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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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    More about this item

    Keywords

    Nonparametric inference; treatment effect; size distortions; Anderson-Rubin test; robust confidence set; class size effect;
    All these keywords.

    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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