Regression discontinuity designs (RDD) identify causal effects of interventions by exploiting treatment assignment mechanisms that are discontinuous functions of observed covariates. In standard RDDs, the probability of treatment changes discontinuously if a covariate exceeds a threshold. We consider a more complex RDD setup where the treatment is determined by both a covariate and an application status. In particular, we focus on a fuzzy RDD with this setup, where the causal estimand and estimation strategies are different from those in the standard instrumental variable approach to fuzzy RDDs. A Bayesian approach is developed for drawing inferences of the causal effect and multivariate outcomes are utilized to sharpen the analysis.
The method is applied to evaluate the effects of Italian university grant on student dropout and academic performances. Sensitivity analysis to choices of key structural and model assumptions are also conducted. This is a joint work with Alessandra Mattei and Fabrizia Mealli.