This Appendix demonstrates that an “adverse self selection” among borrowers in a developing country, or among the projects or policies it undertakes, may cause the credit supply schedule it faces to be a negative function of lending rates. An equilibrium in which credit is rationed will ensue when the demand for credit exceeds its supply at the lending rate where the supply of credit begins to contract with further rate increases. An equilibrium may result where some countries obtain all credit desired, others obtain only some, while others are altogether excluded.
Assume that foreign lenders are able to recognize differences in the expected potential returns on loans, and that they can sort borrowers into broad risk classes, but that they cannot distinguish the different degree of riskiness of loans within the same class. In principle, a risk class may contain all borrowers in several countries, all borrowers from one country, or only a subset of borrowers from one country; to simplify the exposition, assume that all borrowers from one country are in the same risk class.
An external loan to a borrower in a particular class is L, the gross return on this loan is R, and the distribution of gross returns and its density is F(r, ξ) and f(R, ξ), respectively. The variable ξ is the risk associated with this particular loan; the larger is ξ, the larger is the risk. The measure of increasing risk employed here is that of a mean-preserving spread (Rothschild and Stiglitz (1971)). In particular, let F and G be the two distributions of returns to two different loans. Then G is more risky than F if G can be derived from F by adding an uncorrelated random term. Equivalently, G is more risky than F if G can be derived from F by taking probability mass from the center of the distribution and adding it to the tails, so as to keep the mean constant (Figure 6).17 The advantage of this method of defining risk is that it allows unambiguous comparative-static conclusions about the effects of an increase in lending risk on the banks’ expected profits, and it permits an analysis of the relation between the borrower’s expected benefit from a loan and changes in its risk.18
where the first condition says that the density of returns on L1 has more weight in the tails, while the second condition implies equality of expected value of returns on L1 and L2.
The individual borrower maximizes his expected returns from the loan. Let R denote the gross return to the borrower of using a bank loan of size L, and let r denote the interest rate charged by the banking market. The net benefit to the borrower of using a loan of size L with return R is given by:
Assuming that the lender has first claim on the returns, the borrower will be in default on this loan if:
Figure 7 shows that the borrower’s net benefits from the loan are a convex function of gross returns. Hence, any change to a more risky policy or project (an increase in ξ), results in an increase in expected net benefits to the borrower.19 Only policies or projects with risk greater than some risk level ξ* will be undertaken, where ξ* is the risk at which the borrower’s expected net benefits from a loan are zero:
An increase in the rate of interest charged by the bank reduces the expected net benefit of loans to the borrower and hence requires an increase in the cutoff level of risk ξ* necessary for loans to have a positive expected net return. To establish this rigorously, differentiate equation (3):
This conclusion establishes the possibility that the interest rate itself can be used by the lender to screen borrowers: the risk of any given amount of lending to a particular risk class will increase with a rise in the interest rate charged, because some of the less risky projects or policies are no longer profitable at the higher interest rate. An increase in the interest rate produces an adverse selection among potential borrowers; that is, the bank’s composition of borrowers becomes more risky.
The concentration of risk within a country, which arises from explicit or implicit public guarantees for private borrowing and cross-default clauses, implies that the total external bank debt of a country is the variable of interest to the bank lenders. Let ΣR be the total return on external bank loans. When total returns fall below (1 + r)ΣL then the country will be induced to undertake a stabilization program in order to obtain a rescheduling of its debt. Assume that debt rescheduling is such that the bank lenders’ loss increases proportionately to the shortfall in total return, so the bank’s net return (see Figure 8) is given by:
The international banking market is taken to be competitive in the sense that there are many noncollusive bank lenders and borrowers. The banks are price-takers in the deposit markets, while they set their lending rates so as to maximize expected profits. Since the national monetary authorities have assumed most of the risk of banks’ deposit liabilities, the banks’ choice of assets does not influence their cost of deposits. The interest rate on deposits is determined by the assumption that banks do not earn excess profit from external lending.
