This paper studies estimation of causal effects in a panel data setting. We introduce a new estimator, the Triply RObust Panel (TROP) estimator, that combines (i) a flexible model for the potential outcomes based on a low-rank factor structure on top of a two-way-fixed effect specification, with (ii) unit weights intended to upweight units similar to the treated units and (iii) time weights intended to upweight time periods close to the treated time periods. We study the performance of the estimator in a set of simulations designed to closely match several commonly studied real data sets. We find that there is substantial variation in the performance of the estimators across the settings considered. The proposed estimator outperforms two-way-fixed-effect/difference-in-differences, synthetic control, matrix completion and synthetic-difference-in-differences estimators. We investigate what features of the data generating process lead to this performance, and assess the relative importance of the three components of the proposed estimator. We have two recommendations. Our preferred strategy is that researchers use simulations closely matched to the data they are interested in, along the lines discussed in this paper, to investigate which estimators work well in their particular setting. A simpler approach is to use more robust estimators such as synthetic difference-in-differences or the new triply robust panel estimator which we find to substantially outperform two-way fixed effect estimators in many empirically relevant settings.

翻译：本文研究面板数据设定下的因果效应估计问题。我们提出了一种新的估计量——三重稳健面板（TROP）估计量，该估计量融合了三个要素：（i）基于双向固定效应设定之上低秩因子结构的潜在结果灵活模型；（ii）旨在提升与处理单元相似单元权重的单元权重；（iii）旨在提升接近处理时期时间权重的时期权重。我们通过一系列与常见实证数据集高度匹配的模拟实验来评估该估计量的性能。研究发现，在不同设定下各估计量的表现存在显著差异。所提出的估计量在性能上优于双向固定效应/双重差分法、合成控制法、矩阵补全法以及合成双重差分法估计量。我们探究了数据生成过程的哪些特征导致了这种性能差异，并评估了所提出估计量三个组成部分的相对重要性。我们提出两条建议：首选策略是研究者采用与本文讨论思路一致的、与其关注数据高度匹配的模拟实验，以探究何种估计量在其特定设定下表现良好；更简化的方法是采用更具稳健性的估计量，如合成双重差分法或本文提出的新三重稳健面板估计量——我们在许多实证相关设定中发现后者显著优于双向固定效应估计量。