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Jumpy or Kinky? Regression Discontinuity without the Discontinuity

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  • Dong, Yingying

Abstract

Regression Discontinuity (RD) models identify local treatment effects by associating a discrete change in an outcome with a corresponding discrete change in the probability of treatment at a known threshold of a running variable. This paper shows that it is possible to identify RD model treatment effects without a discontinuity. The intuition is that identification can come from a slope change (a kink) instead of a discrete level change (a jump) in the treatment probability. Formally this can be shown using L'hopital's rule. I also interpret the identification results intuitively using instrumental variable models. Estimators are proposed that can be applied in the presence or absence of a discontinuity, by exploiting either a jump or a kink.

Suggested Citation

  • Dong, Yingying, 2010. "Jumpy or Kinky? Regression Discontinuity without the Discontinuity," MPRA Paper 25427, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:25427
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    References listed on IDEAS

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    1. Pedro Carneiro & James J. Heckman & Edward Vytlacil, 2010. "Evaluating Marginal Policy Changes and the Average Effect of Treatment for Individuals at the Margin," Econometrica, Econometric Society, vol. 78(1), pages 377-394, January.
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    4. Hahn, Jinyong & Todd, Petra & Van der Klaauw, Wilbert, 2001. "Identification and Estimation of Treatment Effects with a Regression-Discontinuity Design," Econometrica, Econometric Society, vol. 69(1), pages 201-209, January.
    5. James J. Heckman, 2010. "Building Bridges between Structural and Program Evaluation Approaches to Evaluating Policy," Journal of Economic Literature, American Economic Association, vol. 48(2), pages 356-398, June.
    6. Guido W. Imbens & Jeffrey M. Wooldridge, 2009. "Recent Developments in the Econometrics of Program Evaluation," Journal of Economic Literature, American Economic Association, vol. 47(1), pages 5-86, March.
    7. 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.
    8. David S. Lee & Thomas Lemieux, 2010. "Regression Discontinuity Designs in Economics," Journal of Economic Literature, American Economic Association, vol. 48(2), pages 281-355, June.
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    Citations

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    Cited by:

    1. Richard Murphy & Gill Wyness, 2023. "Testing Means-Tested Aid," Journal of Labor Economics, University of Chicago Press, vol. 41(3), pages 687-727.
    2. Engels, Barbara & Geyer, Johannes & Haan, Peter, 2017. "Pension incentives and early retirement," Labour Economics, Elsevier, vol. 47(C), pages 216-231.
    3. 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.
    4. 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).
    5. Jaeger, Simon C & Ganong, Peter Nathan, 2014. "A Permutation Test and Estimation Alternatives for the Regression Kink Design," Scholarly Articles 34222894, Harvard University Department of Economics.
    6. Yingying Dong & Arthur Lewbel, 2011. "Regression Discontinuity Marginal Threshold Treatment Effects," Working Papers 111205, University of California-Irvine, Department of Economics.

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    More about this item

    Keywords

    Regression Discontinuity; Fuzzy design; Average treatment effect; Identification; Jump; Kink; Threshold;
    All these keywords.

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities

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