Indeterminacy in credit economies

Abstract

We characterize the equilibrium set of a two-good, pure-credit economy with limited commitment, under both pairwise and centralized meetings. We show that the set of equilibria derived under "not-tootight" solvency constraints (Alvarez and Jermann, 2000) commonly used in the literature is of measure zero in the whole set of Perfect Bayesian Equilibria. There exist a continuum of stationary equilibria, a continuum of endogenous credit cycles of any periodicity, and a continuum of sunspot equilibria, irrespective of the assumed trading mechanism. Equilibria featuring "too-tight" solvency constraints can generate growing credit limits over time, periodic credit shutdowns, and heterogeneous debt limits across ex-ante identical borrowers. Moreover, we provide examples of credit cycles that dominate, from a social welfare point of view, all equilibria with "not-too-tight" solvency constraints.

Optimal monetary interventions in credit markets

“…This would in turn deter sellers from extending loans larger than the debt limit. Bethune, Hu, and Rocheteau (2018) have proved this in a pure-credit economy and their results can be easily generalized to our setting.…”

“…In this case, the pair (y 1 , y 2 ) that solves (2)-(3) satisfies (5) and (6). The latter is true because the pair (y 1 , y 2 ) that solves (2)-(3) satisfies (3) with equality, which implies that (4) is equivalent to (6).…”

“…If, instead, r > r c , the optimal allocation is given by the unique solution, denoted by (y c 1 , y c 2 ), to (5) and (6) at equality. In this case,…”

“…The optimal allocation maximizes (1) subject to (5) and (6). Lemma 1 shows that we can ignore (5). The problem then becomes a standard maximization problem: the objective function (1) is strictly concave, and the constraint (6) gives a convex set, and hence it has a unique solution characterized by first-order conditions, which turn out to coincide with (5).…”

“…In turn, for any given τ , the equilibrium allocation solves a modified version of equation (9) in which the real interest rate r is replaced with the nominal interest rate i. 5 Note that, since τ ≥ 0 implies i ≥ r, welfare is maximized under no intervention.…”