With the model $y=\beta_0+\beta_1x+u$ where $var(u|x) = \sigma^2$ and $cov(x,u)>0$
And assuming the $cov(x,u)>cov(z,u)>0$, how can I show the asymptotic bias of $\hat\beta_1^{IV}$ is $\frac{corr(Z,u)}{corr(Z,x)}\frac{\sigma_u}{\sigma_x}$
How would I prove this through logical reasoning rather than the "Matrix Algebra" approach?
