Fixed Effets vs GMM

[Leticia R]

Hi everyone,

I am estimating four models (OLS, fixed effects, difference GMM and system GMM) with the purpose of comparing the empirical results. The l.depvar is significant in all models and positive in OLS, difference GMM and system GMM, but only in fixed effect model the l.depvar is negative (and significant). I know that the explanatory variables might be endogenous and thus correlated with the error term (as result, the FE is inconsistent).
However, the result not make sense for me.
Can someone please help me?


Thanks!!!

[Jeff Wooldridge]

Just a correction in terminology: OLS and GMM are not "models." They are estimation methods. I would say that about FE, too. You have one model -- an AR(1) model with an unobserved effect -- and you are estimating in four different ways: OLS, FE, difference GMM, system GMM.

Just using OLS never consistently estimates the coefficient on l.depvar unless there is no heterogeneity, and there is an upward biase. FE is also biased, usually downward, and the bias can be substantial unless T is large. So you get a large positive estimate using OLS and a negative estimate using FE? That is perfectly consistent with what is known about the estimators. GMM using the Arellano-Bond conditions is the most robust: It only uses the moment conditions implied by the AR(1) model, and it properly removes the heterogeneity. GMM system adds extra moment conditions that may be false. If the difference GMM estimate seems reasonable precise, and there is no evidence of weak instruments, I would go with that.

Why are OLS and FE even in the running? Maybe FE with a very large T, but it has nothing over GMM unless GMM produces large standard errors. But you haven't even shown us the Stata commands and output.

[Leticia R]

Thanks for your response. I am working with 800 municipalities for a period of 8 years. The Stata commands are: