Hybrid halide perovskites exhibit nearly 20% power conversion efficiency, but the origin of their high efficiency is still unknown. Here, we compute the shift current, a dominant mechanism of bulk photovoltaic (PV) effect for ferroelectric photovoltaics, in CH$_3$NH$_3$PbI$_3$ and CH$_3$NH$_3$PbI$_{3-x}$Cl$_{x}$ from first principles. We find that these materials give approximately three times larger shift current PV response to near-IR and visible light than the prototypical ferroelectric photovoltaic BiFeO$_3$. The molecular orientations of CH$_3$NH$_3^{+}$ can strongly affect the corresponding PbI$_3$ inorganic frame so as to alter the magnitude of the shift current response. Specifically, configurations with dipole moments aligned in parallel distort the inorganic PbI$_3$ frame more significantly than configurations with near net zero dipole, yielding a larger shift current response. Furthermore, we explore the effect of Cl substitution on shift current, and find that Cl substitution at the equatorial site induces a larger response than does substitution at the apical site.
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