  We conduct a comprehensive study of the effects of incorporating galaxy
morphology information in photometric redshift estimation. Using machine
learning methods, we assess the changes in the scatter and catastrophic outlier
fraction of photometric redshifts when galaxy size, ellipticity, S\'{e}rsic
index and surface brightness are included in training on galaxy samples from
the SDSS and the CFHT Stripe-82 Survey (CS82). We show that by adding galaxy
morphological parameters to full $ugriz$ photometry, only mild improvements are
obtained, while the gains are substantial in cases where fewer passbands are
available. For instance, the combination of $grz$ photometry and morphological
parameters almost fully recovers the metrics of $5$-band photometric redshifts.
We demonstrate that with morphology it is possible to determine useful redshift
distribution $N(z)$ of galaxy samples without any colour information. We also
find that the inclusion of quasar redshifts and associated object sizes in
training improves the quality of photometric redshift catalogues, compensating
for the lack of a good star-galaxy separator. We further show that
morphological information can mitigate biases and scatter due to bad
photometry. As an application, we derive both point estimates and posterior
distributions of redshifts for the official CS82 catalogue, training on
morphology and SDSS Stripe-82 $ugriz$ bands when available. Our redshifts yield
a 68th percentile error of $0.058(1+z)$, and a catastrophic outlier fraction of
$5.2$ per cent. We further include a deep extension trained on morphology and
single $i$-band CS82 photometry.
