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Nonlinear Policy Rules and the Identification and Estimation of Causal Effects in a Generalized Regression Kink Design
Card, David
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Lee, David
;
Pei, Zhuan
;
Weber, Andrea
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URL:
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http://www.nber.org/papers/w18564.pdf
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Document Type:
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Working paper
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Year of publication:
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2012
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The title of a journal, publication series:
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NBER Working Paper
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Volume:
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18564
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Place of publication:
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Cambridge, Mass.
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Publication language:
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English
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Institution:
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School of Law and Economics > VWL, Angewandte Politische Ökonomie (Weber, A. 2010-2016)
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Subject:
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330 Economics
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Abstract:
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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
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