On Nonparametric Inference in the Regression Discontinuity Design

TL;DR

This paper examines the limitations of nonparametric tests in regression discontinuity designs, revealing that under common assumptions, these tests cannot have power against alternatives without size distortions, but proposes a strengthened assumption for valid testing.

Contribution

The paper identifies fundamental limitations of existing nonparametric tests in RDD and introduces a strengthened assumption to enable valid size control for a new test.

Findings

Any test under standard assumptions has limited power and size distortions.

A strengthened assumption allows a novel test to control limiting size.

The results highlight fundamental challenges in nonparametric inference in RDD.

Abstract

This paper studies the validity of nonparametric tests used in the regression discontinuity design. The null hypothesis of interest is that the average treatment effect at the threshold in the so-called sharp design equals a pre-specified value. We first show that, under assumptions used in the majority of the literature, for \emph{any} test the power against any alternative is bounded above by its size. This result implies that, under these assumptions, any test with nontrivial power will exhibit size distortions. We next provide a sufficient strengthening of the standard assumptions under which we show that a novel test in the literature can control limiting size.