Regression Discontinuity Designs with a Continuous Treatment

The standard regression discontinuity (RD) design deals with a binary treatment. Manyempirical applications of RD designs involve continuous treatments. This paper establishesidentification and robust bias-corrected inference for such RD design. Causal identificationis achieved by utilizing any changes in the distribution of the continuous treatment at the RDthreshold (including the usual mean change as a special case). Our robust estimand incorporatesthe standard RD estimand as a special case. Applying the proposed approach, we estimatethe impacts of capital holdings on bank failure in the pre-Great Depression era in the UnitedStates. Our RD design takes advantage of the minimum capital requirements, which changediscontinuously with town size