Doubly Robust Uniform Confidence Bands for Group-Time Conditional Average Treatment Effects in Difference-in-Differences

We consider a panel data analysis to examine the heterogeneity in treatment effects with respect to groups, periods, and a pre-treatment covariate of interest in the staggered difference-in-differences setting of Callaway and Sant’Anna. Under standard identification conditions, a doubly robust estimand conditional on the covariate identifies the group-time conditional average treatment effect given the covariate. Focusing on the case of a continuous covariate, we propose a three-step estimation procedure based on nonparametric local polynomial regressions and parametric estimation methods. Using uniformly valid distributional approximation results for empirical processes and weighted/multiplier bootstrapping, we develop doubly robust inference methods to construct uniform confidence bands for the group-time conditional average treatment effect function and a variety of useful summary parameters. The accompanying R package didhetero allows for easy implementation of our methods.

本文基于Callaway与Sant’Anna提出的渐进双重差分（staggered difference-in-differences）框架，开展面板数据分析，以考察分组、时期以及关注的前处理协变量下的处理效应异质性。在标准识别假设下，基于协变量的双重稳健（doubly robust）估计量可识别给定协变量的分组-时期条件平均处理效应（conditional average treatment effect）。针对连续型协变量场景，本文提出一种基于非参数局部多项式回归（nonparametric local polynomial regressions）与参数估计方法的三步估计流程。借助经验过程（empirical processes）的一致有效分布近似结果与加权/乘数Bootstrap（weighted/multiplier bootstrapping）法，本文构建了双重稳健推断方法，可用于构建分组-时期条件平均处理效应函数以及各类实用汇总参数的一致置信带（uniform confidence bands）。配套的R包didhetero可便捷实现本文所提方法的落地应用。