consequence monetary policy can be analyzed only trough its effect on the bond market and the
price of securities in general. The model could easily be changed though to study the discount
window or other forms of direct lending form the central bank to the banking system. In this case
the formal structure would remain unchanged, but F would change sign and indicate a liability
rather than an asset. The only necessary modification would be the need to introduce a non-linear
cost on this liability, because the cost of borrowing for any firm is always convex since the risk
grows non-linearly with the amount borrowed, and the amount of finance provided by the central
bank is always limited. In this case the results would be quite similar, and the coefficient of the
cost function would play the same role as the coefficient of the default cost function. The model
could similarly be extended to include any number of assets and liabilities. We have not shown
these different cases because the solution becomes heavy whenever another liability is added to the
problem, since the value of the roots cannot be simplified. On the contrary the pattern of results
would remain similar since the formal structure of the model would remain unchanged.
The results of our basic model show that higher interest rates on securities reduce the size of
the portfolio and alter the composition in favour of bonds. Banks set the rate on loans in function
of the rate on bonds, smoothing transitory interest rates shocks, while in the case of permanent
shocks they may even amplify the shocks. Besides we have seen that the change of the portfolio
would depend on the initial level of the rates, because the impact of interest rates shocks on the
cash-flow of borrowers is likely to be much stronger when the rates are high. If we would have
considered direct lending of the central bank, the results would have been very similar, but the
forward looking part of the solutions would be smaller in absolute value, because of the presence
of a second cost coefficient in the denominator. This implies that the shock would be smoothed a
bit more.
These results suggest that the credit channel tends to increase the effectiveness of monetary
policy when interest rates are low, while in the case of high interest rates banks might even offset
the result of the policy. This explains why central banks need to impose quantitative restrictions
on the issuance of loans in order to fight high inflations. The interest rate is a very good instrument
as long as interest rates are not very high. In the last case the imposition of ceilings on the issuance
on loans can be necessary to control the endogenous growth of money supply.
In order to control the quantity of monetary aggregates the endogenous process of supply of
deposits by means of the feedback of loans must be considered. This model provides a useful
insight since it considers the incentives that a profit maximising banking firm faces in the process.
The model showed that capital requirements are much more effective than reserve coefficients as a
constraint on the size of the portfolio, because they affect the scale of the whole dynamic process.
Another crucial factor is the value of the parameters of the default cost function, since the size of
the portfolio is ultimately constrained by default costs. This implies that regulatory requirements
regarding the write-off of bad loans are crucial not just for the efficiency of the banking industry,
but for the health of the economic system as a whole. When banks are allowed to roll over loans
that should be written off, the constraint on the size of the portfolio is virtually removed, since
default costs can be indefinitely postponed. This implies that any investment could in principle be
financed, without any selection, producing permanent distortions in the productive structure.
The strength of the results depends on the sensitivity of the demand for loans on the rate on
bonds. The development of the bond market tends to reduce the market power of banks, reducing
the strength of the previous results. But since they can never be overturned, even in the limit case
of perfect competition in the market for loans, the results seem quite robust. It must finally be
observed that the results do not depend on the particular feedback process assumed, since it can
be shown that using different assumptions regarding the time profile of the feedback process the
model provides results that are almost identical.
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