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Robust Inference with Multi-way Clustering

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  • A. Colin Cameron
  • Jonah B. Gelbach
  • Douglas L. Miller

Abstract

In this paper we propose a new variance estimator for OLS as well as for nonlinear estimators such as logit, probit and GMM, that provcides cluster-robust inference when there is two-way or multi-way clustering that is non-nested. The variance estimator extends the standard cluster-robust variance estimator or sandwich estimator for one-way clustering (e.g. Liang and Zeger (1986), Arellano (1987)) and relies on similar relatively weak distributional assumptions. Our method is easily implemented in statistical packages, such as Stata and SAS, that already offer cluster-robust standard errors when there is one-way clustering. The method is demonstrated by a Monte Carlo analysis for a two-way random effects model; a Monte Carlo analysis of a placebo law that extends the state-year effects example of Bertrand et al. (2004) to two dimensions; and by application to two studies in the empirical public/labor literature where two-way clustering is present.

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Bibliographic Info

Paper provided by National Bureau of Economic Research, Inc in its series NBER Technical Working Papers with number 0327.

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Date of creation: Sep 2006
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Handle: RePEc:nbr:nberte:0327

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  1. Jonathan Gruber & Brigitte Madrian, 1993. "Health Insurance and Early Retirement: Evidence from the Availability of Continuation Coverage," NBER Working Papers 4594, National Bureau of Economic Research, Inc.
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  6. Kloek, T, 1981. "OLS Estimation in a Model Where a Microvariable Is Explained by Aggregates and Contemporaneous Disturbances Are Equicorrelated," Econometrica, Econometric Society, vol. 49(1), pages 205-07, January.
  7. Hersch, Joni, 1998. "Compensating Differentials for Gender-Specific Job Injury Risks," American Economic Review, American Economic Association, vol. 88(3), pages 598-627, June.
  8. Angrist, Joshua & Lavy, Victor, 2002. "The Effect of High School Matriculation Awards: Evidence from Randomized Trials," CEPR Discussion Papers 3827, C.E.P.R. Discussion Papers.
  9. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-38, May.
  10. Mitchell A. Petersen, 2009. "Estimating Standard Errors in Finance Panel Data Sets: Comparing Approaches," Review of Financial Studies, Society for Financial Studies, vol. 22(1), pages 435-480, January.
  11. Moulton, Brent R, 1990. "An Illustration of a Pitfall in Estimating the Effects of Aggregate Variables on Micro Unit," The Review of Economics and Statistics, MIT Press, vol. 72(2), pages 334-38, May.
  12. Pepper, John V., 2002. "Robust inferences from random clustered samples: an application using data from the panel study of income dynamics," Economics Letters, Elsevier, vol. 75(3), pages 341-345, May.
  13. David S. Lee & David Card, 2006. "Regression Discontinuity Inference with Specification Error," NBER Technical Working Papers 0322, National Bureau of Economic Research, Inc.
  14. Hansen, Christian B., 2007. "Asymptotic properties of a robust variance matrix estimator for panel data when T is large," Journal of Econometrics, Elsevier, vol. 141(2), pages 597-620, December.
  15. Doug Miller & A. Colin Cameron & Jonah B. Gelbach, 2006. "Bootstrap-Based Improvements for Inference with Clustered Errors," Working Papers 621, University of California, Davis, Department of Economics.
  16. Jeffrey M. Wooldridge, 2003. "Cluster-Sample Methods in Applied Econometrics," American Economic Review, American Economic Association, vol. 93(2), pages 133-138, May.
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