Estimating the Variance of Measurement Errors in Running Variables of Sharp Regression Discontinuity Designs

TL;DR

This paper introduces two data-driven estimators for the variance of measurement errors in running variables of sharp regression discontinuity designs, addressing a key challenge in bias correction and identification.

Contribution

It proposes novel estimators that rely solely on observed data, eliminating the need for external information to estimate measurement error variance.

Findings

Two estimators for measurement error variance are proposed.

Estimators are constructed from observed running variable and treatment data.

Method enhances bias correction in regression discontinuity analysis.

Abstract

Estimation of a treatment effect by a regression discontinuity design faces a severe challenge when the running variable contains measurement errors since the errors smoothen the discontinuity on which the identification depends. The existing studies show that the variance of the measurement errors plays a vital role in both bias correction and identification under such situations. However, the methodologies to estimate the variance from data are relatively undeveloped. This paper proposes two estimators for the variance of measurement errors of running variables of sharp regression continuity designs. The proposed estimators can be constructed merely from data of observed running variable and treatment assignment, and do not require any other external source of information.