Combining Experimental and Observational Data for Identification and Estimation of Long-Term Causal Effects
This addresses the challenge of causal inference in settings with limited data for researchers in statistics and social sciences, though it is incremental by extending existing frameworks like proximal causal inference.
The paper tackles the problem of estimating long-term causal effects when neither experimental nor observational data alone suffice due to unobserved confounding and missing long-term outcomes, proposing three data fusion approaches and applying them to estimate the effect of class size on 8th-grade SAT scores.
We study identifying and estimating the causal effect of a treatment variable on a long-term outcome using data from an observational and an experimental domain. The observational data are subject to unobserved confounding. Furthermore, subjects in the experiment are only followed for a short period; thus, long-term effects are unobserved, though short-term effects are available. Consequently, neither data source alone suffices for causal inference on the long-term outcome, necessitating a principled fusion of the two. We propose three approaches for data fusion for the purpose of identifying and estimating the causal effect. The first assumes equal confounding bias for short-term and long-term outcomes. The second weakens this assumption by leveraging an observed confounder for which the short-term and long-term potential outcomes share the same partial additive association with this confounder. The third approach employs proxy variables of the latent confounder of the treatment-outcome relationship, extending the proximal causal inference framework to the data fusion setting. For each approach, we develop influence function-based estimators and analyze their robustness properties. We illustrate our methods by estimating the effect of class size on 8th-grade SAT scores using data from the Project STAR experiment combined with observational data from the Early Childhood Longitudinal Study.