  We formulate an {\it effective cone conjecture} for klt Calabi--Yau pairs
$(X,\Delta)$, pertaining to the structure of the cone of effective divisors
$\mathrm{Eff}(X)$ modulo the action of the subgroup of pseudo-automorphisms
$\mathrm{PsAut}(X,\Delta)$. Assuming the existence of good minimal models in
dimension $\dim(X)$, known to hold in dimension up to $3$, we prove that the
effective cone conjecture for $(X,\Delta)$ is equivalent to the
Kawamata--Morrison--Totaro movable cone conjecture for $(X,\Delta)$. As an
application, we show that the movable cone conjecture unconditionally holds for
the smooth Calabi--Yau threefolds introduced by Schoen and studied by Namikawa,
Grassi and Morrison. We also show that for such a Calabi--Yau threefold $X$,
all of its minimal models, apart from $X$ itself, have rational polyhedral nef
cones.
