  We test the theoretical predictions of several cosmological models against
different observables to compare the indirect estimates of the current
expansion rate of the Universe determined from model fitting with the direct
measurements based on Cepheids data published recently. We perform a
statistical analysis of type Ia supernova (SN Ia), Hubble parameter, and baryon
acoustic oscillation data. A joint analysis of these datasets allows us to
better constrain cosmological parameters, but also to break the degeneracy that
appears in the distance modulus definition between $H_0$ and the absolute
B-band magnitude of SN Ia, $M_0$. From the theoretical side, we considered
spatially flat and curvature-free $\Lambda$CDM, $w$CDM, and inhomogeneous
Lema\^{i}tre-Tolman-Bondi (LTB) models. To analyse SN Ia we took into account
the distributions of SN Ia intrinsic parameters. For the $\Lambda$CDM model we
find that $\Omega_m=0.35\pm0.02$, $H_0=(67.8\pm1.0)\,$km$\,$s$^{-1}/$Mpc, while
the corrected SN absolute magnitude has a normal distribution ${\cal
N}(19.13,0.11)$. The $w$CDM model provides the same value for $\Omega_m$, while
$H_0=(66.5\pm1.8)\,$km$\,$s$^{-1}/$Mpc and $w=-0.93\pm0.07$. When an
inhomogeneous LTB model is considered, the combined fit provides
$H_0=(64.2\pm1.9)\,$km$\,$s$^{-1}/$Mpc. Both the Akaike information criterion
and the Bayes factor analysis cannot clearly distinguish between $\Lambda$CDM
and $w$CDM cosmologies, while they clearly disfavour the LTB model. For the
$\Lambda$CDM, our joint analysis of the SN Ia, the Hubble parameter, and the
baryon acoustic oscillation datasets provides $H_0$ values that are consistent
with CMB-only Planck measurements, but they differ by $2.5\sigma$ from the
value based on Cepheids data.
