Exogenous treatment and endogenous factors: Vanishing of omitted variable bias on the interaction term

Whether interested in the differential impact of a particular factor in various institutional settings or in the heterogeneous effect of policy or random experiment, the empirical researcher confronts a problem if the factor of interest is correlated with an omitted variable. This paper considers circumstances under which the estimate of the mentioned effect is consistent. We find that if the source of heterogeneity and omitted variable are jointly independent of policy or treatment, then the OLS estimate on the interaction term between the treatment and endogenous factor turns out to be consistent.