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

Author

Listed:
  • David E. Card
  • David S. Lee

    (Princeton University and NBER)

  • Zhuan Pei

    (W. E. Upjohn Institute for Employment Research, Kalamazoo, Michigan)

  • Andrea Weber

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

  • David E. Card & David S. Lee & Zhuan Pei & Andrea Weber, 2012. "Nonlinear Policy Rules and the Identification and Estimation of Causal Effects in a Generalized Regression Kink Design," NRN working papers 2012-14, The Austrian Center for Labor Economics and the Analysis of the Welfare State, Johannes Kepler University Linz, Austria.
  • Handle: RePEc:jku:nrnwps:2012_14
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    Regression Discountinuity Design; Regression Kink Design; Treatment Effects; Nonseparable Models; Nonparametric Estimation;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models

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