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Robust Inference with Multi-way Clustering

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Listed:
  • 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.

Suggested Citation

  • A. Colin Cameron & Jonah B. Gelbach & Douglas L. Miller, 2006. "Robust Inference with Multi-way Clustering," NBER Technical Working Papers 0327, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberte:0327
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    References listed on IDEAS

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    1. Gabor Kezdi, 2005. "Robus Standard Error Estimation in Fixed-Effects Panel Models," Econometrics 0508018, University Library of Munich, Germany.
    2. 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.
    3. 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.
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    12. Cameron,A. Colin & Trivedi,Pravin K., 2008. "Microeconometrics," Cambridge Books, Cambridge University Press, number 9787111235767, October.
    13. Marianne Bertrand & Esther Duflo & Sendhil Mullainathan, 2004. "How Much Should We Trust Differences-In-Differences Estimates?," The Quarterly Journal of Economics, Oxford University Press, vol. 119(1), pages 249-275.
    14. 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.
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    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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