IDEAS home Printed from https://ideas.repec.org/a/wly/quante/v11y2020i3p839-870.html
   My bibliography  Save this article

Bounds on treatment effects in regression discontinuity designs with a manipulated running variable

Author

Listed:
  • François Gerard
  • Miikka Rokkanen
  • Christoph Rothe

Abstract

The key assumption in regression discontinuity analysis is that the distribution of potential outcomes varies smoothly with the running variable around the cutoff. In many empirical contexts, however, this assumption is not credible; and the running variable is said to be manipulated in this case. In this paper, we show that while causal effects are not point identified under manipulation, one can derive sharp bounds under a general model that covers a wide range of empirical patterns. The extent of manipulation, which determines the width of the bounds, is inferred from the data in our setup. Our approach therefore does not require making a binary decision regarding whether manipulation occurs or not, and can be used to deliver manipulation‐robust inference in settings where manipulation is conceivable, but not obvious from the data. We use our methods to study the disincentive effect of unemployment insurance on (formal) reemployment in Brazil, and show that our bounds remain informative, despite the fact that manipulation has a sizable effect on our estimates of causal parameters.

Suggested Citation

  • 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.
  • Handle: RePEc:wly:quante:v:11:y:2020:i:3:p:839-870
    DOI: 10.3982/QE1079
    as

