This post covers the same ground as my previous post, but it's written for a different audience. It's written for those people who approach monetary policy from a banking/finance perspective.
Suppose you are running a commercial bank. Let's call it "BMO". And let's simplify massively. On the asset side of your balance sheet you have "loans". On the liability side of your balance sheet you have demand deposits. Let's call those demand deposits "BMO dollars", because that's what they are.
Again simplifying massively, you have three instruments, or control levers:
1. You set the interest rate on loans. Yes, you have to watch the competition when you set it, but you set it. (And you also care about risk, term to maturity, liquidity, etc., but let's abstract from those things.)
2. You set the interest rate on deposits. Yes, you have to watch the competition when you set it, and you might set it at 0%, or even negative, but you set it. (And you also set fees for cheques, and paying bills, etc., but let's abstract from those things.)
3. You set the exchange rate at which you promise to convert BMO dollars into Bank of Canada dollars. And you fix that exchange rate permanently at one, of course.
It's very easy to forget that third instrument, because it's just so natural that it goes without saying. Of course you promise to convert BMO dollars into Bank of Canada dollars at par. That's what "demand deposit" means. And as long as your promise is credible, the market value of a BMO dollar will stay at one Bank of Canada dollar. That third instrument is sufficient to determine the value of the BMO dollar, in terms of Bank of Canada dollars.
Here's my question: but is it necessary? In other words, if you dropped that third instrument, and dropped any pretence that you might restore convertibility in future, so you dropped that third instrument permanently, would you still be able to control the value of the BMO dollar by using interest rate instruments alone?
Because the Bank of Canada tries to target the value of the Bank of Canada dollar in terms of the CPI basket of goods, but does not use that third instrument. You cannot walk up to the Bank of Canada and demand it redeem your $100 note in CPI baskets of goods as specified by the inflation target. The Bank of Canada targets a 2% crawling peg exchange rate between the Bank of Canada dollar and the CPI basket of goods, without using that third instrument of direct convertibility. The BMO has a stock of Bank of Canada dollars behind the counter. The Bank of Canada does not have a stock of CPI baskets of goods behind the counter.
The Bank of Canada tries to control the value of the Bank of Canada dollar using interest rate instruments only. It sets (1) the interest rate on loans, and (2) the interest rate on deposits. Is that sufficient? If it is sufficient for the Bank of Canada, why wouldn't it also be sufficient for the BMO?
I can't help but recall the old joke about economists: interest rate control seems to have worked in practice, but does it work in theory? But maybe, just maybe, theory is trying to tell us something important about what happens in practice at the Zero Lower Bound, when interest rate instruments hit their limits.
[Update: my answer is "no". BMO would need a third instrument. That third instrument could be convertibility into something at some exchange rate it sets, or it could be direct control over the quantity of deposits, by buying or selling loans for BMO dollars in the secondary market (Open Market Operations). Setting two interest rates, and letting the quantities of loans and deposits be demand-determined at those interest rates, is not sufficient to control the value of the BMO dollar.]