On the role of the quark mass thresholds in extrapolations of the running \alpha_s

The accuracy of the conventional treatment of quark mass thresholds in the QCD running coupling constant ${\alpha }_s$, based on the step approximation to the $\beta$–function, is investigated. The errors of extrapolating $\text{ase}(\mu )$ from low energies to $\mu =M_Z$, implied by this approximation, are shown to be of the same magnitude as the typical next–to–next–to–leading order contributions to \as and tend to increase the resulting \as. The importance of the proper choice of matching points is emphasized.