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A Permutation Test and Estimation Alternatives for the Regression Kink Design

Author

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  • Ganong, Peter

    () (Harvard University)

  • Jäger, Simon

    () (Massachusetts Institute of Technology)

Abstract

The Regression Kink (RK) design is an increasingly popular empirical method, with more than 20 studies circulated using RK in the last 5 years since the initial circulation of Card, Lee, Pei and Weber (2012). We document empirically that these estimates, which typically use local linear regression, are highly sensitive to curvature in the underlying relationship between the outcome and the assignment variable. As an alternative inference procedure, motivated by randomization inference, we propose that researchers construct a distribution of placebo estimates in regions without a policy kink. We apply our procedure to three empirical RK applications – two administrative UI datasets with true policy kinks and the 1980 Census, which has no policy kinks – and we find that statistical significance based on conventional p-values may be spurious. In contrast, our permutation test reinforces the asymptotic inference results of a recent Regression Discontinuity study and a Difference-in-Difference study. Finally, we propose estimating RK models with a modified cubic splines framework and test the performance of different estimators in a simulation exercise. Cubic specifications – in particular recently proposed robust estimators (Calonico, Cattaneo and Titiunik 2014) – yield short interval lengths with good coverage rates.

Suggested Citation

  • 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).
  • Handle: RePEc:iza:izadps:dp8282
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    Cited by:

    1. Jonas Kolsrud & Camille Landais & Peter Nilsson & Johannes Spinnewijn, 2018. "The Optimal Timing of Unemployment Benefits: Theory and Evidence from Sweden," American Economic Review, American Economic Association, vol. 108(4-5), pages 985-1033, April.
    2. David Card & David S. Lee & Zhuan Pei & Andrea Weber, 2015. "Inference on Causal Effects in a Generalized Regression Kink Design," Econometrica, Econometric Society, vol. 83, pages 2453-2483, November.
    3. Jonas Kolsrud & Camille Landais & Peter Nilsson & Johannes Spinnewijn, 2015. "The Optimal Timing of UI Benefits: Theory and Evidence from Sweden," CEP Discussion Papers dp1361, Centre for Economic Performance, LSE.
    4. David Card & Andrew Johnston & Pauline Leung & Alexandre Mas & Zhuan Pei, 2015. "The Effect of Unemployment Benefits on the Duration of Unemployment Insurance Receipt: New Evidence from a Regression Kink Design in Missouri, 2003-2013," American Economic Review, American Economic Association, vol. 105(5), pages 126-130, May.
    5. David Card & David S. Lee & Zhuan Pei & Andrea Weber, 2017. "Regression Kink Design: Theory and Practice," Advances in Econometrics,in: Regression Discontinuity Designs, volume 38, pages 341-382 Emerald Publishing Ltd.
    6. Camille Landais, 2015. "Assessing the Welfare Effects of Unemployment Benefits Using the Regression Kink Design," American Economic Journal: Economic Policy, American Economic Association, vol. 7(4), pages 243-278, November.
    7. Böckerman, Petri & Kanninen, Ohto & Suoniemi, Ilpo, 2014. "A Kink that Makes You Sick: the Effect of Sick Pay on Absence in a Social Insurance System," MPRA Paper 61010, University Library of Munich, Germany.
    8. George B. Bulman & Caroline M. Hoxby, 2015. "The Returns to the Federal Tax Credits for Higher Education," Tax Policy and the Economy, University of Chicago Press, vol. 29(1), pages 13-88.
    9. Alexander Gelber & Timothy J. Moore & Alexander Strand, 2017. "The Effect of Disability Insurance Payments on Beneficiaries' Earnings," American Economic Journal: Economic Policy, American Economic Association, vol. 9(3), pages 229-261, August.
    10. Therese C. Scharlemann & Stephen H. Shore, 2015. "The Effect of Negative Equity on Mortgage Default: Evidence from HAMP PRA," Working Papers 15-06, Office of Financial Research, US Department of the Treasury.
    11. D. G. C. Britto, 2016. "Unemployment Insurance and the Duration of Employment: Evidence from a Regression Kink Design," Working Papers wp1058, Dipartimento Scienze Economiche, Universita' di Bologna.

    More about this item

    Keywords

    randomization inference; placebo test; cubic splines;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • 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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