These two first-year textbook models — the simple money supply multiplier model; and the simple keynesian income-expenditure multiplier model — are formally identical. Translated into math, or game theory, you can't tell the difference between them. They contain exactly the same important insight: that what is true for the individual bank/household is not true for all banks/households. And they both contain the same flaw: they ignore interest rates.
This is really just a rhetorical device, designed for people who understand and appreciate the keynesian multiplier but not the money supply multiplier. Or vice versa.
Assume a closed economy, with no government. For "bank" read "household" throughout. The other translations are obvious (S=savings, I=investment, Y=income, C=consumption).
Let S be desired reserves. Let Y be deposits. Assume desired reserves are a constant fraction s of deposits: S=sY. Let I be the supply of reserves. In equilibrium the supply of reserves must equal the demand for reserves (desired reserves equal actual reserves), so S=I. In equilibrium therefore, deposits Y must adjust so that sY=I, which means we get the multiplier Y=(1/s)I. Just to complete the model, recognise that accounting reminds us that loans C plus reserves S must equal deposits Y, so that C+S=Y=C+I.
One important insight of this model is that the supply of reserves I determines desired reserves S, not the other way round. Deposits Y adjust to ensure that desired reserves S equals the supply of reserves I.
A second important insight is the difference between the individual bank and the banking system as a whole. An individual bank, one that is small relative to the system as a whole, will take deposits Y as given. The individual bank that increases loans C will suffer a dollar for dollar reduction in reserves S. But for the banking system as a whole, an increase in loans C will cause an equal increase in deposits Y, with no change in reserves S.
If banks are at less than "full employment", they could all be better off if they jointly increased loans C and deposits Y. They don't need extra reserves S to do this. And aggregate reserves S would not decrease if they did this. But this expansion of loans C and deposits Y can never happen, without an increase in the supply of reserves I. That's because any individual bank that increased its own loans C would see no corresponding increase in its own deposits Y, merely a reduction in its reserves S. All the benefits of increased loans C would be an increased level of deposits Y at other banks.
People who miss this important insight, who miss the distinction between desired reserves S and actual reserves I, end up with Say's Law of Banking, which states that there can never be a general shortage of reserves I, so banks must always be at full employment.
Now it is true that one bank's deposits Y are not strictly speaking exogenous to that bank. By offering better terms to its customers, it can increase its deposits Y at the expense of other banks' deposits Y. But that does nothing to increase aggregate deposits Y to the banking system as a whole, and get all banks to full employment. It simply redistributes a fixed amount of deposits Y among the different banks. One bank gets to full employment, but only by reducing employment for other banks. The only way to get to full employment of all banks, without an increase in the supply of reserves I is if all banks decrease their desired reserve ratio s. But no individual bank has any incentive to do that.
So the policy message is clear. The only way to get the total level of deposits Y to that required for full employment of banks is to increase the total supply of reserves I. And then hope that banks don't just increase their desired reserves S by the same amount. Ricardian Equivalence Theory, based on the permanent deposits Y theory of loans C, argues that any transitory increase in the supply of reserves I will indeed be mostly hoarded with a corresponding increase in desired reserves S. So lets make the increased supply of reserves I permanent.
Worthwhile Canadian Initiative 
thanks Scott and Rebeleconomist, very helpful
Let me reframe the question just one more time. I’m kind of thinking in terms of “at-the-limit”:
If a bank were to be right up against its capital ratio requirements (has the bare minimum of capital), and currently has pledged all of its low-risk assets as collateral, and then the BOC decides that the rest of their assets (consumer loans, etc.) have become more risky and demands more collateral – is the only way of satisfying that by raising more capital to purchase low risk assets? If they just borrowed those assets, wouldn’t that put them under the required capital ratio?
Yes it would put them under the required capital ratio bob, because borrowing, say, treasuries for, say, ABS would increase the size of the bank’s balance sheet and increase their capital shortfall. As per my previous comment, the loaned ABS rather than the borrowed treasuries would still count as part of the bank’s capital.
