The Surrogate Index: Combining Short-Term Proxies to Estimate Long-Term Treatment Effects More Rapidly and Precisely

72 Pages Posted: 18 Nov 2019 Last revised: 23 Apr 2023

See all articles by Susan Athey

Susan Athey

Stanford Graduate School of Business

Raj Chetty

Harvard University

Guido W. Imbens

Stanford Graduate School of Business

Hyunseung Kang

University of Wisconsin - Madison - Department of Statistics

Date Written: November 2019

Abstract

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.

Suggested Citation

Carleton Athey, Susan and Chetty, Raj and Imbens, Guido W. and Kang, Hyunseung, The Surrogate Index: Combining Short-Term Proxies to Estimate Long-Term Treatment Effects More Rapidly and Precisely (November 2019). NBER Working Paper No. w26463, Available at SSRN: https://ssrn.com/abstract=3488963

Susan Carleton Athey (Contact Author)

Stanford Graduate School of Business ( email )

655 Knight Way
Stanford, CA 94305-5015
United States

Raj Chetty

Harvard University ( email )

1875 Cambridge Street
Cambridge, MA 02138
United States

Guido W. Imbens

Stanford Graduate School of Business ( email )

655 Knight Way
Stanford, CA 94305-5015
United States

Hyunseung Kang

University of Wisconsin - Madison - Department of Statistics ( email )

United States

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