[Sebastian Kripfganz]

1. Yes. 2. Yes. 3. Yes. 4. Yes.

[Prateek Bedi]

Alright, Prof. Kripfganz. Your remarkable expertise in dynamic panel estimation and helpful attitude has benefited me a great deal in my doctoral work. Although a thank you is not at all enough, still thank you so much!

[Prateek Bedi]

I have one more doubt: For a dependent variable, Y which follows a dynamic data generating process, what should we assume its lag to be: predetermined or endogenous. I ask this because we need to put this lag also in a gmmiv() or iv() and specify model() for the same in the command.

Thanks!

[Sebastian Kripfganz]

If there is no serial correlation in the idiosyncratic error term, then the lagged dependent variable, L.Y, is predetermined.

[Prateek Bedi]

If there is no serial correlation in the idiosyncratic error term, then the lagged dependent variable, L.Y, is predetermined.

Ok.

1. By idiosyncratic error term, do you mean that time-varying and cross-section varying part of the composite error term which excludes fixed effects?
2. Is there an empirical way of checking this serial correlation in the idiosyncratic error term or is it a theoretical call?

[Sebastian Kripfganz]

1. Yes.
2. That is precisely what the Arellano-Bond test is doing (for the first-differenced error term). The AR(1) should reject the null hypothesis. The AR(2) test should not reject the null hypothesis.

[Prateek Bedi]

Right, Prof. Kripfganz. So in all my regressions, null hypothesis of AR(1) test is indeed rejected and null hypothesis of AR(2) is not rejected. Thus, since there is serial correlation of the first order (in the first-differenced error term) as shown by results of AR(1) test, should I consider the lag of my dependent variable to be endogenous instead of predetermined?

[Sebastian Kripfganz]

If there is no serial correlation in the level errors, there will be first-order serial correlation in the first-differenced errors. This is why the AR(1) test should reject. A rejection of the AR(1) test does not imply that there is serial correlation in the level errors. Thus, you can continue treating the lagged dependent variable as predetermined.

[Prateek Bedi]

Thank you Prof. Kripfganz for such a clear explanation. Things are much more clear now to me. Thanks a lot!!

[Prateek Bedi]

If there is no serial correlation in the idiosyncratic error term, then the lagged dependent variable, L.Y, is predetermined.

Can we use 0 as the starting and ending lag length for lagged dependent variable i.e. gmmiv(L.Y, lag(0 0) model(fodev))?

[Sebastian Kripfganz]

Yes.

[Prateek Bedi]

Yes.

Ok, Prof. Kripfganz. Since the theory is not very much clear regarding some of the explanatory variables as to whether they should be considered as predetermined or not, I thought of looking at the correlation of the lagged dependent variable with the concerned independent variable in question. The idea is to support my theoretical arguments concerning my decision to consider an independent variable as predetermined or not with the result of this pairwise correlation. If the correlation is not significant, I can support my decision to not consider an independent variable as predetermined. Does this approach sound sensible to you?

Thanks!

[Sebastian Kripfganz]

Not really. Since the lagged dependent variable is part of the model, the error term only captures effect not measured by the lagged dependent variable. Thus, looking at the correlation with the lagged dependent variable does not tell you anything about the correlation with the error term. In that regard, my response to point 1 in my earlier post #152 was not accurate.

[Prateek Bedi]

Ok, Prof. Kripfganz. I understand your viewpoint to an extent. However, I have a doubt. The lagged error term, say u_it-1, is actually the residual part of Y_it-1, which could not be explained by the model. Hence, if I were to make a sense of the relationship between X_it-1 and u_it-1, why can't I just look at the relationship between Y_it-1 and X_it-1 since we cannot practically examine the relationship between X_it-1 and u_it-1 as they are uncorrelated by construction.

For a time point 't', I agree that since Y_it-1 is a part of our model, u_it only captures the effect not measured by Y_it-1. However, we are trying to estimate a relationship between X_it and u_it-1 (and not X_it and u_it).

Apologies in advance if the question sounds silly.

Thanks!

[Sebastian Kripfganz]

I see your point, but u_it-1 is just one part of Y_it-1. X_it-1 as well is part of the process determining Y_it-1. If X_it itself is serially correlated, i.e. correlated with X_it-1, then X_it will be correlated with Y_it-1 because of its correlation with X_it-1. Any observed correlation between X_it and Y_it-1 is thus not informative about a potential correlation of X_it with u_it-1.

The way to address the question whether X_it is predetermined, is by looking at difference-in-Hansen tests as done in the model selection part of my 2019 London Stata Conference presentation.