1932

Abstract

The regression discontinuity (RD) design is one of the most widely used nonexperimental methods for causal inference and program evaluation. Over the last two decades, statistical and econometric methods for RD analysis have expanded and matured, and there is now a large number of methodological results for RD identification, estimation, inference, and validation. We offer a curated review of this methodological literature organized around the two most popular frameworks for the analysis and interpretation of RD designs: the continuity framework and the local randomization framework. For each framework, we discuss three main topics: () designs and parameters, focusing on different types of RD settings and treatment effects of interest; () estimation and inference, presenting the most popular methods based on local polynomial regression and methods for the analysis of experiments, as well as refinements, extensions, and alternatives; and () validation and falsification, summarizing an array of mostly empirical approaches to support the validity of RD designs in practice.

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2022-08-12
2024-04-30
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Literature Cited

  1. Abadie A, Cattaneo MD. 2018. Econometric methods for program evaluation. Annu. Rev. Econ. 10:465–503
    [Google Scholar]
  2. Angrist JD, Rokkanen M. 2015. Wanna get away? Regression discontinuity estimation of exam school effects away from the cutoff. J. Am. Stat. Assoc. 110:5121331–44
    [Google Scholar]
  3. Arai Y, Hsu Y, Kitagawa T, Mourifié I, Wan Y. 2022. Testing identifying assumptions in fuzzy regression discontinuity designs. Quant. Econ. 13:11–28
    [Google Scholar]
  4. Arai Y, Ichimura H. 2016. Optimal bandwidth selection for the fuzzy regression discontinuity estimator. Econ. Lett. 141:1103–6
    [Google Scholar]
  5. Arai Y, Ichimura H. 2018. Simultaneous selection of optimal bandwidths for the sharp regression discontinuity estimator. Quant. Econ. 9:1441–82
    [Google Scholar]
  6. Arai Y, Otsu T, Seo MH. 2021. Regression discontinuity design with potentially many covariates. arXiv:2109.08351 [econ.EM]
  7. Armstrong T, Kolesar M. 2020. Simple and honest confidence intervals in nonparametric regression. Quant. Econ. 11:11–39
    [Google Scholar]
  8. Babii A, Kumar R. 2021. Isotonic regression discontinuity designs. J. Econom. In press. https://doi.org/10.1016/j.jeconom.2021.01.008
    [Crossref] [Google Scholar]
  9. Backus GE. 1989. Confidence set inference with a prior quadratic bound. Geophys. J. Int. 97:1119–50
    [Google Scholar]
  10. Bajari P, Hong H, Park M, Town R 2011. Regression discontinuity designs with an endogenous forcing variable and an application to contracting in health care NBER Work. Pap. 17643
  11. Barreca AI, Guldi M, Lindo JM, Waddell GR. 2011. Saving babies? Revisiting the effect of very low birth weight classification. Q. J. Econ. 126:42117–23
    [Google Scholar]
  12. Barreca AI, Lindo JM, Waddell GR. 2016. Heaping-induced bias in regression-discontinuity designs. Econ. Inq. 54:1268–93
    [Google Scholar]
  13. Bartalotti O, Brummet Q. 2017. Regression discontinuity designs with clustered data. See Cattaneo & Escanciano 2017 383–420
  14. Bartalotti O, Brummet Q, Dieterle S. 2021. A correction for regression discontinuity designs with group-specific mismeasurement of the running variable. J. Bus. Econ. Stat. 39:3833–48
    [Google Scholar]
  15. Bartalotti O, Calhoun G, He Y 2017. Bootstrap confidence intervals for sharp regression discontinuity designs. See Cattaneo & Escanciano 2017 421–53
