  We theoretically discuss analogues of the anomalous and the integer quantum
Hall effect in driven-dissipative two-dimensional photonic lattices in the
presence of a synthetic gauge field. Photons are coherently injected by a
spatially localized pump, and the transverse shift of the in-plane light
distribution under the effect of an additional uniform force is considered.
Depending on pumping parameters, the transverse shift turns out to be
proportional either to the global Chern number (integer quantum Hall effect) or
to the local Berry curvature (anomalous Hall effect). This suggests a viable
route to experimentally measure these quantities in photonic lattices.
