Equivalence between Mean Independence and Zero Correlation of the Error Term with any Function of the Covariates

This paper proves that the mean independence of the error term from the covariates in a linear regression model is equivalent to, rather than just a sufficient condition for, the error term being uncorrelated with any function of the covariates. Therefore, correct functional form specification of the conditional mean E(y|x) is equivalent to, rather than only a consequence of, the zero conditional mean assumption E(ε|x)=0. This fact may provide students and researchers with a helpful way of understanding the full logical content of this important classical linear model assumption.