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Inference on Causal Effects in a Generalized Regression Kink Design

Author

Listed:
  • David Card

    (UC Berkeley, NBER, and IZA)

  • Zhuan Pei

    () (Brandeis University)

  • David S. Lee

    (Princeton University and NBER)

  • Andrea Weber

    (University of Mannheim and IZA)

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 sharp “Regression Kink Design” (RKD, or RK Design) identifies a readily interpretable treatment-on-the-treated parameter (Florens et al. (2008)). We also introduce a “fuzzy regression kink design” generalization that allows for omitted variables in the assignment rule, noncompliance, and certain types of measurement errors in the observed values of the assignment variable and the policy variable. Our identifying assumptions give rise to testable restrictions on the distributions of the assignment variable and predetermined covariates around the kink point, similar to the restrictions delivered by Lee (2008) for the regression discontinuity design. 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 preferred estimates suggest that changes in UI benefit generosity exert a relatively large effect on the duration of joblessness of both low-wage and high-wage UI recipients in Austria.Length: 91 pages

Suggested Citation

  • David Card & Zhuan Pei & David S. Lee & Andrea Weber, 2014. "Inference on Causal Effects in a Generalized Regression Kink Design," Working Papers 83, Brandeis University, Department of Economics and International Businesss School, revised Jan 2015.
  • Handle: RePEc:brd:wpaper:83
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    File URL: http://www.brandeis.edu/economics/RePEc/brd/doc/Brandeis_WP83R.pdf
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    References listed on IDEAS

    as
    1. Bent Jesper Christensen & Rasmus Lentz & Dale T. Mortensen & George R. Neumann & Axel Werwatz, 2005. "On-the-Job Search and the Wage Distribution," Journal of Labor Economics, University of Chicago Press, vol. 23(1), pages 31-58, January.
    2. Dahlberg, Matz & Mörk, Eva & Rattsø, Jørn & Ågren, Hanna, 2008. "Using a discontinuous grant rule to identify the effect of grants on local taxes and spending," Journal of Public Economics, Elsevier, vol. 92(12), pages 2320-2335, December.
    3. Arie Kapteyn & Jelmer Y. Ypma, 2007. "Measurement Error and Misclassification: A Comparison of Survey and Administrative Data," Journal of Labor Economics, University of Chicago Press, vol. 25, pages 513-551.
    4. Rafael Lalive & Jan Van Ours & Josef Zweimuller, 2006. "How Changes in Financial Incentives Affect the Duration of Unemployment," Review of Economic Studies, Oxford University Press, vol. 73(4), pages 1009-1038.
    5. 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.
    6. David Card & David Lee & Zhuan Pei & Andrea Weber, 2012. "Nonlinear Policy Rules and the Identification and Estimation of Causal Effects in a Generalized Regression Kink Design," NBER Working Papers 18564, National Bureau of Economic Research, Inc.
    7. David Card & Zhuan Pei & David S. Lee & Andrea Weber, 2014. "Local Polynomial Order in Regression Discontinuity Designs," Working Papers 81, Brandeis University, Department of Economics and International Businesss School.
    8. Ganong, Peter & Jäger, Simon, 2014. "A Permutation Test and Estimation Alternatives for the Regression Kink Design," IZA Discussion Papers 8282, Institute of Labor Economics (IZA).
    9. Michihito Ando, 2017. "How much should we trust regression-kink-design estimates?," Empirical Economics, Springer, vol. 53(3), pages 1287-1322, November.
    10. repec:taf:jnlasa:v:113:y:2018:i:522:p:494-504 is not listed on IDEAS
    11. 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, July.
    12. Peter Ganong & Simon Jäger, 2018. "A Permutation Test for the Regression Kink Design," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 494-504, April.
    13. Edward Vytlacil, 2002. "Independence, Monotonicity, and Latent Index Models: An Equivalence Result," Econometrica, Econometric Society, vol. 70(1), pages 331-341, January.
    14. repec:hrv:faseco:34222894 is not listed on IDEAS
    15. Philippe Robert-Demontrond & R. Ringoot, 2004. "Introduction," Post-Print halshs-00081823, HAL.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Regression Discontinuity Design; Regression Kink Design; Treatment Effects; nonseparable Models; Nonparametric Estimation;

    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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