THE WILD BOOTSTRAP WITH A SMALL NUMBER OF LARGE CLUSTERS

• 成果类型: Article
• 署名作者: Canay, Ivan A.; Santos, Andres; Shaikh, Azeem M.
• 署名单位: Northwestern University; University of California System; University of California Los Angeles; University of Chicago
• 刊物名称: REVIEW OF ECONOMICS AND STATISTICS
• ISSN/ISSBN: 0034-6535
• DOI: 10.1162/rest_a_00887
• 发表日期: 2021-05
• 页码: 346-363
• 关键词: in-differences; inference; robust

摘要

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.