Halide perovskites have recently been shown to exhibit excellent carrier transport properties. Density functional calculations are performed to study the electronic structure, dielectric properties, and defect properties of β-CH₃NH₃PbI₃. The results show that Pb chemistry plays an important role in a wide range of material properties, i.e., small effective masses, enhanced Born effective charges and lattice polarization, and the suppression of the formation of deep defect levels, all of which contribute to the exceptionally good carrier transport properties observed in CH₃NH₃PbI₃. Defect calculations show that, among native point defects (including vacancies, interstitials, and antisites), only iodine vacancy is a low-energy deep trap and non-radiative recombination centre. Alloying iodide with chloride reduces the lattice constant of the iodide and significantly increases the formation energy of interstitial defects, which explains the observed substantial increase in carrier diffusion length in mixed halide CH₃NH₃PbI₂Cl compared to that in CH₃NH₃PbI₃.