6. Futuras tendencias
6.6 Nuevas tecnologías al servicio de las finanzas
The central objective of STIGLITZ and WEISS (1981) is to demonstrate the possi-
bility of a stable equilibrium where demand for loans exceeds supply with no tendency for the interest rate to clear the market (see Figure 2-3). In this situa- tion, banks deny loans to borrowers who are observationally indistinguishable from those who receive loans (STIGLITZ and WEISS 1981, p. 394) although all
market participants behave in a rational, profit maximising way. The ultimate reason for this form of credit rationing is that banks have only limited informa- tion about the riskiness of projects to be financed. This fact can explain the exis- tence of a bank optimal interest rate, beyond which, at an increasing interest rate, the loan supply of the bank actually decreases. In the following, I concen- trate on the case where a rise in the interest rate leads to an adverse selection
process regarding the pool of loan applicants (section I of STIGLITZ and WEISS
1981).
STIGLITZ and WEISS (1981) consider the lender-borrower relationship on a loan
market as follows. They assume that the bank faces a group of prospective bor- rowers, each of whom holds a project with uncertain outcome to be credit funded. Borrowers and lenders are risk neutral, and the supply of loanable funds available to the bank is unaffected by the interest rate it charges borrowers. Banks act as price setters on the credit market and as quantity setters on the de- posit market. They simultaneously choose a capacity of funds on the deposit market and a nominal loan rate in such a way that their profit is maximised, tak- ing as given the return demanded by depositors and the loan rates set by other banks (see FREIXAS and ROCHET 1997, p. 140).
Projects are assumed to be not divisible, that is, unless a borrower is successful in getting a loan, the project cannot be carried out. For simplicity it is assumed
that the amount borrowed for each project is identical. However, for each project there is a probability distribution of gross return y which cannot be altered by the borrower. All projects have the same mean return but differ by a risk parameter
θ
, which only the borrowers know. The bank thus cannot ascertain the riskiness of an individual project, but it knows the statistical distribution of returns among the population of potential borrowers. Let the distribution of returns be G(y,θ
) and the density function g(y,θ
). Greaterθ
corresponds with greater risk in the sense of mean preserving spreads. This implies the following (see ROTHSCHILDand STIGLITZ 1970): in case that
θ
a <θ
b, if∫
∫
∞ = ∞0
0 yg(y,
θ
a)dy yg(y,θ
b)dythen for a given return ~y ≥0,
∫
∫
yG y a dy≤ yG y b dy ~ 0 ~ 0 ( ,θ
) ( ,θ
) ,that is the distribution of the riskier project has more weight in the tails.
Borrowers are required to pledge a certain amount of collateral C. Since the bank cannot discriminate between borrowers, the bank offers all borrowers the same standard debt contract, in which the borrower either repays a fixed amount
R (if she can) or her collateral plus cash flow is seized by the bank. The profit of each borrower can thus be written as:
) , max( ) , (y R = −C y−R
π
. (2-1)Figure 2-4: Profit of the borrower as a function of project return Profit of the borrower π C Return of the project y R
Source: Adapted from STIGLITZ andWEISS (1981, p. 396).
To the contrary, the return to the bank
ρ
is a concave function of y (Figure 2-5): ) , min( ) , (y R = R C+ yρ
. (2-2)Figure 2-5: Return to the bank as a function of project re- turn Return to the bank ρ C Return of the project y R
Source: Adapted from STIGLITZ andWEISS (1981, p. 396).
Borrower and bank are thus affected differently by an increasing riskiness of projects: while borrowers gain if the return of the project undergoes a mean pre- serving spread, the bank loses. The downside risk is borne by the bank alone. This is an application of Jensen’s inequality, which states that the expected value of a convex (concave) function increases (decreases) as its argument undergoes a mean preserving spread.29 As a consequence, within the pool of borrowers with the same expected project returns, the more risky borrowers generate the largest profits. However, the projects with the lowest risk generate the highest return for the bank. Since all borrowers are offered the same interest rate, low- risk borrowers implicitly subsidise high-risk borrowers, which is a special form of externality.
Under these circumstances, STIGLITZ and WEISS (1981) establish that the effect
of an increase in interest rates on the bank’s return is twofold. On the one hand, it increases the return the bank makes on any individual loan granted to a bor-
29
Jensen’s inequality does not appear in the original paper of STIGLITZ and WEISS (1981).
However, it is a useful formalisation of their argument (see LENSINK et al. 2001, p. 17 and
rower with given risk
θ
. On the other hand, it also decreases the return of the bank: a rising interest rate decreases the profits of borrowers, probably below zero (or any reservation level). The crucial fact is that, as explicated above, the projects with the lowest risk drop out of the market first, since they generate the lowest profits for borrowers. In turn, the pool of borrowers becomes more risky, which decreases the return of the bank. Therefore, an increase in the interest rateneed not necessarily increase the return to the bank. If the adverse selection ef- fect outweighs the increased return from interest rates, the total return of the bank declines. Whether and when this is the case depends on the distribution of
θ
. For some of these distributions, the bank’s expected return on loans will be single-peaked with a maximum for a repayment R* (see the simulation in NEYER2000, pp. 95-100). Under the assumption that the supply of deposits is not fully elastic, this results in a backward bending supply of credit and, therefore, a situation of equilibrium credit rationing as shown in Figure 2-3.
STIGLITZ and WEISS (1981) also consider a case where moral hazard induces a
backward bending loan supply curve (in section II of their paper). In this in- stance, each borrower has available a choice of projects with different risks. In- creasing the interest rate increases the relative attractiveness of the riskier pro- jects, for which the return to the bank is lower. Raising the interest rate may thus lead borrowers to take actions that are contrary to the objectives of the bank. This establishes a similar case to the one above, where the bank may ration credit instead of raising the interest rate.
The results of STIGLITZ and WEISS stand in marked contrast to the conventional
perfect market model (see STIGLITZ 1987; HILLIER and IBRAHIMO 1993, pp. 284-
288):
1. Equilibrium credit rationing is inconsistent with the orthodox view that in equilibrium supply equals demand (the ‘law of supply and demand’).
STIGLITZ and WEISS (1981, p. 409) conclude their paper by saying that “The
usual result of economic theorizing: that prices clear markets, is model spe- cific and is not a general property of markets – unemployment and credit ra- tioning are not phantasms.”
2. Conventional comparative static analysis breaks down in the presence of asymmetric information. For example, a shift in demand, that is an increase in demand at every interest rate level, would usually be expected to increase both the interest rate and the loan volume traded. If the market is character- ised by equilibrium credit rationing, such as with regard to Demand 2 in Figure 2-3, neither of the two effects will occur.
3. Supply and demand are no longer independent, if informational asymmetries are important. Suppose that an external shock makes all projects to be fi- nanced less likely to be successful. This would affect the demand for funds and also the banks’ willingness to supply funds, since both functions partly depend upon the distribution of projects’ risk.
4. If there are observationally distinguishable groups of borrowers, particularly risky groups may be denied credit at any rate; a phenomenon known as ‘red- lining’. This may be the case if there is no interest rate at which the bank re- ceives a certain minimum return. Although these borrowers have particularly profitable projects, the market equilibrium fails to allocate credit to them
(STIGLITZ and WEISS 1981, pp. 406-407).
Welfare and policy implications will be treated in more detail below (section 2.2.3). I now turn first to the question of how sensitive the previously presented model is to changes in assumptions.