Bounds On Treatment Effects On Transitions

This paper considers the definition and identification of treatment effects on conditional transition probabilities. We show that even under sequential random assignment only the instantaneous average treatment effect is point identified. Because treated and control units drop out at different rates, randomization only ensures the comparability of treatment and controls at the time of randomization, so that long run average treatment effects are not point identified. Instead we derive informative bounds on these average treatment effects. Our bounds do not impose (semi)parametric restrictions, as e.g. proportional hazards, that would narrow the bounds or even allow for point identification. We also explore various assumptions such as monotone treatment response, common shocks and positively correlated outcomes.