log differenced model and GMM Estimator

[Sehri Far]

Hi all,

I have panel data (T=30) and due to potential threat of non stationarity in my data i've transformed my data into log differences.
There is endogeneity bias in my model as well, i want to apply GMM estimator. Since GMM apply differenced transformation on data so it would be double differencing in my case.

In this case can I use Difference or System GMM on the model? if not which estimator would be appropriate?

I'll appreciate early response.
Thanks

[Sebastian Kripfganz]

If you worry about nonstationarity, you can normally just use the difference GMM estimator (without pre-differencing your data). The assumptions for the system GMM estimator are probably not satisfied.

[Sehri Far]

Thanks. But confusion is still there, why I cannot use GMM on the model with growth rates(log difference), secondly System GMM use differenced lags and levels of the variables as instruments, if there is non stationarity in levels, system GMM wont provide reliable estimates, isn't that the case?

[Sebastian Kripfganz]

The system GMM estimator may not be reliable if used with nonstationary levels data.

You can use GMM on the model with growth rates. However, since the model is then estimated in second differences, there is a chance that your instruments may not be strong enough anymore. First, you should ask yourself what the effects are you are interested in: Do you want to estimate long-run effects for the level variables or for the growth rates. This should inform your decision whether to pre-difference your data prior to the estimation. In the next step, you then decide about the appropriate estimator.