Bias-Aware Inference in Fuzzy Regression Discontinuity Designs

TL;DR

This paper introduces bias-aware confidence sets for fuzzy regression discontinuity designs that improve inference accuracy, especially in complex scenarios like weak identification or discrete running variables.

Contribution

It develops new bias-aware confidence sets based on local linear regression that are valid under a wider range of conditions than existing methods.

Findings

The proposed confidence sets are asymptotically equivalent to existing methods in ideal settings.

They remain valid in scenarios where traditional methods fail, such as weak identification.

The approach explicitly accounts for bias, improving inference robustness.

Abstract

We propose new confidence sets (CSs) for the regression discontinuity parameter in fuzzy designs. Our CSs are based on local linear regression, and are bias-aware, in the sense that they take possible bias explicitly into account. Their construction shares similarities with that of Anderson-Rubin CSs in exactly identified instrumental variable models, and thereby avoids issues with "delta method" approximations that underlie most commonly used existing inference methods for fuzzy regression discontinuity analysis. Our CSs are asymptotically equivalent to existing procedures in canonical settings with strong identification and a continuous running variable. However, due to their particular construction they are also valid under a wide range of empirically relevant conditions in which existing methods can fail, such as setups with discrete running variables, donut designs, and weak identification.