THE IMPACT OF THE CAPITAL MARKET
CHAPTER 8 CREDIT RATIONING
8.3 THEORIES OF CREDIT RATIONING
Early theories of credit rationing were based on the notion of sticky interest rates caused by institutional, legal or cultural factors such as usury laws, transactions costs, inertia or inelastic expectations. These approaches are tantamount to assuming the existence of credit rationing, or it exists because of governmental controls rather than showing that it comes out of optimizing behaviour. Later theories concentrated on the risk of default. The main thrust of this argument is that the
¢nancial intermediary could not be compensated for an increase in risk by an increase in the rate of interest. Beyond some speci¢c loan exposure by the bank, the risk will always outweigh the rate of interest and the expected pro¢t would decline as the rate of interest increases beyond some given point, as shown in Figure 8.2.
Figure 8.2 shows that expected pro¢t for the bank increases as the rate of interest rises. This arises because a rising rate of interest will have two opposing e¡ects on the bank’s loan revenue. First, expected revenue increases because of the increase in price (assuming loan demand is interest-inelastic) and, second, a fall in expected revenue as the risk of default increases. After a certain point the second factor will outweigh the ¢rst factor and total expected revenue/pro¢ts will decline. Hence, expected pro¢t increases at a declining rate because the increase in the rate of interest also increases the risk of default. Beyond some particular rate of interestfRg, the risk of default reduces expected pro¢t faster than the rise in the rate of interest will increase expected pro¢t. The result is that there is a maximum expected pro¢t given byEðÞat the rate of interestfRg, and beyond this point a higher rate of interest reduces expected pro¢t.
Hodgman (1960) was one of the ¢rst to develop a theory of endogenous credit rationing that was consistent with pro¢t-maximizing behaviour. In this framework, which remains at the heart of the credit-rationing literature, is the notion that the bank’s risk of loss (risk of default) is positively related to loan exposure.
The bank’s expected return therefore consists of two components, the minimum return in the event of default and, in the absence of default, the full
THEORIES OF CREDIT RATIONING 115
return given by the loan rate less the cost of raising deposits on the money market.
This analysis is set out more formally in Box 8.1.
Each of these two components has an attached probability. For very small loans the probability of default is virtually zero. As the loan size increases after a certain point the probability of default rises so that the pro¢t on the loan starts to decrease such that the loan o¡er curve bends backwards. This is demonstrated in Figure 8.3.
In the rangeA, loans are small and risk-free. In this rangeL<l=ð1þÞ, the project yields the minimum outcome discounted by the interest cost of funds. In the rangeB, the probability of default rises with loan size. The maximum loan size is given byL. When the demand for loans isD2, the equilibrium rate of interest is r2and loan supply is the regionBwith no excess demand. When the demand for loans is given byD1the rate of interest isr1and the loan o¡ered isL, which is less than the demand at the rate of interestr1. At D1 the size of the loan demanded would always exceed the maximum o¡ered, so that credit rationing occurs.
Even if the demand curve lies betweenD1andD2and does intersect the loan o¡er curve but at a higher interest rate thanr1, the loan o¡ered will still beL. The Hodgman Model is able to explain the possibility of type 1 rationing but is unable to explain type 2 rationing. There is a group demand for credit but at a group interest rate.
Models of limited loan rate di¡erentiation were developed in an attempt to extend the Hodgman analysis, but ended up raising more questions than answers.
In Ja¡ee and Modigliani (1969) a monopolistic bank is assumed to face rigidities in FIGURE 8.2
The interest rate and expected profit Expected
profit
Interest rate Max expected profit E(π*)
R*
the setting of di¡erential loan rates. The question that arises in such models is: When is it optimal for a bank to set a rate of interest such that the demand exceeds supply, as in the case ofD? The problem is that by assuming constraints to setting interest rates it should not be surprising that a nonmarket clearing outcome for the credit market could arise. The more interesting issue is the reasoning and origin for the constraints.
The origin of the practice of limited loan rate di¡erentiation is to do with custom and practice, goodwill, legal constraints (such as usury laws), and
THEORIES OF CREDIT RATIONING 117
BOX 8.1
The Hodgman Model
A risk-neutral bank is assumed to make a one-period loan to a firm. The firm’s investment project provides outcome fxg, which has a minimum flg and maximumfugvalue; sol<x<u. The probability distribution function ofx is described byfðxÞ. The contracted repayment isð1þrÞL, whereLis the loan andr is the rate of interest. The bank obtains funds in the deposit market at a cost. Expected profit is given by the following function:
EðÞ ¼ ðð1þrÞL
l xfðxÞdxþ ðu
ð1þrÞLð1þrÞLfðxÞdx ð1þÞL ð8:1:1Þ If default occurs (x<ð1þrÞL) the bank receivesx. The first term is the income the bank receives ifx<ð1þrÞL; that is, if there is a default. The second term represents bank income if the loan is repaid. The first two terms represent the weighted average of expected revenue from the loan. The weights are prob- abilistic outcomes. The third term is the bank’s cost of funds.
FIGURE 8.3 Type 1 rationing
δ + 1
l r
L
A B
D1
D2
L*
Loan offer curve
r1
r2
institutional rigidities. Interest rates are kept at below market rates as a preferential price to blue-chip customers, emphasizing the customer^loan relationship. Such explanations recognize the fundamental nature of the loan market as being made up of heterogeneous customers. The lender is a price setter and the borrower is a price taker. Di¡erent borrowers have di¡erent quality characteristics. If the lender is a perfectly discriminating monopolist, it would lend according to the borrower’s quality characteristics; hence, there would be no rationing. But the underpinnings of this approach remainad hocand not founded in theory.