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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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    1. J. P. Florens & J. J. Heckman & C. Meghir & E. Vytlacil, 2008. "Identification of Treatment Effects Using Control Functions in Models With Continuous, Endogenous Treatment and Heterogeneous Effects," Econometrica, Econometric Society, vol. 76(5), pages 1191-1206, September.
    2. 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.
    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. Helena Skyt Nielsen & Torben Sørensen & Christopher Taber, 2010. "Estimating the Effect of Student Aid on College Enrollment: Evidence from a Government Grant Policy Reform," NBER Chapters, in: Income Taxation, Trans-Atlantic Public Economics Seminar (TAPES), pages 185-215, National Bureau of Economic Research, Inc.
    5. Sebastian Calonico & Matias D. Cattaneo & Rocio Titiunik, 2014. "Robust data-driven inference in the regression-discontinuity design," Stata Journal, StataCorp LP, vol. 14(4), pages 909-946, December.
    6. Raj Chetty & Adam Looney & Kory Kroft, 2009. "Salience and Taxation: Theory and Evidence," American Economic Review, American Economic Association, vol. 99(4), pages 1145-1177, September.
    7. Per Engström & Katarina Nordblom & Henry Ohlsson & Annika Persson, 2015. "Tax Compliance and Loss Aversion," American Economic Journal: Economic Policy, American Economic Association, vol. 7(4), pages 132-164, November.
    8. Sebastian Calonico & Matias D. Cattaneo & Rocio Titiunik, 2014. "Robust Nonparametric Confidence Intervals for Regression‐Discontinuity Designs," Econometrica, Econometric Society, vol. 82, pages 2295-2326, November.
    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.
    11. Rosenbaum P. R, 2001. "Stability in the Absence of Treatment," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 210-219, March.
    12. Jens Ludwig & Douglas L. Miller, 2007. "Does Head Start Improve Children's Life Chances? Evidence from a Regression Discontinuity Design," The Quarterly Journal of Economics, Oxford University Press, vol. 122(1), pages 159-208.
    13. Ho, Daniel E. & Imai, Kosuke, 2006. "Randomization Inference With Natural Experiments: An Analysis of Ballot Effects in the 2003 California Recall Election," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 888-900, September.
    14. Sebastian Calonico & Matias D. Cattaneo & Rocío Titiunik, 2015. "Optimal Data-Driven Regression Discontinuity Plots," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1753-1769, December.
    15. 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.
    16. Guido Imbens & Karthik Kalyanaraman, 2012. "Optimal Bandwidth Choice for the Regression Discontinuity Estimator," Review of Economic Studies, Oxford University Press, vol. 79(3), pages 933-959.
    17. Marianne Bertrand & Esther Duflo & Sendhil Mullainathan, 2004. "How Much Should We Trust Differences-In-Differences Estimates?," The Quarterly Journal of Economics, Oxford University Press, vol. 119(1), pages 249-275.
    18. Lee, David S., 2008. "Randomized experiments from non-random selection in U.S. House elections," Journal of Econometrics, Elsevier, vol. 142(2), pages 675-697, February.
    19. Imbens, Guido W. & Lemieux, Thomas, 2008. "Regression discontinuity designs: A guide to practice," Journal of Econometrics, Elsevier, vol. 142(2), pages 615-635, February.
    20. Andrew Gelman & Guido Imbens, 2019. "Why High-Order Polynomials Should Not Be Used in Regression Discontinuity Designs," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(3), pages 447-456, July.
    21. Alberto Abadie & Susan Athey & Guido W. Imbens & Jeffrey M. Wooldridge, 2014. "Finite Population Causal Standard Errors," NBER Working Papers 20325, National Bureau of Economic Research, Inc.
    22. Guido W. Imbens & Paul R. Rosenbaum, 2005. "Robust, accurate confidence intervals with a weak instrument: quarter of birth and education," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 168(1), pages 109-126, January.
    23. 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.
    24. Abadie, Alberto & Diamond, Alexis & Hainmueller, Jens, 2010. "Synthetic Control Methods for Comparative Case Studies: Estimating the Effect of California’s Tobacco Control Program," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 493-505.
    25. Imbens,Guido W. & Rubin,Donald B., 2015. "Causal Inference for Statistics, Social, and Biomedical Sciences," Cambridge Books, Cambridge University Press, number 9780521885881, May.
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