Robust Inference with Clustered Data

A. Colin Cameron · Douglas L. Miller

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Spatial and Panel Data Analysis Advanced Statistical Methods and Models Advanced Causal Inference Techniques

Abstract

In this paper we survey methods to control for regression model error that is correlated within groups or clusters, but is uncorrelated across groups or clusters. Then failure to control for the clustering can lead to understatement of standard errors and overstatement of statistical significance, as emphasized most notably in empirical studies by Moulton (1990) and Bertrand, Duflo and Mullainathan (2004). We emphasize OLS estimation with statistical inference based on minimal assumptions regarding the error correlation process. Complications we consider include cluster-specific fixed effects, few clusters, multi-way clustering, more efficient feasible GLS estimation, and adaptation to nonlinear and instrumental variables estimators.

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References

2001Econometric Analysis of Cross Section and Panel Data 2008Estimating Standard Errors in Finance Panel Data Sets: Comparing Approaches 1998Consistent Covariance Matrix Estimation with Spatially Dependent Panel Data 2008Bootstrap-Based Improvements for Inference with Clustered Errors 2011Robust Inference With Multiway Clustering 1999GMM estimation with cross sectional dependence 1990An Illustration of a Pitfall in Estimating the Effects of Aggregate Variables on Micro Units 1986Random group effects and the precision of regression estimates

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