From sunspots to black holes: Singular dynamics in macroeconomic models

We present conditions for the emergence of singularities in DGE models. We distinguish between slow-fast and impasse singularity types, review geometrical methods to deal with both types of singularity and apply them to DGE dynamics. We find that impasse singularities can generate new types of DGE dynamics, in particular temporary determinacy/indeterminacy. We illustrate the different nature of the two types of singularities and apply our results to two simple models: the Benhabib and Farmer (1994) model and one with a cyclical fiscal policy rule.