Regression discontinuity designs assess causal effects in settings where treatment is determined by whether an observed running variable crosses a pre-specified threshold. Here we propose a new approach to identification, estimation, and inference in regression discontinuity designs that uses knowledge about exogenous noise (e.g., measurement error) in the running variable. In our strategy, we weight treated and control units to balance a latent variable of which the running variable is a noisy measure. Our approach is explicitly randomization-based and complements standard formal analyses that appeal to continuity arguments while ignoring the stochastic nature of the assignment mechanism.

翻译：断点回归设计通过观察运行变量是否跨越预设阈值来决定处理分配，从而评估因果效应。本文提出了一种基于运行变量中外生噪声（如测量误差）信息的断点回归识别、估计与推断新方法。该策略通过对处理组与控制组进行加权，以平衡运行变量作为噪声测度的潜变量。本方法明确基于随机化原理，弥补了依赖连续性假设而忽视分配机制随机性的标准形式化分析。