A Convenient Omitted Variable Bias Formula for Treatment Effect Models - Clarke, D (Elsevier B.V., 2019)
Generally, determining the size and magnitude of the omitted variable bias (OVB) in regression models is challenging when multiple included and omitted variables are present. Here, I describe a convenient OVB formula for treatment effect models with potentially many included and omitted variables. I show that in these circumstances it is simple to infer the direction, and potentially the magnitude, of the bias. In a simple setting, this OVB is based on mutually exclusive binary variables, however I provide an extension which loosens the need for mutual exclusivity of variables, deriving the bias in difference-in-differences style models with an arbitrary number of included and excluded “treatment” indicators. © 2018 Elsevier B.V.
Keywords: Omitted variable bias; Ordinary least squares regression; Treatment effects; Difference-in-differences