[This is aimed at intermediate-level students. It's "big picture" stuff, and doesn't go into all the institutional details. And it's already too long.]
Banks are financial intermediaries that create money. Banks are special because money is special. If we used cows as money, then dairy farms would be special, because dairy farms would create money.
Why is money special (and important)? Money is the medium of exchange (we buy and sell all other goods for money). Money is the medium of account (we quote the prices of all other goods in money). (The store of value function doesn't make money special, because lots of goods are stores of value.)
If there were a fall in the supply of apples, the price of apples would need to rise to clear the market for apples.
But if we used apples as the MOA, apples would not have a price of their own; the price of apples would be the reciprocal of the price of everything else. So the price of everything else would have to fall instead. And that's hard, because some prices are sticky, which means the price of apples would be sticky. And some prices are stickier than others, so a fall in the supply of apples would distort relative prices across the whole economy.
If the price of apples were sticky, a fall in the supply of apples would create an excess demand for apples. Some people would be unable to buy as many apples as they want. But if we used apples as the MOE, apples would not have a market of their own; the market for apples would be the market for every other good. An excess demand for apples would mean people would want to sell more other goods and buy fewer other goods. But if people are buying fewer other goods, they would actually be able to sell fewer other goods than before, and this would mean they would buy even fewer other goods, and so on. If barter is hard, which it is, an excess demand for the MOE disrupts trade of all other goods. It causes a recession.
That's why money is special and important. Changes in the supply and demand for money have macroeconomic consequences.
There are three types of goods that might be used as money: 1. goods that would be valuable in their own right even if they weren't used as money; 2. IOUs, or promises to pay goods that are valuable; 3. none of the above, or goods that are valuable only because they are used as money.
Suppose people like wearing shells as jewelry. That creates a demand for shells. If the supply of shells is not perfectly elastic at a zero price, demand and supply means shells will be valuable. People might use shells as money, as well as for jewelry. That's an example of the first type of money. But notice that the demand to use shells as money adds to the demand to use shells as jewelry, so this monetary demand makes shells more valuable than they would otherwise be.
Suppose now that fashions change, and people stop wearing shells as jewelry, and only the monetary demand remains. People now hold shells in their pockets, and not around their necks. Demand is less than before, but there's still a demand for shells, so they can still be valuable, though not as valuable as before. That's an example of the third type of money.
But notice there's also a second equilibrium, where shells are worthless, and so can't be used as money, and so there is no monetary demand for shells. The demand curve for shells slopes down, but suddenly drops to zero demand when the price of shells drops to zero, so the demand curve crosses the supply curve twice.
What keeps us in the first equilibrium and not the second equilibrium? I think the answer is "network externalities and custom". If everyone else I trade with is using shells as money, I will want to use shells as money too, because it will be easier to buy and sell things for shells. This means it is hard to change what we use as money, because we either all change at once or not at all, and it's hard to coordinate everyone changing at once. Just like languages or computer programs.
Suppose we are using shells as money. If I write "IOU 10 shells, signed Nick Rowe" on a sheet of paper, I might be able to persuade my local supermarket to give me some apples in exchange for my IOU, if they know me and trust me. But if my local supermarket redeems my IOU with me next week, then my IOU is not money. I have simply postponed payment for the apples. But if the supermarket uses my IOU to buy something else, from someone who uses it to buy something else, and it keeps on circulating around my village because everyone in the village trusts my signature, then my IOU is money, because it is being used as a medium of exchange.
I have now created money. But I am not a bank. Because a bank is a financial intermediary that creates money, and I am not a financial intermediary.
"Liquidity" is hard to define precisely, but it means how easy it is to buy or sell an asset quickly at a good price with low transactions costs. Some assets are more liquid than other assets. Other things equal, people prefer holding more liquid assets to less liquid assets. So in equilibrium the more liquid assets will pay lower rates of interest (or lower rates of return). Money is the most liquid asset, so money will pay a lower rate of interest than other assets. (Bank of Canada currency pays 0% nominal interest and usually pays around minus 2% real interest.)
As long as my IOU for 10 shells continues to circulate around the village rather than being returned to me for redemption, and if my IOU pays 0% interest, the village has, in effect, made me an interest-free loan.
If I can lend at a higher interest rate than I can borrow, I might decide to become a financial intermediary, which means I both borrow and lend, and make an income off the spread between my borrowing and lending rates.
If I can create this spread by creating money, I might decide to become a bank, which means a financial intermediary whose liabilities are used as money.
So if you want to borrow 100 shells to buy a bike, you give me your signed IOU for 100 shells plus 5% interest, and I give you my signed IOU for 100 shells plus 0% interest. You take my IOU to the village bike store, and use it to buy a bike. If my IOU continues to circulate around the village, I am now a bank.
My IOUs are paper currency, convertible on demand at a fixed exchange rate into shells. Paper currency is like a "bearer bond", where simple possession of the bit of paper is normally considered sufficient evidence of ownership. There is no central record kept of who owns what bits of paper with which serial numbers. But if I sell you my car, we have to tell the government the VIN and your name as the new owner, and the government keeps records. This helps prevent theft of cars. Cars are not like bearer bonds; if the police stop you, you have to show the ownership paper, otherwise they'll think you stole it.
