The Wild Bootstrap with a “Small” Number of “Large” Clusters

By Ivan A. Canay, Andrés Santos, A. Shaikh. Review of Economics and Statistics, 2019

115 citations recorded by the source corpus.

Abstract This paper studies the wild bootstrap–based test proposed in Cameron, Gelbach, and Miller (2008). Existing analyses of its properties require that number of clusters is “large.” In an asymptotic framework in which the number of clusters is “small,” we provide conditions under which an unstudentized version of the test is valid. These conditions include homogeneity-like restrictions on the distribution of covariates. We further establish that a studentized version of the test may only overreject the null hypothesis by a “small” amount that decreases exponentially with the number of clusters. We obtain a qualitatively similar result for “score” bootstrap-based tests, which permit testing in nonlinear models.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/f976214e55a8dbfade24c3f10f12a919a2efabcd

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Citations in the corpus

Cluster-robust inference: A guide to empirical practice (2022, background): “The results of Canay et al. (2021) and MacKinnon and Webb (2020b) strongly suggest that homogeneity across clusters is more important for RI than for the WCR bootstrap.”
What’s trending in difference-in-differences? A synthesis of the recent econometrics literature (2022, unknown): “Importantly, Canay et al. (2021) show that the reliability of these bootstrap procedures depends on imposing certain homogeneity conditions on treatment effects, as well as the type of bootstrap weights one uses and the estimation method adopted (e.g., restricted vs. unrestricted OLS).”