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Regression Discontinuity for Binary Response and Local Maximum Likelihood Estimator to Extrapolate Treatment

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  • Goeun Lee
  • Myoung-jae Lee

Abstract

Regression discontinuity is popular in finding treatment/policy effects when the treatment is determined by a continuous variable crossing a cutoff. Typically, a local linear regression (LLR) estimator is used to find the effects. For binary response, however, LLR is not suitable in extrapolating the treatment, as in doubling/tripling the treatment dose/intensity. The reason is that doubling/tripling the LLR estimate can give a number out of the bound [ − 1 ,  1 ] , despite that the effect should be a change in probability. We propose local maximum likelihood estimators which overcome these shortcomings, while giving almost the same estimates as the LLR estimator does for the original treatment. A simulation study and an empirical analysis for effects of an income subsidy program on religion demonstrate these points.

Suggested Citation

  • Goeun Lee & Myoung-jae Lee, 2023. "Regression Discontinuity for Binary Response and Local Maximum Likelihood Estimator to Extrapolate Treatment," Evaluation Review, , vol. 47(2), pages 182-208, April.
    • Handle: RePEc:sae:evarev:v:47:y:2023:i:2:p:182-208
    DOI: 10.1177/0193841X221105968
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    References listed on IDEAS

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    1. Choi, Jin-young & Lee, Myoung-jae, 2018. "Regression Discontinuity with Multiple Running Variables Allowing Partial Effects," Political Analysis, Cambridge University Press, vol. 26(3), pages 258-274, July.
    2. 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.
    3. Imbens, Guido W. & Lemieux, Thomas, 2008. "Regression discontinuity designs: A guide to practice," Journal of Econometrics, Elsevier, vol. 142(2), pages 615-635, February.
    4. David Card & David S. Lee & Zhuan Pei & Andrea Weber, 2017. "Regression Kink Design: Theory and Practice," Advances in Econometrics, in: Regression Discontinuity Designs, volume 38, pages 341-382, Emerald Group Publishing Limited.
    5. Jin-young Choi & Myoung-jae Lee, 2017. "Regression discontinuity: review with extensions," Statistical Papers, Springer, vol. 58(4), pages 1217-1246, December.
    6. Myoung-Jae Lee, 2012. "Semiparametric Estimators for Limited Dependent Variable (LDV) Models with Endogenous Regressors," Econometric Reviews, Taylor & Francis Journals, vol. 31(2), pages 171-214.
    7. Choi, Jin-young & Lee, Myoung-jae, 2018. "Relaxing conditions for local average treatment effect in fuzzy regression discontinuity," Economics Letters, Elsevier, vol. 173(C), pages 47-50.
    8. Steven F. Koch & Jeffrey S. Racine, 2016. "Healthcare facility choice and user fee abolition: regression discontinuity in a multinomial choice setting," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 179(4), pages 927-950, October.
    9. 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, President and Fellows of Harvard College, vol. 122(1), pages 159-208.
    10. Xu, Ke-Li, 2017. "Regression discontinuity with categorical outcomes," Journal of Econometrics, Elsevier, vol. 201(1), pages 1-18.
    11. Thomas Buser, 2015. "The Effect of Income on Religiousness," American Economic Journal: Applied Economics, American Economic Association, vol. 7(3), pages 178-195, July.
    12. Guido Imbens & Karthik Kalyanaraman, 2012. "Optimal Bandwidth Choice for the Regression Discontinuity Estimator," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 79(3), pages 933-959.
    13. Joshua D. Angrist & Miikka Rokkanen, 2015. "Wanna Get Away? Regression Discontinuity Estimation of Exam School Effects Away From the Cutoff," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1331-1344, December.
    14. Paul S. Clarke & Frank Windmeijer, 2012. "Instrumental Variable Estimators for Binary Outcomes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(500), pages 1638-1652, December.
    15. 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.
    16. Imbens, Guido W & Angrist, Joshua D, 1994. "Identification and Estimation of Local Average Treatment Effects," Econometrica, Econometric Society, vol. 62(2), pages 467-475, March.
    17. Choi, Jin-young & Lee, Myoung-jae, 2018. "Minimum distance estimator for sharp regression discontinuity with multiple running variables," Economics Letters, Elsevier, vol. 162(C), pages 10-14.
    18. 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.
    19. Matias D. Cattaneo & Nicolas Idrobo & Rocio Titiunik, 2019. "A Practical Introduction to Regression Discontinuity Designs: Foundations," Papers 1911.09511, arXiv.org.
    20. Lee, Myoung-jae, 2016. "Matching, Regression Discontinuity, Difference in Differences, and Beyond," OUP Catalogue, Oxford University Press, number 9780190258740.
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