The elephant in the corner: A cautionary tale about measurement error in treatment effects models

Researchers in economics and other disciplines are often interested in the causal effect of a binary treatment on outcomes. Econometric methods used to estimate such effects are divided into one of two strands depending on whether they require the conditional independence assumption (i.e., independence of potential outcomes and treatment assignment conditional on a set of observable covariates). When this assumption holds, researchers now have a wide array of estimation techniques from which to choose. However, very little is known about their performance - both in absolute and relative terms - when measurement error is present. In this study, the performance of several estimators that require the conditional independence assumption, as well as some that do not, are evaluated in a Monte Carlo study. In all cases, the data-generating process is such that conditional independence holds with the 'real' data. However, measurement error is then introduced. Specifically, three types of measurement error are considered: (i) errors in treatment assignment, (ii) errors in the outcome, and (iii) errors in the vector of covariates. Recommendations for researchers are provided.