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Identifying the Effect of Changing the Policy Threshold in Regression Discontinuity Models

Author

Listed:
  • Yingying Dong

    () (University of California Irvine)

  • Arthur Lewbel

    () (Boston College)

Abstract

Regression discontinuity models are commonly used to nonparametrically identify and estimate a local average treatment effect (LATE).We show that the derivative of the treatment effect with respect to the running variable at the cutoff, referred to as the treatment effect derivative (TED), is nonparametrically identified, easily estimated, and has implications for testing external validity and extrapolating the estimated LATE away from the cutoff. Given a local policy invariance assumption, we further show this TED equals the change in the treatment effect that would result from a marginal change in the threshold, which we call the marginal threshold treatment effect (MTTE). We apply these results to Goodman (2008), who estimates the effect of a scholarship program on college choice. MTTE in this case identifies how this treatment effect would change if the test score threshold to qualify for a scholarship were changed, even though no such change in threshold is actually observed.

Suggested Citation

  • Yingying Dong & Arthur Lewbel, 2015. "Identifying the Effect of Changing the Policy Threshold in Regression Discontinuity Models," The Review of Economics and Statistics, MIT Press, vol. 97(5), pages 1081-1092, December.
  • Handle: RePEc:tpr:restat:v:97:y:2015:i:5:p:1081-1092
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    Cited by:

    1. Dong, Yingying, 2010. "Jumpy or Kinky? Regression Discontinuity without the Discontinuity," MPRA Paper 25461, University Library of Munich, Germany.
    2. Sebastian Galiani & Patrick J. McEwan & Brian Quistorff, 2017. "External and Internal Validity of a Geographic Quasi-Experiment Embedded in a Cluster-Randomized Experiment," Advances in Econometrics,in: Regression Discontinuity Designs, volume 38, pages 195-236 Emerald Publishing Ltd.
    3. YANAGI, Takahide, 2015. "Regression Discontinuity Designs with Nonclassical Measurement Error," Discussion Papers 2015-09, Graduate School of Economics, Hitotsubashi University.
    4. David Pence Slichter, 2015. "The Employment Effects of the Minimum Wage: A Selection Ratio Approach to Measuring Treatment Effects," 2015 Papers psl76, Job Market Papers.
    5. Yingying Dong, 2012. "Regression Discontinuity Applications with Rounding Errors in the Running Variable," Working Papers 111206, University of California-Irvine, Department of Economics.
    6. Nirav Mehta, 2015. "An Economic Approach to Generalize Findings from Regression-Discontinuity Designs," University of Western Ontario, Centre for Human Capital and Productivity (CHCP) Working Papers 20156, University of Western Ontario, Centre for Human Capital and Productivity (CHCP).
    7. BARGAIN Olivier & DOORLEY Karina, 2016. "The Effect of Social Benefits on Youth Employment: Combining RD and a Behavioral Model," LISER Working Paper Series 2016-12, LISER.
    8. Bertanha, Marinho Angelo & Moreira, Marcelo J., 2017. "Impossible inference in econometrics: theory and applications to regression discontinuity, bunching, and exogeneity tests," FGV/EPGE Economics Working Papers (Ensaios Economicos da EPGE) 787, FGV/EPGE - Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
    9. Susan Athey & Guido W. Imbens, 2017. "The State of Applied Econometrics: Causality and Policy Evaluation," Journal of Economic Perspectives, American Economic Association, vol. 31(2), pages 3-32, Spring.
    10. Marinho Bertanha & Guido W. Imbens, 2014. "External Validity in Fuzzy Regression Discontinuity Designs," NBER Working Papers 20773, National Bureau of Economic Research, Inc.
    11. Matias D. Cattaneo & Luke Keele & Rocio Titiunik & Gonzalo Vazquez-Bare, 2018. "Extrapolating Treatment Effects in Multi-Cutoff Regression Discontinuity Designs," Papers 1808.04416, arXiv.org.
    12. Jane Cooley Fruehwirth & Salvador Navarro & Yuya Takahashi, 2016. "How the Timing of Grade Retention Affects Outcomes: Identification and Estimation of Time-Varying Treatment Effects," Journal of Labor Economics, University of Chicago Press, vol. 34(4), pages 979-1021.
    13. Joshua Angrist & Miikka Rokkanen, 2012. "Wanna Get Away? RD Identification Away from the Cutoff," NBER Working Papers 18662, National Bureau of Economic Research, Inc.
    14. Booij, Adam S. & Haan, Ferry & Plug, Erik, 2017. "Can Gifted and Talented Education Raise the Academic Achievement of All High-Achieving Students?," IZA Discussion Papers 10836, Institute for the Study of Labor (IZA).

    More about this item

    Keywords

    regression discontinuity; sharp design; fuzzy design; treatment effects; program evaluation; threshold; running variable; forcing variable; marginal effects; external validity;

    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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