Is conditional mean independence, $E(e_i | x_i)=0$, a different assumption from $E(x e) = 0$? (from Hansen)
$E(\mathbf{x}e)=0$ does not imply $E(e|\mathbf{x})=0$, to see that, suppose that x is a variable that always takes the value of zero, but $e$ is independent of $\mathbf x$ and has a mean of, say, $3$. Then the expected value of the product is necessarily $0$, but the conditional expectation will be equal to 3 (given independence, the conditional mean is equal to the unconditional mean).