On the relationship between prediction intervals, tests of sharp nulls and inference on realized treatment effects in settings with few treated units

2025/06/17 by Luis Ignacio Ortega Álvarez, Bruno Ferman, Alvarez, Luis +1
Mathematics · #Econometrics (econ.EM) #FOS: Economics and business #Statistical Methods in Clinical Trials

paper · pdf · doi:10.48550/arxiv.2506.14998

openalex publication_date 2025/06/17 · openalex created_date 2025/10/19 · openalex updated_date 2026/07/28

Abstract

We study how inference methods for settings with few treated units that rely on treatment effect homogeneity extend to alternative inferential targets when treatment effects are heterogeneous -- namely, tests of sharp null hypotheses, inference on realized treatment effects, and prediction intervals. We show that inference methods for these alternative targets are deeply interconnected: they are either equivalent or become equivalent under additional assumptions. Our results show that methods designed under treatment effect homogeneity can remain valid for these alternative targets when treatment effects are stochastic, offering new theoretical justifications and insights on their applicability.

Citations

• Inference with few treated units
• Extensions for Inference in Difference-in-Differences with Few Treated Clusters
• Uncertainty Quantification in Synthetic Controls with Staggered Treatment Adoption
• Conformal Inference of Counterfactuals and Individual Treatment Effects
• Conformal prediction intervals for the individual treatment effect
• Prediction Intervals for Synthetic Control Methods
• Debiasing and t-tests for synthetic control inference on average causal effects
• Inference with “Difference in Differences” with a Small Number of Policy Changes

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• Individual Treatment Effect: Prediction Intervals and Sharp Bounds
• Randomization Inference beyond the Sharp Null: Bounded Null Hypotheses and Quantiles of Individual Treatment Effects
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• Beyond the Sharp Null: Randomization Inference, Bounded Null Hypotheses, and Confidence Intervals for Maximum Effects