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

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.