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Robust Inference with Multi-way Clustering

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

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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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
Date of revision:
Handle: RePEc:nbr:nberte:0327
Note: TWP
Contact details of provider: Postal: National Bureau of Economic Research, 1050 Massachusetts Avenue Cambridge, MA 02138, U.S.A.
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  1. Marianne Bertrand & Esther Duflo & Sendhil Mullainathan, 2004. "How Much Should We Trust Differences-in-Differences Estimates?," The Quarterly Journal of Economics, MIT Press, vol. 119(1), pages 249-275, February.
  2. Jonathan Gruber & Brigitte C. Madrian, 1993. "Health Insurance Availability and the Retirement Decision," NBER Working Papers 4469, National Bureau of Economic Research, Inc.
  3. 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.
  4. Jonathan Gruber & Brigitte C. Madrian, 1996. "Health Insurance and Early Retirement: Evidence from the Availability of Continuation Coverage," NBER Chapters, in: Advances in the Economics of Aging, pages 115-146 National Bureau of Economic Research, Inc.
  5. 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.
  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. Moulton, Brent R., 1986. "Random group effects and the precision of regression estimates," Journal of Econometrics, Elsevier, vol. 32(3), pages 385-397, August.
  8. Joshua D. Angrist & Victor Lavy, 2002. "The Effect of High School Matriculation Awards: Evidence from Randomized Trials," NBER Working Papers 9389, National Bureau of Economic Research, Inc.
  9. A. Colin Cameron & Jonah B. Gelbach & Douglas L. Miller, 2008. "Bootstrap-Based Improvements for Inference with Clustered Errors," The Review of Economics and Statistics, MIT Press, vol. 90(3), pages 414-427, August.
  10. 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.
  11. repec:cup:cbooks:9780521848053 is not listed on IDEAS
  12. 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.
  13. Jeffrey M. Wooldridge, 2003. "Cluster-Sample Methods in Applied Econometrics," American Economic Review, American Economic Association, vol. 93(2), pages 133-138, May.
  14. David S. Lee & David Card, 2006. "Regression Discontinuity Inference with Specification Error," NBER Technical Working Papers 0322, National Bureau of Economic Research, Inc.
  15. Hersch, Joni, 1998. "Compensating Differentials for Gender-Specific Job Injury Risks," American Economic Review, American Economic Association, vol. 88(3), pages 598-627, June.
  16. 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.
  17. Gabor Kezdi, 2005. "Robus Standard Error Estimation in Fixed-Effects Panel Models," Econometrics 0508018, EconWPA.
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