[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/a/sae/evarev/v47y2023i2p182-208.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.1177/0193841X221105968
    Download Restriction: no
    File URL: https://libkey.io/10.1177/0193841X221105968?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Choi, Jin-young & Lee, Myoung-jae, 2023. "Complier and monotonicity for Fuzzy Multi-score Regression Discontinuity with partial effects," Economics Letters, Elsevier, vol. 228(C).
    2. Matias D. Cattaneo & Rocío Titiunik, 2022. "Regression Discontinuity Designs," Annual Review of Economics, Annual Reviews, vol. 14(1), pages 821-851, August.
    3. Jin-young Choi & Myoung-jae Lee, 2017. "Regression discontinuity: review with extensions," Statistical Papers, Springer, vol. 58(4), pages 1217-1246, December.
    4. Giuseppe Francesco Gori & Patrizia Lattarulo & Marco Mariani, 2021. "The Expediting Effect of Monitoring on Infrastructural Works. A Regression-Discontinuity Approach with Multiple Assignment Variables," Papers 2102.09625, arXiv.org.
    5. Blaise Melly & Rafael Lalive, 2020. "Estimation, Inference, and Interpretation in the Regression Discontinuity Design," Diskussionsschriften dp2016, Universitaet Bern, Departement Volkswirtschaft.
    6. Carolina Caetano & Gregorio Caetano & Juan Carlos Escanciano, 2023. "Regression discontinuity design with multivalued treatments," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(6), pages 840-856, September.
    7. 'Agoston Reguly, 2021. "Heterogeneous Treatment Effects in Regression Discontinuity Designs," Papers 2106.11640, arXiv.org, revised Oct 2021.
    8. Carolina Caetano & Gregorio Caetano & Juan Carlos Escanciano, 2023. "Regression discontinuity design with multivalued treatments," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(6), pages 840-856, September.
    9. Yu-Chin Hsu & Chung-Ming Kuan & Giorgio Teng-Yu Lo, 2017. "Quantile Treatment Effects in Regression Discontinuity Designs with Covariates," IEAS Working Paper : academic research 17-A009, Institute of Economics, Academia Sinica, Taipei, Taiwan.
    10. Xu, Ke-Li, 2018. "A semi-nonparametric estimator of regression discontinuity design with discrete duration outcomes," Journal of Econometrics, Elsevier, vol. 206(1), pages 258-278.
    11. 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.
    12. Mauricio Villamizar‐Villegas & Freddy A. Pinzon‐Puerto & Maria Alejandra Ruiz‐Sanchez, 2022. "A comprehensive history of regression discontinuity designs: An empirical survey of the last 60 years," Journal of Economic Surveys, Wiley Blackwell, vol. 36(4), pages 1130-1178, September.
    13. Porter, Jack & Yu, Ping, 2015. "Regression discontinuity designs with unknown discontinuity points: Testing and estimation," Journal of Econometrics, Elsevier, vol. 189(1), pages 132-147.
    14. Myoung-Jae Lee & Hyae-Chong Shim & Sang Soo Park, 2023. "Regression Discontinuity with Integer Score and Non-Integer Cutoff," Korean Economic Review, Korean Economic Association, vol. 39, pages 73-101.
    15. Mohamed Ebeid & Umut Oguzoglu, 2023. "Short‐term effect of retirement on health: Evidence from nonparametric fuzzy regression discontinuity design," Health Economics, John Wiley & Sons, Ltd., vol. 32(6), pages 1323-1343, June.
    16. Guido Imbens & Stefan Wager, 2019. "Optimized Regression Discontinuity Designs," The Review of Economics and Statistics, MIT Press, vol. 101(2), pages 264-278, May.
    17. Dong, Yingying, 2010. "Jumpy or Kinky? Regression Discontinuity without the Discontinuity," MPRA Paper 25461, University Library of Munich, Germany.
    18. Sebastian Calonico & Matias D Cattaneo & Max H Farrell, 2020. "Optimal bandwidth choice for robust bias-corrected inference in regression discontinuity designs," The Econometrics Journal, Royal Economic Society, vol. 23(2), pages 192-210.
    19. Gong, Jie & Lu, Yi & Xie, Huihua, 2020. "The average and distributional effects of teenage adversity on long-term health," Journal of Health Economics, Elsevier, vol. 71(C).
    20. Hong Kai, 2017. "School Bond Referendum, Capital Expenditure, and Student Achievement," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 17(4), pages 1-26, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:sae:evarev:v:47:y:2023:i:2:p:182-208. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: SAGE Publications (email available below). General contact details of provider: .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.