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Regression Discontinuity Design with Continuous Measurement Error in the Running Variable

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  • Davezies, Laurent

    (CREST)

  • Le Barbanchon, Thomas

    (Bocconi University)

Abstract

Since the late 90s, Regression Discontinuity (RD) designs have been widely used to estimate Local Average Treatment Effects (LATE). When the running variable is observed with continuous measurement error, identification fails. Assuming non-differential measurement error, we propose a consistent nonparametric estimator of the LATE when the discrepancy between the true running variable and its noisy measure is observed in an auxiliary sample of treated individuals, and when there are treated individuals at any value of the true running variable – two-sided fuzzy designs. We apply our method to estimate the effect of receiving unemployment benefits.

Suggested Citation

  • Davezies, Laurent & Le Barbanchon, Thomas, 2017. "Regression Discontinuity Design with Continuous Measurement Error in the Running Variable," IZA Discussion Papers 10801, Institute of Labor Economics (IZA).
    • Handle: RePEc:iza:izadps:dp10801
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    1. Erich Battistin & Agar Brugiavini & Enrico Rettore & Guglielmo Weber, 2009. "The Retirement Consumption Puzzle: Evidence from a Regression Discontinuity Approach," American Economic Review, American Economic Association, vol. 99(5), pages 2209-2226, December.
    2. Xiaohong Chen & Demian Pouzo, 2015. "Sieve Wald and QLR Inferences on Semi/Nonparametric Conditional Moment Models," Econometrica, Econometric Society, vol. 83(3), pages 1013-1079, May.
    3. Davezies, Laurent & Le Barbanchon, Thomas, 2017. "Regression discontinuity design with continuous measurement error in the running variable," Journal of Econometrics, Elsevier, vol. 200(2), pages 260-281.
    4. Alan I. Barreca & Jason M. Lindo & Glen R. Waddell, 2016. "Heaping-Induced Bias In Regression-Discontinuity Designs," Economic Inquiry, Western Economic Association International, vol. 54(1), pages 268-293, January.
    5. Dale T. Mortensen, 1977. "Unemployment Insurance and Job Search Decisions," ILR Review, Cornell University, ILR School, vol. 30(4), pages 505-517, July.
    6. Sebastian Calonico & Matias D. Cattaneo & Rocio Titiunik, 2014. "Robust data-driven inference in the regression-discontinuity design," Stata Journal, StataCorp LP, vol. 14(4), pages 909-946, December.
    7. Richard Blundell & Xiaohong Chen & Dennis Kristensen, 2003. "Nonparametric IV estimation of shape-invariant Engel curves," CeMMAP working papers CWP15/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    8. 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.
    9. 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, President and Fellows of Harvard College, vol. 122(4), pages 1511-1560.
    10. S. Darolles & Y. Fan & J. P. Florens & E. Renault, 2011. "Nonparametric Instrumental Regression," Econometrica, Econometric Society, vol. 79(5), pages 1541-1565, September.
    11. 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.
    12. Yingyao Hu & Susanne M. Schennach, 2008. "Instrumental Variable Treatment of Nonclassical Measurement Error Models," Econometrica, Econometric Society, vol. 76(1), pages 195-216, January.
    13. 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.
    14. Richard Blundell & Xiaohong Chen & Dennis Kristensen, 2007. "Semi-Nonparametric IV Estimation of Shape-Invariant Engel Curves," Econometrica, Econometric Society, vol. 75(6), pages 1613-1669, November.
    15. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504.
    16. Xiaohong Chen & Demian Pouzo, 2012. "Estimation of Nonparametric Conditional Moment Models With Possibly Nonsmooth Generalized Residuals," Econometrica, Econometric Society, vol. 80(1), pages 277-321, January.
    17. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
    18. Imbens, Guido W. & Lemieux, Thomas, 2008. "Regression discontinuity designs: A guide to practice," Journal of Econometrics, Elsevier, vol. 142(2), pages 615-635, February.
    19. Xiaohong Chen & Han Hong & Elie Tamer, 2005. "Measurement Error Models with Auxiliary Data," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(2), pages 343-366.
