A determination of the QED coupling at the $Z$ pole

We critically examine the evaluation of the hadronic contribution to the running of the QED coupling, $\alpha$, from $Q^2=0$ to $Q^2=M_Z^2$. Using data for $e^+e^-\to{}$hadrons we find that $\alpha(M_Z^2)^{-1} = 128.99\pm 0.06$, as compared to the existing value of $128.87\pm 0.12$.