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A Permutation Test for the Regression Kink Design

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  • Peter Ganong
  • Simon Jäger

Abstract

The regression kink (RK) design is an increasingly popular empirical method for estimating causal effects of policies, such as the effect of unemployment benefits on unemployment duration. Using simulation studies based on data from existing RK designs, we empirically document that the statistical significance of RK estimators based on conventional standard errors can be spurious. In the simulations, false positives arise as a consequence of nonlinearities in the underlying relationship between the outcome and the assignment variable, confirming concerns about the misspecification bias of discontinuity estimators pointed out by Calonico, Cattaneo, and Titiunik. As a complement to standard RK inference, we propose that researchers construct a distribution of placebo estimates in regions with and without a policy kink and use this distribution to gauge statistical significance. Under the assumption that the location of the kink point is random, this permutation test has exact size in finite samples for testing a sharp null hypothesis of no effect of the policy on the outcome. We implement simulation studies based on existing RK applications that estimate the effect of unemployment benefits on unemployment duration and show that our permutation test as well as inference procedures proposed by Calonico, Cattaneo, and Titiunik improve upon the size of standard approaches, while having sufficient power to detect an effect of unemployment benefits on unemployment duration. Supplementary materials for this article are available online.

Suggested Citation

  • 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.
  • Handle: RePEc:taf:jnlasa:v:113:y:2018:i:522:p:494-504
    DOI: 10.1080/01621459.2017.1328356
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    References listed on IDEAS

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    3. 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.
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    Cited by:

    1. Huber, Martin, 2019. "An introduction to flexible methods for policy evaluation," FSES Working Papers 504, Faculty of Economics and Social Sciences, University of Freiburg/Fribourg Switzerland.
    2. Ivan A. Canay & Vishal Kamat, 2015. "Approximate permutation tests and induced order statistics in the regression discontinuity design," CeMMAP working papers CWP27/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    3. 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.
    4. Yoici Arai & Taisuke Otsu & Myung Hwan Seo, 2019. "Causal inference on regression discontinuity designs by high-dimensional methods," STICERD - Econometrics Paper Series 601, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    5. 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.
    6. repec:tsj:stataj:y:17:y:2017:i:3:p:630-651 is not listed on IDEAS
    7. Petri Bockerman & Ohto Kanninen & Ilpo Suoniemi, 2014. "A Kink that Makes you Sick: the Effect of Sick Pay on Absence in a Social Insurance System," Discussion Papers 97, Aboa Centre for Economics.
    8. repec:spr:empeco:v:53:y:2017:i:3:d:10.1007_s00181-016-1155-8 is not listed on IDEAS
    9. 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.
    10. Michihito Ando, 2017. "How much should we trust regression-kink-design estimates?," Empirical Economics, Springer, vol. 53(3), pages 1287-1322, November.

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