Primary Submission Category: Instrumental Variables
Few Clusters, Many Problems: A Clustered Wild Bootstrap for Instrumental Variables Estimation with Evidence from School-Board Gender Representation on Achievement Gaps
Authors: Sam Lee,
Presenting Author: Sam Lee*
Empirical researchers often estimate instrumental variables (IV) models to address endogeneity in key regressors. When observations are correlated within clusters, however, conventional inference can fail, particularly when the number of clusters is small. Standard cluster-robust variance estimators may understate uncertainty in these settings. I introduce a finite-sample wild cluster bootstrap procedure for just-identified IV models under arbitrary cluster dependence. The method recovers the consistency properties of the Liang–Zeger cluster-robust variance estimator and is shown to coincide with a restricted wild cluster bootstrap under the null hypothesis. Monte Carlo simulations demonstrate that the proposed procedure achieves rejection rates close to nominal levels and uniformly improves upon existing cluster-robust approaches. An empirical application estimates the causal effect of female school-board representation on gender gaps in scholastic achievement in California from 2014–2024. While the estimates show no significant reduction in within-district gender achievement disparities, the results provide applied researchers with a transparent and reliable framework for inference in clustered IV settings.