IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2402.10836.html
   My bibliography  Save this paper

Manipulation Test for Multidimensional RDD

Author

Listed:
  • Federico Crippa

Abstract

The causal inference model proposed by Lee (2008) for the regression discontinuity design (RDD) relies on assumptions that imply the continuity of the density of the assignment (running) variable. The test for this implication is commonly referred to as the manipulation test and is regularly reported in applied research to strengthen the design's validity. The multidimensional RDD (MRDD) extends the RDD to contexts where treatment assignment depends on several running variables. This paper introduces a manipulation test for the MRDD. First, it develops a theoretical model for causal inference with the MRDD, used to derive a testable implication on the conditional marginal densities of the running variables. Then, it constructs the test for the implication based on a quadratic form of a vector of statistics separately computed for each marginal density. Finally, the proposed test is compared with alternative procedures commonly employed in applied research.

Suggested Citation

  • Federico Crippa, 2024. "Manipulation Test for Multidimensional RDD," Papers 2402.10836, arXiv.org, revised Jun 2024.
    • Handle: RePEc:arx:papers:2402.10836
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2402.10836
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Sebastian Calonico & Matias D. Cattaneo & Max H. Farrell, 2018. "On the Effect of Bias Estimation on Coverage Accuracy in Nonparametric Inference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 767-779, April.
    2. Keele, Luke J. & Titiunik, Rocío, 2015. "Geographic Boundaries as Regression Discontinuities," Political Analysis, Cambridge University Press, vol. 23(1), pages 127-155, January.
    3. Timothy B. Armstrong & Michal Kolesár, 2020. "Simple and honest confidence intervals in nonparametric regression," Quantitative Economics, Econometric Society, vol. 11(1), pages 1-39, January.
    4. 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.
    5. Connan Snider & Jonathan W. Williams, 2015. "Barriers to Entry in the Airline Industry: A Multidimensional Regression-Discontinuity Analysis of AIR-21," The Review of Economics and Statistics, MIT Press, vol. 97(5), pages 1002-1022, December.
    6. Salti, Nisreen & Chaaban, Jad & Moussa, Wael & Irani, Alexandra & Al Mokdad, Rima & Jamaluddine, Zeina & Ghattas, Hala, 2022. "The impact of cash transfers on Syrian refugees in Lebanon: Evidence from a multidimensional regression discontinuity design," Journal of Development Economics, Elsevier, vol. 155(C).
    7. Sarah R. Cohodes & Joshua S. Goodman, 2014. "Merit Aid, College Quality, and College Completion: Massachusetts' Adams Scholarship as an In-Kind Subsidy," American Economic Journal: Applied Economics, American Economic Association, vol. 6(4), pages 251-285, October.
    8. Cattaneo, Matias D & Jansson, Michael & Ma, Xinwei, 2020. "Simple Local Polynomial Density Estimators," Department of Economics, Working Paper Series qt9vt997qn, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
    9. Jonathan Smith & Michael Hurwitz & Christopher Avery, 2017. "Giving College Credit Where It Is Due: Advanced Placement Exam Scores and College Outcomes," Journal of Labor Economics, University of Chicago Press, vol. 35(1), pages 67-147.
    10. 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.
    11. 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.
    12. Papay, John P. & Willett, John B. & Murnane, Richard J., 2011. "Extending the regression-discontinuity approach to multiple assignment variables," Journal of Econometrics, Elsevier, vol. 161(2), pages 203-207, April.
    13. Cattaneo, Matias D & Jansson, Michael & Ma, Xinwei, 2020. "Simple Local Polynomial Density Estimators," University of California at San Diego, Economics Working Paper Series qt9vt997qn, Department of Economics, UC San Diego.
    14. Yusuke Narita & Kohei Yata, 2021. "Algorithm is Experiment: Machine Learning, Market Design, and Policy Eligibility Rules," Working Papers 2021-022, Human Capital and Economic Opportunity Working Group.
    15. Egger, Peter H. & Wamser, Georg, 2015. "The impact of controlled foreign company legislation on real investments abroad. A multi-dimensional regression discontinuity design," Journal of Public Economics, Elsevier, vol. 129(C), pages 77-91.
    16. 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.
    17. 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.
    18. Marco Becht & Andrea Polo & Stefano Rossi, 2016. "Does Mandatory Shareholder Voting Prevent Bad Acquisitions?," The Review of Financial Studies, Society for Financial Studies, vol. 29(11), pages 3035-3067.
