Asymptotic Theory for Clustered Samples

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.

References in corpus (2)

• Asymptotic Refinements of a Misspecification-Robust Bootstrap for Generalized Method of Moments Estimators
• Inference with Dyadic Data: Asymptotic Behavior of the Dyadic-Robust t-Statistic

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• Panel Data with Unknown Clusters
• CONQ: CONtinuous Quantile Treatment Effects for Large-Scale Online Controlled Experiments
• Some Finite Sample Properties of the Sign Test