Fallacies of composition and decomposition: the supply of money and reserves

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.

83 comments

  1. winterspeak's avatar

    Nick:
    I don’t know of the arguments between you, Sumner, and Woosley have made you nervous or not. They should.
    Your assertion that PK has missed the fact that reserve outflows (for whatever reason) need to be matched by reserve inflows at an individual bank level reflects poorly on you. PKs talk about this all the time, and it is how the loans->deposits causality works.
    It’s also a pity no one responded to David’s original question about how a bank that’s just enjoyed a $1M deposit isn’t better off than an identical bank that has not. DAVID, if you’re still rolling about this bog, the answer is that the bank with the $1M deposit has a lower cost of capital because of its liability structure, and it can exploit that lower cost in a number of ways, one of which may be making additional loans. Up to the bank.
    This raises two important points. The first is that, at an individual bank level, the entity has a number of strategies it can use to generate a reserve inflow to make up a reserve outflow (for whatever reason). It can seek deposits, it can borrow reserves from another bank, or it can borrow directly at the discount window. These all go up in cost of capital, and banks can and do manage their liquidity risk as fits their business model. PKs have always stressed that capital constrains lending, and cost of capital is a factor in that. But claiming that matching reserve inflows and outflows someone makes the “money multiplier” real again is a fallacy. If you want to say “reserves matter because they impact the cost of capital” that’s fine. But lending remains capital constrained and NOT reserve constrained (as per your “money multiplier”).
    Which brings me to my second point, that if a bank gets lots of deposits, it has the option to make more loans because it enjoys a lower cost of capital and note that the mechanism for loan enablement remains the capital channel. Nick — you have just spilt I don’t know how many pixels arguing with other monetarists about what constrains credit extension and the word “capital” was not mentioned even once. Anyone who knows the first thing about Reality will reject the nonsense based on that alone. And it should make you seriously reconsider the monetarist fairy tale about how all this works.
    You’re getting dangerously close to the last refuge of Monetarists, which is to redefine all fiscal policy as monetary.

  2. Unknown's avatar

    Winslow @10.40: “The small bank will ‘lose’ $100 in deposits not reserves when a deposit is spent.”
    Yes, but when the deposit is spent, and redeposited at bank B, bank A will lose $100 in reserves to bank B.
    The MoneyDemandblog: as in my reply to Winslow above, the immediate cost to bank A is the loss in $100 of reserves, so it must pay interest to Bank B (for example) to borrow those reserves back. I see how it subsequantly responds to that loss, whether by selling $100 of T-bills, or whatever, as a second round response. Yes, I agree, it’s interesting to consider such things. Beyond the scope of my post though.
    Winslow @11.25: Look, just because some people disagree with you on public policy questions (and on the proper sphere of public policy vs private policy) doesn’t mean they “lack intellectual integrity”.

  3. Unknown's avatar

    Winterspeak: welcome to the “car crash”! I knew you wouldn’t be able to resist doing more than just “rubbernecking” 😉
    “I don’t know of the arguments between you, Sumner, and Woosley have made you nervous or not. They should.”
    Paradoxically, they cheer me. You and I both know there is something unhealthy about a science that claims a monolithic orthodoxy of mainstream knowledge. And PK’s apparent sense that there is a monolithic mainstream is I think mistaken. Plus, in some ways, the PKs are actually closer to any mainstream than me, Scott, or Bill.
    Bill’s an my views don’t seem to differ much on this particular issue. And Scott’s view is internally consistent. The banking system matters to me (and Bill?) because I think money’s role as medium of exchange is important, and bank deposits are media of exchange. If I didn’t hold those beliefs, and were interested only in money as unit of account, and the equilibrium price level, then I would I think agree with Scott. Any model of banks’ creating money would not be so much wrong as irrelevant.
    “Your assertion that PK has missed the fact that reserve outflows (for whatever reason) need to be matched by reserve inflows at an individual bank level reflects poorly on you. PKs talk about this all the time, and it is how the loans->deposits causality works.”
    There is a lot of heterogeneity among PKs, as they themselves generally acknowledge. Perhaps those who commented on David Beckworth’s post, and here, who seemed to me to disagree with this point, are not a representative sample? So I am (mostly) preaching to the converted? OK.
    Now, you are really losing me on the question of the cost of capital. Because as I understood it, the idea that bank lending is capital constrained (as well-articulated by JKH for example), when it talks about a bank’s “capital” means by that the bank’s equity (total assets minus total liabilities). I know I’m probably over-simplifying, but getting lots of extra deposits does not increase the bank’s capital in that sense of the word (except perhaps slowly, over time, if it can increase retained earnings as a result). The way for a bank to get more “capital”, for example, would be to issue more shares (or preferred shares?). So the “cost of capital”, in that sense, would be (inversely) related to the P/E ratio at which it could sell new shares, for example. The interest rate on deposits is not a cost of bank “capital”, in that sense.
    The idea that bank lending is capital constrained is interesting and important. How important it is will depend on the supply curve of new capital (people’s willingness to buy newly-issued bank shares, and at what P/E ratio. But that’s more relevant to the supply of bank loans. As I said in the post, the textbook model is not a theory of the supply of bank loans, it’s a theory of the supply of bank deposits, i.e. money.
    “You’re getting dangerously close to the last refuge of Monetarists, which is to redefine all fiscal policy as monetary.”
    “Close”?! If you adopt the standard monetarist definition of monetary policy — anything that affects the (current or expected future) supply (function) of money — and then take the standard MMT definition of fiscal policy — any change in G and/or T that is financed my changing the stock of money — then I am not “close” to that “last refuge”. Monetarists always and everywhere have already been there!

