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Weak Identification in Fuzzy Regression Discontinuity Designs


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


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.

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Bibliographic Info

Paper provided by Vancouver School of Economics in its series working papers with number vadim_marmer-2010-19.

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Length: 50 pages
Date of creation: 15 May 2010
Date of revision: 23 Jan 2014
Handle: RePEc:ubc:pmicro:vadim_marmer-2010-19

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Related research

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

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  1. Miguel Urquiola & Eric A. Verhoogen, 2007. "Class size and sorting in market equilibrium: Theory and evidence," Discussion Papers 0607-14, Columbia University, Department of Economics.
  2. Imbens, Guido W. & Lemieux, Thomas, 2008. "Regression discontinuity designs: A guide to practice," Journal of Econometrics, Elsevier, vol. 142(2), pages 615-635, February.
  3. Taisuke Otsu & Ke-Li Xu, 2011. "Empirical Likelihood for Regression Discontinuity Design," Cowles Foundation Discussion Papers 1799, Cowles Foundation for Research in Economics, Yale University.
  4. 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, 05.
  5. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, 07.
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Cited by:
  1. Feir, Donna & Lemieux, Thomas & Marmer, Vadim, 2014. "Supplement To "Weak Identification in Fuzzy Regression Discontinuity Designs"," working papers vadim_marmer-2014-3, Vancouver School of Economics, revised 23 Jan 2014.
  2. Yukitoshi Matsushita & Taisuke Otsu & Ke-Li Xu, 2014. "Empirical Likelihood for Regression Discontinuity Design," STICERD - Econometrics Paper Series /2014/573, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  3. 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.
  4. Fe, Eduardo, 2012. "Efficient estimation in regression discontinuity designs via asymmetric kernels," MPRA Paper 38164, University Library of Munich, Germany.


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