It has recently been found that anti-Stokes photoluminescence can be observed in degenerately n-doped indium phosphide nanowires, when exciting directly into the electron gas. This anti-Stokes mechanism has not been observed before and allows the study of carrier relaxation and recombination using standard photoluminescence techniques. It is important to know if this anti-Stokes photoluminescence also occurs in bulk semiconductors as well as its relation to carrier recombination and relaxation. Here we show that similar anti-Stokes photoluminescence can indeed be observed in degenerately doped bulk indium phosphide and gallium arsenide and is caused by minority carriers scattering to high momenta by phonons. We find in addition that the radiative electron-hole recombination is highly momentum-conserving and that photogenerated minority carriers recombine before relaxing to the band edge at low temperatures. These observations challenge the use of models assuming thermalization of minority carriers in the analysis of highly doped devices.