Weak Identification in Fuzzy Regression Discontinuity Designs
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.
|Date of creation:||15 May 2010|
|Date of revision:||02 Mar 2015|
|Publication status:||Forthcoming in Journal of Business & Economic Statistics|
|Contact details of provider:|| Web page: http://www.economics.ubc.ca/|
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