The Surrogate Index: Combining Short-Term Proxies to Estimate Long-Term Treatment Effects More Rapidly and Precisely
A common challenge in estimating the long-term impacts of treatments (e.g., job training programs) is that the outcomes of interest (e.g., lifetime earnings) are observed with a long delay. We address this problem by combining several short-term outcomes (e.g., short-run earnings) into a “surrogate index,” the predicted value of the long-term outcome given the short-term outcomes. We show that the average treatment effect on the surrogate index equals the treatment effect on the long-term outcome under the assumption that the long-term outcome is independent of the treatment conditional on the surrogate index. We then characterize the bias that arises from violations of this assumption, deriving feasible bounds on the degree of bias and providing simple methods to validate the key assumption using additional outcomes. Finally, we develop efficient estimators for the surrogate index and show that even in settings where the long-term outcome is observed, using a surrogate index can increase precision. We apply our method to analyze the long-term impacts of a multi-site job training experiment in California. Using short-term employment rates as surrogates, one could have estimated the program's impacts on mean employment rates over a 9 year horizon within 1.5 years, with a 35% reduction in standard errors. Our empirical results suggest that the long-term impacts of programs on labor market outcomes can be predicted accurately by combining their short-term treatment effects into a surrogate index.
We are grateful for discussions with James Dailey, Lawrence Katz, Dylan Small, Scott Stern, and Liang Xu and for comments from numerous seminar participants. We thank Emanuel Schertz and James Stratton for outstanding research assistance. This research was funded through National Science Foundation Grant DMS-1502437, the Chan-Zuckerberg Initiative, the Bill & Melinda Gates Foundation, and the Overdeck Foundation. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research.
Guido W. Imbens
I have consulted for Microsoft Corporation, Facebook, Amazon, and Lilly Corporation.