[Sebastian Kripfganz]

1.
Once you have specified the teffects option, you do not need to explicitly specify the time dummies in the list of instruments. That is done automatically.
For L.CashHoldings1 as GMM-type instruments in the FOD model, you could already start with the 0-th lag. See the example in my previous post.
You have specified Size1 Profitability4 WPromoterSharesin1 CashFlowVol15years OperatingCashflow as instruments for the level model. By doing so, you are implicitly assuming that all of these variables are strictly exogenous and, in particular, uncorrelated with the unobserved group-specific effects. This is a strong assumption, although not necessarily wrong.

2.
Yes, they are supportive. These are the two statistics that are usually reported in empirical research.

3.
Both versions are asymptotically equivalent. They just use different estimates of the weighting matrix. The second-step weighting matrix is estimated with the first-step residuals. The third-step weighting matrix is estimated using the second-residuals. (This would be the weighting matrix for a 3-step GMM estimator.) You can usually just ignore the second version and only report the test based on the two-step weighting matrix.

4.
The degrees of freedom for the overidentification tests equal the number of instruments minus the number of estimated coefficients (not including "empty" or "omitted" coefficients). The problem with xtabond2 is that it counts those omitted coefficients as well.

5.
There was an update to xtabond2 last December. You may want to check if you have the latest version. In any case, not all problems have been fixed in this update, unfortunately. There might be good reasons from a programmer's perspective for not modifying the code, but I do not want to speak for David Roodman here. Regarding the FOD, it is probably anything but easy to deal with the problems while ensuring that previous do-files will still run and deliver correct results.
As to why xtabond2 is still the primary choice for GMM estimation: Most people probably do not know about the problems with that program. If you are a beginner and ask someone how to estimate dynamic panel models with GMM in Stata, they will almost inevitably point you towards xtabond2 because everyone knows it. The popularity of the program is self-reinforcing. xtdpdgmm is a rather new program still under development and there is not yet a documentation (beyond the help files) or a Stata Journal article (to be written in the hopefully near future) about it.

[Prateek Bedi]

Thank you so much for your detailed response once again, Prof. Sebastian. Please consider my follow-up queries below.

1. In your response in point #1, I assume you mean "firm fixed effects" (as applicable to my model) when you mention "unobserved group-specific effects". Since I am working on firm data, I should ensure that variables specified by me as exogenous should not be correlated with "firm fixed effects". Right? Further, as you mentioned in an earlier post, this assumption of no correlation between exogenous variables and firm fixed effects is a theoretical call of the researcher and cannot be tested empirically. Right?

2. In my model, I suppose I can claim that I have controlled for firm fixed effects (although I haven't included firm dummies but since I use FODEV, firm fixed effects should get wiped out). Right?

3. In some of my models, although the first lag of the dependent variable is highly significant, AB test for serial correlation does not reject the null hypothesis for first order serial correlation (for all such cases, the null hypothesis for second order serial correlation is not rejected). Should I change the specification of my model in such cases to ensure that AB test for serial correlation rejects the null hypothesis for first order serial correlation.

4. For some of my models, although the null hypothesis of Sargan-Hansen test for 2-step moment functions, 2-step weighting matrix is not rejected, the null hypothesis of Sargan-Hansen test for 3-step moment functions, 3-step weighting matrix is rejected. Should I change the specification of my model in such cases to ensure that both the null hypotheses are not rejected?

5. There are some models for which I have changed the "lags" of the endogenous variables (in order to achieve "desired" results). How do we decide on the correct lag limits. I ask this because the results are significantly dependent on the lag limits used in the model.

Thanks

[Sebastian Kripfganz]

1. Yes, these are firm-fixed effects in your case. You are actually able to test the validity of the overidentifying restrictions with a (Difference-in-)Hansen test.

2. Firm-fixed effects are wiped out from the FOD model, yes. Your claim requires that the exogeneity assumption from point 1 holds.