  4. winterspeak's avatar

    Nick:
    I tip my hat to Sumner’s consistency just as I do to your graciousness. As for the rubbernecking and involvement, I am weak : (
    If you want to find complete confusion about the basic mechanisms of banking cheering, that is up to you. Perhaps you are similarly invigorated by debates concerning the flatness of the Earth?
    The capital question is easy to understand. JKHs point about equity liability is exactly correct. Banks with large deposit bases find it cheaper to raise additional equity and thus have lower CoCs than comparables without those deposit bases.
    I find your distinction between bank loans and bank deposits trivial.
    And yes, once PKs demolish the point of reserves, FFR, QE, and the entire steaming pile that is monetary policy in general, and point out the centrality of fiscal, Monetarists say “fiscal is monetary too”. Then they start arguing about the money multiplier again.

  5. TheMoneyDemand blog's avatar

    “The MoneyDemandblog: as in my reply to Winslow above, the immediate cost to bank A is the loss in $100 of reserves, so it must pay interest to Bank B (for example) to borrow those reserves back. I see how it subsequantly responds to that loss, whether by selling $100 of T-bills, or whatever, as a second round response. Yes, I agree, it’s interesting to consider such things. Beyond the scope of my post though.”
    In practice selling $100 of T-bills or repoing $100 of longer term securities is what happens in the first round. Especially now in the US when reserves yield more than T-bills.

  6. TheMoneyDemand blog's avatar

    Nick, winterspeak – capital constraints have a serious impact on the money multiplier model as thay sharply increase what Nick calls “an allowance for risk and admin costs”. Money multiplier model is 100% correct, you just have to map it correctly to the reality.

  7. Scott Sumner's avatar
    Scott Sumner · · Reply

    Nick, I understand why you say that DDs associated with a new loan will disappear almost immediately. But that is not true for the entire stock of DDs held by the loan-making bank. Suppose a bank attracts $100 in new base money via an OMO. The bank may decide to increase loans by $900 and DDs by $1000 in equilibrium. The fact that most of the specific DDs associated with the loan may soon disappear is not important. Even if they do, they will be replaced by other DDs. Even if those other DDs come from another bank, that’s no problem, as other banks will also be attracting DDs as the loan money is withdraw from the original bank, and deposited elsewhere. I still don’t see any problem with analyzing the process by assuming a single monopoly bank. For instance, suppose you had a single monopoly bank with many branches. Wouldn’t the process look exactly the same, even if you broke down the accounting statements on a branch by branch basis?
    In my view the expected future supply and demand for base money determines the expected future NGDP (perhaps with help from an explicit central bank target). The expected future NGDP determines near-term NGDP. Near term NGDP determines current demand for M2. (M2 is endogenous in that sense). So current M2 is determined by future expected MB supply and demand, nothing at all like the way it’s taught in the textbooks. You say you are being attacked on 5 sides? I’m disappointed, there are at least ten ways of thinking about banking. You’ve got to broaden your readership! (Seriously, you have great commenters.)
    If C/D and R/D go to zero, then the price level goes to infinity, in other words people use cash in their fireplace for heat. You can’t buy anything with currency.
    Bill, I did not mean to assume no demand for base money, just no demand for reserves. I was still assuming a demand for currency, which pins down the price level.

  8. Winslow R.'s avatar
    Winslow R. · · Reply

    Winslow @11.25: Look, just because some people disagree with you on public policy questions (and on the proper sphere of public policy vs private policy) doesn’t mean they “lack intellectual integrity”.
    If I gave the impression that I believe anyone that disagrees with me “lacks intellectual integrity, I apologize. Economists lack intellectual integrity when their jobs ‘keep’ them from publicly questioning or stating their stance on the proper sphere of public policy vs private policy.
    From your statements I can only infer you believe the printing press should be fully privatized. You still haven’t stated your stance, so how can we disagree?

