Title: Bayesian analysis of regression discontinuity designs with heterogeneous treatment effects Show Chinese title

Title: 具有异质处理效应的回归断点设计的贝叶斯分析

Abstract: Regression Discontinuity Design (RDD) is a popular framework for estimating a causal effect in settings where treatment is assigned if an observed covariate exceeds a fixed threshold. We consider estimation and inference in the common setting where the sample consists of multiple known sub-populations with potentially heterogeneous treatment effects. In the applied literature, it is common to account for heterogeneity by either fitting a parametric model or considering each sub-population separately. In contrast, we develop a Bayesian hierarchical model using Gaussian process regression which allows for non-parametric regression while borrowing information across sub-populations. We derive the posterior distribution, prove posterior consistency, and develop a Metropolis-Hastings within Gibbs sampling algorithm. In extensive simulations, we show that the proposed procedure outperforms existing methods in both estimation and inferential tasks. Finally, we apply our procedure to U.S. Senate election data and discover an incumbent party advantage which is heterogeneous over different time periods. Show Chinese abstract

Abstract: 断点回归设计（RDD）是一种流行的框架，用于估计在处理分配取决于观测协变量超过固定阈值的情况下因果效应。 我们考虑了常见的情况，即样本由多个已知的子总体组成，并且这些子总体可能具有异质的处理效应。 在应用文献中，通常通过拟合参数模型或分别考虑每个子总体来考虑异质性。 相比之下，我们开发了一种基于高斯过程回归的贝叶斯分层模型，该模型允许非参数回归同时跨子总体借用信息。 我们推导出后验分布，证明后验一致性，并开发了一个吉布斯采样内的Metropolis-Hastings采样算法。 在广泛的模拟研究中，我们表明所提出的方法在估计和推断任务中均优于现有方法。 最后，我们将我们的方法应用于美国参议院选举数据，并发现执政党优势在不同的时间段内存在异质性。