A Bootstrap Method for Conducting Statistical Inference with Clustered Data

Abstract

U.S. state politics researchers often analyze data with observations grouped into clusters. This structure commonly produces unmodeled correlation within clusters, leading to downward bias in the standard errors of regression coefficients. Estimating robust cluster standard errors (RCSE) is a common approach to correcting this bias. However, despite their frequent use, recent work indicates that RCSE can also be biased downward. Here the author provides evidence of that bias and offers a potential solution. Through Monte Carlo simulation of an ordinary least squares (OLS) regression model, the author compares conventional standard error (OLS-SE) and RCSE performance to that of a bootstrap method that resamples clusters of observations (BCSE). The author shows that both OLS-SE and RCSE are biased downward, with OLS-SE being the most biased. In contrast, BCSE are not biased and consistently outperform the other two methods. The author concludes with three replications from recent work and offers recommendations to researchers.