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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 causal inference. Analogous to the Regression Discontinuity design, which evaluates discontinuous changes in the level of an outcome variable with respect to the running variable at a point at which the level of a policy changes, the RK design evaluates discontinuous changes in the slope of an outcome variable with respect to the running variable at a kink point at which the slope of a policy with respect to the running variable changes. We document empirically that RK estimates are highly sensitive to nonlinearity in the underlying relationship between the outcome and the assignment variable. As an alternative to standard 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. In simulation studies with policy kinks, we find that statistical significance based on conventional standard errors may be spurious. In contrast, our permutation test has exact size even in the presence of non-linearity.

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  • Peter Ganong & Simon Jäger, 2015. "A Permutation Test for the Regression Kink Design," Working Paper 174531, Harvard University OpenScholar.
  • Handle: RePEc:qsh:wpaper:174531
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    File URL: http://scholar.harvard.edu/jaeger/node/174531
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    1. Erik Hurst & Benjamin Wild Pugsley, 2011. "What Do Small Businesses Do?," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 42(2 (Fall)), pages 73-142.
    2. Miguel Jaramillo, 2013. "Is there demand for formality among informal firms? Evidence from microfirms in downtown Lima," Avances de Investigación 0013, Grupo de Análisis para el Desarrollo (GRADE).
    3. Suresh de Mel & David McKenzie & Christopher Woodruff, 2013. "The Demand for, and Consequences of, Formalization among Informal Firms in Sri Lanka," American Economic Journal: Applied Economics, American Economic Association, vol. 5(2), pages 122-150, April.
    4. Rauch, James E., 1991. "Modelling the informal sector formally," Journal of Development Economics, Elsevier, vol. 35(1), pages 33-47, January.
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    Cited by:

    1. repec:spr:empeco:v:53:y:2017:i:3:d:10.1007_s00181-016-1155-8 is not listed on IDEAS
    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. 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. Michihito Ando, 2017. "How much should we trust regression-kink-design estimates?," Empirical Economics, Springer, pages 1287-1322.
    6. 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.
    7. 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, pages 13-88.
    8. repec:tsj:stataj:y:17:y:2017:i:3:p:630-651 is not listed on IDEAS

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