  The shift current in bulk photovoltaics is commonly attributed to a shift in
non-interacting charge centres. We show that the origin of shift currents in
the many-body picture is fundamentally different. Here the shift current arises
largely from a many-body shift vector that also involves shifts in charge
centres, but these are associated with pairs of nearly-degenerate excitons
overlapping in k-space. The shift current can thus be enhanced by
nearly-degenerate, optically-active and tightly-bound excitons, spread out in
k-space. Ab initio results are presented for BaTiO$_3$, NbOCl$_2$ and MoS$_2$.
