We investigate the role of the mass scale parameter μ2 that naturally arises in the course of computing radiative corrections in quantum-field theory when using operator regularization. When dealing with renormalizable theories, a change in the value of μ2 can be compensated for by a change in the physical parameters that characterize the theory, and a set of renormalization group equations similar to those of Gell-Mann and Low are derived. As operator regularization does not give rise to divergences at any stage of a calculation, it is possible to compute radiative corrections in so-called nonrenormalizable interactions. In these theories, a change in the physical parameters of the theory cannot compensate for a change in the value of μ2; rather, μ2 is fixed by the strength of effective interactions generated by radiative processes. Finally, we suggest that even in renormalizable theories, the value of μ2 is determined by a mechanism for mass generation, suggested by Nambu and Jona-Lasinio.