Partial identification of average treatment effects on the treated through difference-in-differences
研究了在只有重复截面数据、无法获知处理组后处理状态时，如何利用双重差分法部分识别处理组平均处理效应，并探讨了工具变量和匹配子样本的识别能力。
The difference-in-differences (DID) method is widely used as a tool for identifying causal effects of treatments in program evaluation. When panel data sets are available, it is well-known that the average treatment effect on the treated (ATT) is point-identified under the DID setup. If a panel data set is not available, repeated cross sections (pretreatment and posttreatment) may be used, but may not point-identify the ATT. This paper systematically studies the identification of the ATT under the DID setup when posttreatment treatment status is unknown for the pretreatment sample. This is done through a novel application of an extension of a continuous version of the classical monotone rearrangement inequality which allows for general copula bounds. The identifying power of an instrumental variable and of a ‘matched subsample’ is also explored. Finally, we illustrate our approach by estimating the effect of the Americans with Disabilities Act of 1991 on employment outcomes of the disabled.