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. We show that the completeness of the market requires both the set of asset payoffs and collateral levels to be sufficiently rich, so as to allow to decentralize the equilibrium allocations obtained in Arrow-Debreu markets subject to a series of appropriate limited pledgeability constraints. We provide then 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 often have finite support. The model is then tractable and its equilibria can be computed with arbitrary accuracy. We carry out on this basis a quantitative assessment of the risk sharing and efficiency properties of equilibria.