Treatment Effects in the Regression Discontinuity Model with Counterfactual Cutoff and Distorted Running Variables

Abstract: We develop a new framework for evaluating the total policy effect in regression discontinuity designs (RDD), incorporating both the direct effect of treatment on outcomes and the indirect effect arising from distortions in the running variable when treatment becomes available. Our identification strategy combines a conditional parallel trend assumption to recover untreated potential outcomes with a local invariance assumption that characterizes how the running variable responds to counterfactual policy cutoffs. These components allow us to identify and estimate counterfactual treatment effects for any proposed threshold. We construct a nonparametric estimator for the total effect, derive its asymptotic distribution, and propose bootstrap inference procedures. Finally, we apply our framework to the Italian Domestic Stability Pact, where population-based fiscal rules generate both behavioral responses and running-variable distortions.