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Asymptotic Theory for Clustered Samples

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  • Bruce E. Hansen
  • Seojeong Lee

Abstract

We provide a complete asymptotic distribution theory for clustered data with a large number of independent groups, generalizing the classic laws of large numbers, uniform laws, central limit theory, and clustered covariance matrix estimation. Our theory allows for clustered observations with heterogeneous and unbounded cluster sizes. Our conditions cleanly nest the classical results for i.n.i.d. observations, in the sense that our conditions specialize to the classical conditions under independent sampling. We use this theory to develop a full asymptotic distribution theory for estimation based on linear least-squares, 2SLS, nonlinear MLE, and nonlinear GMM.

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  • Bruce E. Hansen & Seojeong Lee, 2019. "Asymptotic Theory for Clustered Samples," Papers 1902.01497, arXiv.org.
  • Handle: RePEc:arx:papers:1902.01497
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    Cited by:

    1. James G. MacKinnon & Matthew D. Webb, 2020. "When and How to Deal with Clustered Errors in Regression Models," Working Paper 1421, Economics Department, Queen's University.
    2. James G. MacKinnon & Morten Ørregaard Nielsen & Matthew D. Webb, 2020. "Testing for the appropriate level of clustering in linear regression models," Working Paper 1428, Economics Department, Queen's University.
    3. James G. MacKinnon & Morten Ø. Nielsen & Matthew D. Webb, 2019. "Wild Bootstrap and Asymptotic Inference with Multiway Clustering," Working Paper 1415, Economics Department, Queen's University.
    4. Djogbenou, Antoine A. & MacKinnon, James G. & Nielsen, Morten Ørregaard, 2019. "Asymptotic theory and wild bootstrap inference with clustered errors," Journal of Econometrics, Elsevier, vol. 212(2), pages 393-412.
    5. Wang, Wenjie, 2021. "Wild Bootstrap for Instrumental Variables Regression with Weak Instruments and Few Clusters," MPRA Paper 106227, University Library of Munich, Germany.
    6. Alexander Klein & Guy Tchuente, 2020. "Spatial Differencing for Sample Selection Models with Unobserved Heterogeneity," Papers 2009.06570, arXiv.org.
    7. Koen Jochmans, 2020. "Peer effects and endogenous social interactions," Papers 2008.07886, arXiv.org.
    8. Bruce E. Hansen & Seojeong Jay Lee, 2018. "Inference for Iterated GMM Under Misspecification and Clustering," Discussion Papers 2018-07, School of Economics, The University of New South Wales.
    9. Laurent Davezies & Xavier D'Haultfoeuille & Yannick Guyonvarch, 2018. "Asymptotic results under multiway clustering," Papers 1807.07925, arXiv.org, revised Aug 2018.
    10. Yong Cai, 2021. "Some Finite Sample Properties of the Sign Test," Papers 2103.01412, arXiv.org.
    11. Bruno Ferman, 2019. "A simple way to assess inference methods," Papers 1912.08772, arXiv.org, revised Jan 2021.

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    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation

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