Robustness: GMM differences +GMM system

[Jorge Vela]

Dear colleagues

I am analyzing the effect of different kind of variables and the effect of a new law on the local debt.

I estimated two GMM in differences (Arellano and Bond, 1991). A model with dummies that includes the years and another with one temporary dummy (years). The reviewer told me that it is fine but that it would be advisable to raise dynamic panels to the GMM.

He proposed me some of these: Maximum likelihood estimation of Fixed efects dynamic panel data models covering short time periods (Hsiao et al., 2002), Estimation and inference in dynamic unbalanced panel data models with a small number of individuals (Bruno, 2005) or estimating using maximum likelihood and structutural equation modeling (Williams et al., 2015). I have tried with the last suggestion, but my sample is my small one and it is not possible to apply it (command xtdpdml).

As a contribution to the review of the paper, I was able to include two new estimates, including the GMM system estimate with the xtdpdsys command (Arellano and Bover, 1995).

My questions are:

1) Would greater robustness complement the initial estimate in differences with the estimate system? Even though both are GMM

2) Would it be feasible or more appropriate to incorporate some of the other estimates? Are they better than GMM? Basically in my field of study apply all GMM.


Thank you very much to all!!

[Sebastian Kripfganz]

The Hsiao et al. (2002) estimator is implemented in my xtdpdqml command (not to be confused with the Williams et al. (2018) xtdpdml command):

ssc install xtdpdqml

Please see my accompanying article for further background information:
Kripfganz, S. (2018). Quasi-maximum likelihood estimation of linear dynamic short-T panel-data models. Stata Journal 16 (4), 1013-1038.

Difference GMM suffers from a weak instruments problem if the dependent variable is highly autocorrelated. System GMM requires an additional mean stationarity assumption that may not be appropriate in some applications. Several other problems might emerge with GMM estimation. The following article might be useful:
Roodman, D. (2009). A note on the theme of too many instruments. Oxford Bulletin of Economics and Statistics 71 (1). 135-158.

The Hsiao et. al (2002) QML estimator is more efficient than GMM estimators if all assumptions are satisfied. The GMM estimators have the advantage that they can be made more robust, in particular to deviations from strict exogeneity of the regressors (besides the lagged dependent variable).