Dynamic Competitive Economies with Complete Markets and Collateral Constraints

Abstract

In this article we examine the competitive equilibria of a dynamic stochastic economy with complete markets and collateral constraints. We show that, provided the sets of asset pay-offs and of 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 limited pledgeability constraints. We provide both necessary and sufficient conditions for equilibria to be Pareto efficient and show that when collateral is scarce equilibria are not only Pareto inefficient but 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, for the case of two agents, for the existence of equilibria that have finite support. These equilibria can be computed with arbitrary accuracy and the model is very tractable. Abstract In this paper we examine the competitive equilibria of a dynamic stochastic economy with complete markets and collateral constraints. We show that, provided the sets of asset payoffs and of 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 limited pledgeability constraints.We provide both necessary and sufficient conditions for equilibria to be Pareto efficient and show that when collateral is scarce equilibria are not only Pareto inefficient but 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, for the case of two agents, for the existence of equilibria that have finite support. These equilibria can be computed with arbitrary accuracy and the model is very tractable. * We thank seminar participants at various universities and conferences and in particular Arpad Abraham,

Intertemporal equilibrium with heterogeneous agents, endogenous dividends and collateral constraints

“…However, when financial markets are incomplete like in our model, as mentioned by Gottardi and Kubler (2015), it is not easy to find out robust equilibrium properties.…”

“…Since constraint (46) can be interpreted as a collateral constraint, our stochastic model is also related to Gottardi and Kubler (2015) where they construct a tractable model with collateral constraints and complete markets, and provide sufficient conditions for the existence of Markov equilibria. However, when financial markets are incomplete like in our model, as mentioned by Gottardi and Kubler (2015), it is not easy to find out robust equilibrium properties.…”

The Dynamics of Financially Constrained Arbitrage

“…Besides allowing for dynamic contracts, we allow a contract to serve as collateral for other contracts, in a recursive manner. A similar recursive construction can be found in Gottardi and Kubler (). Simsek () characterizes default rates in collateral equilibrium for general distributions in a static setting.…”

Market Selection With Differential Financial Constraints

“…Borrowing constraints have been introduced in the form of liquidity constraints, that is, when certain types of income cannot be traded upon in advance (see, for example, Detemple and Serrat (2003) and Kiyotaki and Moore (2005)), and in the form of collateral requirements (see Geanakoplos and Zame (2014) and Gottardi and Kubler (2015), as well as the references therein). Gottardi and Kubler (2015), in particular, discuss the efficiency of equilibria with collateral requirements and show that, in certain cases, sharper constraints can lead to Pareto improvement. Gottardi and Kubler (2015), in particular, discuss the efficiency of equilibria with collateral requirements and show that, in certain cases, sharper constraints can lead to Pareto improvement.…”