merger changes the merged banks’ deposits, and hence the size of their demand for liquidity.
Corollary 4 shows that the first effect dominates unless cost advantages (efficiency gains and
reduced financing costs) and competition in the loan market (degree of loan differentiation
γ and number of banks N) are so strong that the merged banks increase their balance sheets
substantially relative to two banks in the status quo. From an empirical perspective, such
a strong balance-sheet expansion seems to be a less plausible scenario.
5TheEffects of a Merger on Aggregate Liquidity
Now that we have seen how a merger affects the behavior of individual banks, we can turn
to its implications for the banking system as a whole. To see this, we analyze how changes
in banks’ reserve holdings and in loan market competition modify the aggregate supply and
demand of liquidity, as represented respectively by the sum of all banks’ reserves and of
their demands for liquidity at date 1 when shocks materialize.
We identify two channels. The first one we call reserve channel, as it works through
changes in reserve holdings. When looking at the system as a whole, the distinction be-
tween the internal money market of the merged banks and the interbank market is blurred,
and the total supply of liquidity is composed of the sum of all banks’ reserve holdings.
Nevertheless, the existence of the internal money market affects the total supply of liquidity
through the change in the reserve holdings of the merged banks. The second channel is
an asymmetry channel, which affects the distribution of the aggregate liquidity demand.
This channel originates in the asymmetry of balance sheets across banks, which -as shown
above- depends on both the different amounts of reserves and the different loan market
shares that banks have after the merger.
We start with analyzing each of the two channels in isolation. Then we examine how
they interact in determining aggregate liquidity risk and expected aggregate liquidity needs.
5.1 Asymmetry Channel without Internal Money Market
To isolate the working of the asymmetry channel, we assume for a moment that the merged
banks cannot make use of the internal money market. In this case, they do not have any
financing cost advantages, and they choose the same optimal reserve rule as their competi-
tors. As a consequence, the asymmetry in banks’ balance sheets originates only from the
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