The wild bootstrap with a “small” number of “large” clusters

Ivan A. Canay; Andres Santos; Azeem M. Shaikh

doi:10.1162/rest_a_00887

The wild bootstrap with a “small” number of “large” clusters

Ivan A. Canay, Andres Santos, Azeem M. Shaikh

Economics

Research output: Contribution to journal › Article › peer-review

38 Scopus citations

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.

Original language	English (US)
Pages (from-to)	346-363
Number of pages	18
Journal	Review of Economics and Statistics
Volume	103
Issue number	2
DOIs	https://doi.org/10.1162/rest_a_00887
State	Published - May 14 2021

Funding

We thank Colin Cameron, Patrick Kline, Simon Lee, James MacKinnon, Magne Mogstad, and Ulrich Mueller for helpful comments. The research of I.C. was supported by National Science Foundation grant SES-1530534. The research of A.M.S. was supported by National Science Foundation grants DMS-1308260, SES-1227091, and SES-1530661. We thank Max Tabord-Meehan and Yong Cai for excellent research assistance.

ASJC Scopus subject areas

Social Sciences (miscellaneous)
Economics and Econometrics

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The wild bootstrap with a “small” number of “large” clusters

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