Thus, an increase in the interest rate charged on loans to a particular risk class has two effects on the banks’ expected profits. First, there is the usual direct effect resulting in an increase in expected profits when the composition (and hence the risk) of the borrowers is held constant. Second, an increase in the interest charged by bank lenders has an indirect negative effect on the banks’ expected profits, owing to its adverse selection effect on borrowers. The higher the interest rate, the more likely it is that the latter will dominate the former.
Since the supply of external loans by banks can be assumed to rise with increases in expected profits, the relation between the interest rate charged and the expected profits becomes a relation between the interest rate charged and the supply of loans by the banks. Thus LS in Figure 9 represents the backward-bending relation between the supply of loans and the interest rate charged by international bank lenders for loan financing policies and projects in a particular risk class.
The demand curve for bank financing of development policies and projects is assumed to be downward sloping, as discussed earlier. Hence, it is easily seen (Figure 9) that when the aggregate demand curve for loans, LD in this particular risk class intersects the backward-bending aggregate supply of loans, Ls curve, there will exist an excess demand for loans equal to X. Any increase in the interest rate r beyond r** will reduce the banks’ expected profit. Thus, there is no incentive mechanism to clear the external loan market if there exists excess demand for loans at the interest rate r**, and some potential borrowers will be rationed. On the other hand, if the aggregate demand for loans intersects the aggregate supply below r**, the loan market will clear. An increase in the supply of loanable funds to the banking sector will leave the interest rate-expected profit relation unchanged, and will cause the supply curve in Figure 9 to shift rightward. From this figure it is apparent that such an increase in the supply of loans will first reduce X, the size of the rationed portion of the market, and only then reduce the rates charged to borrowers.
Assume now that the bank can sort potential international borrowers into risk. classes, such that borrowers are known to differ across risk classes, but appear identical within each risk class.20 For each risk class there exists a backward-bending relation between the interest rate charged and expected profits from loans to this risk class. Figure 3 in the text shows the interest rate-expected profit (per dollar lent) relation for three different risk classes, β1(r), β2(r), and β3(r). From this figure, it is clear that if the bank’s cost of deposits exceeds d3 then no borrower in risk class β3(r) will obtain loans from this bank. This is so despite their possible willingness to pay interest charges above the cost of deposits to the bank. For example, if the cost of deposits to the bank is d2, then no borrower in risk class β3(r) will obtain loans, while some, but not necessarily all, borrowers in risk class β2(r) will be able to borrow at interest rate r2, and all borrowers in risk class β1(r) can borrow at interest rate r4. Competition among banks assures that the interest rates charged are such as to equate the expected profits per dollar lent to the various risk classes. Furthermore, profit-maximizing behavior of the individual banks implies that loan credit is available to risk class β1(r) only if risk classes (β2(r) and β3(r) are not rationed.
The shape of the interest rate-expected profits relation for a particular risk class of borrowing countries will be determined by the risk and the distribution of risk among the borrowers in a risk class. For example, if there are only two risk classes, one safe and one risky, then the expected profits will decline steeply once the interest rate is such as to drive the safe borrowers out of the loan market. The position of the interest rate-expected profits relation is determined by the expected return on the total of loans to this particular risk class. Banks will always demand to be compensated for any expected shortfall in loan repayment by raising the contractual interest rate charged. While the lender has no information about the differences in risk among borrowers in a particular risk class, he has knowledge of the interest rate-expected profits relation which permits him to make the kind of lending and interest rate decisions described above.
The argument developed above demonstrates that if international bank lenders have sufficient information about their borrowers and their loans to sort these into risk classes, but not enough information to discriminate among borrowers in the same risk class, then:
(i) an entire risk class of borrowers may be denied access to the international bank loan market;
(ii) there may be one risk class containing both borrowers that obtain bank financing and others that do not;
(iii) all other borrowers will obtain loans at rates reflecting their risk class; and
(iv) banks will not accept offers from the rationed borrowers to pay higher interest charges on loans.