An Effective Treatment Approach to Difference-in-Differences with General Treatment Patterns

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 time 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.