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Bounds on Treatment Effects in Regression Discontinuity Designs with a Manipulated Running Variable

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  • 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, they remain partially identified under a general model that covers a wide range of empirical patterns. We derive sharp bounds on causal parameters for both sharp and fuzzy designs under our general model, and show how additional structure can be used to further narrow the bounds. 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, 2016. "Bounds on Treatment Effects in Regression Discontinuity Designs with a Manipulated Running Variable," NBER Working Papers 22892, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:22892
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    1. 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.
    2. Victor Chernozhukov & Sokbae Lee & Adam M. Rosen, 2013. "Intersection Bounds: Estimation and Inference," Econometrica, Econometric Society, vol. 81(2), pages 667-737, March.
    3. repec:adr:anecst:y:2013:i:111-113:p:2 is not listed on IDEAS
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Jörg Stoye, 2010. "Partial identification of spread parameters," Quantitative Economics, Econometric Society, vol. 1(2), pages 323-357, November.
    10. 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.
    11. 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.
    12. Chetty, Nadarajan & Finkelstein, Amy Nadya, 2013. "Social Insurance: Connecting Theory to Data," Scholarly Articles 34330197, Harvard University Department of Economics.
    13. Alex Solis, 2017. "Credit Access and College Enrollment," Journal of Political Economy, University of Chicago Press, vol. 125(2), pages 562-622.
    14. 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.
    15. 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.
    16. Gerard, François & 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.
    17. Keisuke Hirano & Jack R. Porter, 2012. "Impossibility Results for Nondifferentiable Functionals," Econometrica, Econometric Society, vol. 80(4), pages 1769-1790, July.
    18. 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.
    19. 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.
    20. repec:adr:anecst:y:2013:i: is not listed on IDEAS
    21. 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.
    22. 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.
    23. Jorg Stoye, 2009. "More on Confidence Intervals for Partially Identified Parameters," Econometrica, Econometric Society, vol. 77(4), pages 1299-1315, July.
    24. 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.
    25. 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.
    26. Guido W. Imbens & Charles F. Manski, 2004. "Confidence Intervals for Partially Identified Parameters," Econometrica, Econometric Society, vol. 72(6), pages 1845-1857, November.
    27. 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.
    28. Raj Chetty & Amy Finkelstein, 2012. "Social Insurance: Connecting Theory to Data," NBER Working Papers 18433, National Bureau of Economic Research, Inc.
    29. 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.
    30. Raj Chetty, 2008. "Erratum: Moral Hazard versus Liquidity and Optimal Unemployment Insurance," Journal of Political Economy, University of Chicago Press, vol. 116(6), pages 1197-1197, December.
    31. Manski, Charles F, 1990. "Nonparametric Bounds on Treatment Effects," American Economic Review, American Economic Association, vol. 80(2), pages 319-323, May.
    32. 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.
    33. 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.
    34. 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.
    35. David Card & Laura Giuliano, 2014. "Does Gifted Education Work? For Which Students?," NBER Working Papers 20453, National Bureau of Economic Research, Inc.
    36. 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.
    37. Baily, Martin Neil, 1978. "Some aspects of optimal unemployment insurance," Journal of Public Economics, Elsevier, vol. 10(3), pages 379-402, December.
    38. 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.
    39. Lejeune, Michel & Sarda, Pascal, 1992. "Smooth estimators of distribution and density functions," Computational Statistics & Data Analysis, Elsevier, vol. 14(4), pages 457-471, November.
    40. 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.
    41. 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.
    42. 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.
    43. 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.
    44. 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.
    45. 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.
    46. 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.
    47. 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.
    48. 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.
    49. 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.
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    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

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