Asymptotic theory for clustered samples

By B. Hansen, Seojeong Lee. Journal of Econometrics, 2019

103 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/0afeaf7eea621ed80c061cf7a67ad9c19eaec5e2

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Citations in the corpus

Inference for Iterated GMM Under Misspecification (2021, background): “The asymptotic variance in Theorem 4 differs from the classical formula (Q′W−1Q)−1 ( QWΩ11W −1Q ) ( Q′W−1Q )−1 where Ω11 is (23) with μ = 0, in two ways.”
Various Versatile Variances: An Object-Oriented Implementation of Clustered Covariances in R (2020, methodology): “An alternative but less frequently-used asymptotic framework is the “ﬁxed G ” setup, where the number of clusters is assumed to be ﬁxed (see Bester, Conley, and Hansen 2011; Hansen and Lee 2017).”
Asymptotic theory and wild bootstrap inference with clustered errors (2019, background): “For example, Hansen (2007) showed that, if both the time-series and cross-sectional dimensions in a panel setting diverge, then, in our notation, β̂ is either √ N -convergent or √ G-convergent depending on whether the degree of intra-cluster (time-series) correlation is strong or weak.”
Wild Bootstrap and Asymptotic Inference With Multiway Clustering (2019, background): “Indeed, this is why Carter et al. (2017), Djogbenou et al. (2019), and Hansen and Lee (2019), among others, consider asymptotic limit theory only for studentized (or self-normalized) quantities.”