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Robust Inference with Multi-way Clustering

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Author Info

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

    (Department of Economics, University of California Davis)

Abstract

In this paper we propose a variance estimator for the OLS estimator as well as for nonlinear estimators such as logit, probit and GMM. This variance estimator enables 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 studies in the empirical literature where two-way clustering is present.

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Bibliographic Info

Paper provided by University of California, Davis, Department of Economics in its series Working Papers with number 98.

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Length: 43
Date of creation: 01 May 2009
Date of revision:
Handle: RePEc:cda:wpaper:09-8

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Related research

Keywords: cluster-robust standard errors; two-way clustering; multi-way clustering.;

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References

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  1. Cameron, A. Colin & Miller, Douglas & Gelbach, Jonah B., 2006. "Bootstrap-Based Improvements for Inference with Clustered Errors," Working Papers 06-21, University of California at Davis, Department of Economics.
  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. Gabor Kezdi, 2005. "Robus Standard Error Estimation in Fixed-Effects Panel Models," Econometrics 0508018, EconWPA.
  4. 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.
  5. 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.
  6. Moulton, Brent R., 1986. "Random group effects and the precision of regression estimates," Journal of Econometrics, Elsevier, vol. 32(3), pages 385-397, August.
  7. Lee, David S. & Card, David, 2008. "Regression discontinuity inference with specification error," Journal of Econometrics, Elsevier, vol. 142(2), pages 655-674, February.
  8. 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.
  9. Mitchell A. Petersen, 2005. "Estimating Standard Errors in Finance Panel Data Sets: Comparing Approaches," NBER Working Papers 11280, National Bureau of Economic Research, Inc.
  10. 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.
  11. Hersch, Joni, 1998. "Compensating Differentials for Gender-Specific Job Injury Risks," American Economic Review, American Economic Association, vol. 88(3), pages 598-627, June.
  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. 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.
  15. 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.
  16. 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.
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