When Should You Adjust Standard Errors for Clustering?

When Should You Adjust Standard Errors for Clustering?

September 21, 2022 | Alberto Abadie, Susan Athey, Guido W. Imbens, Jeffrey M. Wooldridge
The article by Alberto Abadie, Susan Athey, Guido W. Imbens, and Jeffrey M. Wooldridge addresses the common practice of adjusting standard errors for clustering in empirical research, particularly in economics. They question why certain factors, such as geography, are used for clustering but not others, and why conventional clustering is an "all-or-nothing" adjustment. The authors propose a new framework for clustered inference on average treatment effects that incorporates both sampling and design components, accounting for variability induced by treatment assignment. This framework shifts the focus from infinite populations to finite populations, where the choice of clustering level depends on the sampling and assignment mechanisms rather than the presence of unobserved cluster-level components. The authors derive central limit theorems and large sample variances for least squares and fixed effect estimators, showing that conventional cluster standard errors can be severely inflated when a non-negligible fraction of clusters are sampled. They introduce new variance estimators, including an analytic formula (Causal Cluster Variance, CCV) and a bootstrap procedure (Two-Stage-Cluster-Bootstrap, TSCB), which are designed to correct for this bias. The CCV formula uses estimates of cluster-level treatment effects to adjust the conventional cluster variance, while the TSCB procedure involves resampling clusters and their treatment assignments in two stages. The article also highlights three common misconceptions about clustering adjustments: (1) the need for clustering hinges on residual correlations within clusters, (2) there is no harm in using clustering adjustments when they are not required, and (3) researchers have only two choices for standard errors: robust or cluster. The authors demonstrate the empirical relevance of their framework using data from the 2000 U.S. Census, showing that their proposed standard errors are more accurate than both robust and conventional cluster standard errors in estimating the effect of college attendance on earnings.The article by Alberto Abadie, Susan Athey, Guido W. Imbens, and Jeffrey M. Wooldridge addresses the common practice of adjusting standard errors for clustering in empirical research, particularly in economics. They question why certain factors, such as geography, are used for clustering but not others, and why conventional clustering is an "all-or-nothing" adjustment. The authors propose a new framework for clustered inference on average treatment effects that incorporates both sampling and design components, accounting for variability induced by treatment assignment. This framework shifts the focus from infinite populations to finite populations, where the choice of clustering level depends on the sampling and assignment mechanisms rather than the presence of unobserved cluster-level components. The authors derive central limit theorems and large sample variances for least squares and fixed effect estimators, showing that conventional cluster standard errors can be severely inflated when a non-negligible fraction of clusters are sampled. They introduce new variance estimators, including an analytic formula (Causal Cluster Variance, CCV) and a bootstrap procedure (Two-Stage-Cluster-Bootstrap, TSCB), which are designed to correct for this bias. The CCV formula uses estimates of cluster-level treatment effects to adjust the conventional cluster variance, while the TSCB procedure involves resampling clusters and their treatment assignments in two stages. The article also highlights three common misconceptions about clustering adjustments: (1) the need for clustering hinges on residual correlations within clusters, (2) there is no harm in using clustering adjustments when they are not required, and (3) researchers have only two choices for standard errors: robust or cluster. The authors demonstrate the empirical relevance of their framework using data from the 2000 U.S. Census, showing that their proposed standard errors are more accurate than both robust and conventional cluster standard errors in estimating the effect of college attendance on earnings.
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