Causal Inference with Latent Treatments

Social scientists are interested in the effects of low-dimensional latent treatments within texts, such as the effect of an attack on a candidate in a political advertisement. We provide a framework for causal inference with latent treatments in high-dimensional interventions. Using this framework, we show that the randomization of texts alone is insufficient to identify the causal effects of latent treatments, because other unmeasured treatments in the text could confound the measured treatment's effect. We provide a set of assumptions that is sufficient to identify the effect of latent treatments and a set of strategies to make these assumptions more plausible, including explicitly adjusting for potentially confounding text features and nontraditional experimental designs involving many versions of the text. We apply our framework to a survey experiment and an observational study, demonstrating how our framework makes text-based causal inferences more credible.