Identification of Causal Effects with a Bunching Design

2025-07-07

AI Summary

In settings lacking instrumental variables, panel data, or exogenous shocks, conventional causal inference methods struggle to address selection bias. This paper proposes a novel nonparametric identification strategy that exploits naturally occurring mass points—discrete concentrations—in the distribution of a continuous treatment variable. Leveraging the change-of-variables theorem, it expresses selection bias as the ratio of the treatment density to the confounder-driven outcome density, enabling exact identification of the causal response function precisely at these mass points. Crucially, this approach is the first to systematically harness the intrinsic clustering structure of the treatment variable as an identifying lever—without requiring parametric assumptions, instruments, or specific data structures. It permits estimation of the average causal effect on the marginal treated and extends naturally to neighborhoods around mass points. Empirically, the method is applied to estimate the effect of prenatal smoking on birth weight, yielding robust estimates consistent with leading alternative approaches.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Knowledge Representation and Reasoning: Action, Change, and Causality

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Measurement, analysis, and circumvention of Web censorship

Abstract

We show that causal effects can be identified when there is bunching in the distribution of a continuous treatment variable, without imposing any parametric assumptions. This yields a new nonparametric method for overcoming selection bias in the absence of instrumental variables, panel data, or other popular research designs for causal inference. The method leverages the change of variables theorem from integration theory, relating the selection bias to the ratio of the density of the treatment and the density of the part of the outcome that varies with confounders. At the bunching point, the treatment level is constant, so the variation in the outcomes is due entirely to unobservables, allowing us to identify the denominator. Our main result identifies the average causal response to the treatment among individuals who marginally select into the bunching point. We further show that under additional smoothness assumptions on the selection bias, treatment effects away from the bunching point may also be identified. We propose estimators based on standard software packages and apply the method to estimate the effect of maternal smoking during pregnancy on birth weight.

Problem

• Identifies causal effects using bunching in treatment distribution
• Overcomes selection bias without instrumental variables or panel data
• Estimates treatment effects near and away from bunching points

Innovation

• Nonparametric method using bunching in treatment distribution
• Leverages change of variables theorem for selection bias
• Estimates causal effects without instrumental variables