Weak Identification in Fuzzy Regression Discontinuity Designs

By D. Feir, Thomas Lemieux, Vadim Marmer. 2016

64 citations recorded by the source corpus.

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. Supplementary materials for this article are available online.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/3867e55e64d87cec64ae30d20388ebe590670548

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Statistics and Probability

Citations in the corpus

Regression Discontinuity Designs (2021, unknown): “Frandsen (2017) proposes a manipulation test for discrete scores and Bugni and Canay (2021) propose a binomial-like test using an asymptotic argument to justify local randomization near the cutoff, both employing a uniform-in-bias approach that requires the manual choice of a theoretical smoothness ”
Regression Discontinuity Design with Continuous Measurement Error in the Running Variable (2017, unknown): “Following the usual strategy (see for instance Newey (1997) or Chen & Pouzo (2012)), we use the triangle inequality to split 1 n ∑n i=1 (ĝp(Zi, ξ)− gp(Zi, ξ)) 2 in three terms: [ 1 n ∑n i=1 (ĝp(Zi, ξ)− gp(Zi, ξ)) 2]1/2 ≤ [ 1 n ∑n i=1 (ĝp(Zi, ξ)− g̃p(Zi, ξ)) 2]1/2”
Randomization Inference in the Regression Discontinuity Design: An Application to Party Advantages in the U.S. Senate (2015, background): “Fuzzy RD designs are local versions of the usual instrumental variables (IV) model and thus concerns about weak instruments may arise in this context as well [34].”