Regression Discontinuity Designs with a Continuous Treatment

65 Pages Posted: 8 May 2018 Last revised: 4 Nov 2020

See all articles by Yingying Dong

Yingying Dong

UC Irvine

Ying-Ying Lee

University of California, Irvine - Department of Economics

Michael Gou

University of California, Irvine

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

Dong, Yingying and Lee, Ying-Ying and Gou, Michael, Regression Discontinuity Designs with a Continuous Treatment (April 1, 2019). Available at SSRN: https://ssrn.com/abstract=3167541 or http://dx.doi.org/10.2139/ssrn.3167541

Yingying Dong (Contact Author)

UC Irvine ( email )

3151 Social Science Plaza
Irvine, CA 92617
United States

Ying-Ying Lee

University of California, Irvine - Department of Economics ( email )

3151 Social Science Plaza
Irvine, CA 92697-5100
United States

Michael Gou

University of California, Irvine ( email )

P.O. Box 19556
Science Library Serials
Irvine, CA California 62697-3125
United States

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