IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v241y2024i1s0304407624000848.html
   My bibliography  Save this article

Testing identification conditions of LATE in fuzzy regression discontinuity designs

Author

Listed:
  • Hsu, Yu-Chin
  • Shiu, Ji-Liang
  • Wan, Yuanyuan

Abstract

This paper derives testable implications of the identifying conditions for the local average treatment effect in fuzzy regression discontinuity designs. We show that the testable implications of these identifying conditions are a finite number of inequality restrictions on the observed data distribution. We then propose a specification test for the testable implications and show that the proposed test controls the size and is asymptotically consistent. We apply our test to several fuzzy regression discontinuity designs in the literature.

Suggested Citation

  • Hsu, Yu-Chin & Shiu, Ji-Liang & Wan, Yuanyuan, 2024. "Testing identification conditions of LATE in fuzzy regression discontinuity designs," Journal of Econometrics, Elsevier, vol. 241(1).
    • Handle: RePEc:eee:econom:v:241:y:2024:i:1:s0304407624000848
    DOI: 10.1016/j.jeconom.2024.105738
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407624000848
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jeconom.2024.105738?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
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Erich Battistin & Agar Brugiavini & Enrico Rettore & Guglielmo Weber, 2009. "The Retirement Consumption Puzzle: Evidence from a Regression Discontinuity Approach," American Economic Review, American Economic Association, vol. 99(5), pages 2209-2226, December.
    2. Frandsen, Brigham R. & Frölich, Markus & Melly, Blaise, 2012. "Quantile treatment effects in the regression discontinuity design," Journal of Econometrics, Elsevier, vol. 168(2), pages 382-395.
    3. Donald W. K. Andrews & Xiaoxia Shi, 2013. "Inference Based on Conditional Moment Inequalities," Econometrica, Econometric Society, vol. 81(2), pages 609-666, March.
    4. Arai, Yoichi & Ichimura, Hidehiko, 2016. "Optimal bandwidth selection for the fuzzy regression discontinuity estimator," Economics Letters, Elsevier, vol. 141(C), pages 103-106.
    5. Bugni, Federico A. & Canay, Ivan A., 2021. "Testing continuity of a density via g-order statistics in the regression discontinuity design," Journal of Econometrics, Elsevier, vol. 221(1), pages 138-159.
    6. Ivan A Canay & Vishal Kamat, 2018. "Approximate Permutation Tests and Induced Order Statistics in the Regression Discontinuity Design," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 85(3), pages 1577-1608.
    7. 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.
    8. Bertanha, Marinho & Moreira, Marcelo J., 2020. "Impossible inference in econometrics: Theory and applications," Journal of Econometrics, Elsevier, vol. 218(2), pages 247-270.
    9. Matias D. Cattaneo & Michael Jansson & Xinwei Ma, 2020. "Simple Local Polynomial Density Estimators," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(531), pages 1449-1455, July.
    10. François Gerard & Miikka Rokkanen & Christoph Rothe, 2020. "Bounds on treatment effects in regression discontinuity designs with a manipulated running variable," Quantitative Economics, Econometric Society, vol. 11(3), pages 839-870, July.
    11. Yoichi Arai & Yu‐Chin Hsu & Toru Kitagawa & Ismael Mourifié & Yuanyuan Wan, 2022. "Testing identifying assumptions in fuzzy regression discontinuity designs," Quantitative Economics, Econometric Society, vol. 13(1), pages 1-28, January.
    12. Sebastian Calonico & Matias D. Cattaneo & Rocio Titiunik, 2014. "Robust Nonparametric Confidence Intervals for Regression‐Discontinuity Designs," Econometrica, Econometric Society, vol. 82, pages 2295-2326, November.
    13. Yingying Dong, 2018. "Alternative Assumptions to Identify LATE in Fuzzy Regression Discontinuity Designs," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 80(5), pages 1020-1027, October.
    14. Toru Kitagawa, 2015. "A Test for Instrument Validity," Econometrica, Econometric Society, vol. 83(5), pages 2043-2063, September.