  16. Bertanha M. 2020. Regression discontinuity design with many thresholds. J. Econom. 218:1216–41
    [Google Scholar]
  17. Bertanha M, Imbens GW. 2020. External validity in fuzzy regression discontinuity designs. J. Bus. Econ. Stat. 38:3593–612
    [Google Scholar]
  18. Black SE. 1999. Do better schools matter? Parental valuation of elementary education. Q. J. Econ. 114:2577–99
    [Google Scholar]
  19. Blomquist S, Newey WK, Kumar A, Liang CY. 2021. On bunching and identification of the taxable income elasticity. J. Political Econ. 129:82320–43
    [Google Scholar]
  20. Branson Z, Rischard M, Bornn L, Miratrix LW. 2019. A nonparametric Bayesian methodology for regression discontinuity designs. J. Stat. Plan. Inference 202:14–30
    [Google Scholar]
  21. Bugni FA, Canay IA. 2021. Testing continuity of a density via g-order statistics in the regression discontinuity design. J. Econom. 221:1138–59
    [Google Scholar]
  22. Bulus M. 2022. Minimum detectable effect size computations for cluster-level regression discontinuity studies: specifications beyond the linear functional form. J. Res. Educ. Eff. 15:1151–77
    [Google Scholar]
  23. Busse M, Silva-Risso J, Zettelmeyer F. 2006. $1,000 cash back: the pass-through of auto manufacturer promotions. Am. Econ. Rev. 96:41253–70
    [Google Scholar]
  24. Caetano C, Caetano G, Escanciano JC. 2021. Regression discontinuity design with multivalued treatments Work. Pap., Univ. Carlos III, Madrid Spain:
  25. Calonico S, Cattaneo MD, Farrell MH. 2018. On the effect of bias estimation on coverage accuracy in nonparametric inference. J. Am. Stat. Assoc. 113:522767–79
    [Google Scholar]
  26. Calonico S, Cattaneo MD, Farrell MH. 2020. Optimal bandwidth choice for robust bias corrected inference in regression discontinuity designs. Econom. J. 23:2192–210
    [Google Scholar]
  27. Calonico S, Cattaneo MD, Farrell MH. 2022. Coverage error optimal confidence intervals for local polynomial regression. Bernoulli In press
    [Google Scholar]
  28. Calonico S, Cattaneo MD, Farrell MH, Titiunik R. 2019. Regression discontinuity designs using covariates. Rev. Econ. Stat. 101:3442–51
    [Google Scholar]
  29. Calonico S, Cattaneo MD, Titiunik R. 2014. Robust nonparametric confidence intervals for regression-discontinuity designs. Econometrica 82:62295–326
    [Google Scholar]
  30. Calonico S, Cattaneo MD, Titiunik R. 2015. Optimal data-driven regression discontinuity plots. J. Am. Stat. Assoc. 110:5121753–69
    [Google Scholar]
  31. Canay IA, Kamat V. 2018. Approximate permutation tests and induced order statistics in the regression discontinuity design. Rev. Econ. Stud. 85:31577–608
    [Google Scholar]
  32. Card D, Lee DS, Pei Z, Weber A 2015. Inference on causal effects in a generalized regression kink design. Econometrica 83:62453–83
    [Google Scholar]
  33. Card D, Lee DS, Pei Z, Weber A 2017. Regression kink design: Theory and practice. See Cattaneo & Escanciano 2017 341–82
  34. Card D, Mas A, Rothstein J. 2008. Tipping and the dynamics of segregation. Q. J. Econ. 123:1177–218
    [Google Scholar]
  35. Cattaneo MD, Escanciano JC, eds. 2017. Regression Discontinuity Designs: Theory and Applications Bingley, UK: Emerald
  36. Cattaneo MD, Frandsen B, Titiunik R. 2015. Randomization inference in the regression discontinuity design: an application to party advantages in the U.S. Senate. J. Causal Inference 3:11–24
    [Google Scholar]
  37. Cattaneo MD, Idrobo N, Titiunik R 2020a. A Practical Introduction to Regression Discontinuity Designs: Foundations Cambridge, UK: Cambridge Univ. Press
