  The behavior of the vector Adler function at spacelike momenta is studied in
the framework of a covariant chiral quark model with instanton-like quark-quark
interaction. The model reproduces the Adler function and $V-A$ correlator
extracted from the ALEPH and OPAL data on hadronic $\tau$ lepton decays,
transformed into the Euclidean domain via dispersion relations. The leading
order contribution from hadronic part of the photon vacuum polarization to the
anomalous magnetic moment of the muon, $a_{\mu}^{\mathrm{hvp}(1)} $, is
estimated.
