It is sometimes said that banks are more than just financial intermediaries, because they can sort of create their own funds to lend. In this analysis, a simple financial intermediary would be one that takes in funds that the public place with it and then allocates these between different assets. Banks, in contrast, don't need to wait for funds to come in, because the very act of their lending creates the deposits that fund them. It might therefore be concluded that bank decisions matter, whereas those of other financial institutions do not (or at least they matter less).
Whatever the merits of this analysis, I always find it useful to look at things from different angles, so I thought I'd describe a slightly different approach. What I want to do is start from the concept of a completely passive bank, which makes no decisions of any importance, and then see what we need to change to get a more realistic picture.
So, this starts with a bank that does no more than record transactions. Everyone has an account with the bank and each account carries a balance measured in units of the currency. Whenever any one person wants to make a payment to another, they inform the bank of the payment and the bank debits one account and credits the other. The bank only acts on instructions; it makes no decisions for itself.
Account balances can be negative. If a person makes a payment in excess of the positive balance in their account, then the bank simply records that excess as a negative balance. The total balance of all accounts in the black is equal to the total negative balance on all accounts in the red. So whilst individual balances will change from time to time, the total net balance is always zero.
In this model, the balances in these accounts form the medium of account. We could measure the aggregate positive balance of accounts and call this the quantity of the medium of exchange, but this might be misleading as the negative balances are also a part of that medium.
This concept of money might be said to fit with the basic New Keynesian model. Agents can transact and make payments to one another, but the aggregate balance is zero. The total amount of positive balances (which we might want to call the money supply) doesn't really matter. It would be easy to add an interest rate to this picture - with interest charged on negative balances and credited to positive balances. However, there are no credit constraints. Everyone spends purely based on how they wish to spread their expenditure.
So the natural extension is to include credit limits. With what we have here, individuals hold claims on the bank; the exposure to those with negative balances is pooled. So it may be impractical for the individuals to decide on how credit is allocated. This creates a natural role for the bank. For an individual to make any payment which would result in its balance going negative, it has to be first approved by the bank. Furthermore, the bank will then also require that the account is made positive again within a specified length of time.
What we have now is more like our normal simple model of a bank. We have positive balances which we call deposits and negative balances which we call loans. The bank takes an active role in deciding how much is lent, to whom and for how long. Individual depositors have no role in this decision. We could say that loans create deposits, although an alternative would be to say that the two are actually created in parallel by spending decisions.
So we have arrived at the same concept of what a bank does, but via a different route. I think the alternative perspective is useful for a couple of reasons. First, it highlights that the credit rationing aspect of bank activity is critical to why they matter. This helps us frame questions about how credit decisions outside banking might matter as well. Secondly, it gives a different and, I would say, more realistic concept of how the medium of exchange operates in modern economy. Rather than the MOE being a quantifiable thing which is created by lending and then circulated until it is extinguished, it is just a system of payments and balances, both positive and negative.