Abstract
This paper considers identification of treatment effects on conditional transition probabilities. We show that even under 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 bound on these average treatment effects. Our bounds do not impose (semi)parametric restrictions, as e.g. proportional hazards. We also explore various assumptions such as monotone treatment response, common shocks and positively correlated outcomes that tighten the bounds.
Highlights
We consider the effect of an intervention if the outcome is a transition from an initial to a destination state
At later points in time treated units with characteristics that interact with the treatment to increase/decrease the transition probability relative to similar control units leave the initial state sooner/later than comparable control units, so that these characteristics are under/over represented among the remaining treated relative to the remaining controls and this confounds the effect of the treatment
In Illinois Unemployment Insurance (UI) benefits end after 26 weeks and since administrative data were used, all unemployment durations are censored at 26 weeks
Summary
We consider the effect of an intervention if the outcome is a transition from an initial to a destination state. The bounds can be applied if the treatment assignment is unconfounded by creating bounds conditional on the covariates (or the propensity score) that are averaged over the distribution of these covariates (or the propensity score) Besides these general bounds, we derive bounds under additional (weak) assumptions like monotone treatment response and positively correlated outcomes. In the application to a job–bonus experiment considered in this paper, labor supply and search models predict that being eligible for a bonus if a job is found, increases the hazard rate from unemployment to employment. According to these models there is a positive effect only during the eligibility period, and the effect increases shortly before the end of the eligibility period.
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