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

  • David Card
  • David Lee
  • Zhuan Pei
  • Andrea Weber

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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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 18564.

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Date of creation: Nov 2012
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Handle: RePEc:nbr:nberwo:18564
Note: LS
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  1. Guido Imbens & Karthik Kalyanaraman, 2010. "Optimal bandwidth choice for the regression discontinuity estimator," CeMMAP working papers CWP05/10, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  2. Lawrence Katz & Bruce Meyer, 1988. "The Impact of the Potential Duration of Unemployment Benefits on the Duration of Unemployment," Working Papers 621, Princeton University, Department of Economics, Industrial Relations Section..
  3. Marianne Simonsen & Lars Skipper & Niels Skipper, 2010. "Price Sensitivity of Demand for Prescription Drugs: Exploiting a Regression Kink Design," Economics Working Papers 2010-03, School of Economics and Management, University of Aarhus.
  4. J.P. Florensy & J. J. Heckmanz & C. Meghirx & E. Vytlacil, 2008. "Identification of Treatment Effects Using Control Functions in Models with Continuous, Endogenous Treatment and Heterogeneous Effects," Working Papers 200832, Geary Institute, University College Dublin.
  5. David Card & Raj Chetty & Andrea Weber, 2006. "Cash-on-Hand and Competing Models of Intertemporal Behavior: New Evidence from the Labor Market," NBER Working Papers 12639, National Bureau of Economic Research, Inc.
  6. Andrew Chesher, 2003. "Identification in Nonseparable Models," Econometrica, Econometric Society, vol. 71(5), pages 1405-1441, 09.
  7. Emilia Del Bono & Andrea Weber, 2008. "Do Wages Compensate for Anticipated Working Time Restrictions? Evidence from Seasonal Employment in Austria," Journal of Labor Economics, University of Chicago Press, vol. 26, pages 181-221.
  8. Jonathan Guryan, 2001. "Does Money Matter? Regression-Discontinuity Estimates from Education Finance Reform in Massachusetts," NBER Working Papers 8269, National Bureau of Economic Research, Inc.
  9. Han, Aaron K., 1987. "Non-parametric analysis of a generalized regression model : The maximum rank correlation estimator," Journal of Econometrics, Elsevier, vol. 35(2-3), pages 303-316, July.
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  11. Camille Landais, 2012. "Assessing the welfare effects of unemployment benefits using the regression kink design," LSE Research Online Documents on Economics 58025, London School of Economics and Political Science, LSE Library.
  12. Josef Zweimüller & Rudolf Winter-Ebmer & Rafael Lalive & Andreas Kuhn & Jean-Philippe Wuellrich & Oliver Ruf & Simon Büchi, 2009. "Austrian social security database," IEW - Working Papers 410, Institute for Empirical Research in Economics - University of Zurich.
    • Josef Zweimüller & Rudolf Winter-Ebmer & Rafael Lalive & Andreas Kuhn & Jean-Philippe Wuellrich & Oliver Ruf & Simon Büchi, 2009. "Austrian Social Security Database," NRN working papers 2009-03, The Austrian Center for Labor Economics and the Analysis of the Welfare State, Johannes Kepler University Linz, Austria.
  13. Imbens, Guido W & Angrist, Joshua D, 1994. "Identification and Estimation of Local Average Treatment Effects," Econometrica, Econometric Society, vol. 62(2), pages 467-75, March.
  14. Arthur Lewbel, 1998. "Semiparametric Latent Variable Model Estimation with Endogenous or Mismeasured Regressors," Econometrica, Econometric Society, vol. 66(1), pages 105-122, January.
  15. Moffitt, Robert, 1985. "Unemployment insurance and the distribution of unemployment spells," Journal of Econometrics, Elsevier, vol. 28(1), pages 85-101, April.
  16. Kroft, Kory, 2008. "Takeup, social multipliers and optimal social insurance," Journal of Public Economics, Elsevier, vol. 92(3-4), pages 722-737, April.
  17. Baily, Martin Neil, 1978. "Some aspects of optimal unemployment insurance," Journal of Public Economics, Elsevier, vol. 10(3), pages 379-402, December.
  18. Joseph G. Altonji & Rosa L. Matzkin, 2005. "Cross Section and Panel Data Estimators for Nonseparable Models with Endogenous Regressors," Econometrica, Econometric Society, vol. 73(4), pages 1053-1102, 07.
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