does not pass the Hansen test, there is probably little point in worrying about the AR(2) test. On the other hand, if the results are robust and the model passes the Hansen test under several different specifications of the lags used as instruments, this could be taken as some evidence that the model is correctly specified, in which case you may reasonably proceed without the AR(2) test.

An alternative to using System GMM is to use a bias-corrected fixed-effects estimator. You can use the xtlsdvc command for this purpose. See the following article for details: Stata Journal | Article

[Jeff Wooldridge]

Helmi: Just because a lagged dependent variable predicts the current outcome doesn't mean you should estimate a dynamic model. You should ask what effect you're trying to uncover. Is this a policy analysis?

For example, if I want to know the dynamic effects of a job training program, I generally identify different effects depending on whether I include y(i,t-1) or whether I use a difference-in-differences analysis. In the latter case, I can clearly define the parameters of interest, and then ask whether the DID assumptions -- particular parallel trends -- holds. In the dynamic model, I'm always holding fixed y(i,t-1), and so I'm really only estimating the immediate effect, not dynamic effects -- unless I make additional assumptions.

[Helmi Mansour]

Since you only have T=4, while the Arellano–Bond AR(2) test requires at least T=5 (1 for lagged y, 4 for AR2 in Δe_it equation), the AR(2) test cannot be performed because of the data limitation, rather than because of a problem with the method.

One consequence of serial correlation in the error term (e_it) is that some of the lagged instruments may become invalid. I think you could look for evidence of serial correlation indirectly using the Hansen test. If the model does not pass the Hansen test, there is probably little point in worrying about the AR(2) test. On the other hand, if the results are robust and the model passes the Hansen test under several different specifications of the lags used as instruments, this could be taken as some evidence that the model is correctly specified, in which case you may reasonably proceed without the AR(2) test.

An alternative to using System GMM is to use a bias-corrected fixed-effects estimator. You can use the xtlsdvc command for this purpose. See the following article for details: Stata Journal | Article

Thank you for this! The hansen test is good as well as the sargan test for all specifications. I would like to use LSDV but FDI analysis usually requires using a dynamic model in which I can include lags of the dependent variable, can I use lags with LSDV??

[Helmi Mansour]

Helmi: Just because a lagged dependent variable predicts the current outcome doesn't mean you should estimate a dynamic model. You should ask what effect you're trying to uncover. Is this a policy analysis?

For example, if I want to know the dynamic effects of a job training program, I generally identify different effects depending on whether I include y(i,t-1) or whether I use a difference-in-differences analysis. In the latter case, I can clearly define the parameters of interest, and then ask whether the DID assumptions -- particular parallel trends -- holds. In the dynamic model, I'm always holding fixed y(i,t-1), and so I'm really only estimating the immediate effect, not dynamic effects -- unless I make additional assumptions.

Thank you Jeff! If I got your point right, I should first specify whether a dynamic model is suitable or not. You could say that this is a policy analysis: I’m trying to investigate the impact of countries’ reputation on their ability to attract FDI. I’m only interested in the short-term effect. The reason I’m using a dynamic model is that I’ve observed in the recent literature that many FDI studies use dynamic models, where past values of FDI affect future values. Do you think it would be more suitable to use a static model in this case, since the main focus is not to asess the impact of lagged FDI??

[Manh Hoang Ba]

Thank you for this! The hansen test is good as well as the sargan test for all specifications. I would like to use LSDV but FDI analysis usually requires using a dynamic model in which I can include lags of the dependent variable, can I use lags with LSDV??

The bias resulting from the correlation between y(-1) and w_it = u_i + e_it is corrected using the xtlsdvc command—not regress, xtreg, areg, or reghdfe. You really should read the paper I linked to in #2.

[Helmi Mansour]

The bias resulting from the correlation between y(-1) and w_it = u_i + e_it is corrected using the xtlsdvc command—not regress, xtreg, areg, or reghdfe. You really should read the paper I linked to in #2.

I see your point! I’ll check it now. Thank you!

[Sebastian Kripfganz]

While my opinion might be biased in this regard, I would recommend to use my own xtdpdbc command instead of xtlsdvc; see the following presentation:

• Kripfganz, S., and J. Breitung (2022). Bias-corrected estimation of linear dynamic panel data models. Proceedings of the 2022 London Stata Conference.

Regarding serial correlation tests, there are alternative tests that can be used with T=4, as implemented in my xtdpdserial package:

• Kripfganz, S. (2024). Robust testing for serial correlation in linear panel-data models. Proceedings of the 2024 London Stata Conference.

Note, however, that xtdpdserial does not work after xtabond2. I recommend to use instead my xtdpdgmm command:

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