    20. Ivan A. Canay & Andres Santos & Azeem M. Shaikh, 2013. "On the Testability of Identification in Some Nonparametric Models With Endogeneity," Econometrica, Econometric Society, vol. 81(6), pages 2535-2559, November.
    21. Chen, Xiaohong, 2007. "Large Sample Sieve Estimation of Semi-Nonparametric Models," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 76, Elsevier.
    22. Lee, David S. & Card, David, 2008. "Regression discontinuity inference with specification error," Journal of Econometrics, Elsevier, vol. 142(2), pages 655-674, February.
    23. Patrick Hullegie & Tobias J. Klein, 2010. "The effect of private health insurance on medical care utilization and self‐assessed health in Germany," Health Economics, John Wiley & Sons, Ltd., vol. 19(9), pages 1048-1062, September.
    24. Jinyong Hahn & Petra Todd & Wilbert Van der Klaauw, 1999. "Evaluating the Effect of an Antidiscrimination Law Using a Regression-Discontinuity Design," NBER Working Papers 7131, National Bureau of Economic Research, Inc.
    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 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.
    27. Card, David, 2001. "Estimating the Return to Schooling: Progress on Some Persistent Econometric Problems," Econometrica, Econometric Society, vol. 69(5), pages 1127-1160, September.
    28. Yingyao Hu & Geert Ridder, 2012. "Estimation of nonlinear models with mismeasured regressors using marginal information," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(3), pages 347-385, April.
    29. Lalive, Rafael, 2008. "How do extended benefits affect unemployment duration A regression discontinuity approach," Journal of Econometrics, Elsevier, vol. 142(2), pages 785-806, February.
    30. 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.
    31. Battistin, Erich & Chesher, Andrew, 2014. "Treatment effect estimation with covariate measurement error," Journal of Econometrics, Elsevier, vol. 178(2), pages 707-715.
    32. Alan I. Barreca & Melanie Guldi & Jason M. Lindo & Glen R. Waddell, 2011. "Saving Babies? Revisiting the effect of very low birth weight classification," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 126(4), pages 2117-2123.
    33. Bound, John & Brown, Charles & Mathiowetz, Nancy, 2001. "Measurement error in survey data," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 5, chapter 59, pages 3705-3843, Elsevier.
    34. J.J. Heckman & E.E. Leamer (ed.), 2001. "Handbook of Econometrics," Handbook of Econometrics, Elsevier, edition 1, volume 5, number 5.
    35. repec:hal:spmain:info:hdl:2441/4bckbd1dtk8jdp1dnjedlgofe2 is not listed on IDEAS
    36. Carrasco, Marine & Florens, Jean-Pierre & Renault, Eric, 2007. "Linear Inverse Problems in Structural Econometrics Estimation Based on Spectral Decomposition and Regularization," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 77, Elsevier.
    37. Yingying Dong, 2012. "Regression Discontinuity Applications with Rounding Errors in the Running Variable," Working Papers 111206, University of California-Irvine, Department of Economics.
    38. Pierre Cahuc & Stéphane Carcillo & Thomas Le Barbanchon, 2014. "Do Hiring Credits Work in Recessions?: Evidence from France," Sciences Po publications 8330, Sciences Po.
    39. Pierre Cahuc & Stéphane Carcillo & Thomas Le Barbanchon, 2014. "Do Hiring Credits Work in Recessions?," Working Papers hal-03602366, HAL.
    40. Xiaohong Chen & Han Hong & Denis Nekipelov, 2011. "Nonlinear Models of Measurement Errors," Journal of Economic Literature, American Economic Association, vol. 49(4), pages 901-937, December.
    41. 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).
    42. 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.
    43. Patricia M. Anderson & Bruce D. Meyer, 1997. "Unemployment Insurance Takeup Rates and the After-Tax Value of Benefits," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 112(3), pages 913-937.
    44. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, September.
    45. Yingying Dong, 2015. "Regression Discontinuity Applications with Rounding Errors in the Running Variable," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(3), pages 422-446, April.
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    More about this item

    Keywords

    regression discontinuity design; measurement error;

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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