Causal inference with latent outcomes

While causal inference has become front and center in empirical political science, we know little about how to analyze causality with latent outcomes, such as political values, beliefs, and attitudes. In this article, we develop a framework for defining, identifying, and estimating the causal effect of an observed treatment on a latent outcome, which we call the latent treatment effect (LTE). We describe a set of assumptions that allow us to identify the LTE and propose a hierarchical item response model to estimate it. We highlight an often overlooked exclusion restriction assumption, which states that treatment status should not affect the observed indicators other than through the latent outcome. A simulation study shows that the hierarchical approach offers unbiased estimates of the LTE under the identification and modeling assumptions, whereas conventional two-step approaches are biased. We illustrate our proposed methodology using data from two published experimental studies.