3. While most people ignore the AR(1) test, ideally this test should reject the null hypothesis of no first-order serial correlation in the first-differenced model. Otherwise, this would be a contradiction to the assumption that the level residuals are serially uncorrelated.

4. The difference between these two statistics should not be large. If one rejects and the other does not, then your p-values are probably close to the significance level. There are probably many people who would not regard your model as reliable in such a situation. At the end, it is probably still sufficient to look only at one of the two statistics but ensure that the p-value is substantially higher than the significance level.

5. That's indeed a tricky question and I do not have a simple answer for you. You might want to avoid using too many lags because observations far in the past can become weak instruments (plus the familiar too-many-instruments problem).

[Prateek Bedi]

Thanks a ton, Prof. Sebastian for your crystal clear responses. I know I might be bothering you a bit too much. Below are some further questions.

1. I could notice that xtabond2 reports difference-in-Hansen tests for instrument subsets. However, I could not find the output for this test in xtdpdgmm. How do I check validity of the overidentifying restrictions with a (Difference-in-) Hansen test in xtdpdgmm?

2. You mention that AR(1) test should reject the null hypothesis of no first-order serial correlation in the first-differenced model. I just wanted to know that if we use FODEV everywhere in gmmiv sub-option, where does first-differencing come into the picture?

3. I wonder why AR(1) test is not getting rejected in some of my models despite the lagged dependent variable being significant at 1% in the output.

4. Regarding the cases of contradiction between results for Sargan-Hansen test for 2-step moment functions and 3-step moment functions, the null for 2-step moment functions gets accepted comfortable (p-value > 0.50) but the null for 3-step moment functions gets rejected at 0.05. Is it fine to consider the result for 2-step moment functions and show corresponding results? Also, as advised by you, for consistency, I plan to report results for 2-step moment functions for all my models (and stay silent on 3-step moment functions). Hope it is fine.

5. This may sound a bit silly: I would like to understand the basic conceptual difference between gmmiv style treatment and iv style treatment. I understand that we put endogenous variables in gmmiv sub-option and exogenous variables in iv sub-option. However, I would like to know what happens with these variables (mentioned in gmmiv and iv sub-options) when they enter the system of equations in system GMM. For which type of variables (gmmiv or iv) are instruments sought in the background? Why do we usually use "model(level)" for iv-style variables?


Thanks and Regards
Prateek

[Sebastian Kripfganz]

1. Currently, xtdpdgmm computes those tests in a different way compared to xtabond2. You need to separately estimate the two models that you want to compare, e.g.

webuse abdata
xtdpdgmm L(0/1).n w k, two vce(r) gmm(L.n w k, l(1 4) c) m(d)
estimates store ab
xtdpdgmm L(0/1).n w k, two vce(r) gmm(L.n w k, l(1 4) c m(d)) iv(L.n w k, d)
estat overid ab

This performs a Difference-in-Hansen test for the additional instruments in iv(L.n w k, d), given that all other instruments are identical in both model specifications. See help xtdpdgmm postestimation for details.

2. In this case, first-differencing is only used to compute the Arellano-Bond test statistics. Rejecting the AR(1) statistic and not rejecting the AR(2) statistic are nevertheless equally important for the FODEV and the Differencing transformation.

3. Sometimes this could be an indication that a higher-order lag, say a second lag, of the dependent variable is needed as a regressor.

4. That is what people usually do.

5. The iv() option is also often used with model(difference). In fact, the gmmiv() option with a fixed lag length and the collapse option is equivalent to the iv() option. See help xtdpdgmm for details. For a more general discussion of these options, see for example Roodman (2009): How to do xtabond2 ...

[Prateek Bedi]

Dear Prof. Sebastian:

Your priceless responses and unconditional support has helped me a great deal to understand nuances of dynamic panel estimation. It is difficult to thank you in words. I wish you all the luck for your future endeavors and hope that you shall continue to spread the light of knowledge. May God bless you!!

P.S.: I shall be back with more questions in case I have further doubts!!