Omitted Variable Bias in Interacted Models: A Cautionary Tale

Abstract

We highlight that analyses using interaction terms to study treatment effect heterogeneity are susceptible to a form of omitted variable bias that is often overlooked in economics. Unlike most instances of omitted variable bias, the omitted variables in this case are available to the researcher but were not included in the model. We demonstrate that this exclusion matters based on a replication of 205 estimates across 17 papers published in the American Economic Review over a five-year period. For approximately 60% of these papers, failing to account for the omitted variables changes the majority of estimates by more than 100%.