Inference in Regression Discontinuity Designs with a Discrete Running Variable

TL;DR

This paper examines inference methods in regression discontinuity designs with a limited number of discrete running variable values, revealing issues with standard confidence intervals and proposing more reliable alternatives.

Contribution

It demonstrates the inadequacy of common clustered standard error CIs in such settings and introduces two new confidence intervals with guaranteed coverage.

Findings

Standard CIs have poor coverage in discrete RDDs.

Proposed CIs ensure reliable inference under simple restrictions.

Simulation and empirical results support the new methods.

Abstract

We consider inference in regression discontinuity designs when the running variable only takes a moderate number of distinct values. In particular, we study the common practice of using confidence intervals (CIs) based on standard errors that are clustered by the running variable as a means to make inference robust to model misspecification (Lee and Card, 2008). We derive theoretical results and present simulation and empirical evidence showing that these CIs do not guard against model misspecification, and that they have poor coverage properties. We therefore recommend against using these CIs in practice. We instead propose two alternative CIs with guaranteed coverage properties under easily interpretable restrictions on the conditional expectation function.