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Asymptotic Theory for Clustered Samples

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  • Bruce E. Hansen

    (Department of Economics, University of Wisconsin-Madison)

  • Seojeong Jay Lee

    (School of Economics, UNSW Business School, UNSW Sydney)

Abstract

We provide a complete asymptotic distribution theory for clustered data with a large number of 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.

Suggested Citation

  • Bruce E. Hansen & Seojeong Jay Lee, 2017. "Asymptotic Theory for Clustered Samples," Discussion Papers 2017-18, School of Economics, The University of New South Wales.
    • Handle: RePEc:swe:wpaper:2017-18
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    File URL: http://research.economics.unsw.edu.au/RePEc/papers/2017-18.pdf
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    More about this item

    Keywords

    clustered data; law of large numbers; central limit theorem; clustered covariance matrix estimation;
    All these keywords.

    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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