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Tests for Many Treatment Effects in Regression Discontinuity Panel Data Models

Author

Listed:
  • Likai Chen
  • Georg Keilbar
  • Liangjun Su
  • Weining Wang

Abstract

Numerous studies use regression discontinuity design (RDD) for panel data by assuming that the treatment effects are homogeneous across all individuals/groups and pooling the data together. It is unclear how to test for the significance of treatment effects when the treatments vary across individuals/groups and the error terms may exhibit complicated dependence structures. This paper examines the estimation and inference of multiple treatment effects when the errors are not independent and identically distributed, and the treatment effects vary across individuals/groups. We derive a simple analytical expression for approximating the variance-covariance structure of the treatment effect estimators under general dependence conditions and propose two test statistics, one is to test for the overall significance of the treatment effect and the other for the homogeneity of the treatment effects. We find that in the Gaussian approximations to the test statistics, the dependence structures in the data can be safely ignored due to the localized nature of the statistics. This has the important implication that the simulated critical values can be easily obtained. Simulations demonstrate our tests have superb size control and reasonable power performance in finite samples regardless of the presence of strong cross-section dependence or/and weak serial dependence in the data. We apply our tests to two datasets and find significant overall treatment effects in each case.

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  • Likai Chen & Georg Keilbar & Liangjun Su & Weining Wang, 2023. "Tests for Many Treatment Effects in Regression Discontinuity Panel Data Models," Papers 2312.01162, arXiv.org.
    • Handle: RePEc:arx:papers:2312.01162
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    References listed on IDEAS

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    1. Gaurav Khanna, 2023. "Large-Scale Education Reform in General Equilibrium: Regression Discontinuity Evidence from India," Journal of Political Economy, University of Chicago Press, vol. 131(2), pages 549-591.
    2. Markus Frölich & Martin Huber, 2019. "Including Covariates in the Regression Discontinuity Design," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(4), pages 736-748, October.
    3. Chin, Aimee & Daysal, N. Meltem & Imberman, Scott A., 2013. "Impact of bilingual education programs on limited English proficient students and their peers: Regression discontinuity evidence from Texas," Journal of Public Economics, Elsevier, vol. 107(C), pages 63-78.
    4. Jonathan Reuter & Eric Zitzewitz, 2021. "How Much Does Size Erode Mutual Fund Performance? A Regression Discontinuity Approach [Mutual fund’s R2 as predictor of performance]," Review of Finance, European Finance Association, vol. 25(5), pages 1395-1432.
    5. 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.
    6. Liangjun Su & Zhentao Shi & Peter C. B. Phillips, 2016. "Identifying Latent Structures in Panel Data," Econometrica, Econometric Society, vol. 84, pages 2215-2264, November.
    7. 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.
    8. Caughey, Devin & Sekhon, Jasjeet S., 2011. "Elections and the Regression Discontinuity Design: Lessons from Close U.S. House Races, 1942–2008," Political Analysis, Cambridge University Press, vol. 19(4), pages 385-408.
    9. Sebastian Calonico & Matias D. Cattaneo & Max H. Farrell & Rocío Titiunik, 2019. "Regression Discontinuity Designs Using Covariates," The Review of Economics and Statistics, MIT Press, vol. 101(3), pages 442-451, July.
    10. Matias D. Cattaneo & Nicolas Idrobo & Rocio Titiunik, 2023. "A Practical Introduction to Regression Discontinuity Designs: Extensions," Papers 2301.08958, arXiv.org, revised Mar 2024.
    11. Imbens, Guido W. & Lemieux, Thomas, 2008. "Regression discontinuity designs: A guide to practice," Journal of Econometrics, Elsevier, vol. 142(2), pages 615-635, February.
    12. Andrew Gelman & Guido Imbens, 2019. "Why High-Order Polynomials Should Not Be Used in Regression Discontinuity Designs," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(3), pages 447-456, July.
    13. Victor Chernozhukov & Denis Chetverikov & Kengo Kato & Aureo de Paula, 2019. "Inference on Causal and Structural Parameters using Many Moment Inequalities," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 86(5), pages 1867-1900.
    14. 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.
    15. Marianne P. Bitler & Jonah B. Gelbach & Hilary W. Hoynes, 2017. "Can Variation in Subgroups' Average Treatment Effects Explain Treatment Effect Heterogeneity? Evidence from a Social Experiment," The Review of Economics and Statistics, MIT Press, vol. 99(4), pages 683-697, July.
    16. Oznur Ozdamar & Eleftherios Giovanis & Cansu Dağlıoğlu & Cemaleddin Gerede, 2021. "The effect of the 2008 employment support programme on young men’s labour market outcomes in Turkey: Evidence from a regression discontinuity design," Manchester School, University of Manchester, vol. 89(3), pages 276-296, June.
    17. Sascha O. Becker & Peter H. Egger & Maximilian von Ehrlich, 2013. "Absorptive Capacity and the Growth and Investment Effects of Regional Transfers: A Regression Discontinuity Design with Heterogeneous Treatment Effects," American Economic Journal: Economic Policy, American Economic Association, vol. 5(4), pages 29-77, November.
    18. 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.
    19. Su, Liangjun & Chen, Qihui, 2013. "Testing Homogeneity In Panel Data Models With Interactive Fixed Effects," Econometric Theory, Cambridge University Press, vol. 29(6), pages 1079-1135, December.
    20. Hsu, Yu-Chin & Shen, Shu, 2019. "Testing treatment effect heterogeneity in regression discontinuity designs," Journal of Econometrics, Elsevier, vol. 208(2), pages 468-486.
    21. Sebastian Calonico & Matias D. Cattaneo & Rocío Titiunik, 2015. "Optimal Data-Driven Regression Discontinuity Plots," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1753-1769, December.
    22. Matias D. Cattaneo & Nicolas Idrobo & Rocio Titiunik, 2019. "A Practical Introduction to Regression Discontinuity Designs: Foundations," Papers 1911.09511, arXiv.org.
    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. Emmanuel Rio, 2009. "Moment Inequalities for Sums of Dependent Random Variables under Projective Conditions," Journal of Theoretical Probability, Springer, vol. 22(1), pages 146-163, March.
    25. Likai Chen & Weining Wang & Wei Biao Wu, 2022. "Inference of Breakpoints in High-dimensional Time Series," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(540), pages 1951-1963, October.
    26. Peter C. B. Phillips & Donggyu Sul, 2003. "Dynamic panel estimation and homogeneity testing under cross section dependence *," Econometrics Journal, Royal Economic Society, vol. 6(1), pages 217-259, June.
    27. 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.
    28. Su, Liangjun & Ju, Gaosheng, 2018. "Identifying latent grouped patterns in panel data models with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 206(2), pages 554-573.
    29. Jonah Berger & Devin Pope, 2011. "Can Losing Lead to Winning?," Management Science, INFORMS, vol. 57(5), pages 817-827, May.
    30. Alexander Kreiss & Christoph Rothe, 2023. "Inference in regression discontinuity designs with high-dimensional covariates," The Econometrics Journal, Royal Economic Society, vol. 26(2), pages 105-123.
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