  38. Cattaneo MD, Idrobo N, Titiunik R 2022a. A Practical Introduction to Regression Discontinuity Designs: Extensions Cambridge, UK: Cambridge Univ. Press. In press
  39. Cattaneo MD, Jansson M, Ma X. 2020b. Simple local polynomial density estimators. J. Am. Stat. Assoc. 115:5311449–55
    [Google Scholar]
  40. Cattaneo MD, Keele L, Titiunik R. 2022b. Covariate adjustment in regression discontinuity designs. Handbook of Matching and Weighting in Causal Inference JR Zubizarreta, EA Stuart, DS Small, PR Rosenbaum London: Chapman & Hall. In press
    [Google Scholar]
  41. Cattaneo MD, Keele L, Titiunik R, Vazquez-Bare G. 2016. Interpreting regression discontinuity designs with multiple cutoffs. J. Politics 78:41229–48
    [Google Scholar]
  42. Cattaneo MD, Keele L, Titiunik R, Vazquez-Bare G. 2021. Extrapolating treatment effects in multi-cutoff regression discontinuity designs. J. Am. Stat. Assoc. 116:5361941–52
    [Google Scholar]
  43. Cattaneo MD, Titiunik R, Vazquez-Bare G. 2017. Comparing inference approaches for RD designs: a reexamination of the effect of head start on child mortality. J. Policy Anal. Manag. 36:3643–81
    [Google Scholar]
  44. Cattaneo MD, Titiunik R, Vazquez-Bare G. 2019. Power calculations for regression discontinuity designs. Stata J. 19:1210–45
    [Google Scholar]
  45. Cattaneo MD, Titiunik R, Vazquez-Bare G. 2020c. The regression discontinuity design. Handbook of Research Methods in Political Science and International Relations L Curini, RJ Franzese 835–57 London: Sage
    [Google Scholar]
  46. Cattaneo MD, Vazquez-Bare G. 2016. The choice of neighborhood in regression discontinuity designs. Obs. Stud. 2:134–46
    [Google Scholar]
  47. Cellini SR, Ferreira F, Rothstein J. 2010. The value of school facility investments: evidence from a dynamic regression discontinuity design. Q. J. Econ. 125:1215–61
    [Google Scholar]
  48. Cerulli G, Dong Y, Lewbel A, Poulsen A. 2017. Testing stability of regression discontinuity models. See Cattaneo & Escanciano 2017 317–39
  49. Chaplin DD, Cook TD, Zurovac J, Coopersmith JS, Finucane MM et al. 2018. The internal and external validity of the regression discontinuity design: a meta-analysis of 15 within-study comparisons. J. Policy Anal. Manag. 37:2403–29
    [Google Scholar]
  50. Chen H, Chiang HD, Sasaki Y. 2020. Quantile treatment effects in regression kink designs. Econom. Theory 36:61167–91
    [Google Scholar]
  51. Cheng MY, Fan J, Marron JS. 1997. On automatic boundary corrections. Ann. Stat. 25:41691–708
    [Google Scholar]
  52. Chiang HD, Hsu YC, Sasaki Y. 2019. Robust uniform inference for quantile treatment effects in regression discontinuity designs. J. Econom. 211:2589–618
    [Google Scholar]
  53. Chiang HD, Sasaki Y. 2019. Causal inference by quantile regression kink designs. J. Econom. 210:2405–33
    [Google Scholar]
  54. Chib S, Jacobi L. 2016. Bayesian fuzzy regression discontinuity analysis and returns to compulsory schooling. J. Appl. Econom. 31:61026–47
    [Google Scholar]
  55. Choi JY, Lee MJ. 2018. Relaxing conditions for local average treatment effect in fuzzy regression discontinuity. Econ. Lett. 173:47–50
    [Google Scholar]
  56. Cook TD. 2008.. “ Waiting for life to arrive'': a history of the regression-discontinuity design in psychology, statistics and economics. J. Econom. 142:2636–54
    [Google Scholar]
  57. Cook TD, Wong VC. 2008. Empirical tests of the validity of the regression discontinuity design. Ann. Econ. Stat. 91–92:127–50
    [Google Scholar]
  58. Crespo C. 2020. Beyond manipulation: administrative sorting in regression discontinuity designs. J. Causal Inference 8:1164–81
    [Google Scholar]
