Regulating Collateral-Requirements when Markets are Incomplete. (2009) Forthcoming Journal of Economic Theory

Abstract. In this paper we examine the effects of default and collateral on risk-sharing. We assume that there is a large set of assets which all promise a risk-less payoff but which distinguish themselves by the collateral requirement. In equilibrium agents default and the assets have different payoffs. If there is an abundance of commodities that can be used as collateral and if each agent owns a large fraction of these commodities, markets are complete and competitive equilibrium allocations are Pareto optimal. If, on the other hand, the collateralizable durable good is scarce or if some agents do not own enough of this good in the first period, markets are endogenously incomplete, only few of the available assets are traded in the competitive equilibrium and allocations are not Pareto optimal. We examine a series of examples to understand which collateral-levels prevail in the sub-optimal equilibrium and under which conditions there is scope for regulating the collateral, that is restricting the sets of tradable assets through a government intervention. Assets with very low collateral requirements can be interpreted as sub-prime loans and in our examples these assets are often traded actively in the competitive equilibrium. However, in our examples it turns out that a regulation of collateral requirements can never lead to a Pareto-improvement. While the competitive equilibria are constrained efficient, there do exist regulations which make a majority of agents in the economy better off. These regulations typically restrict all trade to take place in the low-collateral loans and benefit the poor and the rich agents in the economy through their effects on the equilibrium interest rate and the equilibrium price of the durable goods