The Clustered Dose-Response Function Estimator for continuous treatment with heterogeneous treatment effects

Abstract: Many treatments are non-randomly assigned, continuous in nature, and exhibit heterogeneous effects even at identical treatment intensities. Taken together, these characteristics pose significant challenges for identifying causal effects, as no existing estimator can provide an unbiased estimate of the average causal dose-response function. To address this gap, we introduce the Clustered Dose-Response Function (Cl-DRF), a novel estimator designed to discern the continuous causal relationships between treatment intensity and the dependent variable across different subgroups. This approach leverages both theoretical and data-driven sources of heterogeneity and operates under relaxed versions of the conditional independence and positivity assumptions, which are required to be met only within each identified subgroup. To demonstrate the capabilities of the Cl-DRF estimator, we present both simulation evidence and an empirical application examining the impact of European Cohesion funds on economic growth.