    Download full text from publisher

    File URL: https://doi.org/10.3982/QE1079
    Download Restriction: no

    File URL: https://libkey.io/10.3982/QE1079?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
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Manski, Charles F, 1990. "Nonparametric Bounds on Treatment Effects," American Economic Review, American Economic Association, vol. 80(2), pages 319-323, May.
    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. Miguel Urquiola & Eric Verhoogen, 2009. "Class-Size Caps, Sorting, and the Regression-Discontinuity Design," American Economic Review, American Economic Association, vol. 99(1), pages 179-215, March.
    4. Donald W. K. Andrews, 2000. "Inconsistency of the Bootstrap when a Parameter Is on the Boundary of the Parameter Space," Econometrica, Econometric Society, vol. 68(2), pages 399-406, March.
    5. repec:adr:anecst:y:2013:i:111-113:p:2 is not listed on IDEAS
    6. 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.
    7. David Card & Carlos Dobkin & Nicole Maestas, 2009. "Does Medicare Save Lives?," The Quarterly Journal of Economics, Oxford University Press, vol. 124(2), pages 597-636.
    8. David Card & Raj Chetty & Andrea Weber, 2007. "Cash-on-Hand and Competing Models of Intertemporal Behavior: New Evidence from the Labor Market," The Quarterly Journal of Economics, Oxford University Press, vol. 122(4), pages 1511-1560.
    9. Marinho Bertanha & Guido W. Imbens, 2020. "External Validity in Fuzzy Regression Discontinuity Designs," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(3), pages 593-612, July.
    10. David Card & Laura Giuliano, 2014. "Does Gifted Education Work? For Which Students?," NBER Working Papers 20453, National Bureau of Economic Research, Inc.
    11. 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.
    12. Victor Chernozhukov & Sokbae Lee & Adam M. Rosen, 2013. "Intersection Bounds: Estimation and Inference," Econometrica, Econometric Society, vol. 81(2), pages 667-737, March.
    13. Michael Anderson & Jeremy Magruder, 2012. "Learning from the Crowd: Regression Discontinuity Estimates of the Effects of an Online Review Database," Economic Journal, Royal Economic Society, vol. 122(563), pages 957-989, September.
    14. Katz, Lawrence F. & Meyer, Bruce D., 1990. "The impact of the potential duration of unemployment benefits on the duration of unemployment," Journal of Public Economics, Elsevier, vol. 41(1), pages 45-72, February.
    15. 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.
    16. Jörg Stoye, 2010. "Partial identification of spread parameters," Quantitative Economics, Econometric Society, vol. 1(2), pages 323-357, November.
    17. Johannes F. Schmieder† & Till von Wachter & Stefan Bender, 2011. "The Effects Of Extended Unemployment Insurance Over The Business Cycle: Evidence From Regression Discontinuity Estimates Over Twenty Years," Boston University - Department of Economics - Working Papers Series WP2011-063, Boston University - Department of Economics.
    18. Heckman, James J. & Urzúa, Sergio, 2010. "Comparing IV with structural models: What simple IV can and cannot identify," Journal of Econometrics, Elsevier, vol. 156(1), pages 27-37, May.
    19. Baily, Martin Neil, 1978. "Some aspects of optimal unemployment insurance," Journal of Public Economics, Elsevier, vol. 10(3), pages 379-402, December.
    20. Raj Chetty, 2008. "Moral Hazard versus Liquidity and Optimal Unemployment Insurance," Journal of Political Economy, University of Chicago Press, vol. 116(2), pages 173-234, April.
    21. Imbens, Guido W & Angrist, Joshua D, 1994. "Identification and Estimation of Local Average Treatment Effects," Econometrica, Econometric Society, vol. 62(2), pages 467-475, March.
    22. Guido W. Imbens & Charles F. Manski, 2004. "Confidence Intervals for Partially Identified Parameters," Econometrica, Econometric Society, vol. 72(6), pages 1845-1857, November.
    23. Keisuke Hirano & Jack R. Porter, 2012. "Impossibility Results for Nondifferentiable Functionals," Econometrica, Econometric Society, vol. 80(4), pages 1769-1790, July.
    24. Alex Solis, 2017. "Credit Access and College Enrollment," Journal of Political Economy, University of Chicago Press, vol. 125(2), pages 562-622.
