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

AI Summary

This paper systematically investigates the intrinsic relationships among three inferential objectives—sharp null hypothesis testing, inference on the realized treatment effect, and construction of prediction intervals—under settings characterized by small sample sizes and heterogeneous treatment effects. Leveraging randomization-based inference and finite-sample theory, we establish, for the first time, that these three objectives admit a unified robust inferential framework even when treatment effects are stochastic rather than homogeneous. Crucially, validity of this framework does not require the conventional homogeneity assumption but only a specific exchangeability condition. Our result demonstrates conditional equivalence among the three inferential goals in finite samples, thereby providing a novel theoretical justification for classical homogeneity-based methods and substantially broadening the applicability and interpretability of causal inference techniques in heterogeneous settings.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Calibration & Uncertainty Quantification
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Extend inference methods for few treated units to heterogeneous effects
• Connect tests of sharp nulls with realized treatment effects inference
• Validate homogeneity-based methods under stochastic treatment effects

Innovation

• Extends homogeneity methods to heterogeneous effects
• Connects tests, inference, and prediction intervals
• Validates methods under stochastic treatment effects