  We use a first-principles density functional theory approach to calculate the
shift current and linear absorption of uniformly illuminated single-layer Ge
and Sn monochalcogenides. We predict strong absorption in the visible spectrum
and a large effective three-dimensional shift current ($\sim$100 $\mu$A/V$^2$),
larger than has been previously observed in other polar systems. Moreover, we
show that the integral of the shift-current tensor is correlated to the large
spontaneous effective three-dimensional electric polarization ($\sim$1.9
C/m$^2$). Our calculations indicate that the shift current will be largest in
the visible spectrum, suggesting that these monochalcogenides may be promising
for polar optoelectronic devices. A Rice-Mele tight-binding model is used to
rationalize the shift-current response for these systems, and its dependence on
polarization, in general terms with implications for other polar materials
