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Main Authors: Lal, Apoorva, Imbens, Guido, Hull, Peter
Format: Preprint
Published: 2026
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Online Access:https://arxiv.org/abs/2601.06359
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author Lal, Apoorva
Imbens, Guido
Hull, Peter
author_facet Lal, Apoorva
Imbens, Guido
Hull, Peter
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2601_06359
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Long-Term Causal Inference with Many Noisy Proxies
Lal, Apoorva
Imbens, Guido
Hull, Peter
Econometrics
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.
title Long-Term Causal Inference with Many Noisy Proxies
topic Econometrics
url https://arxiv.org/abs/2601.06359