Weak Identification in Fuzzy Regression Discontinuity Designs
AbstractIn fuzzy regression discontinuity (FRD) designs, the treatment effect is identified through a discontinuity in the conditional probability of treatment assignment. As in a standard instrumental variables setting, 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. This finite-sample 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 the FRD estimator and its 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 InfoPaper provided by Microeconomics.ca Website in its series Micro Theory Working Papers with number vadim_marmer-2010-19.
Length: 51 pages
Date of creation: 15 May 2010
Date of revision: 03 Nov 2012
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Nonparametric inference; treatment effect; size distortions; Anderson-Rubin test; robust confidence set; class size effect;
Find related papers by 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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- 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.
- Fe, Eduardo, 2012. "Efficient estimation in regression discontinuity designs via asymmetric kernels," MPRA Paper 38164, University Library of Munich, Germany.
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