Repercussions of default, particularly in modern economies where promises greatly exceed physical endowments, highlight the importance of the careful design of any mechanism which proposes to be an improvement. Whether better results may be obtained by a purely endogenous approach or by one involving government regulation, is often a quantitative issue. While several enforcement mechanisms may be present in an actual economy, a major role is clearly played by collateral. In fact, the vast majority of debt is guaranteed by tangible assets. An important example is given by mortgages, when residential homes serve as collateral for loans to households.

In our work, we consider the general equilibrium model (GEIC) introduced in Geanakoplos, J. and Zame, W.R. (2007) “Collateralized Asset Markets”. It describes a two-period economy where collateral constitutes the only enforcement mechanism. Individuals have to put up durable goods as collateral when they want to take short positions in financial markets. Agents are allowed to default on their promises without any punishment (in particular no reputation effects), but in the case of default, the collateral is seized and distributed among creditors. 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. We use the algorithm described in Schommer, S. (2008) “Computing general equilibrium with incomplete markets and default” to approximate GEIC equilibrium numerically.

A key feature of the model is that scarcity and an unequal distribution of collateralizable goods affects risk-sharing and welfare. If the durable good is plentiful, the model is equivalent to a standard Arrow-Debreu model (and allocations are Pareto-optimal). If, on the other hand, the collateralizable good is scarce, most assets are not traded in equilibrium and markets appear to be incomplete.

In the presence of scarcity, a most interesting question is whether welfare improvements might be achieved through government regulation. It is a quantitative question who in the economy gains and who loses through a regulation of collateral-requirements. We provide a series of examples, some of them illustrative and some realistically calibrated, in order to address this question. The numerical examples illustrate that regulation of margin requirements generally does not lead to Pareto-improvements. However often a majority of agents would favor a regulation since it is welfare improving for them.

In our model, we can interpret the assets with low collateral-requirement as a 'subprime loan'. In particular they carry higher interest rates, and tend to be bought by agents who lack collateralizable goods in the present. Should one banish subprime loans? We find out that restricting trade in the subprime assets tends to hurt all agents. In our numerical examples, it is never optimal to regulate the market for sub-prime loans. On the other hand, in some cases, both rich and poor agents gain if only subprime loans can be traded. However, the middle-class loses if only subprime loans can be traded and it is therefore not Pareto-improving.