We measure the surface of CH$_3$NH$_3$PbI$_3$ single crystals by making use of two photon photoemission spectroscopy. Our method monitors the electronic distribution of photoexcited electrons, explicitly discriminating the initial thermalization from slower dynamical processes. The reported results disclose the fast dissipation channels of hot carriers (0.25 ps), set a upper bound to the surface induced recombination velocity ($<4000$ cm/s) and reveal the dramatic effect of shallow traps on the electrons dynamics. The picosecond localization of excited electrons in degraded CH$_3$NH$_3$PbI$_3$ samples is consistent with the progressive reduction of photoconversion efficiency in operating devices. Minimizing the density of shallow traps and solving the aging problem may boost the macroscopic efficiency of solar cells to the theoretical limit.
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