Bounds on treatment effects on transitions

This paper considers the identification of treatment effects on conditional transition probabilities. We show that even under random assignment only the instantaneous average treatment effect is point identified. Since 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 bounds on these average effects. Our bounds do not impose (semi)parametric restrictions, for example, proportional hazards. We also explore assumptions such as monotone treatment response, common shocks and positively correlated outcomes that tighten the bounds.