Understanding Estimators of Treatment Effects in Regression Discontinuity Designs
提出两种新的断点回归处理效应估计量：部分多项式估计量和工具变量估计量，前者通过引入导数差异改进部分线性估计量，后者适用于模糊设计，并研究了它们的渐近性质。
In this paper, we propose two new estimators of treatment effects in regression discontinuity designs. These estimators can aid understanding of the existing estimators such as the local polynomial estimator and the partially linear estimator. The first estimator is the partially polynomial estimator which extends the partially linear estimator by further incorporating derivative differences of the conditional mean of the outcome on the two sides of the discontinuity point. This estimator is related to the local polynomial estimator by a relocalization effect. Unlike the partially linear estimator, this estimator can achieve the optimal rate of convergence even under broader regularity conditions. The second estimator is an instrumental variable estimator in the fuzzy design. This estimator will reduce to the local polynomial estimator if higher order endogeneities are neglected. We study the asymptotic properties of these two estimators and conduct simulation studies to confirm the theoretical analysis.