Local Polynomial Order in Regression Discontinuity Designs

43 Pages Posted: 29 Jun 2020 Last revised: 8 Jun 2023

See all articles by Zhuan Pei

Zhuan Pei

Cornell University

David Lee

Princeton University

David Card

University of California, Berkeley - Department of Economics; Institute for the Study of Labor (IZA); National Bureau of Economic Research (NBER)

Andrea Weber

Central European University (CEU)

Date Written: June 2020

Abstract

Treatment effect estimates in regression discontinuity (RD) designs are often sensitive to the choice of bandwidth and polynomial order, the two important ingredients of widely used local regression methods. While Imbens and Kalyanaraman (2012) and Calonico, Cattaneo and Titiunik (2014) provide guidance on bandwidth, the sensitivity to polynomial order still poses a conundrum to RD practitioners. It is understood in the econometric literature that applying the argument of bias reduction does not help resolve this conundrum, since it would always lead to preferring higher orders. We therefore extend the frameworks of Imbens and Kalyanaraman (2012) and Calonico, Cattaneo and Titiunik (2014) and use the asymptotic mean squared error of the local regression RD estimator as the criterion to guide polynomial order selection. We show in Monte Carlo simulations that the proposed order selection procedure performs well, particularly in large sample sizes typically found in empirical RD applications. This procedure extends easily to fuzzy regression discontinuity and regression kink designs.

Suggested Citation

Pei, Zhuan and Lee, David and Card, David E. and Weber, Andrea, Local Polynomial Order in Regression Discontinuity Designs (June 2020). NBER Working Paper No. w27424, Available at SSRN: https://ssrn.com/abstract=3637725

Zhuan Pei (Contact Author)

Cornell University ( email )

Ithaca, NY 14853
United States

David Lee

Princeton University ( email )

22 Chambers Street
Princeton, NJ 08544-0708
United States

David E. Card

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

Room 3880
Berkeley, CA 94720-3880
United States
510-642-5222 (Phone)
510-643-7042 (Fax)

Institute for the Study of Labor (IZA)

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Germany

National Bureau of Economic Research (NBER)

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Cambridge, MA 02138
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Andrea Weber

Central European University (CEU) ( email )

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Budapest, H-1051
Hungary

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