When Can We Ignore Measurement Error in the Running Variable?

TL;DR

This paper demonstrates that under certain conditions, ignoring measurement error in the running variable of regression discontinuity designs still allows for valid causal inference, especially with bias-aware inference methods.

Contribution

It establishes conditions under which measurement error can be ignored in RDDs and proposes bias-aware inference techniques for partial identification scenarios.

Findings

Ignoring measurement error can be valid if classification is correct and effects are smooth.

Bias-aware inference methods are effective even with irregular support or discreteness.

The approach is demonstrated in both sharp and fuzzy RDDs with empirical data.

Abstract

In many applications of regression discontinuity designs, the running variable used by the administrator to assign treatment is only observed with error. We show that, provided the observed running variable (i) correctly classifies the treatment assignment, and (ii) affects the conditional means of the potential outcomes smoothly, ignoring the measurement error nonetheless yields an estimate with a causal interpretation: the average treatment effect for units whose observed running variable equals to the cutoff. We show that, possibly after doughnut trimming, these assumptions accommodate a variety of settings where support of the measurement error is not too wide. We propose to conduct inference using bias-aware methods, which remain valid even when discreteness or irregular support in the observed running variable may lead to partial identification. We illustrate the results for both sharp and fuzzy designs in an empirical application.