Local Polynomial Order in Regression Discontinuity Designs
针对断点回归中多项式阶数选择难题，基于渐近均方误差准则提出阶数选择方法，蒙特卡洛模拟显示在大样本下表现良好，并推广到模糊断点回归和回归扭结设计。
Treatment effect estimates in regression discontinuity (RD) designs are often sensitive to the choice of bandwidth and polynomial order, the two important ingredients of widely used local regression methods. While Imbens and Kalyanaraman and Calonico, Cattaneo, and Titiunik provided guidance on bandwidth, the sensitivity to polynomial order still poses a conundrum to RD practitioners. It is understood in the econometric literature that applying the argument of bias reduction does not help resolve this conundrum, since it would always lead to preferring higher orders. We therefore extend the frameworks of Imbens and Kalyanaraman and Calonico, Cattaneo, and Titiunik and use the asymptotic mean squared error of the local regression RD estimator as the criterion to guide polynomial order selection. We show in Monte Carlo simulations that the proposed order selection procedure performs well, particularly in large sample sizes typically found in empirical RD applications. This procedure extends easily to fuzzy regression discontinuity and regression kink designs.