Start with a fractional reserve banking system, like Canada's for example. Canadian banks are not required by law to hold any reserves, and choose to hold very little. They hold a small amount of currency, plus a very small amount of deposits at the Bank of Canada. Those deposits pay interest, but that rate of interest is always set below market rates.
Now consider two different ways Canada could move to a banking system with 100% reserves:
1. Regulation. Require banks to hold reserves against deposits, and slowly increase the legally required reserve ratio to 100%.
2. Interest on reserves. The Bank of Canada currently pays interest on reserves, but that rate of interest is below the expected return on their other assets, so Canadian banks choose to hold very small amounts of reserves. Slowly increase the rate of interest paid on reserves, relative to market rates of interest, until banks choose to hold 100% reserves.
The first method makes it illegal for banks to borrow short and lend long. The second method flattens the term structure of interest rates so that banks choose to borrow short and lend short.
What is the difference between those two methods of getting 100% reserve banking?
First let's note the similarities:
In both cases, banks would stop making loans. Or if you prefer, the only loans they would make would be to the central bank. If you deposited $100 at your bank, your bank in turn would deposit $100 at the central bank.
In both cases, banks would stop creating money. Instead, they would simply transform one form of money (currency) into another form of money (chequable deposits) which many people find more convenient for many purposes.
In both cases, banks would not be subject to runs.
In both cases, the balance sheet of the central bank would be bigger than the balance sheets of all the commercial banks combined. (It would be the same size if people used only bank money and did not use central bank currency too.)
In both cases, the central bank would need to take offsetting action to prevent aggregate demand falling and inflation falling below target. If the banks are selling assets (to hold reserves instead), the central bank would need to buy those assets. The central bank would need to use Open Market Operations (aka "QE") to prevent aggregate demand from falling. If the only assets the banks held were government bonds, this would be simple. The banks sell their government bonds to the central bank, and get deposits at the central bank in exchange. If the banks hold other assets, like mortgages, and if the central bank doesn't want to hold mortgages, it's a little more complicated. The banks and central bank would need to persuade some third party, like pension plans, to buy mortgages from the banks and sell government bonds to the central bank, so the pension plans hold more mortgages and fewer government bonds.
Now let's look at the differences between these two methods of getting to 100% reserves:
There is only one difference I can think of. Relative to the second method, the first method is a tax on banking. Equivalently, relative to the first method, the second method is a subsidy to banking. Banks would pay higher interest rates on deposits if the central bank paid higher interest on reserves. (With a competitive banking system this is obvious, but even a monopoly will change its profit-maximising price if its marginal cost curve shifts up or down.)
So the second method would create higher interest rates on bank money than the first method. And the quantity of bank money demanded would be higher, the higher the rate of interest paid on bank money, relative to other rates of interest. And that would mean aggregate demand would fall more under the second method than under the first method, if the central bank took no offsetting action. And that would mean the central bank would need to take bigger offsetting action under the second method than under the first method.
Another way of saying the same thing is that the second method would mean a larger banking system than the first method. Whether you think of the first method as a tax on banking, or the second method as a subsidy on banking, the result is the same: you get a bigger banking system with a subsidy than a tax. Both the commercial banks and the central bank would need to have bigger balance sheets, if commercial banks were persuaded to hold 100% reserves rather than being forced by law to hold 100% reserves. 100% required reserves would mean a bigger central bank than now. Paying sufficiently high interest on reserves to get 100% reserves voluntarily held would mean a much bigger central bank than now.
How big do we want the central bank to be? And do we want the national debt to be big enough for the central bank to be big enough while holding only government debt? Or do we want the central bank to hold other assets as well? I need to write a second post showing that if the government-owned central bank is large enough we end up with the Fiscal Theory of the Price Level.
One way to think of the US banking system, in recent years, is that it has gone part way towards 100% reserves using the second method. It is the spread between the interest rate on reserves and market rates that matters, and it doesn't matter whether the former rises or the latter falls to narrow that spread. And aggregate demand fell because the Fed increased the size of its balance sheet in response, but not by enough.
(I ought to be crediting someone for inspiring this blog post, but my memory is getting worse and worse. All I can remember is that a few days ago someone said that someone else (John Cochrane?) said something like the US recovery was heading in the direction of 100% reserves?)