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



expected aggregate needs, whereas the effect on loan rates may still depend on their sizes.

The interesting features of these results are that mergers are likely, ceteris paribus, to
increase expected aggregate liquidity needs more in developing countries than in industrial
ones, as they lead to lower reserve holdings for higher cost of refinancing; and that there
is more complementarity between competition and liquidity in industrial countries than in
developing ones. In terms of policy implications, these results suggest that policies aiming
at promoting loan market competition may also prevent the adverse effects of consolidation
for interbank liquidity in industrial countries, but not necessarily in developing countries.

7 Conclusions

This paper analyzes the impact of bank mergers on credit market competition, reserves
and banking system liquidity. A merger creates an internal money market, which modifies
merged banks’ optimal choice of reserves holdings, either decreasing them through a diver-
sification effect or
-more surprisingly- increasing them through an internalization effect.
In both situations, merged banks benefit from a better estimate of future shocks and scope
economies in their liquidity management, and they lower their financing costs and liquidity
risk.

The change in merged banks’ reserve holdings, together with the change in the size of
banks’ balance sheets due to altered loan competition, affect the functioning of the interbank
market. Changes in reserve holdings modify the aggregate supply of private liquidity, while
increased balance-sheet asymmetry raises aggregate liquidity needs by altering the distribu-
tion of the aggregate liquidity demand. These reserve and asymmetry channels can work in
the same or in opposite directions, depending on the cost of refinancing in the money market
as compared to the cost of financing through retail deposits. We conclude that mergers are
more likely to increase aggregate liquidity needs when they involve large banks leading to a
‘polarization’ of the banking system. Moreover, the risk of adverse liquidity effects of bank
consolidation is likely to be more relevant when the ratio of interbank to deposit funding
costs is high. In this case there is also a lower complementarity between competition and
liquidity, so that the effects of consolidation on loan rates and aggregate liquidity do not
necessarily go hand in hand. These results have important implications for central banks’
money market operations.

27



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