On a Unique Nondegenerate Distribution of Agents in a Heterogeneous Agent Model

The seminal work of Huggett [“The risk-free rate in heterogeneous-agent incompleteinsurance economies”, Journal of Economic Dynamics and Control, 1993, 17(5-6), 953969] showed that there exists a unique stationary distribution of agent types, given by their individual states of asset and income endowment pairs. However, the question remains open if the equilibrium individual state space might turn out to be such that either: (i) every agent’s common borrowing constraint binds forever, so that the distribution of agents will be degenerate; or (ii) that the individual state space might be unbounded, so that there could be multiple stationary equilibrium distributions of assets. By invoking a simple comparative-static 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. We expand on Huggett’s result of a unique stationary equilibrium distribution of agents by showing that it must also be one that is nontrivial or nondegenerate.