Fuzzy Difference-in-Discontinuities: Identification Theory and Application to the Affordable Care Act

TL;DR

This paper develops a new fuzzy difference-in-discontinuities method for causal inference with multiple treatments at a cutoff, applies it to evaluate the ACA's impact on healthcare access, and discusses its assumptions and biases.

Contribution

It introduces a novel identification strategy for fuzzy RD with multiple treatments, addressing biases and proposing milder assumptions for causal effect estimation.

Findings

The simple fuzzy difference-in-discontinuities estimator can be biased if treatment probabilities differ.

Modified approaches relying on weaker assumptions are proposed to improve accuracy.

Application to ACA data reveals significant effects on healthcare access and utilization.

Abstract

This paper explores the use of a fuzzy regression discontinuity design where multiple treatments are applied at the threshold. The identification results show that, under the very strong assumption that the change in the probability of treatment at the cutoff is equal across treatments, a difference-in-discontinuities estimator identifies the treatment effect of interest. The point estimates of the treatment effect using a simple fuzzy difference-in-discontinuities design are biased if the change in the probability of a treatment applying at the cutoff differs across treatments. Modifications of the fuzzy difference-in-discontinuities approach that rely on milder assumptions are also proposed. Our results suggest caution is needed when applying before-and-after methods in the presence of fuzzy discontinuities. Using data from the National Health Interview Survey, we apply this new identification strategy to evaluate the causal effect of the Affordable Care Act (ACA) on older Americans' health care access and utilization.