New Developments in Regression Discontinuity Designs: Covariates Adjustment and Coverage Optimal Inference

本计画提出一种新的方法，将协变量纳入回归不连续性（RD）设计。它将协变量平衡条件表示为过识别矩限制。经验似然（EL）RD估计有效地结合了协变量平衡的信息，并具有不大于无协变量的标准估计的渐近方差。该项目然后提出了一个强大的校正EL置信集，实现了更快的覆盖错误衰减率。建议的置信区间的覆盖准确度自动鲁棒对抗协变量平衡条件的轻微扰动，这可能发生在数据污染和错误指定的“未受影响”结果用作协变量的情况下。本计画亦提出当研究者欲使用不连续回归与协变量调整时，在频宽选择上进行敏感度分析的方法。这个项目进行蒙特卡罗模拟，以评估有限样本性能的建议的推理方法，然后将其应用到一个真实的数据集。

This project proposes a novel approach to incorporate covariates in regression discontinuity (RD) designs. It represents the covariate balance condition as over-identifying moment restrictions. The empirical likelihood (EL) RD estimator efficiently incorporates the information from covariate balance and has an asymptotic variance no larger than that of the standard estimator without covariates. This project then proposes a robust corrected EL confidence set which achieves a faster coverage error decay rate. The coverage accuracy of the proposed confidence interval is automatically robust against slight perturbation to the covariate balance condition, which may happen in cases such as data contamination and misspecified “unaffected” outcomes used as covariates. This project also propose a way to conduct sensitivity analysis in the bandwidth choice when the researcher wants to use regression discontinuity with covariate adjustment. This project conducts Monte Carlo simulations to assess the finite-sample performance of the proposed inference method and then applies it to a real dataset.