Proper treatment of the variables that have unit root when System GMM is used

[Laura FR]

Dear everyone,

I have a doubt with respect to the need of first differencing the variables cointaining unit root before estimating a model using System GMM with xtabond2.

According to the Im-Pesaran-Shin test results (xtunitroot ips), some of the variables in the model I want to estimate are I(1) and some others are stationary. There is also another potential regressor, population density, which is I(2).

Would it be correct to include the I(2) variable first differenced twice, the I(1) variables in first differences and the stationary ones in levels?
Or since GMM uses the first differences it is not necessary to compute the first differences for the I(1) variables? Therefore to include the I(0) and the I(1) variables in levels (and only to first difference once the I(2) variables if included)(?)

If it is informative, I must say that the panel dimensions are N=170 and T=21, so a quite long time dimension. I use the collapse option of xtabond2 in order to minimize the proliferation of instruments.

Thank you very much for any comment and help.

Laura

[Anastasia Giannioti]

Hi Laura,

I have the same problem now with my model. I have done unit root tests before my system GMM estimation and some of my variables are I(0) but some I(1). Did you find a solution?? Thank you!

[Sebastian Kripfganz]

With a large-N, small-T dynamic panel data model, there is usually no need to conduct unit root tests. I recommend to address the matter primarily from a modeling point of view: Do you suspect a relationship between the levels of your variables, or does it make more sense to postulate a relationship between the changes (growth rates, if variables are in logs)?! In other words, specify the regression model in the way your theory would suggest.

The following presentation might contain further useful information:

• Kripfganz, S. (2019). Generalized method of moments estimation of linear dynamic panel data models. Proceedings of the 2019 London Stata Conference.