  We consider the problem of determining the beta-functions for any reduced
effective field theory. Even though not all the Green's functions of a reduced
effective field theory are renormalizable, unlike the full effective field
theory, certain effective beta- functions for the reduced set of couplings may
be calculated without having to introduce vertices in the Feynman rules for
redundant operators. These effective beta-functions suffice to apply the
renormalization group equation to any transition amplitude (i.e., S- matrix
element), thereby rendering reduced effective field theories no more cumbersome
than traditionally renormalizable field theories. These effective
beta-functions may equally be regarded as the running of couplings for a
particular redefinition of the fields.
