Boundary Discontinuity (BD) designs are used in empirical research to learn about causal treatment effects along a continuous assignment boundary defined by a bivariate score. These designs are also known as multi-score regression discontinuity (RD) designs, and include geographic RD designs as a prominent example. This article introduces \pkg{rd2d}, a statistical software package for \proglang{R}, \proglang{Python}, and \proglang{Stata} that implements local polynomial estimation and inference for BD designs using either the bivariate score or a univariate signed distance-to-boundary score. The software covers sharp and fuzzy BD designs, providing automatic bandwidth selection, robust bias-corrected pointwise inference, uniform confidence bands, cluster-robust inference with joint or separate fitting conventions, covariate-adjusted efficiency improvements, mass-point checks, and covariance regularization, among other features. We illustrate the package with an empirical application to Opportunity Zones, where eligibility has a strong first-stage effect on designation but no significant effects on early workplace-job growth.

翻译：边界断点（BD）设计用于实证研究中，以了解沿由二元评分定义的连续分配边界的因果处理效应。这类设计也被称为多评分回归断点（RD）设计，其中地理RD设计是重要的一例。本文介绍rd2d——一个适用于R、Python和Stata的统计软件包，该包通过使用二元评分或单变量符号化距离边界评分，实现了BD设计的局部多项式估计与推断。该软件涵盖精确BD设计和模糊BD设计，提供自动带宽选择、稳健偏差校正逐点推断、统一置信带、采用联合或分离拟合惯例的聚类稳健推断、协变量调整效率提升、质量点检查及协方差正则化等功能。我们通过机会区的一项实证应用展示该软件包——在该区中，资格对指定具有强烈的第一阶段效应，但对早期就业岗位增长无显著影响。