Association for Public Policy Analysis & Management

Conventional estimates of causal effects from regression discontinuity designs (RDDs) apply only to the cutoff value of the forcing variable. Several methods have recently been proposed for generalizing RDDs to estimate impacts away from the cutoff by imposing stronger assumptions on the distribution of potential outcomes, obtaining greater external validity by accepting additional threats to internal validity. We focus on three methods in which the key assumptions are that (1) potential outcomes are unrelated to the forcing variable after conditioning on covariates (Angrist and Rokkanen 2014); (2) potential untreated outcomes have the same degree of association with the forcing variable in a completely untreated comparison group as in the group subject to the cutoff rule (Tang, Cook, and Kisbu-Sakarya 2015); or (3) potential outcomes are unrelated to noncompliance with assignment status after conditioning on the forcing variable (Battistin and Rettore 2008; Bertanha and Imbens 2014). In this paper, we compare and contrast the three methods with respect to the theoretical conditions under which they are expected to succeed in identifying causal effects away from the cutoff. We then present empirical evidence on the degree to which estimates from each method approximate estimated impacts obtained from random assignment along the full support of the forcing variable.