According to Malinvaud (see footnote 11), the assumption that E(u_i | X_i) = 0 is quite important. To see this, consider the PRF: Y = β₁ + β₂X_i + u_i . Now consider two situations:

(i) β₁ = 0, β₂ = 1, and E(ui ) = 0;

(ii) β₁ = 1, β₂ = 0, and E(u_i ) = (X_i − 1).

Now take the expectation of the PRF conditional upon X in the two preceding cases and see if you agree with Malinvaud about the significance of the assumption E(u_i | X_i ) = 0.