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Corrected Standard Errors with Clustered Data

Published online by Cambridge University Press:  15 October 2019

John E. Jackson Open the ORCID record for John E. Jackson [Opens in a new window]
John E. Jackson*
Affiliation:
Department of Political Science, University of Michigan, Ann Arbor, MI 48109, USA. Email: jjacksn@umich.edu
*
*Email: jjacksn@umich.edu
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Abstract

The use of cluster robust standard errors (CRSE) is common as data are often collected from units, such as cities, states or countries, with multiple observations per unit. There is considerable discussion of how best to estimate standard errors and confidence intervals when using CRSE (Harden 2011; Imbens and Kolesár 2016; MacKinnon and Webb 2017; Esarey and Menger 2019). Extensive simulations in this literature and here show that CRSE seriously underestimate coefficient standard errors and their associated confidence intervals, particularly with a small number of clusters and when there is little within cluster variation in the explanatory variables. These same simulations show that a method developed here provides more reliable estimates of coefficient standard errors. They underestimate confidence intervals for tests of individual and sets of coefficients in extreme conditions, but by far less than do CRSE. Simulations also show that this method produces more accurate standard error and confidence interval estimates than bootstrapping, which is often recommended as an alternative to CRSE.

Keywords

clustered robust standard errorsclustered dataconfidence intervals
Type
Articles
Information
Political Analysis , Volume 28 , Issue 3 , July 2020 , pp. 318 - 339
Copyright
Copyright © The Author(s) 2019. Published by Cambridge University Press on behalf of the Society for Political Methodology.

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Footnotes

Author’s note: I want to thank Ken Kollman, Chuck Shipan, Matthew Webb and the ubiquitous anonymous referee for their helpful comments and Diogo Ferrari for his comments and the R package “ceser” for computing CESE. All are absolved from any and all errors.

Contributing Editor: Jeff Gill

References

Angrist, J. D., and Pischke, J.-S.. 2009. Mostly Harmless Econometrics: An Empiricist’s Companion. Princeton, NJ: Princeton University Press.Google Scholar
Bell, R. M., and McCaffery, D. F.. 2002. “Bias Reduction and Standard Errors for Linear Regression with Multi-Stage Samples.” Survey Methodology 26(2):169–181.Google Scholar
Bormann, N.-C., and Golder, M.. 2013. “Democratic Electoral Systems Around the World, 1946–2011.” Electoral Studies 32:360–369.Google Scholar
Brown, R. D., Jackson, R. A., and Wright, G. C.. 1999. “Registration, Turnout, and State Party Systems.” Political Research Quarterly 52(3):463–479.Google Scholar
Cameron, C. A., Gelbach, J. B., and Miller, D. L.. 2008. “Bootstrap-Based Improvements for Inference with Clustered Errors.” Review of Economics and Statistics 90(3):414–427.Google Scholar
Davidson, R., and MacKinnon, J. G.. 1993. Estimation and Inference in Econometrics. New York, NY: Oxford University Press.Google Scholar
Eicker, F. 1967. “Limit Theorems for Regressions with Unequal and Dependent Errors.” In Proceedings of the Berkeley Symposium on Mathematical Statistics and Probability, edited by Le Cam, L. M. and Heyman, J., 59–82. Berkeley, CA: California University Press.Google Scholar
Elgie, R., Bueur, C., Dolez, B., and Laurent, A.. 2014. “Proximity, Candidates, and Presidential Power: How Directly Elected Presidents Shape the Legislative Party System.” Political Research Quarterly 67(3):467–477.Google Scholar
Esarey, J., and Menger, A.. 2019. “Practical and Effective Approaches to Dealing with Clustered Data.” Political Science Research and Methods 7(3):541–559.Google Scholar
Franzese, R. J. Jr.. “Empirical Strategies for Various Manifestations of Multilevel Data.” Political Analysis 13(4):430–446.Google Scholar
Golder, M. 2005. “Democratic Electoral Systems Around the World, 1946–2000.” Electoral Studies 24:103–121.Google Scholar
Golder, M. 2006. “Presidential Coattails and Legislative Fragmentation.” American Journal of Political Science 50(1):34–48.Google Scholar
Greene, W. H. 2012. Econometric Analysis. Upper Saddle River, NJ: Prentice-Hall.Google Scholar
Harden, J. J. 2011. “A Bootstrap Method for Conducting Statistical Inference with Clustered Data.” State Politics and Policy Quarterly 11(2):223–246.Google Scholar
Hicken, A., and Stoll, H.. 2012. “Are All Presidents Created Equal? Presidential Powers and the Shadow of Presidential Elections.” Comparative Political Studies 46(3):291–319.Google Scholar
Huber, P. J. 1967. “The Behavior of Maximum Likelihood Estimates Under Nonstandard Conditions.” In Proceedings of the Berkeley Symposium on Mathematical Statistics and Probability, edited by Le Cam, L. M. and Heyman, J., 221–223. Berkeley, CA: California University Press.Google Scholar
Ibragimov, R., and Muller, U. K.. 2002. “t-Statistic Based Correlation and Heterogeneity Robust Inference.” Journal of Business and Economic Statistics 28(4):453–468.Google Scholar
Imbens, G. W., and Kolesár, M.. 2016. “Robust Standard Errors in Small Samples: Some Practical Advice.” The Review of Economics and Statistics 98(4):701–712.Google Scholar
Jackson, J. E.2019 “Replication Data for: Corrected Standard Errors with Clustered Data.” https://doi.org/10.7910/DVN/IABJEB, Harvard Dataverse, V1.Google Scholar
Liang, K.-Y., and Zeger, S. L.. 1986. “Longitudinal Data Analysis for Generalized Linear Models.” Biometrika 73:13–22.Google Scholar
Long, J. S., and Ervin, L. H.. 2000. “Using Heteroscedasticity Consistent Standard Errors in the Linear Regression Model.” The American Statistician 54(3):217–224.Google Scholar
MacKinnon, J. G., and Webb, M. D.. 2017. “Wild Bootstrap Inference for Wildly Different Cluster Sizes.” Journal of Applied Econometrics 32(2):233–254.Google Scholar
Roodman, D., Nielsen, M. Ø., MacKinnon, J. G., and Webb, M. D.. 2019. “Fast and Wild: Bootstrap Inference in Stata Using Boottest.” The Stata Journal 19(1):4–60.Google Scholar
Wasserstein, R. L., Schirm, A. L., and Lazar, N. A.. 2019. “Moving to a World Beyond ‘$p<0.05$’.” The American Statistician 73(1):1–19.Google Scholar
White, H. 1980. “A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity.” Econometrica 48:817–838.Google Scholar
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