Regression Discontinuity Designs with a Continuous Treatment
65 Pages Posted: 8 May 2018 Last revised: 4 Nov 2020
Date Written: April 1, 2019
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.
Keywords: Distributional change, Treatment Quantile, Rank invariance, Rank similarity, Capital regulation
JEL Classification: C21, C25, I23
Suggested Citation: Suggested Citation