Recent literature proposes combining short-term experimental and long-term observational data to provide alternatives to conventional observational studies for the identification of long-term average treatment effects (LTEs). This paper re-examines the identification problem and uncovers that assumptions restricting temporal link functions -- relationships between short-term and mean long-term potential outcomes -- are central in this context. The experimental data serve to amplify the identifying power of such assumptions; absent them, the combined data are no more informative than the observational data alone. Plausible inference thus hinges on justifiable restrictions in this class. Motivated by this, I introduce two treatment response assumptions that may be defensible based on economic theory or intuition. To utilize them and facilitate future developments, I develop a novel unifying identification framework that computationally produces sharp bounds on the LTE for a general class of temporal link function restrictions and accommodates imperfect experimental compliance -- thereby also extending existing approaches. I illustrate the method by estimating the long-term effects of Head Start participation. The findings indicate that the effects on educational attainment, employment, and criminal involvement are lasting but smaller in magnitude than those established by sibling comparisons.

翻译：近期文献提出将短期实验数据与长期观测数据相结合，作为传统观测研究的替代方案，用于识别长期平均处理效应。本文重新审视了该识别问题，并发现限制时间链接函数（即短期结果与平均长期潜在结果之间的关系）的假设在这一背景下具有核心作用。实验数据有助于增强此类假设的识别能力；若无实验数据，则组合数据并不比单独的观测数据提供更多信息。因此，合理的推断取决于该类假设中可辩护的限制条件。基于此，我引入了两种可能基于经济理论或直觉进行辩护的处理响应假设。为利用这些假设并促进未来发展，我建立了一个新颖的统一识别框架，该框架能够针对一般类别的时间链接函数限制，计算性地给出处理效应的尖锐界限，并包容实验中的非完全依从性——从而也扩展了现有方法。我通过估算"启智计划"参与的长期效果来演示该方法。研究结果表明，该计划对教育成就、就业及犯罪参与的影响具有持续性，但其效应幅度小于基于兄弟姐妹比较所确立的结果。