This article reports ab initio Fermi surfaces and conduction-band calculations of both stoichiometric and oxygen-reduced MoO3. The data, based on a TB-LMTO approach in LDA, provide a convincing and detailed interpretation of the one-electron removal XPS valence bands, where a clear energy gap is observed for the stoichiometric samples, whereas a significant emission at the Fermi edge is measured for the oxygen reduced system. In addition, the electrical conductivity, as deduced from the shape of the calculated Fermi surface, is confined in the xz plane of the crystal, as required for Luttinger-liquid behavior. These results, when compared to the conduction mechanism observed in the blue bronze K0.3MoO3, clearly suggest that oxygen reduction and doping can bring to very different processes for the electronic transport.