The Surrogate Index: Combining Short-Term Proxies to Estimate Long-Term Treatment Effects More Rapidly and Precisely
Review of Economic Studies · 2026 · Susan Athey、Raj Chetty、Guido W. Imbens、Hyunseung Kang
中文摘要
估计干预措施（如职业培训项目、教育项目）影响时的一个常见挑战是，许多所关注的结果（如终身收入或其他劳动力市场结果）需要经过很长时间才能观测到。在生物医学领域，通常通过使用短期结果作为所关注结果的所谓“替代指标”来解决这一问题，例如在癌症研究中以肿瘤大小作为死亡率的替代指标。我们在这类文献的基础上，将多个可能在性质上不同的短期结果（如短期收入和就业指标）系统地组合成一个“替代指数”。Prentice替代性假设要求，在给定替代指标的条件下，主要结果与处理相互独立。我们表明，在这一假设下，处理对替代指数的平均效应等于其对长期结果的效应。我们还将替代性假设与一组结构性因果假设联系起来。随后，我们刻画了违反各项关键假设所产生的偏误，并提供了利用额外观测到的结果来验证这些假设的简单方法。我们将该方法应用于分析加利福尼亚州一项多地点职业培训实验的长期影响。我们表明，无需等待整整9年以直接观测长期影响，就可以使用短期（前六个季度）结果作为替代指标。在替代性假设成立的情况下，本可利用前六个季度观测到的就业率来估计该项目对平均就业率的长期影响；相对于基于全部9年数据的简单均值差估计量，其标准误可降低35%。
Abstract
Abstract A common challenge in estimating the impact of interventions (e.g. job training programmes, educational programmes) is that many outcomes of interest (e.g. lifetime earnings or other labour market outcomes) are observed with a long delay. In biomedical settings, this is often addressed by using short-term outcomes as so-called “surrogates” for the outcome of interest, e.g. tumour size as a surrogate for mortality in cancer studies. We build on this literature by combining multiple, possibly qualitatively distinct, short-term outcomes (e.g. short-run earnings and employment indicators) systematically into a “surrogate index”. Under the Prentice surrogacy assumption, which requires that the primary outcome is independent of the treatment conditional on the surrogates, we show that the average treatment effect on the surrogate index equals the treatment effect on the long-term outcome. We also relate the surrogacy assumption to a set of structural, causal assumptions. We then characterize the bias that arises from violations of each of the key assumptions, and we provide simple methods to validate these assumptions using additional observed outcomes. We apply our method to analyse the long-term impacts of a multi-site job training experiment in California. Rather than waiting a full 9 years to directly observe the long-term impact, we show that it is possible to use short-term (the first six quarters) outcomes as surrogates. Given the surrogacy assumption one could have estimated the programme’s long-term impacts on mean employment rates using the employment rates observed in the first six quarters, with a 35% reduction in standard errors relative to a simple difference in means estimator based on all 9 years of data.