Causal Mediation in Natural Experiments

TL;DR

This paper introduces an instrumental variable approach to causal mediation analysis in natural experiments, allowing unbiased estimation of mediation effects even when the mediator is not randomly assigned, demonstrated through health insurance data.

Contribution

It proposes a novel method using instrumental variation to identify causal mediation effects despite unobserved selection bias.

Findings

Medicaid increased healthcare usage significantly.

A substantial part of health improvements was mediated through healthcare utilization.

Conventional methods would have misattributed the effects without this approach.

Abstract

Natural experiments are a cornerstone of applied economics, providing settings for estimating causal effects with a compelling argument for treatment randomisation, but give little indication of the mechanisms behind causal effects. Causal Mediation (CM) is a framework for sufficiently identifying a mechanism behind the treatment effect, decomposing it into an indirect effect channel through a mediator mechanism and a remaining direct effect. By contrast, a suggestive analysis of mechanisms gives necessary but not sufficient evidence. Conventional CM methods require that the relevant mediator mechanism is as-good-as-randomly assigned; when people choose the mediator based on costs and benefits (whether to visit a doctor, to attend university, etc.), this assumption fails and conventional CM analyses are at risk of bias. I propose an alternative strategy that delivers unbiased estimates of CM effects despite unobserved selection, using instrumental variation in mediator take-up costs. The method identifies CM effects via the marginal effect of the mediator, with parametric or semi-parametric estimation that is simple to implement in two stages. Applying these methods to the Oregon Health Insurance Experiment reveals a substantial portion of the Medicaid lottery's effect on subjective health and well-being flows through increased healthcare usage -- an effect that a conventional CM analysis would mistake. This approach gives applied researchers an alternative method to estimate CM effects when an initial treatment is quasi-randomly assigned, but a mediator mechanism is not, as is common in natural experiments.