  We perform \textit{ab initio} no-core shell-model calculations for $A=18$ and
$19$ nuclei in a $4\hbar\Omega$, or $N_{\rm max}=4$, model space by using the
effective JISP16 and chiral N3LO nucleon-nucleon potentials and transform the
many-body effective Hamiltonians into the $0\hbar\Omega$ model space to
construct the $A$-body effective Hamiltonians in the $sd$-shell. We separate
the $A$-body effective Hamiltonians with $A=18$ and $A=19$ into inert core,
one-, and two-body components. Then, we use these core, one-, and two-body
components to perform standard shell-model calculations for the $A=18$ and
$A=19$ systems with valence nucleons restricted to the $sd$ shell. Finally, we
compare the standard shell-model results in the $0\hbar\Omega$ model space with
the exact no-core shell model results in the $4\hbar\Omega$ model space for the
$A=18$ and $A=19$ systems and find good agreement.
