  In this work, we perform steady-state continuous wave (cw) photoluminescence
(PL) measurements on a MAPbI$_3$ thin film in the temperature range of 10-160
K, using excitation densities spanning over almost seven orders of magnitude,
in particular investigating very low densities, rarely used in the published
literature. The temperature range used in this study is below or at the edge of
the orthorhombic-tetragonal phase transition in MAPbI$_3$. In particular, we
show that even in high quality MAPbI$_3$, capable of providing high
photovoltaic efficiency, the defect density is high enough to give rise to an
energy level band. Furthermore, we show that the intensity ratio between the
two PL components related to the two crystalline phases, is a function of
temperature and excitation. At high excitation intensities, we show that
amplified spontaneous emission is attainable even in cw conditions.
Time-resolved PL is also performed to justify some assignments of the PL
features. Finally, our systematic approach, typical for the characterization of
semiconductors, suggests that it should also be applied to hybrid halide
perovskites and that, under suitable conditions, the PL characteristics of
MAPbI$_3$ can be reconciled with those of conventional inorganic
semiconductors.
