Finely Stratified Rerandomization Designs

Abstract

Finely stratified randomization makes unadjusted treatment effect estimation efficient when matches are tight. However, match quality deteriorates rapidly as covariate dimension increases, attenuating the gains from stratification. Motivated by this problem, we study designs that finely stratify on a few important covariates, then rerandomize within matched groups to balance the remainder. We derive the asymptotic distribution for GMM estimators of general causal parameters under such designs, showing that they provide nonparametric control over the stratification covariates and linear control over the rerandomization covariates. The resulting distribution is generally non-normal, but optimal linear adjustment restores asymptotic normality. For finite population parameters, we derive upper bounds on the non-identified asymptotic variance, enabling conservative inference that accounts for the efficiency gains from both design stages. An empirical application to estimating treatment effect heterogeneity among compliers illustrates the gains from adding rerandomization to a stratified design.