Heterogeneous Responses to Continuous Treatments: A Cluster-Based Causal Framework

TL;DR

This paper introduces the Cl-DRF estimator to identify subgroup-specific causal effects of continuous treatments, addressing heterogeneity and limited support issues in observational studies.

Contribution

The paper proposes a novel cluster-based estimator for continuous causal effects that relaxes key assumptions and captures heterogeneity across subgroups.

Findings

Higher funding boosts growth in developed regions without diminishing returns.

Limited absorptive capacity hinders benefits in less developed regions.

The estimator effectively uncovers subgroup-specific dose-response relationships.

Abstract

When treatments are non-randomly assigned, continuous, and yield heterogeneous effects at the same intensity, causal identification becomes particularly challenging. In such contexts, existing approaches often fail to provide policy-relevant estimates of the relationship between treatment intensity and outcomes, especially in the presence of limited common support. To fill this gap, we introduce the Clustered Dose-Response Function (Cl-DRF), a novel estimator designed to uncover the continuous causal relationship between treatment intensity and the dependent variable across distinct subgroups. Our approach leverages both theoretical and data-driven sources of heterogeneity, relying on relaxed versions of the conditional independence and positivity assumptions that are plausible across various observational settings. We apply the Cl-DRF estimator to estimate subgroup-specific dose-response relationships between European Cohesion Funds and economic growth. In contrast to much of the literature, higher funding increases growth in more developed regions without diminishing returns, while limited absorptive capacity prevents other regions from fully benefiting.