Empirical regression discontinuity (RD) studies often use covariates to increase the precision of their estimates. In this paper, we propose a novel class of estimators that use such covariate information more efficiently than the linear adjustment estimators that are currently used widely in practice. Our approach can accommodate a possibly large number of either discrete or continuous covariates. It involves running a standard RD analysis with an appropriately modified outcome variable, which takes the form of the difference between the original outcome and a function of the covariates. We characterize the function that leads to the estimator with the smallest asymptotic variance, and show how it can be estimated via modern machine learning, nonparametric regression, or classical parametric methods. The resulting estimator is easy to implement, as tuning parameters can be chosen as in a conventional RD analysis. An extensive simulation study illustrates the performance of our approach.

翻译：实证断点回归研究常通过引入协变量来提高估计精度。本文提出一类新型估计量，相较于当前实践中广泛使用的线性调整估计量，能更有效地利用协变量信息。本方法可处理包含离散或连续变量在内的较多协变量情形，其核心思想是通过构建经适当修正的指标变量（即原始结果变量与协变量函数之差），对修正后的结果进行标准断点回归分析。我们刻画了使估计量渐近方差最小化的函数形式，并展示了如何通过现代机器学习、非参数回归或经典参数方法对其进行估计。所得估计量易于实现，其调参方式与常规断点回归分析一致。大范围仿真研究验证了本方法的有效性。