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.

翻译：许多处理并非随机分配，具有连续型特征，且即使在相同处理强度下仍表现出异质性效应。这些特性共同对因果效应识别构成了重大挑战，因为现有估计器均无法提供平均因果剂量-响应函数的无偏估计。为填补这一空白，我们提出了聚类剂量-响应函数（Cl-DRF）——一种新颖的估计器，旨在识别不同亚组中处理强度与因变量之间的连续因果关联。该方法同时利用理论驱动与数据驱动的异质性来源，并在放松版本的条件下独立性与正性假设下运行，这些假设仅需在每个识别出的亚组内部满足。为展示Cl-DRF估计器的性能，我们通过模拟证据与实证应用（考察欧洲凝聚基金对经济增长的影响）进行验证。