Abstract:

We consider the problem of stabilising the income of a country, henceforth the borrower, which would always prefer a stable income to a random income with the same average, i.e. a country which is risk-averse. This would be appropriate for countries which are heavily reliant upon agricultural output, or those whose exports are concentrated in a few markets with prices which fluctuate considerably. We suppose that there is another country, or possibly an international organisation, which is risk-neutral and has access to relatively large financial resources. We shall refer to this country as the lender. We further suppose that there is asymmetric information: the lender cannot observe the borrower's income. This is extreme though not that unrealistic in many cases. If there is more than one period a simple loan scheme can provide some insurance (Grossman, Levhari and Mirman [5], Yaari [11]). Townsend [10] has shown that it is possible to do better than these simple loan schemes by using efficient contracts. Our purpose is to examine the properties of efficient loan contracts for any time horizon and any discount factor. The efficient contract corresponds to the solution of a dynamic programming problem. So it can be calculated in a straightforward recursive manner. We can show directly that the second-best Pareto-frontier converges to the first-best frontier as the discount factor tends to one. So the efficient contract nearly provides the first-best utilities if the time horizon is sufficiently long and the discount factor is sufficiently high (Section 7). If the contract is fully enforeable and the time horizon is infinite then the borrower's utility becomes arbitrarily negative with probability one. This could be interpreted as saying that a debt crisis will develop with probability one. It also suggests that the contract will become difficult to enforce. Nevertheless even if the borrower is not legally bound by the contract it will still not break down (Section 6). In the special case where the borrower's utility function is exponential the contract transfers consumption between any two states at a constant rate of interest which is less than the rate of time preference (Section 8). This can be interpreted as saying that soft loans are optimal under these circumstances.