Structural models with no solution are incoherent, and those with multiple solutions are incomplete. We develop a method to study coherency and completeness conditions for linear dynamic forward-looking rational expectations models under an occasionally binding constraint. In the context of the simple New Keynesian model with a zero lower bound, this method shows that the coherency and completeness condition generally violates the Taylor principle. Rational expectations require time-varying and correlated support restrictions on the distribution of the structural shocks. With appropriate restrictions, a very large number of equilibria can be supported.
Link to paper: arxiv.org/abs/2006.12966