We consider a general difference-in-differences model in which the treatment variable of interest may be non-binary and its value may change in each period. It is generally difficult to estimate treatment parameters defined with the potential outcome given the entire path of treatment adoption, because each treatment path may be experienced by only a small number of observations. We propose an alternative approach using the concept of effective treatment, which summarizes the treatment path into an empirically tractable low-dimensional variable, and develop doubly robust identification, estimation, and inference methods. We also provide a companion R software package.

翻译：我们考虑一个一般的双重差分模型，其中感兴趣的处理变量可能不是二元的，且其取值可能在每个时期发生变化。通常，针对基于整个处理采用路径所定义的反事实结果来估计处理参数是困难的，因为每条处理路径可能仅被少量观测样本经历。我们提出了一种替代方法，该方法利用有效处理（effective treatment）的概念，将处理路径总结为一个经验上易于处理的低维变量，并开发了双重稳健的识别、估计和推断方法。我们还提供了一个配套的R软件包。