Nonparametric Identification and Estimation of Causal Effects on Latent Outcomes

Abstract

How can we conduct causal inference when the outcome of interest is latent and imperfectly measured by multiple indicators? We develop a nonparametric framework for identifying and estimating average treatment effects on latent outcomes in randomized experiments. Researchers commonly aggregate multiple outcome indicators into a summary measure before estimating treatment effects. We identify a fundamental but often overlooked comparability problem arising from this practice: adding, removing, or replacing indicators can alter the causal estimand. We formalize this problem and show that commonly used procedures generally fail to preserve comparability across measurement sets. To address this problem, we propose a design-based approach that uses nonparametric bridge functions. We further characterize the semiparametric efficiency bound, construct an efficient estimator, and establish necessary and sufficient conditions under which additional measurements yield strict efficiency gains. We illustrate our approach through an application to the Hajj visa lottery. Our framework provides practical guidance for measurement design, identification, and efficient causal estimation with latent outcomes.