Inference on Causal Effects in a Generalized Regression Kink Design

93 Pages Posted: 24 Jan 2015

See all articles by David Card

David Card

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

David Lee

Princeton University

Zhuan Pei

W.E. Upjohn Institute for Employment Research

Andrea Weber

Austrian Institute of Economic Research (WIFO); Vienna University of Economics and Business; Institute for the Study of Labor (IZA); CESifo (Center for Economic Studies and Ifo Institute)

Multiple version iconThere are 2 versions of this paper

Abstract

We consider nonparametric identification and estimation in a nonseparable model where a continuous regressor of interest is a known, deterministic, but kinked function of an observed assignment variable. This design arises in many institutional settings where a policy variable (such as weekly unemployment benefits) is determined by an observed but potentially endogenous assignment variable (like previous earnings). We provide new results on identification and estimation for these settings, and apply our results to obtain estimates of the elasticity of joblessness with respect to UI benefit rates. We characterize a broad class of models in which a sharp "Regression Kink Design" (RKD, or RK Design) identifies a readily interpretable treatment-on-the-treated parameter (Florens et al. (2008)). We also introduce a "fuzzy regression kink design" generalization that allows for omitted variables in the assignment rule, noncompliance, and certain types of measurement errors in the observed values of the assignment variable and the policy variable. Our identifying assumptions give rise to testable restrictions on the distributions of the assignment variable and predetermined covariates around the kink point, similar to the restrictions delivered by Lee (2008) for the regression discontinuity design. We then use a fuzzy RKD approach to study the effect of unemployment insurance benefits on the duration of joblessness in Austria, where the benefit schedule has kinks at the minimum and maximum benefit level. Our preferred estimates suggest that changes in UI benefit generosity exert a relatively large effect on the duration of joblessness of both low-wage and high-wage UI recipients in Austria.

Keywords: regression discontinuity design, regression kink design, treatment effects, nonseparable models, nonparametric estimation

JEL Classification: C13, C14, C31

Suggested Citation

Card, David E. and Lee, David and Pei, Zhuan and Weber, Andrea Michaela and Weber, Andrea Michaela, Inference on Causal Effects in a Generalized Regression Kink Design. IZA Discussion Paper No. 8757, Available at SSRN: https://ssrn.com/abstract=2554885 or http://dx.doi.org/10.2139/ssrn.2554885

David E. Card (Contact Author)

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)

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

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

David Lee

Princeton University ( email )

22 Chambers Street
Princeton, NJ 08544-0708
United States

Zhuan Pei

W.E. Upjohn Institute for Employment Research ( email )

300 South Westnedge Avenue
Kalamazoo, MI 49007-4686
United States

Andrea Michaela Weber

Austrian Institute of Economic Research (WIFO) ( email )

P.O. Box 91
Wien, A-1103
Austria

Vienna University of Economics and Business ( email )

Welthandelsplatz 1
Vienna, 1020
Austria

Institute for the Study of Labor (IZA)

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

CESifo (Center for Economic Studies and Ifo Institute)

Poschinger Str. 5
Munich, DE-81679
Germany

Do you have negative results from your research you’d like to share?

Paper statistics

Downloads
46
Abstract Views
737
PlumX Metrics