, 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.

The difference and system generalized method of moments (GMM) estimators are growing in popularity. As implemented in popular software, the estimators easily generate instruments that are numerous and, in system GMM, potentially suspect. A large instrument collection overfits endogenous variables even as it weakens the Hansen test of the instruments' joint validity. This paper reviews the evidence on the effects of instrument proliferation, and describes and simulates simple ways to control it. It illustrates the dangers by replicating Forbes [American

, 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.

The Difference and System generalized method of moments (GMM) estimators are growing in popularity, thanks in part to specialized software. But as implemented in these packages, the estimators easily generate results by default that are at once invalid yet appear valid in specification tests. The culprit is their tendency to generate instruments that are a) numerous and, in System GMM, b) suspect. A large collection of instruments, even if individually valid, can be collectively invalid in finite samples because they overfit endogenous variables. They also weaken the Hansen test of overidentifying restrictions, which is commonly relied upon to check instrument validity. This paper reviews the evidence on the effects of instrument proliferation, and describes and simulates simple ways to control it. It illustrates the dangers by replicating two early applications to economic growth: Forbes (2000) on income inequality and Levine, Loayza, and Beck (2000) on financial sector development. Results in both papers appear driven by previously undetected endogeneity.The Center for Global Development is an independent think tank that works to reduce global poverty and inequality through rigorous research and active engagement with the policy community. Use and dissemination of this working paper is encouraged, however, reproduced copies may not be used for commercial purposes. Further usage is permitted under the terms of the Creative Commons License. The views expressed in this paper are those of the author and should not be attributed to the directors or funders of the Center for Global Development. JEL codes: C23, G0, O40. Keywords: difference GMM, system GMM, Hansen test, small-sample properties of GMM, financial development, inequality. AbstractThe Difference and System GMM estimators are growing in popularity. As implemented in popular software, the estimators easily generate instruments that are numerous and, in System GMM, potentially suspect. A large instrument collection overfits endogenous variables even as it weakens the Hansen test of the instruments' joint validity. This paper reviews the evidence on the effects of instrument proliferation, and describes and simulates simple ways to control it. It illustrates the dangers by replicating Forbes (2000) on income inequality and Levine et al. (2000) on financial sector development. Results in both papers appear driven by previously undetected endogeneity.Emperor Joseph II: My dear young man, don't take it too hard. Your work is ingenious. It's quality work. And there are simply too many notes, that's all. Just cut a few and it will be perfect. Mozart: Which few did you have in mind, Majesty?- Amadeus (1984)

At the heart of many econometric models are a linear function and a normal error. Examples include the classical small-sample linear regression model and the probit, ordered probit, multinomial probit, tobit, interval regression, and truncated-distribution regression models. Because the normal distribution has a natural multidimensional generalization, such models can be combined into multiequation systems in which the errors share a multivariate normal distribution. The literature has historically focused on multistage procedures for fitting mixed models, which are more efficient computationally, if less so statistically, than maximum likelihood. Direct maximum likelihood estimation has been made more practical by faster computers and simulated likelihood methods for estimating higherdimensional cumulative normal distributions. Such simulated likelihood methods include the Geweke-Hajivassiliou-Keane algorithm (