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

Stuart Lane

Papers from arXiv.org

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.

Date: 2025-11, Revised 2026-04
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-mac
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