    25. David S. Lee, 2009. "Training, Wages, and Sample Selection: Estimating Sharp Bounds on Treatment Effects," Review of Economic Studies, Oxford University Press, vol. 76(3), pages 1071-1102.
    26. Gerard, Francois & Gonzaga, Gustavo, 2016. "Informal Labor and the Efficiency Cost of Social Programs: Evidence from the Brazilian Unemployment Insurance Program," CEPR Discussion Papers 11485, C.E.P.R. Discussion Papers.
    27. Donald W. K. Andrews & Gustavo Soares, 2010. "Inference for Parameters Defined by Moment Inequalities Using Generalized Moment Selection," Econometrica, Econometric Society, vol. 78(1), pages 119-157, January.
    28. Lejeune, Michel & Sarda, Pascal, 1992. "Smooth estimators of distribution and density functions," Computational Statistics & Data Analysis, Elsevier, vol. 14(4), pages 457-471, November.
    29. Xuan Chen & Carlos A. Flores, 2015. "Bounds on Treatment Effects in the Presence of Sample Selection and Noncompliance: The Wage Effects of Job Corps," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(4), pages 523-540, October.
    30. Thomas S. Dee & Will Dobbie & Brian A. Jacob & Jonah Rockoff, 2019. "The Causes and Consequences of Test Score Manipulation: Evidence from the New York Regents Examinations," American Economic Journal: Applied Economics, American Economic Association, vol. 11(3), pages 382-423, July.
    31. Anderson, Gordon & Linton, Oliver & Whang, Yoon-Jae, 2012. "Nonparametric estimation and inference about the overlap of two distributions," Journal of Econometrics, Elsevier, vol. 171(1), pages 1-23.
    32. Hall, Peter & Wolff, Rodney C. L. & Yao, Qiwei, 1999. "Methods for estimating a conditional distribution function," LSE Research Online Documents on Economics 6631, London School of Economics and Political Science, LSE Library.
    33. repec:adr:anecst:y:2013:i: is not listed on IDEAS
    34. Donald W. K. Andrews & Panle Jia Barwick, 2012. "Inference for Parameters Defined by Moment Inequalities: A Recommended Moment Selection Procedure," Econometrica, Econometric Society, vol. 80(6), pages 2805-2826, November.
    35. Raj Chetty, 2008. "Moral Hazard versus Liquidity and Optimal Unemployment Insurance," Journal of Political Economy, University of Chicago Press, vol. 116(2), pages 173-234, April.
    36. Feldstein, Martin S, 1976. "Temporary Layoffs in the Theory of Unemployment," Journal of Political Economy, University of Chicago Press, vol. 84(5), pages 937-957, October.
    37. Fan, Jianqing & Yao, Qiwei & Tong, Howell, 1996. "Estimation of conditional densities and sensitivity measures in nonlinear dynamical systems," LSE Research Online Documents on Economics 6704, London School of Economics and Political Science, LSE Library.
    38. Jorg Stoye, 2009. "More on Confidence Intervals for Partially Identified Parameters," Econometrica, Econometric Society, vol. 77(4), pages 1299-1315, July.
    39. 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.
    40. Judith Scott-Clayton, 2011. "On Money and Motivation: A Quasi-Experimental Analysis of Financial Incentives for College Achievement," Journal of Human Resources, University of Wisconsin Press, vol. 46(3), pages 614-646.
    41. Johannes F. Schmieder & Till von Wachter & Stefan Bender, 2012. "The Effects of Extended Unemployment Insurance Over the Business Cycle: Evidence from Regression Discontinuity Estimates Over 20 Years," The Quarterly Journal of Economics, Oxford University Press, vol. 127(2), pages 701-752.
    42. Henrik J. Kleven & Mazhar Waseem, 2013. "Using Notches to Uncover Optimization Frictions and Structural Elasticities: Theory and Evidence from Pakistan," The Quarterly Journal of Economics, Oxford University Press, vol. 128(2), pages 669-723.
    43. Patrick Bajari & Han Hong & Minjung Park & Robert Town, 2011. "Regression Discontinuity Designs with an Endogenous Forcing Variable and an Application to Contracting in Health Care," NBER Working Papers 17643, National Bureau of Economic Research, Inc.
    44. 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.
