Regression Discontinuity Designs with a Continuous Treatment

Abstract

The standard regression discontinuity (RD) design deals with a binary treatment. Many empirical applications of RD designs involve continuous treatments. This paper establishes identification and robust bias-corrected inference for such RD design. Causal identification is achieved by utilizing any changes in the distribution of the continuous treatment at the RD threshold (including the usual mean change as a special case). Our robust estimand incorporates the standard RD estimand as a special case. Applying the proposed approach, we estimate the impacts of capital holdings on bank failure in the pre-Great Depression era in the United States. Our RD design takes advantage of the minimum capital requirements, which change discontinuously with town size.