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

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  • David Card
  • David Lee
  • Zhuan Pei
  • 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.

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Bibliographic Info

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

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References

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  1. 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, Geary Institute, University College Dublin 200832, Geary Institute, University College Dublin.
  2. Han, Aaron K., 1987. "Non-parametric analysis of a generalized regression model : The maximum rank correlation estimator," Journal of Econometrics, Elsevier, Elsevier, vol. 35(2-3), pages 303-316, July.
  3. Lawrence F. Katz & Bruce D. Meyer, 1988. "The Impact of the Potential Duration of Unemployment Benefits on the Duration of Unemployment," NBER Working Papers 2741, National Bureau of Economic Research, Inc.
  4. Kroft, Kory, 2008. "Takeup, social multipliers and optimal social insurance," Journal of Public Economics, Elsevier, Elsevier, vol. 92(3-4), pages 722-737, April.
  5. Joseph G. Altonji & Rosa L. Matzkin, 2005. "Cross Section and Panel Data Estimators for Nonseparable Models with Endogenous Regressors," Econometrica, Econometric Society, Econometric Society, vol. 73(4), pages 1053-1102, 07.
  6. Moffitt, Robert, 1985. "Unemployment insurance and the distribution of unemployment spells," Journal of Econometrics, Elsevier, Elsevier, vol. 28(1), pages 85-101, April.
  7. Guido Imbens & Karthik Kalyanaraman, 2009. "Optimal Bandwidth Choice for the Regression Discontinuity Estimator," NBER Working Papers 14726, National Bureau of Economic Research, Inc.
  8. Joshua D. Angrist & Guido W. Imbens, 1995. "Identification and Estimation of Local Average Treatment Effects," NBER Technical Working Papers, National Bureau of Economic Research, Inc 0118, National Bureau of Economic Research, Inc.
  9. Marianne Simonsen & Lars Skipper & Niels Skipper, 2010. "Price Sensitivity of Demand for Prescription Drugs: Exploiting a Regression Kink Design," Economics Working Papers, School of Economics and Management, University of Aarhus 2010-03, School of Economics and Management, University of Aarhus.
  10. Del Bono, Emilia & Weber, Andrea, 2006. "Do wages compensate for anticipated working time restrictions? Evidence from seasonal employment in Austria," ISER Working Paper Series 2006-37, Institute for Social and Economic Research.
  11. Baily, Martin Neil, 1978. "Some aspects of optimal unemployment insurance," Journal of Public Economics, Elsevier, Elsevier, vol. 10(3), pages 379-402, December.
  12. Josef Zweimüller & Rudolf Winter-Ebmer & Rafael Lalive & Andreas Kuhn & Jean-Philippe Wuellrich & Oliver Ruf & Simon Büchi, 2009. "Austrian Social Security Database," NRN working papers, The Austrian Center for Labor Economics and the Analysis of the Welfare State, Johannes Kepler University Linz, Austria 2009-03, The Austrian Center for Labor Economics and the Analysis of the Welfare State, Johannes Kepler University Linz, Austria.
  13. Lee, David S., 2008. "Randomized experiments from non-random selection in U.S. House elections," Journal of Econometrics, Elsevier, Elsevier, vol. 142(2), pages 675-697, February.
  14. David Card & Raj Chetty & Andrea Weber, 2007. "Cash-On-Hand and Competing Models of Intertemporal Behavior: New Evidence from the Labor Market," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 122(4), pages 1511-1560, November.
  15. Arthur Lewbel, 1998. "Semiparametric Latent Variable Model Estimation with Endogenous or Mismeasured Regressors," Econometrica, Econometric Society, Econometric Society, vol. 66(1), pages 105-122, January.
  16. Landais, Camille, 2013. "Assessing the Welfare Effects of Unemployment Benefits Using the Regression Kink Design," IZA Discussion Papers 7589, Institute for the Study of Labor (IZA).
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Citations

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Cited by:
  1. Ando, Michihito, 2013. "How Much Should We Trust Regression-Kink-Design Estimates?," Working Paper Series, Uppsala University, Department of Economics 2013:22, Uppsala University, Department of Economics.
  2. Dayanand S. Manoli & Nicholas Turner, 2014. "Cash-on-Hand & College Enrollment: Evidence from Population Tax Data and Policy Nonlinearities," NBER Working Papers 19836, National Bureau of Economic Research, Inc.
  3. Landais, Camille, 2013. "Assessing the Welfare Effects of Unemployment Benefits Using the Regression Kink Design," IZA Discussion Papers 7589, Institute for the Study of Labor (IZA).
  4. Parag A. Pathak & Alvin E. Roth, 2013. "Matching with Couples: Stability and Incentives in Large Markets," The Quarterly Journal of Economics, Oxford University Press, vol. 128(4), pages 1585-1632.
  5. Lindo, Jason M. & Siminski, Peter & Yerokhin, Oleg, 2014. "Breaking the Link Between Legal Access to Alcohol and Motor Vehicle Accidents: Evidence from New South Wales," IZA Discussion Papers 7930, Institute for the Study of Labor (IZA).
  6. Arash Nekoei & Andrea Weber, 2014. "Does Extending Unemployment Benefits Improve Job Quality?," NRN working papers, The Austrian Center for Labor Economics and the Analysis of the Welfare State, Johannes Kepler University Linz, Austria 2014-04, The Austrian Center for Labor Economics and the Analysis of the Welfare State, Johannes Kepler University Linz, Austria.
  7. Clark, Damon & Del Bono, Emilia, 2014. "The long-run effects of attending an elite school: evidence from the UK," ISER Working Paper Series 2014-05, Institute for Social and Economic Research.
  8. Böckerman, Petri & Kanninen, Ohto & Suoniemi, Ilpo, 2014. "A Kink that Makes You Sick: The Incentive Effect of Sick Pay on Absence," IZA Discussion Papers 8205, Institute for the Study of Labor (IZA).
  9. Ganong, Peter & Jäger, Simon, 2014. "A Permutation Test and Estimation Alternatives for the Regression Kink Design," IZA Discussion Papers 8282, Institute for the Study of Labor (IZA).

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