Hierarchical and Density-based Causal Clustering

TL;DR

This paper advances causal clustering by integrating hierarchical and density-based algorithms, enabling more flexible and assumption-light identification of subgroups with heterogeneous treatment effects, supported by theoretical analysis and practical applications.

Contribution

It introduces new plug-in estimators for causal clustering that do not rely on strong structural assumptions, expanding the methodological toolkit for subgroup analysis.

Findings

Estimators achieve near-optimal convergence rates.

Methods perform well in finite samples as shown in simulations.

Applied successfully to voting and employment datasets.

Abstract

Understanding treatment effect heterogeneity is vital for scientific and policy research. However, identifying and evaluating heterogeneous treatment effects pose significant challenges due to the typically unknown subgroup structure. Recently, a novel approach, causal k-means clustering, has emerged to assess heterogeneity of treatment effect by applying the k-means algorithm to unknown counterfactual regression functions. In this paper, we expand upon this framework by integrating hierarchical and density-based clustering algorithms. We propose plug-in estimators that are simple and readily implementable using off-the-shelf algorithms. Unlike k-means clustering, which requires the margin condition, our proposed estimators do not rely on strong structural assumptions on the outcome process. We go on to study their rate of convergence, and show that under the minimal regularity conditions, the additional cost of causal clustering is essentially the estimation error of the outcome regression functions. Our findings significantly extend the capabilities of the causal clustering framework, thereby contributing to the progression of methodologies for identifying homogeneous subgroups in treatment response, consequently facilitating more nuanced and targeted interventions. The proposed methods also open up new avenues for clustering with generic pseudo-outcomes. We explore finite sample properties via simulation, and illustrate the proposed methods in voting and employment projection datasets.