Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-31T14:16:23.209Z Has data issue: false hasContentIssue false
Series:   Elements in Quantitative and Computational Methods for the Social Sciences

A Practical Introduction to Regression Discontinuity Designs

Extensions

Published online by Cambridge University Press:  25 March 2024

Matias D. Cattaneo ,
Nicolas Idrobo  and
Rocío Titiunik
Matias D. Cattaneo
Affiliation:
Princeton University
Nicolas Idrobo
Affiliation:
University of Pennsylvania
Rocío Titiunik
Affiliation:
Princeton University

Summary

In this Element, which continues our discussion in Foundations, the authors provide an accessible and practical guide for the analysis and interpretation of Regression Discontinuity (RD) designs that encourages the use of a common set of practices and facilitates the accumulation of RD-based empirical evidence. The focus is on extensions to the canonical sharp RD setup that we discussed in Foundations. The discussion covers (i) the local randomization framework for RD analysis, (ii) the fuzzy RD design where compliance with treatment is imperfect, (iii) RD designs with discrete scores, and (iv) and multi-dimensional RD designs.
Get access

Keywords

regression discontinuityRD designfuzzy RD designlocal randomization RD designmultidimensional RD designgeographic RD design
Type
Element
Information
Series: Elements in Quantitative and Computational Methods for the Social Sciences
Online ISBN: 9781009441896
Publisher: Cambridge University Press
Print publication: 11 April 2024