If I wanted to prevent theft of my IOUs, I might keep a record of the serial numbers on my IOUs and who owned them, and require you to inform me that the ownership of my IOU serial number 12345 had been transferred from you to the bike seller. And the bike seller would want to make sure you had informed me of this. To make it easier for you to do this, I might give you a form letter, where you could fill in the name of the bike seller, then give the letter to the bike seller, who could then mail it to me. That way, I know the bike seller now owns the IOU, and he knows I know this.
But if I'm keeping a record of who owns which of my IOUs, and since the only thing that matters is how many shells' worth of my IOUs different people own, we can dispense with the sheets of paper on which I have written "IOU 10 shells signed Nick Rowe" altogether. As long as you trust me to keep good records. I simply give you a stack of form letters, stapled together for convenience. We call those form letters "cheques". You now have a chequing account instead of currency, and you give the bike seller a cheque instead of currency.
And if I keep my records on a computer rather than in a book, and if the form letter gets sent by email rather than by Canada Post, and if my computer can understand those email letters, we have electronic money. Currency, chequing accounts, e-money: these are all basically the same. Some are just more convenient and trustworthy than others. But on the other hand, money is all about convenience and trust. We wouldn't use money if it weren't more convenient than barter. And if everyone's IOUs were trusted, anyone could create money. Or we wouldn't even need money, except as a convenient way to keep track of the value of goods we have taken from other people and given to other people, so we don't take more than we give, or give more than we take.
If using my IOUs as money is sometimes less and sometimes more convenient than using shells as money, some people will be redeeming my IOUs for shells (withdrawing shells from my bank), and other people will be buying my IOUs for shells (depositing shells in my bank). If a lot of people want to redeem my IOUs at the same time, I might run out of shells. In principle, as long as I am solvent, I could always redeem all of my IOUs by selling the IOUs signed by other people that other people have sold me, when they borrowed from me. But those IOUs will be illiquid. Because the whole point of my being a bank is to make an income from the interest rate spread between my liquid IOUs and your illiquid IOUs. So if I had to sell those illiquid IOUs quickly, I would make a loss, and that loss might be big enough to make me insolvent, so I couldn't redeem all my IOUs quickly. And if people think that might happen, there might be a run on my bank, where everyone tries to redeem before I run out of shells.
If I saw that I would run out of shells, I would suspend convertibility of my IOUs into shells. I would break my promise to redeem my currency on demand at a fixed exchange rate. But if people believed there was some positive probability I would restore convertibility in future, or even if they they expected me to restore convertibility at a lower exchange rate (paying less than 100% of the shells promised), my IOUs would still have some value, even if that value would be lower. But if my IOUs have some value, and they are convenient to use as money, people might still use them as money, so there would still be a demand for my IOUs. And if there is a demand for my IOUs as money, then provided I don't create an unlimited supply, there will be an equilibrium in which my IOUs are valuable even if I renouce any promise of convertibility. (Though there is also a second equilibrium in which my IOUs are worthless and so cannot be used as money and so are not demanded.)
This case of permanent suspension of convertibility is analogous to the case where people use shells as both jewelry and money, and then fashions change so the demand for shells as jewelry disappears, but people keep on using the shells as money.
If I permanently suspend convertibility of my IOUs into shells, my IOUs are now just sheets of paper with ink marks on them. All the number "10" means is that I will convert one "10" into two "5"s or vice versa. If people keep using my sheets of paper as money, I am now a central bank issuing a fiat money with a floating exchange rate. My central bank might get taken over by the government, or it might not. It might depend on whether the government thinks I will do what it wants the central bank to do. Or whether the government wants the profits I can earn.
What happens when there are two (or more) banks? If you bank with Nick, and you buy a bike, and the bike seller uses Mary's bank, then the bike seller sends your cheque to Mary's bank, Mary credits the 100 shells to the bike seller's chequing account, and then brings the cheque to me, and I give Mary 100 shells, and deduct 100 shells from your chequing account. But at the same time, someone else who banks with Mary may have bought something for 90 shells from someone who has an account at my bank. So when Mary and I settle our debts to each other that evening, I only give her 10 shells.
If both banks have lots of customers, and if both banks are doing the same things, the Law of Large Numbers says that most evenings those net transfers of shells will be small in proportion to the gross transfers between me and Mary, and they will average out to zero over time. If Mary and I don't want to keep a lot of shells in reserve to make these payments between us, we could instead just borrow from each other in the overnight market. Instead of me giving Mary 10 shells, she accepts my IOU for 10 shells, but since Mary doesn't need my IOU to use as money, she charges me interest at the overnight rate of interest on loans between banks.
But if Mary succeeds in attracting some of my depositors to switch to her bank, or if I succeed in attracting some of Mary's borrowers to switch to my bank, I will be making net payments of shells to Mary, and unless I want to keep on borrowing from Mary in the overnight market, I won't want this to happen. And I won't want to keep on borrowing from Mary, because Mary charges me a higher rate of interest than I pay my depositors.
