Bounds On Treatment Effects On Transitions

TL;DR

This paper derives bounds on long-term treatment effects on transition probabilities, showing that only instantaneous effects are point identified under randomization, and explores assumptions to tighten these bounds.

Contribution

It provides a method to bound long-term treatment effects on transitions without relying on parametric assumptions, extending the understanding of treatment effect identification.

Findings

Bounds on long-term treatment effects are derived.

Instantaneous effects are point identified under randomization.

Assumptions like monotonicity tighten the bounds.

Abstract

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 informative bounds on these average treatment effects. Our bounds do not impose (semi)parametric restrictions, for example, proportional hazards. We also explore various assumptions such as monotone treatment response, common shocks and positively correlated outcomes that tighten the bounds.