We study the identification and estimation of long-term treatment effects under unobserved confounding by combining an experimental sample, where the long-term outcome is missing, with an observational sample, where the treatment assignment is unobserved. While standard surrogate index methods fail when unobserved confounders exist, we establish novel identification results by leveraging proxy variables for the unobserved confounders. We further develop multiply robust estimation and inference procedures based on these results. Applying our method to the Job Corps program, we demonstrate its ability to recover experimental benchmarks even when unobserved confounders bias standard surrogate index estimates.

翻译：本研究探讨在未观测混杂存在的情况下，通过结合实验样本（长期结果缺失）与观测样本（处理分配未观测）来识别和估计长期处理效应。当未观测混杂存在时，标准代理指标方法失效，我们通过利用未观测混杂的代理变量建立了新的识别结果。基于这些结果，我们进一步开发了多重稳健的估计与推断方法。将我们的方法应用于Job Corps项目，结果表明即使未观测混杂使标准代理指标估计产生偏差，该方法仍能恢复实验基准。