Luminosity density (ρ_L) and cosmic SFR density (﹩{\dot{\rho }}_{\star }﹩) as functions of redshift, derived by integrating the model UV LFs to magnitude limits of ﹩{M}_{{\rm{AB}}}=-17﹩ (green lines) and ﹩{M}_{{\rm{AB}}}=-12﹩ (purple lines). The dust corrected SFR densities for the two magnitude limits are shown as solid lines, dust uncorrected SFR densities are shown as dashed lines. The observed SFR densities from Bouwens et al. (2015a) are shown in black (dust corrected) and gray (dust uncorrected). Shaded regions show the 1σ confidence range.