Using A Fuzzy Regression Discontinuity Designs (Ford) To Estimate Treatments When There Is Insufficient Information About Cut Point Selection: A Review

Abstract

The study aimed to identify and comprehensively review studies related to the use of Fuzzy Regression Discontinuity Designs (FRD) to estimate treatments when there is insufficient information about choosing the cutoff point with reference images illustrating this design. Fuzzy logic and fuzzy inference systems have been used to incorporate imprecise or vaguely-defined information data. fuzzy regression discontinuity design is used to identify the causal effect Fuzzy sets have also been frequently used to model non-precise statistical data . 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. Literature Review has focused on how to use a fuzzy discontinuity regression design to estimate the treatment effect. To eliminate the asymptotic size distortions that the standard error suffers from . Has been reached a new set of testable implications, characterized by a set of inequality restrictions on the joint distribution of observed outcomes and treatment status at the cut-off. We propose a nonparametric test for these testable implications. The test controls size uniformly over a large class of distributions of observables, is consistent against all fixed alternatives violating the testable implications, and has nontrivial power against some local alternatives