higher return of alternative assets (that may even provide monetary services, in some cases). The
negative impact affects the contemporaneous level of deposits but not the level of the following
period. As a consequence, the higher the rate on bonds, the lower the contemporaneous level of
deposits, the higher the difference between the levels of the two periods. This result provides a
theoretical rational for the empirical evidence provided by Chari, Christiano and Eichenbaum [2],
which shows that M1 shows a relevant positive correlation with future values of the interest rate,
while the correlation with contemporaneous and past values is negative.
The covariance between the interest rate on bonds and the reciprocal of the default costs
increases deposits, so a positive correlation between interest rates and default costs reduces the
level of deposits. The opposite is true in the case of a positive correlation between shocks in the
demand for loans and default costs. Default costs shrink the size of the forward looking part of
the equation, reducing the size of the portfolio. They are the true constraint on the size of the
portfolio, putting a limit to the liquidity creation.
Loans
The rational expectation equilibrium quantity of loans can be easily obtained from the budget
constraint L =(1- q)D - F + NW:
Lt+j+1 = ɪLt+j + ɪNW--— C + 1—γYH γ (ɪ) i Et+i Γ Zt+j+i+11. (44)
t+j γγβ t+j + γγβ γγβα + γγβ = YYγJ t+iL α J ()
And:
1 i Γ(1 — d )( yy β — H) + (1 — q ) κH 1 rB+ j+ι + κ ( rR+ j q - rD+ j )
Lt+j+1 =---Lt+j +---NW - —------------------------------------------— +
yy β γγ β γγ βα
-1 βγγ - 1)Γz - * 1 - κu - (1 - d)(γγβ -1) + (1 - q)κCOV(rB, 1 ) + YYβ-1COV(L , i). (45)
γγ βα γγ βα α βγγ α
This result shows that the contemporaneous rate on bonds has a negative impact on the issuance
of loans. Lower interest rates on bonds increase the amount of loans issued and vice-versa. This
is not surprising since the rate on loans depends negatively on the rate on bonds and the rate on
bonds itself represents the opportunity cost of the issuance of loans.
Loans depend positively on the lagged rate on deposits. At the same time, costs of loans
negatively affect the issuance of loans, while the opposite is true for the cost of deposits. In this
model the amount of deposits represents a constraint for the issuance of loans since it cannot be
adjusted in a costless way. Higher industrial costs (which are linear) and interest rates on deposits
have a stronger impact on the alternative investment of the assets portfolio of banks, bonds. Lower
margins in the intermediation due to higher industrial costs and interest rates of deposits push the
bank to issue proportionally more loans. The reason lies in the fact that there is a crucial difference
between the issuance of loans and of the purchase of bonds. Purchasing bonds the size of the bank
does not change, while the issuance of loans increases the size. The constraint on the size is
caused by the default cost, and is increased by the monopoly power. Default costs are the relevant
constraints for the issuance of loans because they work as an adjustment cost on deposits, as shown
before.
The covariance between the rate of interest and the reciprocal of the cost function has a negative
sign. This implies that a positive correlation between the rate of interest and the default cost has
a positive effect on the issuance of loans. This condition states that when higher rates on bonds
are correlated with higher default costs on loans, the banks, not surprisingly, issues more loans.
Any consideration regarding the impact of interest rate shocks must accordingly be qualified.
When the demand for loans is correlated with default costs, the bank issues a proportion-
ally lower quantity of loans, buying more bonds instead. Not surprisingly if a buoyant demand
is regarded as implying higher future default cost, the enthusiasm for the issuance of loans is
proportionally reduced.
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