Hi Rebel,
“Central banks are typically highly risk averse, so insist on high quality collateral to avoid credit losses, even if they do not need it to raise their own funds. Insolvency matters for a central bank, because it would require state recapitalisation, with potential loss of independence.”
I agree that there are political issues for central banks related to its capital, defaults on central bank loans, etc., but there’s no operational need for collateral. That was my point.
Also, the only reason there’s any question about the size of the Fed’s capital is that the Fed has been legally required to send about 95% of its profits for the past 95+ years to the Treasury. I looked this up for all the Fed income statements availabe online going back to the early 1990s, and this amounted to well over $300B just in that period. If the Fed had retained its earnings like any other private bank is allowed to do (not that I’m advocating this), there would be virtually no issue regarding state recapitalization–indeed, it’s the height of hypocrisy to not allow the central bank to retain its earnings and then potentially withhold recapitalization if that were to be necessary. And again, operationally, there’s no need for recapitalizataion of the currency issuer in the first place.
I agree with your 3rd paragraph mostly, though I would say that a reserve balance is a bank asset that doesn’t use up any of the bank’s capital, not that it is capital itself. I see where you are going with that, but 99% of people (economists, in particular) would get confused (more than they already are) if we start conflating reserves and capital.
Best,
Scott
bob at 11:23 . . . I was responding to Adam’s point there. All cleared up now. Thanks!
Note that the bank would not have to issue capital securities (eg shares) to raise capital, however. If the bank sold ABS outright and bought treasuries with the proceeds, that would increase its regulatory (as opposed to economic) capital, because the treasuries get a greater weighting. This is, of course, one reason why treasury yields are lower despite massive government borrowing – a bank can effectively deleverage without actually decreasing the size of its balance sheet.
I agree Scott. I used to call myself a “reserve manager”, and that was yet another type of reserves……lets not go there!
Scott, at 11:23, if you were responding to me you’ve cearly not understood what I was saying.
I was saying that the constraints are only on capital, there is virtually no reserve constraint (though the requirement to have some assets that are acceptable for collateral I guess is a type of liquidity constraint).
I was not implying what you seem to have understood and it’s quite myserious how you could have thought that.
correction, should be “Scott at 12:16”
Adam . . .sorry. When you said “it’s about capital only” I interpreted the “it” as collateral which now I understand you obviously weren’t intending. My misinterpretation was because bob had asked if collateral was from capital and I thought you were responding to that. Sorry again.
Rebeleconomist – good point @ 12:18
would it be possible for the BOC to make the bank rate equal to the deposit rate @ 0.25%? In such a situation the BOC would borrow all settlement balances at 0.25% and lend them at 0.25%
Could that work? Would it be desirable?
bob . . . MMT’ers would say “yes.” Warren Mosler has proposed precisely this frequently. (Note that this would also put the target rate at 0.25%, so if you want the target rate higher you need the other two higher,too.) Charles Goodhart–a non-MMT’er–has also proposed this, by the way, though his proposal would raise the spread between the two after individual banks reach a particular threshold of balances.
Yes bob, I think it would work, but since it would probably mean that the central bank became the intermediary for all reserves loans, I would expect the central bank to prefer to maintain a spread between their lending and deposit rates.
By the way, you might appreciate a post that I wrote to explain quantitative easing:
http://reservedplace.blogspot.com/2009/04/easing-understanding.html
“since it would probably mean that the central bank became the intermediary for all reserves loans, I would expect the central bank to prefer to maintain a spread between their lending and deposit rates.”
Yes, I can see that they wouldn’t want to do anything too radical, but why not really? The BOC would become the intermediary, but is that really a problem? It seems like it would be more efficient than keeping an interbank market for settlement balances where they are constantly intervening to drive the rate down to 0.25% yet leaving the bank rate at 0.50% (under the current post-crisis policy).
that should read “intervening to drive the overnight rate down”
bob . . .exactly. you might find this of interest: http://www.newyorkfed.org/research/staff_reports/sr337.pdf
thanks Scott!
very very interesting paper. I also checked out one of Martin’s other papers on the reason why intraday liquidity is so cheap and overnight liquidity so expensive… good stuff.