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abadie, A., and Cattaneo, M. D. (2018): “Econometric Methods for Program Evaluation,” Annual Review of Economics, 10, 465–503.CrossRefGoogle Scholar
Andrews, I., Stock, J. H., and Sun, L. (2019): “Weak Instruments in Instrumental Variables Regression: Theory and Practice,” Annual Review of Economics, 11, 727–753.CrossRefGoogle Scholar
Arai, Y., Hsu, Y., Kitagawa, T., Mourifié, I., and Wan, Y. (2022): “Testing Identifying Assumptions in Fuzzy Regression Discontinuity Designs,” Quantitative Economics, 13(1), 1–28.CrossRefGoogle Scholar
Banerjee, S. (2005): “On Geodetic Distance Computations in Spatial Modeling,” Biometrics, 61(2), 617–625.CrossRefGoogle ScholarPubMed
Barreca, A. I., Lindo, J. M., and Waddell, G. R. (2016): “Heaping-Induced Bias in Regression-Discontinuity Designs,” Economic Inquiry, 54(1), 268–293.CrossRefGoogle Scholar
Calonico, S., Cattaneo, M. D., and Farrell, M. H. (2018): “On the Effect of Bias Estimation on Coverage Accuracy in Nonparametric Inference,” Journal of the American Statistical Association, 113(522), 767–779.CrossRefGoogle Scholar
Calonico, S., Cattaneo, M. D., and Farrell, M. H. (2020): “Optimal Bandwidth Choice for Robust Bias Corrected Inference in Regression Discontinuity Designs,” Econometrics Journal, 23(2), 192–210.CrossRefGoogle Scholar
Calonico, S., Cattaneo, M. D., and Farrell, M. H. (2022): “Coverage Error Optimal Confidence Intervals for Local Polynomial Regression,” Bernoulli, 28(4), 2998–3022.CrossRefGoogle Scholar
Calonico, S., Cattaneo, M. D., Farrell, M. H., and Titiunik, R. (2017): “rdrobust: Software for Regression Discontinuity Designs,” Stata Journal, 17(2), 372–404.CrossRefGoogle Scholar
Calonico, S., Cattaneo, M. D., Farrell, M. H., and Titiunik, R. (2019): “Regression Discontinuity Designs Using Covariates,” Review of Economics and Statistics, 101(3), 442–451.CrossRefGoogle Scholar
Calonico, S., Cattaneo, M. D., and Titiunik, R. (2014a): “Robust Data-Driven Inference in the Regression-Discontinuity Design,” Stata Journal, 14(4), 909–946.CrossRefGoogle Scholar
Calonico, S., Cattaneo, M. D., and Titiunik, R. (2014b): “Robust Nonparametric Confidence Intervals for Regression-Discontinuity Designs,” Econometrica, 82(6), 2295–2326.CrossRefGoogle Scholar
Calonico, S., Cattaneo, M. D., and Titiunik, R. (2015a): “Optimal Data-Driven Regression Discontinuity Plots,” Journal of the American Statistical Association, 110(512), 1753–1769.CrossRefGoogle Scholar
Calonico, S., Cattaneo, M. D., and Titiunik, R. (2015b): “rdrobust: An R Package for Robust Nonparametric Inference in Regression-Discontinuity Designs,” R Journal, 7(1), 38–51.CrossRefGoogle Scholar
Cattaneo, M. D., Frandsen, B., and Titiunik, R. (2015): “Randomization Inference in the Regression Discontinuity Design: An Application to Party Advantages in the U.S. Senate,” Journal of Causal Inference, 3(1), 1–24.CrossRefGoogle Scholar
Cattaneo, M. D., Idrobo, N., and Titiunik, R. (2020): A Practical Introduction to Regression Discontinuity Designs: Foundations. Cambridge Elements: Quantitative and Computational Methods for Social Science, Cambridge, UK: Cambridge University Press.Google Scholar
Cattaneo, M. D., Jansson, M., and Ma, X. (2018): “Manipulation Testing Based on Density Discontinuity,” Stata Journal, 18(1), 234–261.CrossRefGoogle Scholar
Cattaneo, M. D., Jansson, M., and Ma, X. (2020): “Simple Local Polynomial Density Estimators,” Journal of the American Statistical Association, 115(531), 1449–1455.CrossRefGoogle Scholar
Cattaneo, M. D., Keele, L., and Titiunik, R. (2023a): “Covariate Adjustment in Regression Discontinuity Designs,” in Handbook of Matching and Weighting in Causal Inference, ed. by Zubizarreta, D. S. S. J. R., Stuart, E. A., and Rosenbaum, P. R., chap. 8, pp. 153–168. Chapman & Hall, Boca Raton, FL.CrossRefGoogle Scholar
Cattaneo, M. D., Keele, L., and Titiunik, R. (2023b): “A Guide to Regression Discontinuity Designs in Medical Applications,” Statistics in Medicine, 42(24): 4484–4513.CrossRefGoogle ScholarPubMed
Cattaneo, M. D., Keele, L., Titiunik, R., and Vazquez-Bare, G. (2016): “Interpreting Regression Discontinuity Designs with Multiple Cutoffs,” Journal of Politics, 78(4), 1229–1248.CrossRefGoogle Scholar
Cattaneo, M. D., Keele, L., Titiunik, R., and Vazquez-Bare, G. (2021): “Extrapolating Treatment Effects in Multi-Cutoff Regression Discontinuity Designs,” Journal of the American Statistical Association, 116(536), 1941–1952.CrossRefGoogle Scholar
Cattaneo, M. D., and Titiunik, R. (2022): “Regression Discontinuity Designs,” Annual Review of Economics, 14, 821–851.CrossRefGoogle Scholar
Cattaneo, M. D., Titiunik, R., and Vazquez-Bare, G. (2016): “Inference in Regression Discontinuity Designs under Local Randomization,” Stata Journal, 16(2), 331–367.CrossRefGoogle Scholar
Cattaneo, M. D., Titiunik, R., and Vazquez-Bare, G. (2017): “Comparing Inference Approaches for RD Designs: A Reexamination of the Effect of Head Start on Child Mortality,” Journal of Policy Analysis and Management, 36(3), 643–681.CrossRefGoogle ScholarPubMed
Cattaneo, M. D., Titiunik, R., and Vazquez-Bare, G. (2019): “Power Calculations for Regression Discontinuity Designs,” Stata Journal, 19(1), 210–245.CrossRefGoogle Scholar
