  We determine the Hall conductivity of light-driven graphene, with specific
focus on its frequency dependence, and compare it to the static effective
approximation, based on Floquet states. This approximation gives the Haldane
model as the effective model for light-driven graphene, with a gapped spectrum
and a quantized Hall conductivity of $-2e^2/h$. We simulate both the
light-driven and the effective model, and explicitly include the dissipative
environment in our simulations. We investigate the effect of different driving
regimes and dissipation strengths on the Hall conductivity in graphene. As a
central result, the Hall conductivity of the light-driven system is not well
approximated by the effective model, except for a regime of intermediate
driving frequencies and small dissipation where the Hall conductivity
contribution of the Dirac point approximately recovers the quantized value of
$-2e^2/h$, as well as in the transient dynamics for weak dissipation.
