How to do Xtabond2: An Introduction to Difference and System GMM in Stata

TLDR

Difference and system GMM estimators, developed by Holtz‑Eakin, Newey, Rosen, Arellano, Bond, and Blundell, are increasingly popular for small‑T, large‑N panel data with endogenous regressors, fixed effects, and heteroskedasticity. This pedagogic article introduces linear GMM and demonstrates how to apply it using Stata’s xtabond2 command. It explains how limited time spans and potential fixed effects drive the design of the estimators, provides Stata examples, and shows how to perform the Arellano–Bond autocorrelation test with the abar command. The article concludes with practical tips for proper use of these estimators.

Abstract

The difference and system generalized method-of-moments estimators, developed by Holtz-Eakin, Newey, and Rosen (1988, Econometrica 56: 1371–1395); Arellano and Bond (1991, Review of Economic Studies 58: 277–297); Arellano and Bover (1995, Journal of Econometrics 68: 29–51); and Blundell and Bond (1998, Journal of Econometrics 87: 115–143), are increasingly popular. Both are general estimators designed for situations with “small T, large N″ panels, meaning few time periods and many individuals; independent variables that are not strictly exogenous, meaning they are correlated with past and possibly current realizations of the error; fixed effects; and heteroskedasticity and autocorrelation within individuals. This pedagogic article first introduces linear generalized method of moments. Then it describes how limited time span and potential for fixed effects and endogenous regressors drive the design of the estimators of interest, offering Stata-based examples along the way. Next it describes how to apply these estimators with xtabond2. It also explains how to perform the Arellano–Bond test for autocorrelation in a panel after other Stata commands, using abar. The article concludes with some tips for proper use.