# Validity condition for Instrumental Variables

My professor states the validity condition in the following way: $$W$$ (the matrix of instrumental variables) must be such that $$\text{plim} \, \frac{W'u}{N}=0$$, where $$u$$ is the error term. Intuitively, I can see that in some way, this relates to the covariance between $$W$$ and $$u$$, but am not entirely convinced. Moreover, why do we look at this condition in an asymptotic setting? Why not impose mean independence, i.e., $$E(u|W)=E(u)$$?

Essentially, $$Cov(u,W) = 0$$ is implied by $$E(u|W) = E(u)$$ by the Law of iterated expectations
• I think $\mathrm{Cov}(u,W)=0$ is implied by $E(u|W)=0$, not the other way around. Dec 6 '18 at 21:04