Apoorva Lal, Guido Imbens, Peter Hull
arXiv 9 Jan 2026 · Econometrics
arXiv:2601.06359 · PDF · DOI · OpenAlex · Extracted main text
We propose a method for estimating long-term treatment effects with many short-term proxy outcomes: a central challenge when experimenting on digital platforms. We formalize this challenge as a latent variable problem where observed proxies are noisy measures of a low-dimensional set of unobserved surrogates that mediate treatment effects. Through theoretical analysis and simulations, we demonstrate that regularized regression methods substantially outperform naive proxy selection. We show in particular that the bias of Ridge regression decreases as more proxies are added, with closed-form expressions for the bias-variance tradeoff. We illustrate our method with an empirical application to the California GAIN experiment.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Hotz, V Joseph and Imbens, Guido W and Klerman, Jacob A (2006) Evaluating the differential effects of alternative welfare-to-work training components: A reanalysis of the California GAIN prog… self | 0.644 | 2 | 2 | 100% |
| 2 | Kallus, Nathan and Mao, Xiaojie On the role of surrogates in the efficient estimation of treatment effects with limited outcome data | 0.405 | 1 | 1 | 100% |
| 3 | Anderson, Theodore W (2003) An Introduction to Multivariate Statistical Analysis | 0.405 | 1 | 1 | 100% |
| 4 | Athey, Susan and Chetty, Raj and Imbens, Guido W and Kang, Hyunseung (2019) The surrogate index: Combining short-term proxies to estimate long-term treatment effects more rapidly and precisely self | 0.405 | 1 | 1 | 100% |
| 5 | Bai, Jushan and Ng, Serena (2002) Determining the number of factors in approximate factor models | 0.405 | 1 | 1 | 100% |
| 6 | Berry, Steven T (1994) Estimating discrete-choice models of product differentiation | 0.405 | 1 | 1 | 100% |
| 7 | Chen, Jiafeng and Ritzwoller, David M (2023) Semiparametric estimation of long-term treatment effects | 0.405 | 1 | 1 | 100% |
| 8 | Fuller, Wayne A (1987) Measurement Error Models | 0.405 | 1 | 1 | 100% |
| 9 | Gupta, Somit and Kohavi, Ronny and Tang, Diane and Xu, Ya and Anders… (2019) Top challenges from the first practical online controlled experiments summit | 0.405 | 1 | 1 | 100% |
| 10 | Hastie, Trevor and Tibshirani, Robert and Friedman, Jerome (2009) The elements of statistical learning | 0.405 | 1 | 1 | 100% |
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