Nonlinear Policy Rules and the Identification and Estimation of Causal Effects in a Generalized Regression Kink Design

97 Pages Posted: 22 Nov 2012

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

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

Date Written: November 2012

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 "Regression Kink Design" (RKD, or RK Design) provides valid inferences for the treatment-on-the-treated parameter (Florens et al. (2008)) that would be identified in an ideal randomized experiment. We show that the smooth density condition that is sufficient for identification rules out extreme sorting around the kink, but is compatible with less severe forms of endogeneity. It also places testable restrictions on the distribution of predetermined covariates around the kink point. We introduce a generalization of the RKD - the "fuzzy regression kink design" - that allows for omitted variables in the assignment rule, as well as certain types of measurement errors in the observed values of the assignment variable and the policy variable. We also show how standard local polynomial regression techniques can be adapted to obtain nonparametric estimates for the sharp and fuzzy RKD. 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 estimates suggest that the elasticity of joblessness with respect to the benefit rate is on the order of 1.5.

Suggested Citation

Card, David E. and Lee, David and Pei, Zhuan and Weber, Andrea Michaela, Nonlinear Policy Rules and the Identification and Estimation of Causal Effects in a Generalized Regression Kink Design (November 2012). NBER Working Paper No. w18564. Available at SSRN: https://ssrn.com/abstract=2179402

David E. Card (Contact Author)

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

Room 3880
Berkeley, CA 94720-3880
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510-642-5222 (Phone)
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Institute for the Study of Labor (IZA)

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Germany

National Bureau of Economic Research (NBER)

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David Lee

Princeton University ( email )

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Zhuan Pei

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

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

Andrea Michaela Weber

Vienna University of Economics and Business ( email )

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Vienna, 1020
Austria

Austrian Institute of Economic Research (WIFO) ( email )

P.O. Box 91
Wien, A-1103
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

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