Finite Population Identification and Design-Based Sensitivity Analysis

2025-04-19

AI Summary

This paper addresses the lack of robust design foundations for sensitivity analysis in finite-population causal inference. Methodologically, it introduces a novel sensitivity analysis framework grounded in the experimental design distribution—first integrating design-based distributions with partial identification theory to construct model-free, non-asymptotic confidence intervals for the average treatment effect (ATE). It further reinterprets the role of randomization in sensitivity analysis and provides a new design-driven rationale for covariate balance checks. Key contributions include: (1) model-free, finite-population inference under heterogeneous treatment effects; (2) robust ATE confidence intervals with clear identification-theoretic interpretation; and (3) empirical validation across three real-world applications, demonstrating reliability and practicality in small-sample and highly heterogeneous settings.

Technology Category

Reasoning under Uncertainty: CausalityMachine Learning: Causal LearningMultiagent Systems: Mechanism Design

Application Category

Security and Privacy: Large-scale security measurementsUser Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systemsEconomics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

We develop an approach to sensitivity analysis that uses design distributions to calibrate sensitivity parameters in a finite population model. We use this approach to (1) give a new formal analysis of the role of randomization, (2) provide a new motivation for examining covariate balance, and (3) show how to construct design-based confidence intervals for the average treatment effect, which allow for heterogeneous treatment effects but do not rely on asymptotics. This approach to confidence interval construction relies on partial identification analysis rather than hypothesis test inversion. Moreover, these intervals also have a non-frequentist, identification-based interpretation. We illustrate our approach in three empirical applications.

Problem

• Develops sensitivity analysis using design distributions for finite populations
• Analyzes randomization role and motivates covariate balance examination
• Constructs design-based confidence intervals for heterogeneous treatment effects

Innovation

• Uses design distributions for sensitivity analysis
• Constructs design-based confidence intervals
• Relies on partial identification analysis