Identifying average causal effect in regression discontinuity design with auxiliary data

Abstract: Regression discontinuity designs are widely used when treatment assignment is determined by whether a running variable exceeds a predefined threshold. However, most research focuses on estimating local causal effects at the threshold, leaving the challenge of identifying treatment effects away from the cutoff largely unaddressed. The primary difficulty in this context is that the treatment assignment is deterministically defined by the running variable, violating the commonly assumed positivity assumption. In this paper, we introduce a novel framework for identifying the average causal effect in regression discontinuity designs. Our approach assumes the existence of an auxiliary variable for which the running variable can be seen as a surrogate, and an additional dataset that consists of the running variable and the auxiliary variable alongside the traditional regression discontinuity design setup. Under this framework, we propose three estimation methods for the ATE, which resembles the outcome regression, inverse propensity weighted and doubly robust estimators in classical causal inference literature. Asymptotically valid inference procedures are also provided. To demonstrate the practical application of our method, simulations are conducted to show the good performance of our methods; besides, we use the proposed methods to assess the causal effects of vitamin A supplementation on the severity of autism spectrum disorders in children, where a positive effect is found but with no statistical significance.