Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/115092
Authors: 
Card, David E.
Lee, David S.
Pei, Zhuan
Weber, Andrea
Year of Publication: 
2012
Series/Report no.: 
NRN Working Paper, NRN: The Austrian Center for Labor Economics and the Analysis of the Welfare State 1214
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.
Subjects: 
Regression Discountinuity Design
Regression Kink Design
Treatment Effects
Nonseparable Models
Nonparametric Estimation
JEL: 
C13
C14
C31
Document Type: 
Working Paper

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