Cattaneo, M. D., Titiunik, R., and Vazquez-Bare, G. (2020a): “Analysis of Regression Discontinuity Designs with Multiple Cutoffs or Multiple Scores,” Stata Journal, 20(4), 866–891.CrossRefGoogle Scholar
Cattaneo, M. D., Titiunik, R., and Vazquez-Bare, G. (2020b): “The Regression Discontinuity Design,” in Handbook of Research Methods in Political Science and International Relations, ed. by Curini, L., and Franzese, R. J., chap. 44, pp. 835–857. Sage, London.Google Scholar
Cattaneo, M. D., Titiunik, R., and Yu, R. (2024): “Estimation and Inference in Boundary Discontinuity Designs,” Working Paper.Google Scholar
Dong, Y. (2015): “Regression Discontinuity Applications with Rounding Errors in the Running Variable,” Journal of Applied Econometrics, 30(3), 422–446.CrossRefGoogle Scholar
Dong, Y. (2018): “Alternative Assumptions to Identify LATE in Fuzzy Regression Discontinuity Designs,” Oxford Bulletin of Economics and Statistics, 80(5), 1020–1027.CrossRefGoogle Scholar
Ernst, M. D. (2004): “Permutation Methods: A Basis for Exact Inference,” Statistical Science, 19(4), 676–685.CrossRefGoogle Scholar
Feir, D., Lemieux, T., and Marmer, V. (2016): “Weak Identification in Fuzzy Regression Discontinuity Designs,” Journal of Business & Economic Statistics, 34(2), 185–196.CrossRefGoogle Scholar
Hahn, J., Todd, P., and van der Klaauw, W. (2001): “Identification and Estimation of Treatment Effects with a Regression-Discontinuity Design,” Econometrica, 69(1), 201–209.CrossRefGoogle Scholar
Hyytinen, A., Meriläinen, J., Saarimaa, T., Toivanen, O., and Tukiainen, J. (2018): “When Does Regression Discontinuity Design Work? Evidence from Random Election Outcomes,” Quantitative Economics, 9(2), 1019–1051.CrossRefGoogle Scholar
Imbens, G., and Rubin, D. B. (2015): Causal Inference in Statistics, Social, and Biomedical Sciences. Cambridge, UK: Cambridge University Press.CrossRefGoogle Scholar
Keele, L., and Titiunik, R. (2018): “Geographic Natural Experiments with Interference: The Effect of All-Mail Voting on Turnout in Colorado,” CESifo Economic Studies, 64(2), 127–149.CrossRefGoogle Scholar
Keele, L. J., and Titiunik, R. (2015): “Geographic Boundaries as Regression Discontinuities,” Political Analysis, 23(1), 127–155.CrossRefGoogle Scholar
Lee, D. S. (2008): “Randomized Experiments from Non-random Selection in U.S. House Elections,” Journal of Econometrics, 142(2), 675–697.CrossRefGoogle Scholar
Lee, D. S., and Card, D. (2008): “Regression Discontinuity Inference with Specification Error,” Journal of Econometrics, 142(2), 655–674.CrossRefGoogle Scholar
Lindo, J. M., Sanders, N. J., and Oreopoulos, P. (2010): “Ability, Gender, and Performance Standards: Evidence from Academic Probation,” American Economic Journal: Applied Economics, 2(2), 95–117.Google Scholar
Londoño-Vélez, J., Rodríguez, C., and Sánchez, F. (2020): “Upstream and Downstream Impacts of College Merit-based Financial Aid for Low-Income Students: Ser Pilo Paga in Colombia,” American Economic Journal: Economic Policy, 12(2), 193–227.Google Scholar
McCrary, J. (2008): “Manipulation of the Running Variable in the Regression Discontinuity Design: A Density Test,” Journal of Econometrics, 142(2), 698–714.CrossRefGoogle Scholar
Papay, J. P., Willett, J. B., and Murnane, R. J. (2011): “Extending the Regression-Discontinuity Approach to Multiple Assignment Variables,” Journal of Econometrics, 161(2), 203–207.CrossRefGoogle Scholar
Reardon, S. F., and Robinson, J. P. (2012): “Regression Discontinuity Designs with Multiple Rating-Score Variables,” Journal of Research on Educational Effectiveness, 5(1), 83–104.CrossRefGoogle Scholar
Rosenbaum, P. R. (2010): Design of Observational Studies. Springer, New York.CrossRefGoogle ScholarPubMed
Sekhon, J. S., and Titiunik, R. (2016): “Understanding Regression Discontinuity Designs as Observational Studies,” Observational Studies, 2, 174–182.Google Scholar
Sekhon, J. S., and Titiunik, R. (2017): “On Interpreting the Regression Discontinuity Design as a Local Experiment,” in Regression Discontinuity Designs: Theory and Applications. Advances in Econometrics, volume 38. Bingley, UK: Emerald; distributed by Turpin Distribution, Ashland, OH., ed. by Cattaneo, M. D., and Escanciano, J. C., pp. 1–28. Emerald Group.CrossRefGoogle Scholar
Thistlethwaite, D. L., and Campbell, D. T. (1960): “Regression-Discontinuity Analysis: An Alternative to the Ex-Post Facto Experiment,” Journal of Educational Psychology, 51(6), 309–317.CrossRefGoogle Scholar
Titiunik, R. (2021): “Natural Experiments,” in Advances in Experimental Political Science, ed. by Druckman, J. N., and Gree, D. P., chap. 6, pp. 103–129. Cambridge, UK: Cambridge University Press.CrossRefGoogle Scholar
Wong, V. C., Steiner, P. M., and Cook, T. D. (2013): “Analyzing Regression-Discontinuity Designs with Multiple Assignment Variables A Comparative Study of Four Estimation Methods,” Journal of Educational and Behavioral Statistics, 38(2), 107–141.CrossRefGoogle Scholar

Save element to Kindle

To save this element to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

A Practical Introduction to Regression Discontinuity Designs
Available formats
×

Save element to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

A Practical Introduction to Regression Discontinuity Designs
Available formats
×

Save element to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

A Practical Introduction to Regression Discontinuity Designs
Available formats
×