  Pulsars are rapidly rotating neutron stars that emit radiation across the
electromagnetic spectrum, from radio to gamma-rays. We use the rapid binary
population synthesis suite COMPAS to model the Galactic population of canonical
pulsars. We account for both radio and gamma-ray selection effects, as well as
the motion of pulsars in the Galactic potential due to natal kicks. We compare
our models to the catalogs of pulsars detected in the radio, and those detected
in gamma-rays by Fermi, and find broad agreement with both populations. We
reproduce the observed ratio of radio-loud to radio-quiet gamma-ray pulsars. We
further examine the possibility of low spin-down luminosity (Edot) pulsars
emitting weak, unpulsed gamma-ray emission and attempt to match this with
recent stacking results. We demonstrate that the apparent correlation between
the latitude of a pulsar and its Edot arises due to natal kicks imparted to
pulsars at birth, assuming that all pulsars are born in the Galactic disk.
