1-step gmm-sys VS. 2-step

[Niko Sarafidis]

Dear all,

Estimating a gmm-system model with xtabond2, N=36 T=6, I got results that showed smaller standard errors of estimates using 1-step robust than using 2-step robust.

I have two questions:

I) Why even diminishing the number of instruments, using the command xtabond2, the warning about the singularity of 2-step weighting matrix is singular?

II) In a case of a small sample, is it better to utilise the 1-step procedure or the Windmeijer's correction is sufficient for face the standard-error bias?

[Andrew Matt]

Hi, Niko

I have similar results. Have you got an answer to your question?

[Sebastian Kripfganz]

I) If you are sure that you are doing the correct thing, you can just ignore the warning. Otherwise, it might be an indication that your number of instruments is still too large relative to the sample size.

II) For the system GMM estimator, one-step standard errors are always asymptotically inefficient. In finite samples, in particular when your number of instruments is relatively large compared to the cross-sectional sample size, the two-step procedure is not guaranteed to produce superior results. There is no general answer to this question.

With such a small sample, estimating a dynamic panel model by system GMM is generally difficult. You should try to keep the model as simple as possible.

More on GMM estimation of linear dynamic panel data models:
XTDPDGMM: new Stata command for efficient GMM estimation of linear (dynamic) panel models

[Domenico Candido]

How to justify that results obtained from two-step sys GMM are "better" (for my case) than results obtained from one-step sys GMM in small panels?

[Fernando Martins]

I used to have the same issue with some models from my masters course.

One-step GMM estimations are usually inefficient and, probably, will be a problem for anyone that may comment on your work.

As several persons mentioned to me (including Sebastian itself), these kind of models are usually very sensitive to the sample size, especially small ones. You will always be juggling around to get satisfactory results.

If the One-step GMM is yielding better results, something may be wrong, either the moment conditions included (too many instruments), or maybe the model itself is misspecified (my case) and inconsistent.

Also, I started using Roodman's xtabond2 and ended with Sebastian's xtdpdgmm. I think the syntaxes from the later are better and gives you more space to fine tune your model.

You can also try using the Iterated GMM estimator (IGMM), supported by xtdpdgmm, that should yiled efficient results in small samples.

In the last case, there is also the Continuous Update GMM estimator (CUE), but I don't know the panel command that supports it.

Of course, it's way more probable that you have a instrument/misspecification problem than a problem with the estimator itself.

Also, it will help if you share some results.

Regards,