α_s(m_Z) from tau decays with matching conditions at three loops

Using the recent four-loop calculations of the QCD beta-function and the three-loop matching coefficients we study the induced error in $\alpha_s(m_Z)$ obtained from $\alpha_s(m_tau)$ due to the evolution procedure. We show that, when consistent matching and running is used at this order, these errors are pushed below 0.0005 in $\alpha_s(m_Z)$.