Structural models with no solution are incoherent, and those with multiple
solutions are incomplete. We show that models with occasionally binding
constraints are not generically coherent. Coherency requires restrictions on
the parameters or on the support of the distribution of the shocks. In presence
of multiple shocks, the support restrictions cannot be independent from each
other, so the assumption of orthogonality of structural shocks is incompatible
with coherency. Models whose coherency is based on support restrictions are
generically incomplete, admitting a very large number of minimum state variable
solutions
