Causal Mediation in Natural Experiments

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) provides a framework to analyse mechanisms by identifying the average direct and indirect effects (CM effects), yet conventional CM methods require the relevant mediator 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 a control function strategy that uses instrumental variation in mediator take-up costs, delivering unbiased direct and indirect effects when selection is driven by unobserved gains. 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 self-reported health and happiness 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 the mediator is not, as is common in natural experiments.