This means I won't want to expand my loans without expanding my deposits, and Mary won't want to expand her loans without expanding her deposits. But if we both expand our loans together, and if we are the only two banks, our deposits will expand in line with our loans, and we won't have to worry about this. Unless people withdraw deposits from both our banks because they would rather hold shells instead.
Most countries, like Canada, have several commercial banks that accept deposits from the public and make loans to the public. And a single central bank. The central bank is usually owned by the government, and is an arm of public policy. The commercial banks are usually not owned by the government and can be assumed to maximise profits. The central bank usually has a monopoly on issuing paper currency, but does not normally make loans to the public or accept deposits from the public. It may however, make loans to and accept deposits from the government.
What is the important difference between central banks and commercial banks? What makes a central bank central? What makes central banks powerful? I think there are two important differences.
1. Central banks act as bankers to the commercial banks. [Aside: I'm not satisfied with this section.]
If there are only two banks, mine and Mary's, we don't need a bank to do our settling of accounts every evening. But if there are three or more banks, it gets more complicated. If I owe Mary 100 shells, and Mary owes Harry 100 shells, and Harry owes me 100 shells, we would need all three of us bankers to meet together every evening and do a deal where we agree that none of us owes anything to either of the others. That three-way deal is like a three-way barter deal where a hairdresser gives a haircut to a manicurist, who gives a manicure to a masseuse, who gives a massage to the hairdresser. It's hard for all three to get together and do three-way deals. That's why they use money instead of barter. It's more convenient. And they don't all have to trust the other two to deliver what was agreed on; each needs only to trust one.
It's more convenient, and requires less mutual trust, if each commercial bank has a chequing account at the central bank, and lets the central bank cancel out the circles of obligations. So the central bank acts as banker to the commercial banks, and central bank money is the money the commercial banks use to make payments between themselves. Just as the public uses commercial bank money to buy and sell different goods, so commercial banks use central bank money to buy and sell different commercial bank monies. And just as the public can get an overdraft at a commercial bank to cover unexpected needs for liquidity, so commercial banks can get an overdraft at the central bank to cover unexpected needs for liquidity. The central bank acts as lender of last resort to the commercial banks.
2. Commercial banks promise to redeem their monetary IOUs at fixed exchange rates for central bank monetary IOUs. It's not the other way around. It's the Bank of Montreal's job to make sure a Bank of Montreal dollar is worth the same as a Bank of Canada dollar. Only in an emergency, if there's a run on the Bank of Montreal dollar, will the Bank of Canada act as lender of last resort to make sure the Bank of Montreal dollar doesn't depreciate against the Bank of Canada dollar.
This is analogous to what would happen if the US Fed decided to have a fixed exchange rate between the US dollar and the Canadian dollar, but the Bank of Canada took on no responsibility to keep the exchange rate fixed. The Bank of Canada could do what it liked, and the Fed would have to follow. If the Bank of Canada wanted to create higher inflation and make the Canadian dollar worth less, the Fed would have to make the US dollar worth less too. US monetary policy would be set in Ottawa. Since the Canadian commercial banks fix their exchange rates against the Bank of Canada dollar, Canadian monetary policy is set in Ottawa, by the Bank of Canada. If the Bank of Canada wanted to create higher inflation and make the Bank of Canada dollar worth less, the Bank of Montreal would have to make the Bank of Montreal dollar worth less too.
Right now, the Bank of Canada: charges commercial banks 1.25% interest on overdrafts (negative balances); pays commercial banks 0.75% interest on deposits (positive balances); and has a target of 1.00% for the overnight rate on loans between commercial banks. It nearly always keeps these same 25 basis point spreads between the three rates. Actual positive or negative balances are usually very small. The actual overnight rate cannot be higher than the 1.25% bank rate, because otherwise commercial banks would borrow from the Bank of Canada instead; and cannot be less than the 0.75% deposit rate, because otherwise commercial banks would lend to the Bank of Canada instead. The Bank of Canada keeps the actual overnight rate very close to the target by adjusting, or threatening to adjust, the supply of settlement balances up or down to lower or raise the actual overnight rate. If the Bank of Canada wants to make its dollar more valuable (because it thinks inflation will rise above the 2% target unless it does something different) it raises all three interest rates. That's how the Bank of Canada stops all the commercial banks expanding their total loans and deposits too much. If it wants to make the Canadian dollar less valuable (because it thinks inflation will fall below the 2% target unless it does something different) it lowers all three interest rates. That's how the Bank of Canada stops all the commercial banks expanding their total loans and deposits too little.
You might say the Bank of Canada dollar is an inconvertible fiat money, of the third type. Or you might say that, because the Bank of Canada targets 2% CPI inflation, the Bank of Canada dollar is like an IOU that is indirectly convertible at a slowly depreciating exchange rate into the CPI basket of goods, and is thus a money of the second type.
[Obviously, there's more to say about banks, but for now I'm stopping here.]