    19. Björn Tyrefors Hinnerich & Per Pettersson‐Lidbom, 2014. "Democracy, Redistribution, and Political Participation: Evidence From Sweden 1919–1938," Econometrica, Econometric Society, vol. 82(3), pages 961-993, May.
    20. Frey, Anderson, 2019. "Cash transfers, clientelism, and political enfranchisement: Evidence from Brazil," Journal of Public Economics, Elsevier, vol. 176(C), pages 1-17.
    21. Brent J. Evans, 2017. "SMART Money: Do Financial Incentives Encourage College Students to Study Science?," Education Finance and Policy, MIT Press, vol. 12(3), pages 342-368, Summer.
    22. Matsudaira, Jordan D., 2008. "Mandatory summer school and student achievement," Journal of Econometrics, Elsevier, vol. 142(2), pages 829-850, February.
    23. 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.
    24. Guido Imbens & Stefan Wager, 2019. "Optimized Regression Discontinuity Designs," The Review of Economics and Statistics, MIT Press, vol. 101(2), pages 264-278, May.
    25. Damon Clark & Paco Martorell, 2014. "The Signaling Value of a High School Diploma," Journal of Political Economy, University of Chicago Press, vol. 122(2), pages 282-318.
    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. Matias D. Cattaneo & Rocío Titiunik, 2022. "Regression Discontinuity Designs," Annual Review of Economics, Annual Reviews, vol. 14(1), pages 821-851, August.
    2. Blaise Melly & Rafael Lalive, 2020. "Estimation, Inference, and Interpretation in the Regression Discontinuity Design," Diskussionsschriften dp2016, Universitaet Bern, Departement Volkswirtschaft.
    3. 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.
    4. Babii, Andrii & Kumar, Rohit, 2023. "Isotonic regression discontinuity designs," Journal of Econometrics, Elsevier, vol. 234(2), pages 371-393.
    5. Takuya Ishihara & Masayuki Sawada, 2020. "Manipulation-Robust Regression Discontinuity Designs," Papers 2009.07551, arXiv.org, revised Oct 2023.
    6. 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.
    7. Albert Whata & Charles Chimedza, 2021. "Credibility of Causal Estimates from Regression Discontinuity Designs with Multiple Assignment Variables," Stats, MDPI, vol. 4(4), pages 1-23, November.
    8. Yiqi Liu & Yuan Qi, 2023. "Using Forests in Multivariate Regression Discontinuity Designs," Papers 2303.11721, arXiv.org.
    9. Koki Fusejima & Takuya Ishihara & Masayuki Sawada, 2022. "Joint diagnostic test of regression discontinuity designs: multiple testing problem," Papers 2205.04345, arXiv.org, revised Oct 2023.
    10. 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.
    11. Sacha Kapoor & Matthijs Oosterveen & Dinand Webbink, 2021. "The price of forced attendance," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(2), pages 209-227, March.
    12. Luisa Doerr & Niklas Potrafke & Felix Roesel & Luisa Dörr, 2021. "Populists in Power," CESifo Working Paper Series 9336, CESifo.
    13. Lu, Jiaxuan, 2023. "The economics of China’s between-city height competition: A regression discontinuity approach," Regional Science and Urban Economics, Elsevier, vol. 100(C).
    14. De Benedetto, Marco Alberto & De Paola, Maria & Scoppa, Vincenzo & Smirnova, Janna, 2023. "Erasmus Program and Labor Market Outcomes: Evidence from a Fuzzy Regression Discontinuity Design," IZA Discussion Papers 16181, Institute of Labor Economics (IZA).
    15. Luca Bellodi & Massimo Morelli & Matia Vannoni, 2021. "A Costly Commitment: Populism, Government Performance, and the Quality of Bureaucracy," CESifo Working Paper Series 9470, CESifo.
    16. Vanessa Cirulli & Giuliano Resce & Marco Ventura, 2021. "Co-payment exemption and healthcare consumption. Quasi-experimental evidence from Italy," Working Papers in Public Economics 203, University of Rome La Sapienza, Department of Economics and Law.
    17. Huber, Martin, 2019. "An introduction to flexible methods for policy evaluation," FSES Working Papers 504, Faculty of Economics and Social Sciences, University of Freiburg/Fribourg Switzerland.
    18. Bonilla, Sade, 2020. "The dropout effects of career pathways: Evidence from California," Economics of Education Review, Elsevier, vol. 75(C).
    19. Koohyun Kwon & Soonwoo Kwon, 2020. "Inference in Regression Discontinuity Designs under Monotonicity," Papers 2011.14216, arXiv.org.
    20. Kämpfen, F.; & Gómez-Olivé, X.; & O’Donnell, O.; & Riumallo Herl, C.;, 2023. "Effectiveness of Population-Based Hypertension Screening: A Multidimensional Regression Discontinuity Design," Health, Econometrics and Data Group (HEDG) Working Papers 23/15, HEDG, c/o Department of Economics, University of York.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:arx:papers:2402.10836. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.