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Robust Inference with Multi-way Clustering


  • Jonah B. Gelbach
  • Doug Miller

    (Department of Economics, University of California Davis)


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 en- ables 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 es- timator 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 o¤er cluster-robust standard errors when there is one-way clustering. The method is demonstrated by a Monte Carlo analysis for a two-way random ef- fects model; a Monte Carlo analysis of a placebo law that extends the state-year e¤ects example of Bertrand et al. (2004) to two dimensions; and by application to studies in the empirical literature where two-way clustering is present.

Suggested Citation

  • Jonah B. Gelbach & Doug Miller, 2009. "Robust Inference with Multi-way Clustering," Working Papers 99, University of California, Davis, Department of Economics.
  • Handle: RePEc:cda:wpaper:09-9

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    References listed on IDEAS

    1. Gabor Kezdi, 2005. "Robus Standard Error Estimation in Fixed-Effects Panel Models," Econometrics 0508018, EconWPA.
    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.
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    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. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    14. 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.
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    More about this item


    cluster-robust standard errors; two-way clustering; multi-way clus- tering.;

    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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