Long-term Causal Inference Under Persistent Confounding via Data Combination
This addresses the challenge of causal inference in settings with delayed outcomes and persistent confounding, which is incremental but important for fields like economics and policy evaluation.
The paper tackles the problem of estimating long-term treatment effects when persistent unmeasured confounders invalidate previous methods, by developing novel identification strategies and estimators that outperform existing approaches in semi-synthetic data on job training effects.
We study the identification and estimation of long-term treatment effects when both experimental and observational data are available. Since the long-term outcome is observed only after a long delay, it is not measured in the experimental data, but only recorded in the observational data. However, both types of data include observations of some short-term outcomes. In this paper, we uniquely tackle the challenge of persistent unmeasured confounders, i.e., some unmeasured confounders that can simultaneously affect the treatment, short-term outcomes and the long-term outcome, noting that they invalidate identification strategies in previous literature. To address this challenge, we exploit the sequential structure of multiple short-term outcomes, and develop three novel identification strategies for the average long-term treatment effect. We further propose three corresponding estimators and prove their asymptotic consistency and asymptotic normality. We finally apply our methods to estimate the effect of a job training program on long-term employment using semi-synthetic data. We numerically show that our proposals outperform existing methods that fail to handle persistent confounders.