    15. Müller, Tobias & Shaikh, Mujaheed, 2018. "Your retirement and my health behavior: Evidence on retirement externalities from a fuzzy regression discontinuity design," Journal of Health Economics, Elsevier, vol. 57(C), pages 45-59.
    16. Ismael Mourifié & Yuanyuan Wan, 2017. "Testing Local Average Treatment Effect Assumptions," The Review of Economics and Statistics, MIT Press, vol. 99(2), pages 305-313, May.
    17. Horowitz, Joel L & Manski, Charles F, 1995. "Identification and Robustness with Contaminated and Corrupted Data," Econometrica, Econometric Society, vol. 63(2), pages 281-302, March.
    18. Taisuke Otsu & Ke-Li Xu & Yukitoshi Matsushita, 2013. "Estimation and Inference of Discontinuity in Density," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(4), pages 507-524, October.
    19. Andrews, Donald W.K. & Shi, Xiaoxia, 2014. "Nonparametric inference based on conditional moment inequalities," Journal of Econometrics, Elsevier, vol. 179(1), pages 31-45.
    20. Joshua D. Angrist & Victor Lavy & Jetson Leder-Luis & Adi Shany, 2019. "Maimonides' Rule Redux," American Economic Review: Insights, American Economic Association, vol. 1(3), pages 309-324, December.
    21. 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.
    22. David S. Lee, 2009. "Training, Wages, and Sample Selection: Estimating Sharp Bounds on Treatment Effects," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 76(3), pages 1071-1102.
    23. Santiago Acerenza & Otávio Bartalotti & Désiré Kédagni, 2023. "Testing identifying assumptions in bivariate probit models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(3), pages 407-422, April.
    24. repec:cwl:cwldpp:1840rr is not listed on IDEAS
    25. Lee, David S., 2008. "Randomized experiments from non-random selection in U.S. House elections," Journal of Econometrics, Elsevier, vol. 142(2), pages 675-697, February.
    26. Imbens, Guido W. & Lemieux, Thomas, 2008. "Regression discontinuity designs: A guide to practice," Journal of Econometrics, Elsevier, vol. 142(2), pages 615-635, February.
    27. Ma, Shuangge & Kosorok, Michael R., 2005. "Robust semiparametric M-estimation and the weighted bootstrap," Journal of Multivariate Analysis, Elsevier, vol. 96(1), pages 190-217, September.
    28. Martin Huber & Giovanni Mellace, 2015. "Testing Instrument Validity for LATE Identification Based on Inequality Moment Constraints," The Review of Economics and Statistics, MIT Press, vol. 97(2), pages 398-411, May.
    29. Tomasz Olma, 2021. "Nonparametric Estimation of Truncated Conditional Expectation Functions," Papers 2109.06150, arXiv.org.
    30. McCrary, Justin, 2008. "Manipulation of the running variable in the regression discontinuity design: A density test," Journal of Econometrics, Elsevier, vol. 142(2), pages 698-714, February.
    31. Cristian Pop-Eleches & Miguel Urquiola, 2013. "Going to a Better School: Effects and Behavioral Responses," American Economic Review, American Economic Association, vol. 103(4), pages 1289-1324, June.
    32. Donald, Stephen G. & Hsu, Yu-Chin, 2011. "A new test for linear inequality constraints when the variance–covariance matrix depends on the unknown parameters," Economics Letters, Elsevier, vol. 113(3), pages 241-243.
    33. Grant Miller & Diana Pinto & Marcos Vera-Hernández, 2013. "Risk Protection, Service Use, and Health Outcomes under Colombia's Health Insurance Program for the Poor," American Economic Journal: Applied Economics, American Economic Association, vol. 5(4), pages 61-91, October.
    34. Stephen G. Donald & Yu-Chin Hsu, 2016. "Improving the Power of Tests of Stochastic Dominance," Econometric Reviews, Taylor & Francis Journals, vol. 35(4), pages 553-585, April.
    35. 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.
    36. Lukas Laffers & Giovanni Mellace, 2017. "A note on testing instrument validity for the identification of LATE," Empirical Economics, Springer, vol. 53(3), pages 1281-1286, November.
    37. Joshua D. Angrist & Victor Lavy, 1999. "Using Maimonides' Rule to Estimate the Effect of Class Size on Scholastic Achievement," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(2), pages 533-575.
