Control Variables in Interactive Models

Abstract

Accounting studies often examine whether the relation between X and Y varies with a moderating variable, M, by including an interactive term, X × M, in a regression. We provide plain-English guidance on why, how, and when to use control variables, Z, in interaction tests. A simulation and simple descriptions demonstrate how interacted controls affect coefficient estimates and interpretations. In particular, we demonstrate how controlling for Z without an accompanying interaction of X × Z and/or M × Z generally does not eliminate the confounding effect of Z on X × M. We conclude with guidance for future research. Data Availability: Stata code to produce the simulations in this paper is available, as linked in the text. JEL Classifications: M40; M41; C01; C18.