This paper discusses the evaluation problem using observational data when the timing of treatment is an outcome of a stochastic process. We show that, without additional assumptions, it is not possible to estimate the average treatment effect and treatment on the treated. It is, however, possible to estimate the effect of treatment on the treated up to a certain time point. We propose an estimator to estimate this effect and show that it is possible to test for an average treatment effect.
Treatment effects dynamic treatment assignment program evaluation method of matching