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Weak Identification in Fuzzy Regression Discontinuity Designs

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  • Feir, Donna
  • Lemieux, Thomas
  • Marmer, Vadim

Abstract

In fuzzy regression discontinuity (FRD) designs, the treatment effect is identified through a discontinuity in the conditional probability of treatment assignment. We show that when identification is weak (i.e. when the discontinuity is of a small magnitude) the usual t-test based on the FRD estimator and its standard error suffers from asymptotic size distortions as in a standard instrumental variables setting. This problem can be especially severe in the FRD setting since only observations close to the discontinuity are useful for estimating the treatment effect. To eliminate those size distortions, we propose a modified t-statistic that uses a null-restricted version of the standard error of the FRD estimator. Simple and asymptotically valid confidence sets for the treatment effect can be also constructed using this null-restricted standard error. An extension to testing for constancy of the regression discontinuity effect across covariates is also discussed.

Suggested Citation

  • Feir, Donna & Lemieux, Thomas & Marmer, Vadim, 2010. "Weak Identification in Fuzzy Regression Discontinuity Designs," Microeconomics.ca working papers vadim_marmer-2010-19, Vancouver School of Economics, revised 17 Apr 2016.
  • Handle: RePEc:ubc:pmicro:vadim_marmer-2010-19
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    File URL: http://microeconomics.ca/vadim_marmer/wfrd09.pdf
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    References listed on IDEAS

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    1. Otsu, Taisuke & Xu, Ke-Li & Matsushita, Yukitoshi, 2015. "Empirical likelihood for regression discontinuity design," Journal of Econometrics, Elsevier, vol. 186(1), pages 94-112.
    2. 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.
    3. 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.
    4. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037.
    5. 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.
    6. Wilbert van der Klaauw, 2008. "Regression-Discontinuity Analysis: A Survey of Recent Developments in Economics," LABOUR, CEIS, vol. 22(2), pages 219-245, June.
    7. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, July.
    8. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    9. Donald W. K. Andrews & Marcelo J. Moreira & James H. Stock, 2006. "Optimal Two-Sided Invariant Similar Tests for Instrumental Variables Regression," Econometrica, Econometric Society, vol. 74(3), pages 715-752, May.
    10. Guido W. Imbens & Charles F. Manski, 2004. "Confidence Intervals for Partially Identified Parameters," Econometrica, Econometric Society, vol. 72(6), pages 1845-1857, November.
    11. Hahn, Jinyong & Kuersteiner, Guido, 2002. "Discontinuities of weak instrument limiting distributions," Economics Letters, Elsevier, vol. 75(3), pages 325-331, May.
    12. Imbens, Guido W. & Lemieux, Thomas, 2008. "Regression discontinuity designs: A guide to practice," Journal of Econometrics, Elsevier, vol. 142(2), pages 615-635, February.
    13. Mills, Benjamin & Moreira, Marcelo J. & Vilela, Lucas P., 2014. "Tests based on t-statistics for IV regression with weak instruments," Journal of Econometrics, Elsevier, vol. 182(2), pages 351-363.
    14. Antoine, Bertille & Renault, Eric, 2012. "Efficient minimum distance estimation with multiple rates of convergence," Journal of Econometrics, Elsevier, vol. 170(2), pages 350-367.
    15. Antoine, Bertille & Lavergne, Pascal, 2014. "Conditional moment models under semi-strong identification," Journal of Econometrics, Elsevier, vol. 182(1), pages 59-69.
    16. 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.
    17. Papay, John P. & Willett, John B. & Murnane, Richard J., 2011. "Extending the regression-discontinuity approach to multiple assignment variables," Journal of Econometrics, Elsevier, vol. 161(2), pages 203-207, April.
    18. Jean-Marie Dufour, 1997. "Some Impossibility Theorems in Econometrics with Applications to Structural and Dynamic Models," Econometrica, Econometric Society, vol. 65(6), pages 1365-1388, November.
    19. Bertille Antoine & Eric Renault, 2009. "Efficient GMM with nearly-weak instruments," Econometrics Journal, Royal Economic Society, vol. 12(s1), pages 135-171, January.
    20. 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.
    21. Frank Kleibergen, 2002. "Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression," Econometrica, Econometric Society, vol. 70(5), pages 1781-1803, September.
    22. Joshua D. Angrist & Victor Lavy, 1999. "Using Maimonides' Rule to Estimate the Effect of Class Size on Scholastic Achievement," The Quarterly Journal of Economics, Oxford University Press, vol. 114(2), pages 533-575.
    23. Anna Mikusheva, 2007. "Uniform Inference in Autoregressive Models," Econometrica, Econometric Society, vol. 75(5), pages 1411-1452, September.
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    Cited by:

