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Dynamic Competitive Economies with Complete Markets and Collateral Constraints

In this paper we examine the competitive equilibria of a dynamic stochastic economy with complete markets and collateral constraints. We show that, provided both the set of asset payoffs and collateral levels are sufficiently rich, the equilibrium allocations with sequential trades and collateral constraints are equivalent to those obtained in Arrow-Debreu markets subject to a series of appropriate limited pledgeability constraints. We provide sufficient conditions for equilibria to be Pareto efficient and show that when collateral is scarce equilibria are also often constrained inefficient, in the sense that imposing tighter borrowing restrictions can make everybody in the economy better off. We derive sufficient conditions for the existence of Markov equilibria and show that they typically have finite support when there are two agents' types. The model is then tractable and its equilibria can be computed with arbitrary accuracy. We carry outon this basis a quantitative assessment of the risk sharing and efficiency properties ofequilibria.