Weak Identification in Fuzzy Regression Discontinuity Designs

Donna Feir, Thomas Lemieux, Vadim Marmer
2016 Figshare  
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
more » ... 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. Supplementary materials for this article are available online.
doi:10.6084/m9.figshare.1378716.v2 fatcat:o4tvd35u6nbpzjg2dowgl3ioqm