Estimation and Identification of the Complier Average Causal Effect Parameter in Education RCTs

Abstract

In randomized control trials (RCTs) in the education field, the complier average causal effect (CACE) parameter is often of policy interest, because it pertains to intervention effects for students who receive a meaningful dose of treatment services. This article uses a causal inference and instrumental variables framework to examine the identification and estimation of the CACE parameter for two-level clustered RCTs. The article also provides simple asymptotic variance formulas for CACE impact estimators measured in nominal and standard deviation units. In the empirical work, data from 10 large RCTs are used to compare significance findings using correct CACE variance estimators and commonly used approximations that ignore the estimation error in service receipt rates and outcome standard deviations. The key finding is that the variance corrections have very little effect on the standard errors of standardized CACE impact estimators. Across the examined outcomes, the correction terms typically raise the standard errors by less than 1%, and change p values at the fourth or higher decimal place. Manuscript received April 16, 2010 Revision received April 26, 2010 Accepted May 24, 2010