    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. Yoichi Arai & Yu‐Chin Hsu & Toru Kitagawa & Ismael Mourifié & Yuanyuan Wan, 2022. "Testing identifying assumptions in fuzzy regression discontinuity designs," Quantitative Economics, Econometric Society, vol. 13(1), pages 1-28, January.
    2. Blaise Melly & Rafael Lalive, 2020. "Estimation, Inference, and Interpretation in the Regression Discontinuity Design," Diskussionsschriften dp2016, Universitaet Bern, Departement Volkswirtschaft.
    3. Matias D. Cattaneo & Rocío Titiunik, 2022. "Regression Discontinuity Designs," Annual Review of Economics, Annual Reviews, vol. 14(1), pages 821-851, August.
    4. 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.
    5. Takuya Ishihara & Masayuki Sawada, 2020. "Manipulation-Robust Regression Discontinuity Designs," Papers 2009.07551, arXiv.org, revised Sep 2024.
    6. Yingying DONG & Ying-Ying LEE & Michael GOU, 2019. "Regression Discontinuity Designs with a Continuous Treatment," Discussion papers 19058, Research Institute of Economy, Trade and Industry (RIETI).
    7. Bugni, Federico A. & Canay, Ivan A., 2021. "Testing continuity of a density via g-order statistics in the regression discontinuity design," Journal of Econometrics, Elsevier, vol. 221(1), pages 138-159.
    8. Jin-young Choi & Myoung-jae Lee, 2017. "Regression discontinuity: review with extensions," Statistical Papers, Springer, vol. 58(4), pages 1217-1246, December.
    9. Bertanha, Marinho, 2020. "Regression discontinuity design with many thresholds," Journal of Econometrics, Elsevier, vol. 218(1), pages 216-241.
    10. Ivan A Canay & Vishal Kamat, 2018. "Approximate Permutation Tests and Induced Order Statistics in the Regression Discontinuity Design," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 85(3), pages 1577-1608.
    11. Atı̇la Abdulkadı̇roğlu & Joshua D. Angrist & Yusuke Narita & Parag Pathak, 2022. "Breaking Ties: Regression Discontinuity Design Meets Market Design," Econometrica, Econometric Society, vol. 90(1), pages 117-151, January.
    12. Hsu, Yu-Chin & Shen, Shu, 2019. "Testing treatment effect heterogeneity in regression discontinuity designs," Journal of Econometrics, Elsevier, vol. 208(2), pages 468-486.
    13. Joshua D. Angrist, 2022. "Empirical Strategies in Economics: Illuminating the Path From Cause to Effect," Econometrica, Econometric Society, vol. 90(6), pages 2509-2539, November.
    14. Somdeep Chatterjee & Pushkar Maitra & Manhar Manchanda, 2024. "The Relevant Third: Threat of Coalition and Economic Development," Monash Economics Working Papers 2024-13, Monash University, Department of Economics.
    15. Yu‐Chin Hsu & Shu Shen, 2021. "Testing monotonicity of conditional treatment effects under regression discontinuity designs," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(3), pages 346-366, April.
    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. Babii, Andrii & Kumar, Rohit, 2023. "Isotonic regression discontinuity designs," Journal of Econometrics, Elsevier, vol. 234(2), pages 371-393.
    18. Deng, Taotao & Hu, Yukun & Ma, Mulan, 2019. "Regional policy and tourism: A quasi-natural experiment," Annals of Tourism Research, Elsevier, vol. 74(C), pages 1-16.
    19. Jun Ma & Zhengfei Yu, 2020. "Empirical Likelihood Covariate Adjustment for Regression Discontinuity Designs," Papers 2008.09263, arXiv.org, revised May 2024.
    20. Adam C. Sales & Ben B. Hansen, 2020. "Limitless Regression Discontinuity," Journal of Educational and Behavioral Statistics, , vol. 45(2), pages 143-174, April.

    More about this item

    Keywords

    Fuzzy regression discontinuity design; Moment inequalities; Local continuity in means; Weighted bootstrap;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

    Statistics

    Access and download statistics

    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:eee:econom:v:241:y:2024:i:1:s0304407624000848. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jeconom .

    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.