(Iceland's financial crisis was much worse than other countries', which concentrates their minds to consider radical reforms. But it would be wise for all countries, and that includes Canada, to keep at least one eye on the possibility of radical reforms. We don't really know why Canada has been relatively "lucky" so far.)

This post is just my attempt to get my own head clear on some of the questions this raises. My head is not 100% clear yet.

I was reading Frosti Sigurjonsson's proposal for monetary reform in Iceland . [Click on the document thingy halfway down the page.] His proposal is a variant on 100% reserve banking. I got stuck on page 72 and footnote 66, where he discusses overdrafts.

Suppose we stop keeping our money in our pockets. Instead we each have a box with our name on it at the Bank of Canada, where we keep our paper banknotes issued by the Bank of Canada. When I buy something from you, I send an email to the Bank of Canada, cc'ing you, instructing the Bank of Canada to take a $20 banknote out of my box and put it in your box. The Bank of Canada sends a reply-all email confirming it has done this. Then the boxes and paper banknotes all get destroyed in a fire. But it doesn't matter because the Bank of Canada has a computer record of how many notes are in each person's box, so everything carries on just as before. Paper money that we keep in our pockets is functionally equivalent to electronic money, except for convenience, muggers, etc.

100% reserve banking is exactly like that (all money is central bank money), except that there is limited decentralisation so that commercial banks manage some of the record-keeping and communications. Most proposals for 100% reserve banking require each commercial bank to keep a record of how much is in each customer's box, and the central bank to keep records of the totals for each commercial bank (with an occasional audit to check that the two sets of records match up). Frosti's proposal requires the central bank to keep records of how much is in each individual's box too (the commercial banks just handle the communication).

What happens when we introduce overdrafts into an economy with 100% reserve banking?

There are green notes worth +$1 each and red notes worth -$1 each. If you buy something for $20, you either have 20 green notes taken out of your box or 20 red notes put into your box. There is a limit to how many red notes you may have in your box, to prevent you buying unlimited amounts of goods, and accumulating an unlimited number of red notes. If you have only red notes in your box we call it an "overdraft".

Introducing red notes raises some interesting questions:

1. Who decides the limit on the number of red notes each individual may have in his box? Can it be decentralised so that commercial banks set those limits? If it is decentralised, is the commercial bank liable if the individual holding red notes becomes insolvent? If no, then commercial banks face moral hazard in setting that limit. If yes, then commercial banks can go bust despite 100% reserves, unless the commercial banks are required to hold green notes in their own boxes equal to their customers' holdings of red notes.

2. If the central bank: creates one green note plus one red note on demand; and destroys one green note plus one red note on demand, then the value of one red note will always be minus the value of one green note. (For the same reason that a $20 note will always be worth two $10 notes if the Bank of Canada swaps one $20 note for two $10 notes, or vice versa, on demand.) But then what particular monetary aggregate does the central bank control? Is it the the net stock of notes [the number of green notes minus the number of red notes]? (That is the direct equivalent of the Bank of Canada controlling [10 times the number of $10 notes plus 20 times the number of $20 notes].)

3. If the central bank controls the net stock of notes [green notes minus red notes], and commercial banks control the gross stock of notes [green notes plus red notes], then commercial banks do control the stock of money in one important sense, despite 100% reserve banking. Because red notes are media of exchange too. We can imagine an economy where the net stock of notes is zero, but the gross stock of notes is unlimited. (The simple New Keynesian model is like this.)

And that's as far as I've got.