Does the supply of reserves matter? It certainly matters in the simple textbook ECON 1000 model of the money multiplier. But is that model fatally flawed, especially in the context of zero required reserves, and where central banks target an interest rate, so the quantity of reserves is demand-determined?
Some people do argue that the simple textbook model is fatally flawed, and that the supply of reserves, to a first approximation, doesn't matter. See for example the comments on David Beckworth's post about the Fed's exit strategy. Even if this is a minority view (and I'm not 100% sure it is a minority), it's not an insignificant minority. My sense is that this view is widely held by people who describe themselves as: Post-Keynesians; Neo-Chartalists (Modern Monetary Theorists); and "horizontalists" more generally. And at least some of those people know from personal experience a lot more about how banks and central banks operate than academic economists like me ever will. We should take them seriously.
But I think they are wrong. I think the simple textbook model, despite its simplicity, and "lack of realism", contains important insights that its critics miss.
A fallacy of composition is when you say that what is true of each of the parts must be true of the whole. "If each individual stands up, he can see the stage better; therefore if everybody stands up everybody will see the stage better". A fallacy of decomposition is the same thing in reverse. It's when you say that what is true of the whole must be true of each of the parts.
The fallacy of decomposition is just as important as its reverse. If it weren't a fallacy, there would be no free-rider problem, for example. "If everyone free rides, everyone is worse off; therefore if each individual free rides he is worse off, so he won't ever free ride".
What the simple textbook model of the money supply gets right is precisely that. But only if you teach it right, and don't skip the long boring bit that takes you from one equilibrium to another. You know, the bit where Bank A has $100 excess reserves, and so expands loans and deposits by $100, which then end up in Bank B, which then expands loans and deposits by $90, etc. I've always been tempted to skip that bit (especially since I always screw up the arithmetic) and jump straight to the new equilibrium, where deposits expand by 10 times the increase in reserves. I swear I will never skip that bit again. But I think I may change how I teach it.
That boring bit of the textbook story is not really about dynamics, even though it's usually taught that way. It's about marginal costs: more precisely, about the difference between marginal costs for the individual bank vs marginal costs for the banking system as a whole. With a (say) 10% desired reserve ratio, the marginal cost to the banking system as a whole of a $100 expansion in deposits is the cost of needing an extra $10 in reserves. But for the individual bank, the marginal cost of creating a new $100 deposit is the cost of needing an extra $100 in reserves. At the margin, it is as if an individual bank has a 100% reserve ratio, regardless of the 10% (or 0% or whatever) desired reserve ratio. And whether or not something is an equilibrium is determined by individuals' incentives, at the margin. Does every individual's marginal benefit equal his marginal cost? If not, it's not an equilibrium.
To see the importance of this insight, suppose there were only one big commercial bank. That means there can't be any fallacy of composition or decomposition, because there is only one part, so the part is the whole.
Start in equilibrium, where the bank has exactly the desired reserve/deposit ratio. Ignoring currency drains, the bank know that if it advances an extra $100 loan by creating a $100 deposit, it gets to keep that $100 increase in deposits indefinitely (or, at least until the loan is repaid). When the borrower spends the loan, the deposit changes hands, but stays at the same bank. If there's 5% interest on loans, and 2% interest on deposits, the bank's net revenue is $5 per year loan interest, minus $2 per year deposit interest, minus the cost of borrowing extra reserves (from the central bank). If the desired reserve ratio is 10%, and the interest it pays on borrowed reserves is 3%, the cost of the extra $10 reserves is a mere 30 cents. And as the desired reserve ratio goes to 0%, the cost of those extra reserves disappears from its calculation.
The equilibrium condition assuming 0% desired reserve ratio is that the interest rate on an extra $100 loan equal the interest rate on an extra $100 deposit, plus an allowance for risk and admin costs. The interest rate on reserves is irrelevant.
Now suppose instead that each commercial bank is very small relative to the whole banking system.
Again start in equilibrium, where the bank has exactly the desired reserve/deposit ratio. An individual bank knows that if it advances an extra $100 loan by creating a $100 deposit it will not keep that deposit. The borrower will spend it, and it will be re-deposited at a different bank, and so the first bank will need to transfer $100 in reserves to the second bank. The bank's net revenue is $5 per year loan interest, minus nothing on deposit interest, minus $3 per year on the $100 extra reserves it will need to borrow.
The equilibrium condition assuming 0% desired reserve ratio is that the interest rate on an extra $100 loan equal the interest rate on an extra $100 borrowed reserves, plus an allowance for risk and admin costs. The interest rate on deposits is irrelevant.
Notice two differences between the case where there is one big bank and the case where there are many small banks:
1. The interest rate paid on deposits has a 100% weight in the big bank's decision, but a 0% weight in the small bank's decision.
2. The interest rate paid to borrow reserves has a 100% weight in the small bank's decision, but a weight equal to the desired reserve ratio in the big bank's decision. If the desired reserve ratio were 0%, the interest rate on reserves would be irrelevant to the big bank. At the margin, the small bank acts as if there were a 100% reserve ratio, even if the desired reserve ratio is 0%.
To ignore that distinction between the banking system as a whole and the individual bank, or between one big bank and one of many small banks, is to commit a fallacy of decomposition. With 0% desired reserve ratio, the banking system as a whole can expand loans and deposits without needing to borrow extra reserves. But that does not mean the price and availability of reserves is irrelevant. It is 100% relevant to the individual bank at the margin. And it is individual banks' unwillingness to change their decisions at the margin that determine whether an equilibrium is indeed an equilibrium.
