Dynamically assigned treatments: duration models, binary treatment models, and panel data models

Often, the moment of a treatment and the moment at which the outcome of interest occurs are realizations of stochastic processes with dependent unobserved determinants. Notably, both treatment and outcome are characterized by the moment they occur. We compare different methods of inference of the treatment effect, and we argue that the timing of the treatment relative to the outcome conveys useful information on the treatment effect, which is discarded in binary treatment frameworks