On nonparametric identification of treatment effects in duration models

We show that the main nonparametric identification finding of Abbring and Van den Berg (2003b, Econometrica) for the effect of a timing-chosen treatment on an event duration of interest does not hold. The main problem is that the identification is based on the competing-risks identification result of Abbring and Van den Berg (2003a, Journal of the Royal Statistical Society, Series B) that requires independence between the waiting duration until treatment and the event duration, but the independence assumption does not hold unless there is no treatment effect. We illustrate the problem using constant hazards (i.e., exponential distribution), and as it turns out, there is no constant-hazard data generating process satisfying the assumptions in Abbring and Van den Berg (2003b, Econometrica) so long as the effect is not zero. We also suggest an alternative causal model.