eq(level) or eq(dif) specification

[Anna Bakkers]

Hi users,

I am struggling to understand when to use eq(level) or eq(dif) in the xtabond2 function for the gmmstyle and the ivstyle estimators.
Is it most common/basic to use eq(level) for gmmstyle and eq(dif) for ivstyle? Or how can I figure out which ones to use for my endogenous and exogenous variables?
I have tried to read papers, but I cannot find a clear explanation on how to apply this in Stata.

My goal is to obtain a two-step system gmm. (based on literature).

Thanks a lot. Looking forward to any reply.

[Anna Bakkers]

Additionally, what if the Hansen test excluding group provides good results, but the Difference (null H=exogenous) does not (or other way around). I tend to get contrary results sometimes.
So what do both test statistics indicate? (aka, what part of the model specification is incorrect).
For example

Hansen test excluding group: chi2(131) = 244.95 Prob > chi2 = 0.000
Difference (null H = exogenous): chi2(3) = 1.48 Prob > chi2 = 0.687

Or
Hansen test excluding group: chi2(59) = 50.50 Prob > chi2 = 0.777
Difference (null H = exogenous): chi2(57) = 128.77 Prob > chi2 = 0.000

[Sebastian Kripfganz]

In contrast to the level equation, the first-differenced equation is free of the unobserved group-specific "fixed effects". Specifying instruments for this equation is usually the starting point of GMM estimation for linear dynamic panel models because those instruments do not need to satisfy any assumption with regard to the fixed effects. This leads to the so-called difference-GMM estimator. This is irrespective of whether you use GMM-style or standard instruments.

The system-GMM estimator adds further instruments for the level equation in addition to those already specified for the first-differenced equation. Those additional instruments need to satisfy the assumption that they are uncorrelated with the fixed effects.

Regarding the overidentification tests: If the "Hansen test excluding group" rejects the null hypothesis, then the corresponding difference test becomes meaningless. It indicates a problem with the model specification other than the instrument group investigated here. If the "Hansen test excluding group" does not reject the null hypothesis but the corresponding difference test does, then this indicates that the instrument group investigated here contains invalid instruments.

I have slides about all of these issues in my 2019 London Stata Conference presentation:

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