If there really were just one big commercial bank, so the fallacy of decomposition would not arise, and if the desired reserve ratio were close to zero, I can't see how the central bank could possibly control that bank through changing the interest rate on reserves. The central bank really would need some sort of quantitative controls instead.
Before ending this post, I might as well deal with a couple more criticisms or misunderstandings of the simple textbook model of the money multiplier.
The first criticism/misunderstanding has to do with the "supply of reserves".
This is mostly a terminological issue. In economics the "supply of apples" does not mean the actual quantity of apples sold. It does not even mean the quantity of apples that sellers want to sell (the "quantity supplied"). It means the supply curve, which is the whole relation between the quantity sellers want to sell and the price of apples. Better yet, since price is only one of many variables that affects quantity supplied, the "supply of apples" means the whole functional relation between quantity supplied and everything that affects it.
Furthermore, we can even think of a supply curve, or a supply function, in an inverse form, as Alfred Marshall did. Marshall saw a supply curve as defining the supply price (the price the seller was willing to accept) as a function of quantity sold, rather than quantity supplied as a function of price. (That's the historical accident that explains why economists' supply and demand curves have the dependent variable on the horizontal axis, rather than the vertical; something that always annoys science and engineering students taking ECON 1000.)
Similarly, the "supply of reserves" does not mean the actual stock of reserves. It does not even mean the stock of reserves desired by the central bank. It means the supply curve, which is the whole relation between the central bank's desired stock and the rate of interest on reserves. Better yet, since that desired stock depends on many things, the "supply of reserves" means the whole relationship between the central bank's desired stock of reserves, the rate of interest on reserves, and anything else that affects it.
Furthermore, like Alfred Marshall, if we want to we can think of the "supply of reserves" in its inverse form, as defining the central bank's desired target for the interest rate on reserves as a function of the quantity of reserves and everything else that affects it.
So to argue that the supply of reserves is irrelevant, because when the central bank sets a target for the interest rate on reserves the supply of reserves is demand-determined, is to misunderstand what is meant by "supply of reserves". It's not a quantity; it's a function.
Now there is a difference, it is true, between a perfectly inelastic supply function and a perfectly elastic supply function. A cap-and-trade system for emissions permits (a "verticalist" policy) may give the same equilibrium as a Pigou tax (a "horizontalist" policy), but if the demand curve shifts the former leads to a change in the equilibrium price of emissions, while the latter leads to a change in the equilibrium quantity of emissions. But that's only if the policy-maker holds the supply curve fixed when the demand curve shifts. But central banks don't hold the supply curve of reserves fixed when the demand curve shifts. Depending on the central bank's ultimate target, whether it be the inflation rate, the price level, nominal income, the exchange rate, or whatever, it will almost certainly shift the supply curve in response to a change in demand for reserves.
Except in the very short run (6 weeks or so) the Bank of Canada does not have a perfectly elastic supply curve of reserves (and even then it reserves the right to change the overnight rate target between Fixed Announcement Dates if needed).
(And the elasticity of supply of reserves to an individual bank can be very different from the elasticity of supply to the banking system as a whole, of course. Each buyer of apples in a competitive market faces a perfectly elastic supply curve of apples at the equilibrium price, even if the market supply curve is inelastic.)
The second criticism/misunderstanding has to do with the supply of money vs loans.
The simple textbook model of the money multiplier is not a model of the supply of loans. It's a model of the supply of money. It's about the liability side of the banks' balance sheet, not the asset side.
Banks make loans. So do I. Banks create money. I don't. That's why banks are special.
If the textbook model were intended as a model of the supply of loans, it would fail miserably. Banks are only a part of the overall supply of loans. Plus, it makes no difference whatsoever to the textbook model if banks create deposits by buying bonds, shares, land, computers, or whatever. When a bank makes a loan it buys a non-marketable IOU, and pays for it by creating a demand deposit. But it could buy anything else instead and still pay for it by creating a demand deposit. It would make no difference to the textbook model. It's the demand deposit that matters, not what the bank buys with it. The textbook model is a model of the supply of money, by banks, and those demand deposits are money, that is to say a medium of exchange.
The textbook model is a model of the supply of the medium of exchange. If you are not interested in the supply of the medium of exchange, and are instead interested in the supply of loans, then of course you will find the textbook model of the supply of the medium of exchange totally unsatisfactory. Since loans are usually risky, you will want to look at things like bank capital, etc.
Now, none of the above means the textbook model is perfect. Far from it. It leaves out lots of stuff. But its main insight, the difference between the individual bank and the banking system as a whole, is precisely what its critics miss.
Afterthought: If we want to explain the quantity of apples, we need to look at both the supply and the demand for apples, and put them together. If we want to explain the quantity of money, don't we also need to look at both the supply and the demand for money, and put them together? How can the textbook model get away with ignoring the demand for money?
Actually, that's not a bug; it's a feature. You can already see in the above that an individual bank will ignore the interest rate on deposits when it decides whether to expand loans and deposits. And the borrower will ignore it too, because he got the loan to spend it, not to leave it sitting on deposit at the bank. New money really is always like helicopter money. Changes in the stock of money are always supply-determined, never demand-determined. But that's a subject for another post.