  We use results of fits to the OPAL spectral data, obtained from non-strange
hadronic \tau decays, to evaluate the difference between the vector and axial
current correlators, \Pi_{V-A}(Q^2). The behavior of \Pi_{V-A}(Q^2) near
euclidean momentum Q^2=0 is used to determine the effective low-energy
constants L_10^eff and C_87^eff related to the renormalized low-energy
constants L_10^r and C_87^r in the chiral lagrangian. We also investigate how
well two-loop chiral perturbation theory describes \Pi_{V-A}(Q^2) as a function
of Q^2. This is the first determination of L_10^eff and C_87^eff to employ a
fully self-consistent model for the violations of quark-hadron duality in both
the vector and axial channels. We also discuss the values of the coefficients
C_{6,V-A} and C_{8,V-A} governing the dimension six and eight contributions to
the operator product expansion representation of \Pi_{V-A}(Q^2).
