Indeterminacy, bifurcations and unemployment fluctuations

We incorporate imperfectly insured unemployment in the finance constrained economy proposed by Woodford (1986), by introducing unions and unemployment benefits financed by labor taxation. We show that this simple extension of the Woodford model changes drastically its stability conditions and local dynamics around the steady state. In fact, in contrast to related models in the literature, we find that, under constant returns to scale in production: (i) indeterminacy always prevails in the case of a unitary elasticity of substitution between capital and labor; (ii) flip and Hopf bifurcations occur for empirically credible elasticities of substitution between capital and labor, so that a rich set of dynamics may emerge at "realistic" parameters' values.