centre for microdata methods and practice

ESRC centre

cemmap is an ESRC research centre

ESRC

Keep in touch

Subscribe to cemmap news

The wild bootstrap with a "small" number of "large" clusters

Authors: Ivan A. Canay , Andres Santos and Azeem M. Shaikh
Date: 11 April 2018
Type: cemmap Working Paper, CWP27/18
DOI: 10:1920/wp.cem.2018.2718

Abstract

This paper studies the properties of the wild bootstrap-based test proposed in Cameron et al. (2008) in settings with clustered data. Cameron et al. (2008) provide simulations that suggest this test works well even in settings with as few as fi ve clusters, but existing theoretical analyses of its properties all rely on an asymptotic framework in which the number of clusters is "large." In contrast to these analyses, we employ an asymptotic framework in which the number of clusters is "small," but the number of observations per cluster is "large." In this framework, we provide conditions under which the limiting rejection probability of an un-Studentized version of the test does not exceed the nominal level. Importantly, these conditions require, among other things, certain homogeneity restrictions on the distribution of covariates. We further establish that the limiting rejection probability of a Studentized version of the test does not exceed the nominal level by more than an amount that decreases exponentially with the number of clusters. We study the relevance of our theoretical results for finite samples via a simulation study.

Download full version

Publications feeds

Subscribe to cemmap working papers via RSS

Search cemmap

Search by title, topic or name.

Contact cemmap

Centre for Microdata Methods and Practice

How to find us

Tel: +44 (0)20 7291 4800

E-mail us