  59. Davezies L, Le Barbanchon T 2017. Regression discontinuity design with continuous measurement error in the running variable. J. Econom. 200:2260–81
    [Google Scholar]
  60. De la Cuesta B, Imai K. 2016. Misunderstandings about the regression discontinuity design in the study of close elections. Annu. Rev. Political Sci. 19:375–96
    [Google Scholar]
  61. De Magalhaes L, Hangartner D, Hirvonen S, Meriläinen J, Ruiz NA, Tukiainen J. 2020. How much should we trust regression discontinuity design estimates? Evidence from experimental benchmarks of the incumbency advantage Work. Pap., Univ. Bristol Bristol, UK:
  62. Dell M. 2010. The persistent effects of Peru's mining mita. Econometrica 78:61863–903
    [Google Scholar]
  63. Dong Y. 2015. Regression discontinuity applications with rounding errors in the running variable. J. Appl. Econom. 30:3422–46
    [Google Scholar]
  64. Dong Y. 2018a. Alternative assumptions to identify late in fuzzy regression discontinuity designs. Oxf. Bull. Econ. Stat. 80:51020–27
    [Google Scholar]
  65. Dong Y 2018b. Jump or kink? Regression probability jump and kink design for treatment effect evaluation Work. Pap., Univ. Calif. Irvine:
  66. Dong Y. 2019. Regression discontinuity designs with sample selection. J. Bus. Econ. Stat. 37:1171–86
    [Google Scholar]
  67. Dong Y, Lee YY, Gou M. 2021. Regression discontinuity designs with a continuous treatment. J. Am. Stat. Assoc. https://doi.org/10.1080/01621459.2021.1923509
    [Crossref] [Google Scholar]
  68. Dong Y, Lewbel A. 2015. Identifying the effect of changing the policy threshold in regression discontinuity models. Rev. Econ. Stat. 97:51081–92
    [Google Scholar]
  69. Donoho DL. 1994. Statistical estimation and optimal recovery. Ann. Stat. 22:1238–70
    [Google Scholar]
  70. Dowd C. 2021. Donuts and distant CATEs: Derivative bounds for RD extrapolation. Work. Pap., Booth Sch. Bus., Univ. Chicago Chicago, IL:
  71. Eckles D, Ignatiadis N, Wager S, Wu H. 2021. Noise-induced randomization in regression discontinuity designs. arXiv:2004.09458 [stat.ME]
  72. Fan J, Gijbels I. 1996. Local Polynomial Modelling and Its Applications London: Chapman & Hall
  73. Feir D, Lemieux T, Marmer V. 2016. Weak identification in fuzzy regression discontinuity designs. J. Bus. Econ. Stat. 34:2185–96
    [Google Scholar]
  74. Frandsen B. 2017. Party bias in union representation elections: testing for manipulation in the regression discontinuity design when the running variable is discrete. See Cattaneo & Escanciano 2017 281–315
  75. Frandsen B, Frolich M, Melly B 2012. Quantile treatments effects in the regression discontinuity design. J. Econom. 168:2382–95
    [Google Scholar]
  76. Frolich M, Huber M. 2019. Including covariates in the regression discontinuity design. J. Bus. Econ. Stat. 37:4736–48
    [Google Scholar]
  77. Galiani S, McEwan PJ, Quistorff B. 2017. External and internal validity of a geographic quasi-experiment embedded in a cluster-randomized experiment. See Cattaneo & Escanciano 2017 195–236
  78. Ganong P, Jäger S. 2018. A permutation test for the regression kink design. J. Am. Stat. Assoc. 113:522494–504
    [Google Scholar]
  79. Gelman A, Carlin JB, Stern HS, Dunson DB, Vehtari A, Rubin DB. 2013. Bayesian Data Analysis Boca Raton, FL: CRC Press
  80. Gelman A, Imbens GW. 2019. Why high-order polynomials should not be used in regression discontinuity designs. J. Bus. Econ. Stat. 37:3447–56
    [Google Scholar]
  81. Geneletti S, O'Keeffe AG, Sharples LD, Richardson S, Baio G. 2015. Bayesian regression discontinuity designs: incorporating clinical knowledge in the causal analysis of primary care data. Stat. Med. 34:152334–52
