Isotonic Regression Discontinuity Designs

52 Pages Posted: 2 Oct 2019 Last revised: 18 Mar 2021

See all articles by Andrii Babii

Andrii Babii

University of North Carolina at Chapel Hill

Rohit Kumar

Indian Statistical Institute, Kolkata

Date Written: August 15, 2019


This paper studies the estimation and inference for the isotonic regression at the boundary point, an object that is particularly interesting and required in the analysis of monotone regression discontinuity designs. We show that the isotonic regression is inconsistent in this setting and derive the asymptotic distributions of boundary corrected estimators. Interestingly, the boundary corrected estimators can be bootstrapped without subsampling or additional nonparametric smoothing which is not the case for the interior point. The Monte Carlo experiments indicate that shape restrictions can improve dramatically the finite-sample performance of unrestricted estimators. Lastly, we apply the isotonic regression discontinuity designs to estimate the causal effect of incumbency in the U.S. House elections.

Keywords: regression discontinuity designs, shape constraints, monotonicity, isotonic regression, boundary point, wild bootstrap

JEL Classification: C14, C31

Suggested Citation

Babii, Andrii and Kumar, Rohit, Isotonic Regression Discontinuity Designs (August 15, 2019). Journal of Econometrics, Forthcoming, Available at SSRN: or

Andrii Babii (Contact Author)

University of North Carolina at Chapel Hill ( email )

Gardner Hall, CB 3305
Chapel Hill, NC 27514
United States

Rohit Kumar

Indian Statistical Institute, Kolkata ( email )

203 B.T. Road
Kolkata, West Bengal 700108

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