Replication Data for: A Bayesian Alternative to Synthetic Control for Comparative Case Studies

This paper proposes a Bayesian alternative to the synthetic control method for comparative case studies with a single or multiple treated units. We adopt a Bayesian posterior predictive approach to Rubin's causal model, which allows researchers to make inferences about both individual and average treatment effects on treated observations based on the empirical posterior distributions of their counterfactuals. The prediction model we develop is a dynamic multilevel model with a latent factor term to correct biases induced by unit-specific time trends. It also considers heterogeneous and dynamic relationships between covariates and the outcome, thus improving precision of the causal estimates. To reduce model dependency, we adopt a Bayesian shrinkage method for model searching and factor selection. Monte Carlo exercises demonstrate that our method produces more precise causal estimates than existing approaches and achieves correct frequentist coverage rates even when the sample size is relatively small and rich heterogeneities are present in the data. We illustrate the method with two empirical examples from political economy.

本文针对包含单个或多个干预单元的比较案例研究，提出了合成控制法（Synthetic Control Method）的贝叶斯替代方案。我们采用贝叶斯后验预测方法适配鲁宾因果模型（Rubin's Causal Model），使研究者能够基于干预单元反事实结果的经验后验分布，对个体处理效应与平均处理效应开展统计推断。本文构建的预测模型为含潜在因子项的动态多层模型，可校正由单元特异性时间趋势引发的估计偏误；同时该模型兼顾协变量与结果变量间的异质性动态关联，进而提升因果估计的精度。为降低模型依赖性，我们采用贝叶斯收缩法（Bayesian Shrinkage Method）开展模型搜索与因子筛选。蒙特卡洛（Monte Carlo）模拟实验表明，相较于现有方法，本文所提方法可生成更为精准的因果估计量，即便在样本量相对较小、数据存在丰富异质性的场景下，仍能保证正确的频率学派置信覆盖率。我们采用两个来自政治经济学领域的实证案例对所提方法进行演示说明。