    [Google Scholar]
  82. Gerard F, Rokkanen M, Rothe C. 2020. Bounds on treatment effects in regression discontinuity designs with a manipulated running variable. Quant. Econ. 11:3839–70
    [Google Scholar]
  83. Grembi V, Nannicini T, Troiano U. 2016. Do fiscal rules matter? A difference-in-discontinuities design. Am. Econ. J. Appl. Econ. 8:31–30
    [Google Scholar]
  84. Groeneboom P, Jongbloed G. 2014. Nonparametric Estimation Under Shape Constraints Cambridge, UK: Cambridge Univ. Press
  85. Hahn J, Todd P, van der Klaauw W. 2001. Identification and estimation of treatment effects with a regression-discontinuity design. Econometrica 69:1201–9
    [Google Scholar]
  86. Hansen BE. 2017. Regression kink with an unknown threshold. J. Bus. Econ. Stat. 35:2228–40
    [Google Scholar]
  87. Hartman E. 2021. Equivalence testing for regression discontinuity designs. Political Anal. 29:4505–21
    [Google Scholar]
  88. Hausman C, Rapson DS. 2018. Regression discontinuity in time: considerations for empirical applications. Annu. Rev. Resour. Econ. 10:533–52
    [Google Scholar]
  89. He Y. 2018. Three essays on regression discontinuity design and partial identification PhD Thesis, Iowa State Univ. Ames:
  90. He Y, Bartalotti O. 2020. Wild bootstrap for fuzzy regression discontinuity designs: obtaining robust bias-corrected confidence intervals. Econom. J. 23:2211–31
    [Google Scholar]
  91. Hsu YC, Shen S. 2019. Testing treatment effect heterogeneity in regression discontinuity designs. J. Econom. 208:2468–86
    [Google Scholar]
  92. Hsu YC, Shen S. 2021a. Dynamic regression discontinuity under treatment effect heterogeneity. Work. Pap., Univ. Calif. Davis:
  93. Hsu YC, Shen S. 2021b. Testing monotonicity of conditional treatment effects under regression discontinuity designs. J. Appl. Econom. 36:3346–66
    [Google Scholar]
  94. Huang X, Zhan Z. 2021. Local composite quantile regression for regression discontinuity. J. Bus. Econ. Stat. https://doi.org/10.1080/07350015.2021.1990072
    [Crossref] [Google Scholar]
  95. Hyytinen A, Meriläinen J, Saarimaa T, Toivanen O, Tukiainen J. 2018. When does regression discontinuity design work? Evidence from random election outcomes. Quant. Econ. 9:21019–51
    [Google Scholar]
  96. Imbens GW, Lemieux T. 2008. Regression discontinuity designs: a guide to practice. J. Econom. 142:2615–35
    [Google Scholar]
  97. Imbens GW, Kalyanaraman K. 2012. Optimal bandwidth choice for the regression discontinuity estimator. Rev. Econ. Stud. 79:3933–59
    [Google Scholar]
  98. Imbens GW, Rubin DB. 2015. Causal Inference in Statistics, Social, and Biomedical Sciences Cambridge, UK: Cambridge Univ. Press
  99. Imbens GW, Wager S. 2019. Optimized regression discontinuity designs. Rev. Econ. Stat. 101:2264–78
    [Google Scholar]
  100. Jales H, Ma J, Yu Z 2017. Optimal bandwidth selection for local linear estimation of discontinuity in density. Econ. Lett. 153:23–27
    [Google Scholar]
  101. Jales H, Yu Z. 2017. Identification and estimation using a density discontinuity approach. See Cattaneo & Escanciano 2017 29–72
  102. Kamat V. 2018. On nonparametric inference in the regression discontinuity design. Econom. Theory 34:3694–703
    [Google Scholar]
  103. Karabatsos G, Walker SG. 2015. A Bayesian nonparametric causal model for regression discontinuity designs. Nonparametric Bayesian Inference in Biostatistics R Mitra, P Müller 403–21 Cham, Switz: Springer
    [Google Scholar]
  104. Keele LJ, Lorch S, Passarella M, Small D, Titiunik R. 2017. An overview of geographically discontinuous treatment assignments with an application to children's health insurance. See Cattaneo & Escanciano 2017 147–94
