Credit rationing

Credit rationing is an economics term that has found widespread use in practice. It denotes the blanket rejection of some loan applications , although among them there are also potential borrowers of good quality (definition according to Stiglitz and Weiss 1981).

The question examined is whether banks should raise interest rates in the event of excess demand.

The starting point is that the lender only limited refinancing options has. The bank therefore has two options:

It can either reject any further loan application above a certain loan volume. The ascertained quality of the borrowers does not play a role in this decision.
On the other hand, it can reject potential borrowers with certain negative quality characteristics.

Function of credit rationing

In imperfect markets, credit rationing can make sense. Possible reasons are

Adverse selection : By lowering the loan interest, the average quality of the borrower improves ( quality uncertainty ). A project is only carried out if the expected profit is positive at the given interest rate.
Moral Hazard : By lowering the interest rate, the credit seekers see themselves forced to reduce the risk of their project ( behavioral uncertainty, ex-interim uncertainty).
ex-post uncertainty

The effect of the interest rate cut on bank income can be more than offset by the adverse selection effect.

Theoretical Analysis of Credit Rationing: The Stiglitz and Weiss Model

Basic model

Assumptions

variables

K is the loan amount
r is the lending rate required by the bank
C is the collateral value
R is the agreed repayment in the amount of (1 + r) K

Structural assumptions

Lenders and borrowers are risk neutral
The distribution of borrower qualities is known. However, the investor cannot observe this individually.
The quality of the borrowers depends on the distribution of the project income , whereby the dispersion of the income describes ${\ displaystyle f (y, \ theta)}$ ${\ displaystyle \ theta}$
All projects have the same expected value but different dispersion ${\ displaystyle \ theta}$
A repayment amount R is agreed for the loan: R = (1 + r) K as well as collateral in the amount of C for the default of the borrower.

Profit function of the borrower

The borrower's profit is the maximum from project income minus the agreed repayment and the negative amount of the security:

{\ displaystyle \ max (yR, -C)}

.

The borrower incurs a loss equal to the security as long as the project income is less than the interest-bearing loan amount minus the security. If the project income exceeds this value, the borrower also comes into the profit zone, which is unlimited depending on the project income.

Income function of the lender

The lender's income is the minimum of the agreed repayment and the sum of project income and security:

{\ displaystyle \ min (R, y + C)}

.

The lender's revenue function starts with an amount equal to the security with a project revenue of zero. It then rises with the project income until the agreed repayment amount is reached. Above this, the repayment amount remains constant.

mechanism

An increase in prices has an impact on both demand and the quality and behavior of consumers.

Risk parameters

Borrowers of varying quality are accepted. This is expressed in a different project risk, which can be seen from the distribution of the project income. In order to differentiate between the different project risks, the risk parameter theta is introduced. A high value of the risk parameter theta means a high risk. This is expressed in the probability of low project returns, which is high when the theta is high.

Critical interest rate

For every given loan interest that the bank charges, there is a critical value of the risk parameter theta, above which the borrowers only finance projects that have the optimal risk value, i.e. H. Theta *, exceed. There is therefore an optimal interest rate.

Borrowers only finance projects with risk parameters that exceed the critical theta. If the loan rate rises, the optimal risk value (the critical theta) also rises.

Yield

The bank's expected income from the lending business is lower, the riskier the projects financed. For the lender, increased risk means a lower expected repayment amount per borrower.

Results

For every interest rate r there is a critical value of the risk parameter. From then on, only projects that are riskier than the threshold will be financed.

With the gradual increase in the interest rate r:
- the expected repayment for the investor increases
- however, the critical threshold value of the risk parameter also rises, which can lead to adverse selection or moral hazard.

If the interest rate is optimal, a further increase leads to a loss of income (effect 2 dominates). From then on, it is no longer worthwhile for the bank to raise interest rates. It restricts the supply of credit (credit rationing).

Individual evidence

↑ Article by Stiglitz and Weiss 1981

[1] Article by Stiglitz and Weiss 1981