for 1 - δ . The effect of this legal requirement is to proportionally reduce the forward looking part
of the solution. As a consequence in this case the size of the portfolio is proportionally reduced,
without changing the composition of the assets. Clearly deposits, the only freely chosen liability are
proportionally reduced as well, because deposits positively depend on the main spread Zt . These
constraint virtually acts a reserve coefficients on deposits, but is much more effective. In this case
we did not introduce explicitly net worth in the profit function, assuming that capital could not be
invested and had no cost. The introduction of those cost and revenues function would affect the
optimal composition, that would now take into account this component. But the general result
previously discussed would not change. Variations of the capital requirement coefficient would
affect only the size of the portfolio, not the composition.
3.4 Growth
An increase in the factor of growth of the economy reduces the importance of the backward looking
part of each of the equilibrium equations. The impact on the forward looking part is positive in
the case of deposits, negative for loans. This result reflects the fact that the forward looking part
is a function of the feedback process and of income growth. Income growth increases the demand
of future deposits services exogenously, independently of the feedback process. Since issuing loans
the bank increases the level of deposits through the feedback, when income grows the bank obtains
more deposits independently on the loans issuance. So the bank has to allocate these new deposits
to bonds and reduce proportionally the issuance of loans. This of course assuming that the demand
for loans is not affected by the higher income, which is unlikely. A higher demand for loans could
naturally offset this portfolio composition effect and reverse the result, but that would not be
surprising. The interesting result can be better understood considering the effect of a reduction
of the factor of growth of the economy, ceteris paribus. In this case the bank reacts shifting the
portfolio from bonds to loans, if the demand remains unchanged. This result implies that the
banking system shows a tendency to behave anti-cyclically, smoothing macroeconomic shocks.
Until the very recent past, Anglo-saxon economic systems, where stock and bond markets are a
relevant source of finance, were considered to be more volatile than continental European systems,
where the influence of the banking intermediation is stronger. Our results may help to explain why
banking institutions provide insurance. But the stronger impact of the last recession on continental
European economies has put in question the overall validity of these considerations. The German
banking system in particular has been hardly hit, producing, according to many observers, a credit
crunch. The close ties between banks and firms in the German system, where banks hold a large
portfolio of shares of their own borrowers, can explain the surprising fragility that the system
showed after the bubble in the stock market burst. The main limitation of our work, the absence
of an explicit modelling of the stock market, explains the failure of the model to predict such an
outcome.
3.5 Monetary policy and the control of monetary aggregates
Studying the composition of the portfolio of a bank, this model provides a micro-foundation of
the first step of the credit channel of transmission of monetary policy, showing how banks react
to monetary policy shocks. Most of the literature on the credit channel has focused on explaining
why the intermediation of banking institutions affects the investment behaviour of firms, and the
consumption pattern of households, when interest rates vary. Much less attention has recently
been devoted to understand how variations of market interest rates affect the lending decisions
of banks. This issue has probably neglected because central banks interventions are increasingly
conducted influencing the banking system, for example trough the discount window in the US or
the “corridor” of the ECB. Nevertheless in order to evaluate the importance of the credit channel
it is necessary to study how both the size and the composition of the portfolio of assets of banks
are changed.
The version of the model previously exposed considers interest rates on bonds as a substitute
for loans, and no other liabilities different form deposits are introduced in the problem. The
interest rate movements that we study are changes in the market equilibrium rates, and because
of the timing structure chosen we should consider short term interest rates in particular. As a
18