The moment is here: a generalized class of estimators for fuzzy regression discontinuity designs

TL;DR

This paper introduces a generalized class of fuzzy regression discontinuity estimators that maintain finite moments and improve small-sample performance over standard methods.

Contribution

It proposes a new family of estimators with a tuning parameter that enhances bias and variance properties, unifying fuzzy and sharp RD estimators.

Findings

The generalized estimators have finite moments regardless of kernel or polynomial degree.

They significantly reduce median bias and mean squared error in simulations.

Confidence intervals from the new estimators show reliable coverage in small samples.

Abstract

The standard fuzzy regression discontinuity (FRD) estimator is a ratio of differences of local polynomial estimators. I show that this estimator does not possess any finite integer moments, regardless of local polynomial degree, kernel function, or bandwidth. The estimator is heavy-tailed in small samples or when the treatment probability discontinuity at the cutoff is small. I present a generalized class of FRD estimators which preserves all finite moments from the data, indexed by a single tuning parameter, and nesting both standard FRD and sharp (SRD) estimators. Simple deterministic values of the tuning parameter lead to substantial improvements in median bias, median absolute deviation, and root mean squared error. Confidence intervals typically give reliable small-sample coverage in simulations. Estimator stability and performance are demonstrated using data on class size effects on educational attainment.