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Bootstrap-Based Improvements for Inference with Clustered Errors

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Author Info
Cameron, A. Colin (U of California, Davis)
Miller, Douglas (U of Maryland and Florida State U)
Gelbach, Jonah B. (U of California, Davis)

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Abstract

Microeconometrics researchers have increasingly realized the essential need to account for any within-group dependence in estimating standard errors of regression parameter estimates. The typical preferred solution is to calculate cluster-robust or sandwich standard errors that permit quite general heteroskedasticity and within-cluster error correlation, but presume that the number of clusters is large. In applications with few (5-30) clusters, standard asymptotic tests can over-reject considerably. We investigate more accurate inference using cluster bootstrap-t procedures that provide asymptotic refinement. These procedures are evaluated using Monte Carlos, including the much-cited differences-in-differences example of Bertrand, Mullainathan and Duflo (2004). In situations where standard methods lead to rejection rates in excess of ten percent (or more) for tests of nominal size 0.05, our methods can reduce this to five percent. In principle a pairs cluster bootstrap should work well, but in practice a Wild cluster bootstrap performs better.

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Paper provided by University of California at Davis, Department of Economics in its series Working Papers with number 06-21.

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Date of creation: Jun 2006
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Handle: RePEc:ecl:ucdeco:06-21

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Find related papers by JEL classification:
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing
C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Statistical Simulation Methods
C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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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. [Downloadable!]
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  2. Horowitz, Joel L., 2001. "The Bootstrap," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 5, chapter 52, pages 3159-3228 Elsevier. [Downloadable!] (restricted)
  3. 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. [Downloadable!] (restricted)
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  4. Stephen G Donald & Kevin Lang, 2007. "Inference with Difference-in-Differences and Other Panel Data," The Review of Economics and Statistics, MIT Press, vol. 89(2), pages 221-233, 03. [Downloadable!] (restricted)
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  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. [Downloadable!] (restricted)
  7. Emmanuel Flachaire, 2001. "The Wild Bootstrap, Tamed at Last," STICERD - Distributional Analysis Research Programme Papers 58, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
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  8. Gruber, J. & Poterba, J., 1994. "Tax Incentives and the Decision to Purchase Health Insurance: Evidence from the Self-Employed," Working papers 94-10, Massachusetts Institute of Technology (MIT), Department of Economics.
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  9. 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. [Downloadable!] (restricted)
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  11. Davidson, Russell & MacKinnon, James G., 1999. "The Size Distortion Of Bootstrap Tests," Econometric Theory, Cambridge University Press, vol. 15(03), pages 361-376, June. [Downloadable!]
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  12. James G. MacKinnon, 2002. "Bootstrap inference in econometrics," Canadian Journal of Economics, Canadian Economics Association, vol. 35(4), pages 615-645, November. [Downloadable!] (restricted)
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  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. [Downloadable!] (restricted)
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

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  3. A. Colin Cameron & Jonah B. Gelbach & Douglas L. Miller, 2007. "Bootstrap-Based Improvements for Inference with Clustered Errors," NBER Technical Working Papers 0344, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  8. 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. [Downloadable!] (restricted)
  9. James G. MacKinnon, 2007. "Bootstrap Hypothesis Testing," Working Papers 1127, Queen's University, Department of Economics. [Downloadable!]
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