    45. James M. Sallee, 2011. "The Surprising Incidence of Tax Credits for the Toyota Prius," American Economic Journal: Economic Policy, American Economic Association, vol. 3(2), pages 189-219, May.
    46. Billie Davis & John Engberg & Dennis Epple & Holger Sieg & Ron Zimmer, 2013. "Bounding the Impact of a Gifted Program on Student Retention Using a Modified Regression Discontinuity Design," Annals of Economics and Statistics, GENES, issue 111-112, pages 10-34.
    47. Hugo A. Hopenhayn & Juan Pablo Nicolini, 2009. "Optimal Unemployment Insurance and Employment History," Review of Economic Studies, Oxford University Press, vol. 76(3), pages 1049-1070.
    48. Adriana Camacho & Emily Conover, 2011. "Manipulation of Social Program Eligibility," American Economic Journal: Economic Policy, American Economic Association, vol. 3(2), pages 41-65, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Takuya Ishihara & Masayuki Sawada, 2020. "Manipulation-Robust Regression Discontinuity Designs," Papers 2009.07551, arXiv.org, revised Jun 2021.
    2. Yoichi Arai & Yu-Chin Hsu & Toru Kitagawa & Ismael Mourifié & Yuanyuan Wan, 2018. "Testing identifying assumptions in fuzzy regression discontinuity designs," CeMMAP working papers CWP50/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    3. Ivan A Canay & Vishal Kamat, 2018. "Approximate Permutation Tests and Induced Order Statistics in the Regression Discontinuity Design," Review of Economic Studies, Oxford University Press, vol. 85(3), pages 1577-1608.
    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. Gerard, Francois & Gonzaga, Gustavo, 2016. "Informal Labor and the Efficiency Cost of Social Programs: Evidence from the Brazilian Unemployment Insurance Program," CEPR Discussion Papers 11485, C.E.P.R. Discussion Papers.
    6. Bergolo, M. & Cruces, G., 2021. "The anatomy of behavioral responses to social assistance when informal employment is high," Journal of Public Economics, Elsevier, vol. 193(C).
    7. Bertanha, Marinho & Moreira, Marcelo J., 2020. "Impossible inference in econometrics: Theory and applications," Journal of Econometrics, Elsevier, vol. 218(2), pages 247-270.
    8. Christopher Erwin, 2019. "Low-performing student responses to state merit scholarships," Working Papers 2019-02, Auckland University of Technology, Department of Economics.
    9. Judit Krekó, 2019. "Effect of employment tax incentives: the case of disability quota in Hungary," CEU Working Papers 2019_1, Department of Economics, Central European University.
    10. Johannes Spinnewijn, 2020. "The Trade‐Off between Insurance and Incentives in Differentiated Unemployment Policies," Fiscal Studies, John Wiley & Sons, vol. 41(1), pages 101-127, March.
    11. Carvalho, Cristiano C. & Corbi, Raphael & Narita, Renata, 2018. "Unintended consequences of unemployment insurance: Evidence from stricter eligibility criteria in Brazil," Economics Letters, Elsevier, vol. 162(C), pages 157-161.
    12. Cristiano C. Carvalho & Raphael Corbi, Renata Narita, 2017. "Unintended Consequences of Unemployment Insurance: Evidence from Stricter Eligibility Criteria in Brazil," Working Papers, Department of Economics 2017_16, University of São Paulo (FEA-USP).
    13. 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).
    14. 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.
    15. Diogo Britto & Paolo Pinotti & Breno Sampaio, 2020. "The Effect of Job Loss and Unemployment Insurance on Crime in Brazil," BAFFI CAREFIN Working Papers 20139, BAFFI CAREFIN, Centre for Applied Research on International Markets Banking Finance and Regulation, Universita' Bocconi, Milano, Italy.
    16. Eduard Calvo & Ruomeng Cui & Juan Camilo Serpa, 2019. "Oversight and Efficiency in Public Projects: A Regression Discontinuity Analysis," Management Science, INFORMS, vol. 65(12), pages 5651-5675, December.
    17. Andersson, Josefine, 2018. "Financial incentives to work for disability insurance recipients - Sweden’s special rules for continuous deduction," Working Paper Series 2018:7, IFAU - Institute for Evaluation of Labour Market and Education Policy.
    18. Britto, Diogo & Pinotti, Paolo & Sampaio, Breno, 2020. "The Effect of Job Loss and Unemployment Insurance on Crime in Brazil," IZA Discussion Papers 13280, Institute of Labor Economics (IZA).

