A Permutation Test and Estimation Alternatives for the Regression Kink Design

35 Pages Posted: 5 Jul 2014

See all articles by Peter Ganong

Peter Ganong

University of Chicago

Simon Jäger

Massachusetts Institute of Technology (MIT); CESifo (Center for Economic Studies and Ifo Institute); IZA Institute of Labor Economics; briq- Institute on Behavior & Inequality

Abstract

The Regression Kink (RK) design is an increasingly popular empirical method, with more than 20 studies circulated using RK in the last 5 years since the initial circulation of Card, Lee, Pei and Weber (2012). We document empirically that these estimates, which typically use local linear regression, are highly sensitive to curvature in the underlying relationship between the outcome and the assignment variable. As an alternative inference procedure, motivated by randomization inference, we propose that researchers construct a distribution of placebo estimates in regions without a policy kink. We apply our procedure to three empirical RK applications – two administrative UI datasets with true policy kinks and the 1980 Census, which has no policy kinks – and we find that statistical significance based on conventional p-values may be spurious. In contrast, our permutation test reinforces the asymptotic inference results of a recent Regression Discontinuity study and a Difference-in-Difference study. Finally, we propose estimating RK models with a modified cubic splines framework and test the performance of different estimators in a simulation exercise. Cubic specifications – in particular recently proposed robust estimators (Calonico, Cattaneo and Titiunik 2014) – yield short interval lengths with good coverage rates.

Keywords: randomization inference, placebo test, cubic splines

JEL Classification: C12, C13, C14, C31

Suggested Citation

Ganong, Peter and Jäger, Simon, A Permutation Test and Estimation Alternatives for the Regression Kink Design. IZA Discussion Paper No. 8282. Available at SSRN: https://ssrn.com/abstract=2462714

Peter Ganong (Contact Author)

University of Chicago ( email )

1101 East 58th Street
Chicago, IL 60637
United States

Simon Jäger

Massachusetts Institute of Technology (MIT) ( email )

77 Massachusetts Avenue
50 Memorial Drive
Cambridge, MA 02139-4307
United States

CESifo (Center for Economic Studies and Ifo Institute)

Poschinger Str. 5
Munich, DE-81679
Germany

IZA Institute of Labor Economics

P.O. Box 7240
Bonn, D-53072
Germany

briq- Institute on Behavior & Inequality ( email )

Schaumburg-Lippe-Straße 5-9
Bonn, 53113
Germany

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