  105. Keele LJ, Titiunik R. 2015. Geographic boundaries as regression discontinuities. Political Anal. 23:1127–55
    [Google Scholar]
  106. Keele LJ, Titiunik R, Zubizarreta J. 2015. Enhancing a geographic regression discontinuity design through matching to estimate the effect of ballot initiatives on voter turnout. J. R. Stat. Soc. A 178:1223–39
    [Google Scholar]
  107. Kleven HJ. 2016. Bunching. Annu. Rev. Econ. 8:435–64
    [Google Scholar]
  108. Kolesar M, Rothe C. 2018. Inference in regression discontinuity designs with a discrete running variable. Am. Econ. Rev. 108:82277–304
    [Google Scholar]
  109. Korting C, Lieberman C, Matsudaira J, Pei Z, Shen Y 2021. Visual inference and graphical representation in regression discontinuity designs. arXiv:2112.03096 [econ.EM]
  110. Lee DS. 2008. Randomized experiments from nonrandom selection in U.S. House elections. J. Econom. 142:2675–97
    [Google Scholar]
  111. Lee DS, Card D. 2008. Regression discontinuity inference with specification error. J. Econom. 142:2655–74
    [Google Scholar]
  112. Lee DS, Lemieux T. 2010. Regression discontinuity designs in economics. J. Econ. Lit. 48:2281–355
    [Google Scholar]
  113. Lee MJ. 2017. Regression discontinuity with errors in the running variable: effect on truthful margin. J. Econom. Methods 6:1281355
    [Google Scholar]
  114. Li F, Mattei A, Mealli F. 2015. Evaluating the causal effect of university grants on student dropout: evidence from a regression discontinuity design using principal stratification. Ann. Appl. Stat. 9:41906–31
    [Google Scholar]
  115. Ludwig J, Miller DL. 2007. Does head start improve children's life chances? Evidence from a regression discontinuity design. Q. J. Econ. 122:1159–208
    [Google Scholar]
  116. Lv X, Sun XR, Lu Y, Li R. 2019. Nonparametric identification and estimation of dynamic treatment effects for survival data in a regression discontinuity design. Econ. Lett. 184:108665
    [Google Scholar]
  117. Ma J, Jales H, Yu Z 2020. Minimum contrast empirical likelihood inference of discontinuity in density. J. Bus. Econ. Stat. 38:4934–50
    [Google Scholar]
  118. Ma J, Yu Z 2020. Coverage optimal empirical likelihood inference for regression discontinuity design. arXiv:2008.09263 [econ.EM]
  119. Matzkin RL. 2013. Nonparametric identification in structural economic models. Annu. Rev. Econ. 5:457–86
    [Google Scholar]
  120. McCrary J. 2008. Manipulation of the running variable in the regression discontinuity design: a density test. J. Econom. 142:2698–714
    [Google Scholar]
  121. Mealli F, Rampichini C. 2012. Evaluating the effects of university grants by using regression discontinuity designs. J. R. Stat. Soc. A 175:3775–98
    [Google Scholar]
  122. Mukherjee D, Banerjee M, Ritov Y. 2021. Estimation of a score-explained non-randomized treatment effect in fixed and high dimensions. arXiv:2102.11229 [stat.ME]
  123. Otsu T, Xu KL, Matsushita Y. 2013. Estimation and inference of discontinuity in density. J. Bus. Econ. Stat. 31:4507–24
    [Google Scholar]
  124. Otsu T, Xu KL, Matsushita Y. 2015. Empirical likelihood for regression discontinuity design. J. Econom. 186:194–112
    [Google Scholar]
  125. Owen AB. 2001. Empirical Likelihood London: Chapman & Hall
  126. Owen AB, Varian H. 2020. Optimizing the tie-breaker regression discontinuity design. Electron. J. Stat. 14:24004–27
    [Google Scholar]
  127. Papay JP, Willett JB, Murnane RJ. 2011. Extending the regression-discontinuity approach to multiple assignment variables. J. Econom. 161:2203–7
