  Reionization is thought to have occurred in the redshift range of $6 < z <
9$, which is now being probed by both deep galaxy surveys and CMB observations.
Using halo abundance matching over the redshift range $5<z<8$ and assuming
smooth, continuous gas accretion, we develop a model for the star formation
efficiency $f_{\star}$ of dark matter halos at $z>6$ that matches the measured
galaxy luminosity functions at these redshifts. We find that $f_{\star}$ peaks
at $\sim 30\%$ at halo masses $M \sim 10^{11}$--$10^{12}$~M$_\odot$, in
qualitative agreement with its behavior at lower redshifts. We then investigate
the cosmic star formation histories and the corresponding models of
reionization for a range of extrapolations to small halo masses. We use a
variety of observations to further constrain the characteristics of the galaxy
populations, including the escape fraction of UV photons. Our approach provides
an empirically-calibrated, physically-motivated model for the properties of
star-forming galaxies sourcing the epoch of reionization. In the case where
star formation in low-mass halos is maximally efficient, an average escape
fraction $\sim0.1$ can reproduce the optical depth reported by Planck, whereas
inefficient star formation in these halos requires either about twice as many
UV photons to escape, or an escape fraction that increases towards higher
redshifts. Our models also predict how future observations with JWST can
improve our understanding of these galaxy populations.
