Clustered standard errors (or Liang-Zeger standard errors)[1] are measurements that estimate the standard error of a regression parameter in settings where observations may be subdivided into smaller-sized groups ("clusters") and where the sampling and/or treatment assignment is correlated within each group.[2][3] Clustered standard errors are widely used in a variety of applied econometric settings, including difference-in-differences[4] or experiments.[5]
Analogous to how Huber-White standard errors are consistent in the presence of heteroscedasticity and Newey–West standard errors are consistent in the presence of accurately-modeled autocorrelation, clustered standard errors are consistent in the presence of cluster-based sampling or treatment assignment. Clustered standard errors are often justified by possible correlation in modeling residuals within each cluster; while recent work suggests that this is not the precise justification behind clustering,[6] it may be pedagogically useful.
^Liang, Kung-Yee; Zeger, Scott L. (1986-04-01). "Longitudinal data analysis using generalized linear models". Biometrika. 73 (1): 13–22. doi:10.1093/biomet/73.1.13. ISSN 0006-3444.
^Cameron, A. Colin; Miller, Douglas L. (2015-03-31). "A Practitioner's Guide to Cluster-Robust Inference". Journal of Human Resources. 50 (2): 317–372. CiteSeerX 10.1.1.703.724. doi:10.3368/jhr.50.2.317. ISSN 0022-166X. S2CID 1296789.
^"ARE 212". Fiona Burlig. Retrieved 2020-07-05.
^Bertrand, Marianne; Duflo, Esther; Mullainathan, Sendhil (2004-02-01). "How Much Should We Trust Differences-In-Differences Estimates?". The Quarterly Journal of Economics. 119 (1): 249–275. doi:10.1162/003355304772839588. hdl:1721.1/63690. ISSN 0033-5533. S2CID 470667.
^Yixin Tang (2019-09-11). "Analyzing Switchback Experiments by Cluster Robust Standard Error to prevent false positive results". DoorDash Engineering Blog. Retrieved 2020-07-05.
^Abadie, Alberto; Athey, Susan; Imbens, Guido; Wooldridge, Jeffrey (2017-10-24). "When Should You Adjust Standard Errors for Clustering?". arXiv:1710.02926 [math.ST].
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