    1. Decio Coviello & Andrea Guglielmo & Giancarlo Spagnolo, 2015. "The Effect of Discretion on Procurement Performance," CEIS Research Paper 361, Tor Vergata University, CEIS, revised 17 Nov 2015.
    2. Yoichi Arai & Hidehiko Ichimura, 2018. "Simultaneous selection of optimal bandwidths for the sharp regression discontinuity estimator," Quantitative Economics, Econometric Society, vol. 9(1), pages 441-482, March.
    3. Eduardo Fé, 2010. "An application of local linear regression with asymmetric kernels to regression discontinuity designs," The School of Economics Discussion Paper Series 1016, Economics, The University of Manchester.
    4. repec:eee:ecosta:v:9:y:2019:i:c:p:156-170 is not listed on IDEAS
    5. repec:eee:econom:v:208:y:2019:i:2:p:468-486 is not listed on IDEAS
    6. Gerardino, Maria Paula & Litschig, Stephan & Pomeranz, Dina, 2017. "Can Audits Backfire? Evidence from Public Procurement in Chile," CEPR Discussion Papers 12529, C.E.P.R. Discussion Papers.
    7. Bertanha, Marinho Angelo & Moreira, Marcelo J., 2017. "Impossible inference in econometrics: theory and applications to regression discontinuity, bunching, and exogeneity tests," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 787, FGV EPGE - Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
    8. Otsu, Taisuke & Xu, Ke-Li & Matsushita, Yukitoshi, 2015. "Empirical likelihood for regression discontinuity design," Journal of Econometrics, Elsevier, vol. 186(1), pages 94-112.
    9. Coviello, Decio & Mariniello, Mario, 2014. "Publicity requirements in public procurement: Evidence from a regression discontinuity design," Journal of Public Economics, Elsevier, vol. 109(C), pages 76-100.
    10. Fe, Eduardo & Hollingsworth, Bruce, 2012. "Estimating the eect of retirement on mental health via panel discontinuity designs," MPRA Paper 38162, University Library of Munich, Germany.
    11. Marinho Bertanha & Marcelo J. Moreira, 2016. "Impossible Inference in Econometrics: Theory and Applications," Papers 1612.02024, arXiv.org, revised Nov 2018.
    12. repec:eee:econom:v:201:y:2017:i:1:p:1-18 is not listed on IDEAS
    13. repec:cep:stiecm:/2014/573 is not listed on IDEAS
    14. Mazzutti, Caio Cícero Toledo Piza da Costa, 2016. "Three essays on the causal impacts of child labour laws in Brazil," Economics PhD Theses 0616, Department of Economics, University of Sussex Business School.
    15. Feir, Donna & Lemieux, Thomas & Marmer, Vadim, 2014. "Supplement To "Weak Identification in Fuzzy Regression Discontinuity Designs"," Microeconomics.ca working papers vadim_marmer-2014-3, Vancouver School of Economics, revised 02 Mar 2015.

    More about this item

    Keywords

    Nonparametric inference; treatment effect; size distortions; Anderson-Rubin test; robust confidence set; class size effect;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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