treatment-effect discontinuity analysis

This paper addresses an inherent bias in conventional univariate distance-based methods for boundary discontinuity design (BDD) when assignment boundaries are piecewise-linear or irregularly shaped—bias arising from model misspecification and thus non-eliminable. To resolve this, we propose a novel causal inference framework based on bivariate scores. Theoretically, we establish, for the first time, the fundamental bias of distance-based estimators at boundary kinks and rigorously prove the theoretical superiority and universality of the bivariate-score approach. Methodologically, we develop a robust estimator integrating local polynomial regression with bivariate kernel weighting, and derive uniform inference theory—including consistent confidence band construction—for irregular boundaries. Empirically, we provide open-source software and demonstrate substantial improvements over existing methods in both simulations and real-data applications.

This paper addresses the challenge of identifying heterogeneous treatment effects in regression discontinuity designs (RDD) without prior specification of effect-modifying covariates. We propose an “honest” RDD tree method grounded in supervised machine learning, which—novelty—incorporates honest splitting to ensure valid statistical inference while automatically selecting pre-treatment covariates that drive heterogeneity, without requiring prespecified candidate variables. By integrating RDD theory, decision-tree modeling, and Monte Carlo simulation, our approach achieves superior bias control and nominal coverage of confidence intervals compared to conventional subgroup analyses or interaction-based methods. An empirical application to Romanian secondary education data successfully uncovers multiple sources of treatment-effect heterogeneity, demonstrating the method’s robustness and practical utility for causal inference in RDD settings.

This paper addresses the challenge of accurately estimating and inferring causal treatment effects under multivariate fuzzy regression discontinuity designs (RDDs) and geographic RDDs—settings where treatment assignment depends on a two-dimensional continuous boundary. We propose a novel data-driven, adaptive bandwidth selection method that supports local polynomial estimation either on the original bivariate score or on the Euclidean distance to the boundary. Within a unified bivariate nonparametric regression framework, we develop both pointwise and uniform asymptotic inference procedures. Simulations demonstrate that our approach substantially improves spatial resolution and statistical power while maintaining robustness under complex boundary curvature and heterogeneous sampling density. Our primary contribution is the first theoretically rigorous yet empirically feasible unified estimation and inference toolkit for RDDs with two-dimensional boundaries.

In multivariate regression discontinuity designs (RDD), conventional dimensionality reduction of multidimensional running variables to Euclidean distance leads to suboptimal bandwidth selection, inefficient estimation, and inability to detect heterogeneous treatment effects on the cutoff boundary. This paper proposes a direct local linear estimation framework for multivariate running variables. It establishes, for the first time, the asymptotic normality theory for multivariate local polynomial estimators, enabling boundary-adaptive bandwidth selection and precise identification of heterogeneous treatment effects. The method integrates multivariate local linear regression, asymptotic statistical inference, and numerical simulation, and is applied to evaluate Colombia’s scholarship policy. Results demonstrate substantially improved estimation efficiency and uncover rich heterogeneity masked by traditional univariate approaches—thereby overcoming fundamental limitations of the dimensionality-reduction paradigm.

This paper addresses causal identification in regression discontinuity designs (RDD) under linear mean spillover effects. When treated units generate spillovers onto nearby control units, the interpretation of conventional RDD estimators hinges critically on the relative magnitude of the spillover radius and the bandwidth—potentially capturing the direct effect, total effect, or a mixture thereof. To resolve this ambiguity, we first formally characterize the identification targets of RDD under spillovers. Second, we propose a localized linear regression framework that explicitly incorporates spillover terms, enabling separable identification of direct and spillover effects. Third, we derive necessary and sufficient conditions for the “doughnut-hole” RDD design to eliminate spillover bias, and delineate its validity boundary. Leveraging asymptotic bandwidth analysis and causal identification theory, we establish a spillover-robust RDD estimation framework, substantially broadening the applicability and interpretability of RDD in settings with spatial or social spillovers.

This study addresses the identification of discontinuities in distributional treatment effects where the sign of the marginal effect abruptly changes. To this end, it proposes a unified framework that integrates horizontal discontinuity analysis (HDA) and vertical discontinuity analysis (VDA), leveraging causal forests to estimate the treatment effect curve. The approach enables inference on the non-tangentiality of local slopes through asymptotic crossing-point theory and a bias-corrected Wald statistic. Empirical validation on both synthetic data and real-world data from Mexico’s PROGRESA program demonstrates the method’s ability to reliably detect sign-switching points. By doing so, this work substantially expands the methodological toolkit for analyzing distributional treatment effects and offers a novel pathway for investigating heterogeneous causal effects.

This paper addresses the challenge of modeling heterogeneous treatment effects in boundary discontinuity designs. We propose an isotropic-distance-based local polynomial regression method to systematically estimate and conduct inference on the boundary average treatment effect (BATE) curve. Under regularity conditions on the boundary manifold, we establish— for the first time—the necessary and sufficient conditions for the identifiability, estimability, and inferential validity of the BATE curve, enabling both pointwise and uniform asymptotic inference. Theoretical contributions include a unified nonparametric asymptotic theory for the estimator, explicit convergence rates, and valid confidence band construction. Monte Carlo simulations confirm the method’s finite-sample performance. We also release open-source software implementing the framework. By accommodating complex geographic, administrative, or social boundaries, our approach substantially enhances causal analysis of treatment effect heterogeneity across such boundaries.

Conventional univariate regression discontinuity design (RDD) struggles with multidimensional threshold-based decision rules. Method: We propose boundary discontinuity design (BD design), a novel framework focusing on treatment assignment along arbitrary boundary curves in two-dimensional score space. We develop a unified identification theory characterizing local identifiability conditions, bandwidth selection challenges, and sources of estimation bias, and integrate local polynomial estimation with robust inference procedures. Contribution/Results: Synthesizing over 80 empirical studies, we trace methodological evolution and provide the first theoretical guide and practical implementation protocol for BD design. Our approach substantially improves estimation accuracy of causal effects under multidimensional cutoffs and enhances the reliability and applicability of nonexperimental causal inference in complex policy settings—such as school district zoning and credit approval—where decisions depend on multiple criteria.

This study addresses a key limitation of traditional regression discontinuity and kink designs, which focus solely on average treatment effects while ignoring how policies reshape the entire outcome distribution. The authors propose a novel distributional framework that introduces the Wasserstein distance into causal inference to quantify discrepancies between conditional distributions at the treatment threshold. By leveraging an L-moments-based orthogonal decomposition, the method disentangles changes in distributional features—such as location, scale, and skewness—to uncover sources of treatment effect heterogeneity. In the fuzzy kink setting, this approach yields new identification results. Empirical applications to two real-world natural experiments demonstrate that distributional effects can differ markedly from conventional average effects, underscoring the method’s explanatory power and practical relevance.

本文提出了一种非参数测试方法，用于检测回归断点设计中未观察到的处理效应异质性问题。