Are there random-effects GMM models?

[Sang-Bum Park]

One of my key variables is time-invariant. Thus, fixed-effects models do not suit my research. As far as I know, GMM models follow fixed-effects models. Thus, do GMM models not fit with my study as well?

[Sebastian Kripfganz]

You can use a GMM estimator to estimate unobserved effects models. Whether these unobserved effects are "fixed" or "random" informs the choice of your instruments. Random-effects models assume that the regressors are uncorrelated with the unobserved effects. Thus, assuming that there is no other source of endogeneity, you can use the regressor as an instrument for itself without the need for a transformation of the variables or the model.

You might find the following paper interesting:

• Kripfganz, S., and C. Schwarz (2019). Estimation of linear dynamic panel data models with time-invariant regressors. Journal of Applied Econometrics 34 (4), 526-546.

[Sang-Bum Park]

Sebastian Kripfganz Thank you. Can you also provide some Stata code examples that can help me readily adapt your methodology?

[Sebastian Kripfganz]

Replication files for the article referenced in my previous post are available in the JAE data archive. I also provide a brief example on slides 82-86 of the following presentation:

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