It seems like the interbank market for overnight balances may actually be pretty useless, just a big waste of time really.
I’m going to take one last crack at this thread, then leave it.
I agree with Scott Fulwiler, at least on this point, 😉
” Whether we critique you or vice versa, everyone ends up talking past each other, unfortunately. Don’t really know how to fix that, but I wish I did.”
Yes, it’s sort of depressing, isn’t it. I don’t know how to fix it either.
But, on the bright side: I now think I understand and appreciate the other side’s (or it should be “other sides'”, because there’s more than one or two) positions now, even if I don’t agree. And, most importantly, I understand my own position better now than I did before this debate. (I know that’s sort of selfish, but so what?)
I’m going to make just one last point before leaving this topic. It may help clarify a source of disagreement, or (more likely) it may fail totally. But I’m going to make it anyway.
Banks (either individually, or in total) need a lot of different things if they want to expand. Reserves, capital, yes. But also loan officers, computers, tellers, etc. Not to mention people and firms who want to lend or borrow from banks. Why should I “privilege” just one of those many things (reserves)? Why should others “privilege” capital? Aren’t the others on the list equally important?
Here’s my answer: I privilege reserves because I am interested in the public policy question. The Bank of Canada controls one aspect of public policy (monetary policy), and the Bank of Canada controls the supply of reserves to the banking system. (Again, you can read “the supply of reserves” as either an interest rate (price) or a quantity, but better yet as a functional relationship.) The Bank of Canada does not (except when it bails out banks) directly control the supply of capital, reserve officers, tellers, or anything else.
Anyway, thanks all for the argument!
Nick,
your last comment has inspired me to write a post called “Loan officer theory of helicopter drop monetary policy”:
http://themoneydemand.blogspot.com/2010/02/loan-officer-theory-of-helicopter-drop.html
Nick, it’s such a cop-out, very disappointing.
The basic question is: will a bank with a binding capital constraint make new loans no matter now large or permanent is the reserve injection?
You have no comment?
What about this scenario, due to the recent economical crisis, a lot of banks went bust. But what about a bank going bust due to the panic reaction of their clients. People have become very jumpy when it comes to having money on the bank.
Just a little bad news of a bank can cause the clients to massively take their money out of the bank, which result in a downward spiral that the bank doesn’t recover off.
If the banks clients wouldn’t pull their capital out of the bank it would not go bust. Theire are no safe assets that the bank can have if a large part of capital is pulled out of the bank. Even the most profitable bank won’t recover from that.
Adam P: OK then!
“The basic question is: will a bank with a binding capital constraint make new loans no matter now large or permanent is the reserve injection?”
No, but:
Or yes, but:
1. It could get more capital, by issuing new shares, or preferred shares, if the price is right.
2. If (say) bonds have a lower required/desired capital ratio than loans, it can buy bonds, sell loans (or not renew them when they get repaid), thereby changing the mix of assets on the asset side of its balance sheet, to relax the capital constraint, and then expand both assets and deposits. Again, the simple multiplier model is a model of deposits, not loans. Loans are just one part of banks’ assets. And banks aren’t the only source of loans.
Fine Nick, but then what does all of this have to do with an “excess demand for the medium of exchange”?
Adam: chequable demand deposits at the commercial banks are media of exchange. An increased supply of reserves at the BoC causes the commercial banks to buy something (loans, bonds, antique furniture), creating demand deposits to pay for them, which reduces the excess demand for media of exchange.
(Glad to see a very good Canada/Russia game last night.)
surely reserves and govie bonds, both being government debt, have similar capital charges. How did the reserve injection help them do something they couldn’t already do?
It was a fantastic game:). left me feeling much better.