increases ceteris paribus the marginal value of one unit of reserves and has a positive
impact on the demand for reserves.
Whether the merged banks choose a higher reserve-deposit ratio depends on which of
the two effects dominate. Proposition 2 suggests that the internalization effect dominates
when the relative cost of refinancing is low, whereas the diversification effect prevails when
it is high. The intuition behind this result can be explained in terms of the link between the
marginal value of reserves, the initial level of reserves and banks’ ability to estimate future
liquidity needs.7
The marginal value of reserves depends on the amount of reserves a bank has at date
0 and on the probability it will need more liquidity at date 1. The merged banks face less
uncertainty about future liquidity needs than the individual banks, because their demand
for liquidity is more concentrated around the mean. This means that at low initial level
of reserves, a marginal increase of reserves is worth more to the merged banks than to the
individual banks who are less certain of needing more liquidity at date 1. Conversely, when
banks keep high levels of reserves, a marginal increase of reserves is worth less to the merged
banks than to the individual banks, since the merged banks know they will be less likely to
need liquidity at date 1. Whether the merged banks increase their reserve holdings compared
to before merging depends on the relative cost of refinancing pID. When this ratio is low, all
banks keep low reserves because refinancing is not very expensive. Then the merged banks
increase their reserves relative to before merging, since they have a higher marginal value
of further reserve units. The opposite happens when r⅛ is high. In this case reserves are
high, and the merged banks value further increases of reserves less than individual banks,
because they are more confident that they will not need them.
The readjustment of the merged banks’ reserve holdings changes also their refinancing
costs relative to the status quo, and we have the following.
Corollary 2 The merged banks have lower financing costs than the competitors.
This cost advantage for the merged banks is endogenous to the model in that it is
determined not only by diversification, but also by the optimal reserve readjustment. In
7We thank Loretta Mester for suggesting this explanation.
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