Manipulation Testing in Boundary Discontinuity Designs

2026-08-31

AI Summary

本文提出了一种针对具有任意边界形状的边界不连续设计(BDD)的操纵测试方法，通过k-均值聚类和二项平衡测试来检测处理组与对照组的均衡性。

Abstract

We propose the first manipulation test designed for boundary discontinuity designs (BDDs) with general boundary shapes. A BDD is a multidimensional extension of the regression discontinuity design (RDD) in which treatment assignment is determined by whether the multidimensional running variable crosses a lower-dimensional boundary set. The test avoids multivariate density estimation and builds on the observation that, in the absence of manipulation, observations near the boundary should be approximately evenly split between treatment and control within arbitrary groups defined by their projections onto the boundary. We test this implication using a collection of binomial balance tests on observations near the boundary, with groups formed by k-means clustering. We establish the asymptotic validity of the test under suitable regularity conditions. We also evaluate finite-sample performance through Monte Carlo simulations and illustrate the test in three empirical applications.

Problem

• Boundary Discontinuity Designs
• Manipulation Testing
• Regression Discontinuity Design

Innovation

• boundary discontinuity designs
• manipulation test
• k-means clustering
• binomial balance tests