CONTAMINATION BIAS IN LINEAR REGRESSIONS:
This paper studies identification problems in linear regressions with multiple treatments and rich control sets intended to eliminate omitted variable bias. The central result is that, even when controls are sufficiently flexible, standard OLS regressions with multiple treatment variables generally fail to recover meaningful convex combinations of heterogeneous treatment effects. Instead, each estimated coefficient is a contaminated mixture of the true causal effects of all included treatments.
The key insight is that in a multi-treatment setting, partialling out controls induces a re-weighting of variation in treatment variables that is not orthogonal across treatments. As a result, the coefficient on any given treatment reflects not only its own causal effect but also linear combinations of the effects of other treatments. These weights can be negative or exceed one, implying that regression estimands are not convex averages and may lie outside the support of true treatment effects. This phenomenon is termed contamination bias.
The authors derive the exact algebraic representation of OLS coefficients under multiple treatments, showing how the projection of one treatment onto others enters the estimand. They characterize conditions under which contamination disappears—essentially requiring orthogonality or special designs where treatments vary independently conditional on controls. However, such conditions are rarely satisfied in observational data, especially in applied economics where multiple policy variables are often correlated.
To address the problem, the paper proposes alternative estimands that target interpretable weighted averages of treatment effects. One approach involves constructing weights that explicitly account for the covariance structure among treatments, ensuring that identified estimands correspond to meaningful convex averages. Another approach focuses on estimating “easiest-to-learn” or most precisely identified linear combinations of treatment effects, trading off interpretability and statistical precision.
The authors also conduct a re-analysis of nine empirical applications from the applied microeconomics literature. They find substantial contamination bias in observational studies, often leading to sign changes or magnitude distortions in reported treatment effects. In contrast, randomized experimental settings exhibit less severe contamination due to more balanced treatment assignment and reduced correlation among treatments, though some bias can still remain when propensity scores vary.
Overall, the paper highlights a fundamental limitation of standard regression-based causal interpretation in multi-treatment environments. It shows that even with rich controls, OLS coefficients may not correspond to any meaningful average treatment effect unless additional structure or alternative estimators are used. The results motivate caution in interpreting multi-variable regressions causally and provide practical tools for more robust estimation strategies.
Paper: https://t.co/KSrZGVNJVd
Goldsmith-Pinkham, @instrumenthull, Kolesár (2024)
IMSのreview誌のStatistical Scienceにアクセプトされた論文
A unified approach to penalized likelihood estimation of covariance matrices in high dimensions
https://t.co/5GYfy55E3N
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Today, neural network distillation is a technique that drives all commercially successful LLMs. Modern inference speed and low cost would be impossible without distillation.
Authored by Google's Geoffrey Hinton, Oriol Vinyals, and Jeff Dean, the paper was rejected by the reviewers at NIPS 2014 (now NeurIPS) as "unlikely to have a significant impact."
The paper was published on arXiv and has gotten more than 30,000 citations.
Learn from this foundational paper on ChapterPal: https://t.co/WGDibzk3xE
PDF: https://t.co/1SyoQiqeaJ
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Preprint: https://t.co/ktSPX2mWWH
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The Cline Center is pleased to announce the 2024-2025 David F. Linowes Faculty Fellows: JungHwan Yang of @illinoiscomm and Yun Huang of @iSchoolUI
You can learn more about their projects and the Linowes Fellowship here: https://t.co/Em6qomdohy