Stata First-difference and system GMM model - one-step or two-step?

[Aneta Joanna]

Hi,

I estimate in Stata two dynamic panel models using first-difference GMM and system GMM.

For first-difference GMM and one-step approach I use command: xi: xtabond lnr_fpl i.year year, twostep. Here you have a part of my results:

Estat sargan: Prob > chi2 = 1.0000

I add vce(robust) option and I have:

Estat abond:

So when I use two-step estimator, Sargan test presents good results, but I have a significant autocorrelation order 1. Moreover, my variable in lag 1 (lnr_fpl) is not statistically significant


When I use one-step estimator without vce(robust), I have estat sargan: Prob > chi2 = 0.1623:

Estat abond with vce(robust): AR(1) Prob>z: 0.0024; AR(2) Prob>z: 0.4622

Based on above results, I have several questions:
1. Should I use i.year and year together, if I want to include time effects? Maybe should I use only i.year?
2. Why does two-step gives so bad results? Autocorrelation of order 1, main variable (lnr_fpl) is not significant.... One-step is better a lot. Why? The same situuation is in SYS-GMM model (xtdpdsys command in stata).
3. How can I add individual effects to first-difference and system GMM models?

[Aneta Joanna]

I add one question.

[Sebastian Kripfganz]

• First of all, your number of groups (25) is very small, usually too small to expect reliable results from this type of estimator. If anything, then you should only use the one-step estimator which avoids estimating the weighting matrix. But again, any inference is quite unreliable with such a small number of groups.
• The Sargan test makes strong assumptions about the error variance structure (similar to not specifying robust standard errors). But again, with such a small number of groups, there is not much hope for getting reliable results from any overidentification test.
• Your number of instruments is way too large. It should be substantially smaller than the number of groups. You need to radically limit the lag order for your instruments and use the collapse option.
• year is redundant once you included i.year.
• There is no need to include individual effects. These are left in the error term. The whole idea of the estimator is to use instruments orthogonal to those effects.

More on the GMM estimation of linear dynamic panel models:

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