Mean Variance Optimization of Non-Linear Systems and Worst-case Analysis

The model implies some empirical hypotheses, which would be interesting to test in fu-
ture research. While the competition effects of bank mergers are already quite well covered
in the empirical literature, the same does not apply to the liquidity effects. At the individual
level it would be interesting to estimate the effects of mergers on reserve holdings, and in
particular the role of refinancing costs for the sign of reserve changes. At the aggregate level,
it would be important to examine how asymmetry in bank sizes relates to liquidity fluctua-
tions. Moreover, it could be tested whether countries with relatively high refinancing costs
experiencing banking consolidation display a deterioration in aggregate liquidity, whereas
others don’t. Finally, it could be interesting to examine econometrically whether countries
with greater bank competition face larger or smaller aggregate liquidity fluctuations.

Some features of the model deserve further discussion. The interbank market works
in a very simple way. In the ultra-short interbank market, the central bank adjusts the
liquidity supply to accommodate changes in the aggregate demand, and banks can always
meet the repayment to depositors without suffering any liquidity crisis. In a similar spirit,
long-term loans are totally illiquid, or, equivalently, the costs of liquidation are higher than
the relative cost of refinancing. This framework allows us to focus on pure liquidity issues,
and isolate reserve management from other considerations. An interesting extension of this
model would be to analyze the functioning of other, longer term interbank markets, where
the central bank would not be active and banks could modify the liquidity supply only by
selling their long-term assets. We leave this for future research.

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