  In this paper, we prove that the log minimal model program in dimension $d-1$
implies the existence of log minimal models for effective lc pairs (eg of
nonnegative Kodaira dimension) in dimension $d$. In fact, we prove that the
same conclusion follows from a weaker assumption, namely, the log minimal model
program with scaling in dimension $d-1$. This enables us to prove that
effective lc pairs in dimension five have log minimal models. We also give new
proofs of the existence of log minimal models for effective lc pairs in
dimension four and the Shokurov reduction theorem. Other applications appear in
a paper of Birkar-Paun.
