# Can someone explain 2SLS - GMM?

I believe I have a dynamic relationship within my panel dataset, with heteroscedasticity and autocorrelation. I've been instructed to look into GMM as it is the solution.

What is it and how can I do it? Most textbooks are so formal I cannot grasp what they are trying to say.

• I found these slides to be a good intro (though focused on stata users): fmwww.bc.edu/EC-C/.../EC823.S2014.nn05.slides.pdf. Dynamic panel models are inescapably technical. Actually fitting them requires specifying several assumptions and checking various measures of fit to those assumptions. I wouldn't recommend fitting these models until you can get yourself to a point where you understand what is going on. This is in contrast to something like OLS, where someone who hasn't learned a lot of basic properties can still reliably use the method. May 28, 2015 at 17:05
• Stupid google won't let me copy the URL of a pdf result. Try googling for "dynamic panel data nickell bias baum boston college". it will be in the top results. May 28, 2015 at 17:08

## 1 Answer

I'll try to answer your questions with as little formality as possible

## 1. What is GMM?

GMM is an estimation methode that turns out to be the mother of most common econometric estimators. Basically we use the fact that empirical moments (which can be determined from the data) are consistent estimators (="good" estimators in a statistical sense) for their theoretical population counterpart. These theoretical moments are functions of parameters that you are interested in (in your case coefficients).

If you have as many empirical moments as there are parameters to estimate, all you do is to equate empirical and theoretical moments and solve for the set of unknown parameters. Since there might be more such so called "moment equations" than there are parameters to estimate, a weigted minimization of the quadratic difference between empirical and theoretical moments is done. This is technically more complicated than simply solving a set of K equations with K unknowns, however, in princial the idea is the same.

## 2. What is GMM in a panel data context?

If you have panel data things look (and are indeed) more complicated but in fact the underlying logic is the same. We use our empirical moments to estimate the parameters of their theoretical counterpart. Generally, we distinguish between difference GMM and system GMM. These estimators are mainly attributed to the works of Arellano, Bond, Bover and Blundell (hence the GMM panel data estimator is often called Arellano-Bond estimator).

## 3. How can you do it?

As it makes no sense to dive into a general description of how it works I would recommend you read this article from the Stata journal. This should also help you to implement dynamic panel data estimators without to much technical knowledge. Yes, the article is still partly technical, but this is impossible to avoid.

If you have any specific questions concering dynamic panel and/or GMM in general feel free to ask.