assuming that banks operate in regions that are homogeneous. For simplicity loans are assumed
to affect deposits for the following period only.12
Summing deposits of firms and households we can obtain the expected level of deposits of the
bank as:
E[Dt+1]=γYDt + g3E[rtD+1] - g4E[rtB+1] + κE[Lt+1] (15)
where g3 =[f4 - (γY - 1)f2] and g4 =[f5 - (γY - 1)f3].
Interest rates on deposits are assumed to affect equilibrium levels, but not the dynamic behaviour
of deposits. The assumption of a unit root implicitly excludes the existence of a trend, and it
seems reasonable because of the infinite time period of the maximization problem. In the long run
the interest rate should in fact ultimately depend on the productivity of capital and the average
time-preference coefficient, both of which are unlikely to follow a trend, neither deterministic nor
stochastic. The interest rate has increasingly been been model as a mean-reverting stochastic
process, such as the Uhlenberg-Ulbeck in continuous time.
In conclusion, the demand for deposits services is assumed to have three components. One
component is completely exogenous and cannot be influenced by the bank in any way, and it is
the behaviour of income. The second depends on the portfolio choices of the bank, since a fixed
proportion of loans has to be kept or feedbacks in deposits. The interest rate on deposits represents
just the third component. If banks are willing to increase deposits further than they could achieve
with just the normal flow plus the component dependent on the loans issued, they have to pay
an interest rate. But since they cannot separate different components of the demand banks can’t
price discriminate and have to pay the interest rate on all their deposits
2.0.4 The demand for loans
The costly availability of information generates monopoly power in the market for loans. Rela-
tionship lending allows the bank to price monopolistically and the higher return due to the market
power makes the higher risks of the project worth. Sharpe [25] has shown that establishing long-
term relationships with its customers, a bank learns more than others about the business and the
capability of the borrower. This information asymmetry generates a rent that allows banks to
finance risky projects whose information is very opaque, which cannot be financed in the market.
Establishing the relationship and developing their knowledge, banks provide a valuable service,
they create the knowledge necessary to price the risk. The price that firms pay for this service is
the monopolistic rent that they pay on loans.
The empirical tests for the presence of market power were traditionally performed studying the
behaviour of the rate on loans, which has been found to be stickier than the rate on bonds, in
different estimates conducted in different periods of time and different countries. This evidence
though was not uncontroversial, since the stickyness of the rate can be explained as well as the
outcome of credit rationing, or the result of implicit contracts for the smoothing of interest rate
shocks. An important recent result has been provided by Cosimano and Mc Donald [5], which,
analysing a large panel of bank loans, have shown that banks in the US exploit significant market
power in the market for loans.
2.0.5 Revenues
The main stream of profits of the bank stems from the difference between the interests rate rLt ,
that the bank charges on loans, and the interest rate rDt , that it pays to depositors. For simplicity
we assume that banks do not buy shares, and that the only available alternative to the issuance of
loans is the purchase of bonds. The alternative source of revenues is given by the spread between
the interest rate on bonds rBt and the rate on deposits:
υt = rB - rD. (16)
12This assumption is necessary in order to make the model tractable. But it can be justified considering that the
lag in the operation of the feedback should not be too long: firms keep part of their loans as deposits, and in general
most of the portfolio of retail banks is made of short-term loans.