This paper explores the use of fuzzy regression-discontinuity design in the context where multiple treatments are applied at the threshold. The identification result shows that, under a very strong assumption of equality of treatment probability changes at the cutoff point, a difference in fuzzy discontinuity identify a treatment effect of interest. Using the data from the National Health Interview Survey (NHIS) , we apply this  identification strategy to evaluate the causal effect of the Affordable Care Act (ACA) on  health care access and utilization of old Americans. We find results suggesting that the implementation of the Affordable Care Act has led to an increase in the hospitalization rate of elderly American--5\% more hospitalization. It has caused a minor increase of cost-related direct barrier to access to care--3.6\% increase in the probability of delaying care for cost reasons . The ACA has also exacerbated cost-related barriers to follow-up and continuity care -- 7\% more elderly couldn't afford prescriptions, 7\% more couldn't see a specialist and, 5.5\% more couldn't afford a follow-up visit -- as result of ACA
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 . Our results suggest that the ACA has (1) led to a 5\% increase in the hospitalization rate of elderly Americans, (2) increased the probability of delaying care for cost reasons by 3.6\%, and (3) exacerbated cost-related barriers to follow-up care and continuity of care: 7\% more elderly individuals could not afford prescriptions, 7\% more could not see a specialist , and 5.5\% more could not afford a follow-up visit . Our results can be explained by an increase in the demand for health services without a corresponding adjustment in supply following the implementation of the ACA.
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