    [Google Scholar]
  128. Pei Z, Lee DS, Card D, Weber A. 2021. Local polynomial order in regression discontinuity designs. J. Bus. Econ. Stat. 31:4507–24
    [Google Scholar]
  129. Pei Z, Shen Y. 2017. The devil is in the tails: regression discontinuity design with measurement error in the assignment variable. See Cattaneo & Escanciano 2017 455–502
  130. Peng S, Ning Y. 2021. Regression discontinuity design under self-selection. Proc. Mach. Learn. Res. 130:118–26
    [Google Scholar]
  131. Porter J. 2003. Estimation in the regression discontinuity model. Work. Pap., Univ. Wis. Madison:
  132. Porter J, Yu P. 2015. Regression discontinuity designs with unknown discontinuity points: testing and estimation. J. Econom. 189:1132–47
    [Google Scholar]
  133. Qu Z, Yoon J. 2019. Uniform inference on quantile effects under sharp regression discontinuity designs. J. Bus. Econ. Stat. 37:4625–47
    [Google Scholar]
  134. Reardon SF, Robinson JP. 2012. Regression discontinuity designs with multiple rating-score variables. J. Res. Educ. Eff. 5:183–104
    [Google Scholar]
  135. Rokkanen M. 2015. Exam schools, ability, and the effects of affirmative action: latent factor extrapolation in the regression discontinuity design Discuss. Pap. 1415-03 Dep. Econ., Columbia Univ. New York:
  136. Rosenbaum PR. 2010. Design of Observational Studies New York: Springer
  137. Schochet PZ. 2009. Statistical power for regression discontinuity designs in education evaluations. J. Educ. Behav. Stat. 34:2238–66
    [Google Scholar]
  138. Sekhon JS, Titiunik R. 2016. Understanding regression discontinuity designs as observational studies. Obs. Stud. 2:174–82
    [Google Scholar]
  139. Sekhon JS, Titiunik R. 2017. On interpreting the regression discontinuity design as a local experiment. See Cattaneo & Escanciano 2017 1–28
  140. Shen S, Zhang X. 2016. Distributional tests for regression discontinuity: theory and empirical examples. Rev. Econ. Stat. 98:4685–700
    [Google Scholar]
  141. Sun Y. 2005. Adaptive estimation of the regression discontinuity model. Work. Pap., Univ. Calif. San Diego:
  142. Thistlethwaite DL, Campbell DT. 1960. Regression-discontinuity analysis: an alternative to the ex post facto experiment. J. Educ. Psychol. 51:6309–17
    [Google Scholar]
  143. Titiunik R 2021. Natural experiments. Advances in Experimental Political Science JN Druckman, DP Green 103–29 Cambridge, UK: Cambridge Univ. Press
    [Google Scholar]
  144. Tuvaandorj P. 2020. Regression discontinuity designs, white noise models, and minimax. J. Econom. 218:2587–608
    [Google Scholar]
  145. Urquiola M, Verhoogen E. 2009. Class-size caps, sorting, and the regression-discontinuity design. Am. Econ. Rev. 99:1179–215
    [Google Scholar]
  146. van der Klaauw W. 2008. Regression–discontinuity analysis: a survey of recent developments in economics. Labour 22:2219–45
    [Google Scholar]
  147. Wing C, Cook TD. 2013. Strengthening the regression discontinuity design using additional design elements: a within-study comparison. J. Policy Anal. Manag. 32:4853–77
    [Google Scholar]
  148. Wong VC, Steiner PM, Cook TD. 2013. Analyzing regression-discontinuity designs with multiple assignment variables: a comparative study of four estimation methods. J. Educ. Behav. Stat. 38:2107–41
    [Google Scholar]
  149. Xu KL. 2017. Regression discontinuity with categorical outcomes. J. Econom. 201:11–18
    [Google Scholar]
  150. Xu KL. 2018. A semi-nonparametric estimator of regression discontinuity design with discrete duration outcomes. J. Econom. 206:1258–78
    [Google Scholar]
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