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.

翻译：当干预非随机分配、连续施加且在同一强度下产生异质性效应时，因果识别变得尤为困难。在此类情境下，现有方法往往无法提供具有政策参考价值的处理强度与结果变量间关系的估计，尤其在共同支撑域受限的情况下更为突出。为填补这一空白，我们提出了聚类剂量响应函数（Cl-DRF），这是一种新颖的估计量，旨在揭示不同亚组中处理强度与因变量之间连续的因果关系。我们的方法同时利用了理论驱动和数据驱动的异质性来源，依赖于条件独立性和正概率假设的宽松版本，这些假设在各种观察性研究设定中具有合理性。我们应用Cl-DRF估计量来评估欧洲凝聚基金与经济增长之间亚组特异性的剂量响应关系。与多数文献结论不同，研究发现更高额度的资金投入会促进较发达地区的经济增长且未出现收益递减现象，而其他地区则因吸收能力有限无法充分获益。