This paper studies the identification, estimation, and inference of long-term (binary) treatment effect parameters when balanced panel data is not available, or consists of only a subset of the available data. We develop a new estimator: the chained difference-in-differences, which leverages the overlapping structure of many unbalanced panel data sets. This approach consists in efficiently aggregating a collection of short-term treatment effects estimated on multiple incomplete panels. Our estimator accommodates (1) multiple time periods, (2) variation in treatment timing, (3) treatment effect heterogeneity, and (4) general missing data patterns. We establish the asymptotic properties of the proposed estimator and discuss identification and efficiency gains in comparison to existing methods. Finally, we illustrate its relevance through (i) numerical simulations, and (ii) an application about the effects of an innovation policy in France.

翻译：本文研究在无法获得平衡的小组数据时,或仅包括可用数据的一个子集时,长期(二元)处理效果参数的确定、估计和推论。我们开发了一个新的估算器:链条差异,利用许多不平衡的小组数据集的重叠结构。这一方法包括有效地汇集对多个不完全的小组估计的短期处理效果。我们的估算器包含:(1) 多个时间段,(2) 治疗时间的变异,(3) 治疗效果异质性,(4) 缺少的一般数据模式。我们确定了拟议估算器的无症状特性,并讨论了与现有方法相比的识别和效率收益。最后,我们通过(一) 数字模拟和(二) 应用法国创新政策的效果来说明其相关性。