A Modified Randomization Test for the Level of Clustering

Abstract

Suppose a researcher observes individuals within a county within a state. Given concerns about correlation across individuals, it is common to group observations into clusters and conduct inference treating observations across clusters as independent. However, a researcher that has chosen to cluster at the county level may be unsure of their decision, given knowledge that observations are independent across states. This article proposes a modified randomization test as a robustness check for the chosen level of clustering in a linear regression setting. Existing tests require either the number of states or number of counties to be large. Our method is designed for settings with few states and few counties. While the method is conservative, it has competitive power in settings that may be relevant to empirical work.

Keywords:

• Clustered standard errors
• Linear regression
• Small-cluster asymptotics

Supplementary Materials

Extended Appendices

Technical details including proof of Theorem 1, details concerning the application and additional Monte Carlo simulations.

Acknowledgments

I thank the editor Jianqing Fan, an associate editor, and two anonymous referees for comments and suggestions that greatly improved the article. I am grateful to Ivan Canay for extensive guidance on this project. I have also benefited from conversations with Eric Auerbach, Eduardo Campillo Betancourt, Grant Goehring and Joel Horowitz.

Disclosure Statement

The author reports there are no competing interests to declare.