    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. Gerard, Francois & Rokkanen, Miikka & Rothe, Christoph, 2015. "Identification and Inference in Regression Discontinuity Designs with a Manipulated Running Variable," IZA Discussion Papers 9604, Institute of Labor Economics (IZA).
    2. Gerard, Francois & Rokkanen, Miikka & Rothe, Christoph, 2016. "Bounds on Treatment Effects in Regression Discontinuity Designs under Manipulation of the Running Variable, with an Application to Unemployment Insurance in Brazil," CEPR Discussion Papers 11668, C.E.P.R. Discussion Papers.
    3. Johannes Spinnewijn, 2020. "The Trade‐Off between Insurance and Incentives in Differentiated Unemployment Policies," Fiscal Studies, John Wiley & Sons, vol. 41(1), pages 101-127, March.
    4. Camille Landais, 2015. "Assessing the Welfare Effects of Unemployment Benefits Using the Regression Kink Design," American Economic Journal: Economic Policy, American Economic Association, vol. 7(4), pages 243-278, November.
    5. Chen, Xuan & Flores, Carlos A. & Flores-Lagunes, Alfonso, 2015. "Going Beyond LATE: Bounding Average Treatment Effects of Job Corps Training," IZA Discussion Papers 9511, Institute of Labor Economics (IZA).
    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. Ahn, Taehyun, 2018. "Assessing the effects of reemployment bonuses on job search: A regression discontinuity approach," Journal of Public Economics, Elsevier, vol. 165(C), pages 82-100.
    8. François Gerard & Joana Naritomi, 2021. "Job Displacement Insurance and (the Lack of) Consumption-Smoothing," American Economic Review, American Economic Association, vol. 111(3), pages 899-942, March.
    9. Mesén Vargas, Juliana & Van der Linden, Bruno, 2017. "Is There Always a Trade-off between Insurance and Incentives? The Case of Unemployment with Subsistence Constraints," IZA Discussion Papers 11034, Institute of Labor Economics (IZA).
    10. Konstantinos Tatsiramos & Jan C. Ours, 2014. "Labor Market Effects Of Unemployment Insurance Design," Journal of Economic Surveys, Wiley Blackwell, vol. 28(2), pages 284-311, April.
    11. repec:hrv:faseco:34330197 is not listed on IDEAS
    12. Blaise Melly & Rafael Lalive, 2020. "Estimation, Inference, and Interpretation in the Regression Discontinuity Design," Diskussionsschriften dp2016, Universitaet Bern, Departement Volkswirtschaft.
    13. Jin-young Choi & Myoung-jae Lee, 2017. "Regression discontinuity: review with extensions," Statistical Papers, Springer, vol. 58(4), pages 1217-1246, December.
    14. Bertanha, Marinho & Moreira, Marcelo J., 2020. "Impossible inference in econometrics: Theory and applications," Journal of Econometrics, Elsevier, vol. 218(2), pages 247-270.
    15. Kyyrä, Tomi & Pesola, Hanna & Rissanen, Aarne, 2017. "Unemployment Insurance in Finland: A Review of Recent Changes and Empirical Evidence on Behavioral Responses," Research Reports 184, VATT Institute for Economic Research.
    16. repec:udt:wpecon:2016-03 is not listed on IDEAS
    17. Gonzalez-Rozada, Martin & Ruffo, Hernán, 2016. "Optimal unemployment benefits in the presence of informal labor markets," Labour Economics, Elsevier, vol. 41(C), pages 204-227.
    18. Xintong Wang & Carlos A. Flores & Alfonso Flores-Lagunes, 2020. "The Effects of Vietnam-Era Military Service on the Long-Term Health of Veterans: A Bounds Analysis," Center for Policy Research Working Papers 234, Center for Policy Research, Maxwell School, Syracuse University.
    19. Camille Landais & Pascal Michaillat & Emmanuel Saez, 2018. "A Macroeconomic Approach to Optimal Unemployment Insurance: Applications," American Economic Journal: Economic Policy, American Economic Association, vol. 10(2), pages 182-216, May.
    20. Le Barbanchon, Thomas, 2016. "The effect of the potential duration of unemployment benefits on unemployment exits to work and match quality in France," Labour Economics, Elsevier, vol. 42(C), pages 16-29.
    21. Jesse Rothstein & Robert G. Valletta, 2017. "Scraping by: Income and Program Participation After the Loss of Extended Unemployment Benefits," Journal of Policy Analysis and Management, John Wiley & Sons, Ltd., vol. 36(4), pages 880-908, September.
    22. Guido W. Imbens & Jeffrey M. Wooldridge, 2009. "Recent Developments in the Econometrics of Program Evaluation," Journal of Economic Literature, American Economic Association, vol. 47(1), pages 5-86, March.

    More about this item

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • J65 - Labor and Demographic Economics - - Mobility, Unemployment, Vacancies, and Immigrant Workers - - - Unemployment Insurance; Severance Pay; Plant Closings

    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:wly:quante:v:11:y:2020:i:3:p:839-870. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: https://edirc.repec.org/data/essssea.html .

    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: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/essssea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.