On stationary recursive equilibria and nondegenerate state spaces: The Huggett model

The seminal work of Huggett (1993) showed that in a stationary recursive equilibrium, there exists a unique stationary distribution of agent types. However, the question remains open as to whether an equilibrium's individual state space might turn out to be such that: either (i) every agent's common borrowing constraint binds forever, and so the distribution of agents will be degenerate; or (ii) the individual state space might be unbounded. By invoking a simple comparative-statics argument, we provide closure to this open question. We show that the equilibrium individual state space must be compact and that this set has positive measure. From Huggett's result that there is a unique distribution of agents in a stationary equilibrium, our result implies that it must also be one that is nontrivial or nondegenerate.