The PCDID Approach: Difference-in-Differences when Trends are Potentially Unparallel and Stochastic

We develop a class of regression-based estimators, called Principal Components Differ-ence-in-Differences estimators (PCDID), for treatment effect estimation. Analogous to a control function approach, PCDID uses factor proxies constructed from control units to control for unobserved trends, assuming that the unobservables follow an interactive effects structure. We clarify the conditions under which the estimands in this regression-based approach represent useful causal parameters of interest. We establish consistency and asymptotic normality results of PCDID estimators under minimal assumptions on the specification of time trends. The PCDID approach is illustrated in an empirical exercise that examines the effects of welfare waiver programs on welfare caseloads in the US.

本文提出了一类用于处理效应估计的基于回归的估计量，命名为主成分双重差分估计量（Principal Components Difference-in-Differences Estimators，缩写为PCDID）。与控制函数方法思路一致，PCDID通过从控制组单元构建的因子代理变量对未观测到的时间趋势进行控制，假设不可观测变量服从交互效应结构。我们阐明了该回归类估计方法中，估计量可作为有效目标因果参数的前提条件。在仅对时间趋势设定施加最弱假设的前提下，我们证明了PCDID估计量的一致性与渐近正态性。本文通过一项考察美国福利豁免计划对福利经办个案数影响的实证研究，演示了PCDID方法的应用。