  We analyze the twist-4 contributions to Bjorken and Ellis-Jaffe sum rules for
spin-dependent structure function $g_1(x, Q^2 )$. We investigate the anomalous
dimensions of the twist-4 operators which determine the logarithmic correction
to the $1/Q^2$ behavior of the twist-4 contribution by evaluating off-shell
Green's functions in both flavor non-singlet and singlet case. It is shown that
the EOM operators play an important role to extract the anomalous dimensions of
physical operators. The calculations to solve the operator mixing of
higher-twist operators are given in detail.
