arXiv 3 Jul 2026 · Econometrics
arXiv:2607.02898 · PDF · DOI · OpenAlex · Extracted main text
Empirical studies often observe outcomes only for selected units, and treatment may change who is observed. This paper studies prediction in randomized studies with one-sided selection. Standard prediction intervals can fail because treated selected observations are not the same group as selected controls. The paper asks how to predict missing treated outcomes and individual treatment effects for always-observed units. The proposed conformalized Lee procedure uses treated selected observations to train and check any prediction rule, then adjusts the cutoff using the observed treatment-control selection gap. For selected controls, the missing treated-outcome interval is shifted by the observed untreated outcome to produce an individual treatment-effect interval. The method provides reliable coverage without requiring the prediction rule to be correctly specified. The key result shows that the proposed adjustment uses the exact amount of uncertainty implied by the monotone selection logic of Lee [2009]. In simulations, ordinary conformal prediction demonstrates a lower coverage rate under selection-induced distribution shift, while the Lee-adjusted methods achieve the desired coverage rate. The results show that the proposed selection correction method can support reliable counterfactual prediction, while retaining practical implementation with modern prediction tools.
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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 | Lee, David S (2009) Training, Wages, and Sample Selection: Estimating Sharp Bounds on Treatment Effects | 1.000 | 13 | 3 | 100% |
| 2 | Jin, Ying and Ren, Zhimei and Candès, Emmanuel J (2023) Sensitivity analysis of individual treatment effects: A robust conformal inference approach | 1.000 | 8 | 3 | 100% |
| 3 | Horowitz, Joel L and Manski, Charles F (1995) Identification and Robustness with Contaminated and Corrupted Data | 0.811 | 4 | 2 | 100% |
| 4 | Huber, Peter J (1981) Robust statistics | 0.811 | 4 | 2 | 100% |
| 5 | Semenova, Vira (2025) Generalized lee bounds | 0.585 | 3 | 1 | 100% |
| 6 | Chernozhukov, Victor and Wüthrich, Kaspar and Zhu, Yinchu (2021) An exact and robust conformal inference method for counterfactual and synthetic controls | 0.511 | 2 | 1 | 100% |
| 7 | Dong, Yingying and Heiler, Phillip (2026) Sharp Bounds and Inference in Sample Selection Models with Treatment Endogeneity | 0.511 | 2 | 1 | 100% |
| 8 | Dorn, Jacob and Guo, Kevin (2023) Sharp sensitivity analysis for inverse propensity weighting via quantile balancing | 0.511 | 2 | 1 | 100% |
| 9 | Dorn, Jacob and Guo, Kevin and Kallus, Nathan (2025) Doubly-valid/doubly-sharp sensitivity analysis for causal inference with unmeasured confounding | 0.511 | 2 | 1 | 100% |
| 10 | Frangakis, Constantine E and Rubin, Donald B (2002) Principal stratification in causal inference | 0.511 | 2 | 1 | 100% |
Showing the top 10 of 28 scored citations.