论文标题
模糊回归不连续设计中的非线性和不可分割的结构功能
Nonlinear and Nonseparable Structural Functions in Fuzzy Regression Discontinuity Designs
论文作者
论文摘要
回归不连续性（RD）设计的许多经验例子涉及连续的治疗变量，但是对此类模型的理论方面进行了较少的研究。这项研究检查了具有连续处理变量的模糊RD设计中结构功能的识别和估计。结构功能充分描述了治疗对结果的因果影响。我们表明，在形状限制下，在RD截止下，非线性和不可分割的结构函数可以在RD截止下识别，包括单调性和平滑度条件。基于非参数识别方程，我们提出了一个三步的半参数估计程序，并建立了估计量的渐近正态性。半参数估计器的收敛速率与二进制治疗变量相同。作为该方法的应用，我们通过在时区域边界上使用自然光计时中的不连续性来估计睡眠时间对健康状况的因果影响。
Many empirical examples of regression discontinuity (RD) designs concern a continuous treatment variable, but the theoretical aspects of such models are less studied. This study examines the identification and estimation of the structural function in fuzzy RD designs with a continuous treatment variable. The structural function fully describes the causal impact of the treatment on the outcome. We show that the nonlinear and nonseparable structural function can be nonparametrically identified at the RD cutoff under shape restrictions, including monotonicity and smoothness conditions. Based on the nonparametric identification equation, we propose a three-step semiparametric estimation procedure and establish the asymptotic normality of the estimator. The semiparametric estimator achieves the same convergence rate as in the case of a binary treatment variable. As an application of the method, we estimate the causal effect of sleep time on health status by using the discontinuity in natural light timing at time zone boundaries.