  9. RSJ's avatar

    Nick,
    You are using the wrong definition of “equilibrium” in this context. The outflows from the bank will be the rate of increase in loans net of the rate of repayment, with interest. The inflows will be the rate of increase in (time and demand) deposits. “Equilibrium” means that the difference between these two rates is constant, so that the size of reserves is a constant fraction of the size of the bank’s assets (or liabilities). All these variables — loans outstanding, reserves, and deposits, are growing with the overall economy, and are set by the bank’s relative aggressiveness in expanding its market share of loans vis-a-vis its aggressiveness in expanding it’s market share of deposits.
    To deviate from equilibrium means that the bank changes it’s policy, i.e. becomes more loose with lending in a way that is not offset with being more aggressive in attracting deposits. Therefore the desired reserve level is a function of overall bank policy (underwriting standards), and the marginal cost of reserves allocated to each loan is the same given that policy. This is where the law of large numbers comes in — i.e. the bank assumes that if the observed rate of growth of loans given a certain lending standard was on average X, then it will remain X. In the same way, if the rate of growth of deposits due to a certain competitive position was Y yesterday, then it will remain Y today. Therefore the difference, X-Y will remain constant unless the policy changes. So the bank can go ahead and keep making loans under that policy, and each loan will have a marginal reserve cost of (X-Y), because just as the loan officer is busy approving customers at one rate, the depositors are arriving at another rate, and the bank knows this.

  10. Unknown's avatar

    TheMoneyDemandblog: “Nick, winterspeak – capital constraints have a serious impact on the money multiplier model as thay sharply increase what Nick calls “an allowance for risk and admin costs”. Money multiplier model is 100% correct, you just have to map it correctly to the reality.”
    I really like that statement. Nice and clear. I think the practical importance, though, depends on the state of the market for new bank shares. If banks face a perfectly elastic demand for new shares (to take an extreme case) then there isn’t really a capital constraint. Just a fixed markup for risk.

  11. Unknown's avatar

    Curses! I wrote a long comment in reply to Winslow on whether I want to privatise money. And it disappeared!
    Short version: Winslow: basically, I want to keep the Bank of Canada as a Crown Corporation acting (or trying to, as best it can) in the public interest. But if a bunch of hippies (or whoever) want to set up their own private money on the side, as long as they don’t infringe in ANY way on the Bank of Canada’s brand name “the Canadian Dollar”, then I think that’s probably OK too.
    Those are tentative views, of course.

  12. Unknown's avatar

    Scott: “If C/D and R/D go to zero, then the price level goes to infinity, in other words people use cash in their fireplace for heat. You can’t buy anything with currency.”
    I’m not sure on this. Suppose the commercial banks are still using the Bank of Canada as a clearing house. So each commercial bank has a deposit at the BoC, which can have a positive or negative balance. Suppose the desired balance of each bank is zero. Now suppose the BoC buys or sells (say) gold for settlement balances at a fixed price P*. I think that pins down the price level. If there were an incipient rise in the CPI and price of gold above P*, the BoC would sell gold, so aggregate settlement balances would go negative, so there would be excess demand for reserves, and so an (infinite) multiplier process would kick in, contracting the money supply (all DDs), until the CPI and price of gold fell back to P*. (That’s a stability experiment, by the way).

  13. TheMoneyDemand blog's avatar

    “I really like that statement. Nice and clear. I think the practical importance, though, depends on the state of the market for new bank shares. If banks face a perfectly elastic demand for new shares (to take an extreme case) then there isn’t really a capital constraint. Just a fixed markup for risk.”
    State of the market for new bank shares is reflected in the Price/Book or even better in the “Price/Tangible book” ratio. If Price/Book ratio is low then banks are capital constrained. The period of too low inflation expectations in the US in late 2008- early 09 had a nice overlap with a period of low price/book ratios in the banking sector. When Price/Book is high as it was in 2007, there are no capital constraints.

  14. winterspeak's avatar

    TheMoneyDemand:
    No. When an individual bank credits a receivable, or debits/credits a deposit as part of payment clearance, it does so without reference to its reserve position. It gets back to its reserve target via operational activities, interbank lending overnight, or the discount window. In no way, and at no point, is an individual bank or the banking system reserve constrained, unless credit concerns shut down its reserve account or the Fed decides to close the discount window.
    Nick, Sumner, and every monetarist on planet earth tries desperately to jam a money multiplier into this and it is nonsense. Read through earlier comments, and the post itself, to smell the nonsense for yourself.
    The CoC for a bank depends on its cost structure, and risk profile (particularly the riskiness of its assets). Remember — equity is in first loss position against default, at least in theory. Maybe you are now starting to see why banks are pro-cyclical, which adds to the impotence of monetary policy. But I doubt it.
    If banks can raise capital at will, then there is no medium/long term capital constraint. Nevertheless, in the short term, there really is a hard capital constraint as you will hit regulatory limits and actually have to raise the capital, without being able to lend more (legally) until you do. This is what a “constraint” is btw., and there is no analogous situation with reserves as that is managed, after COB essentially, to balance the books.
    You guys see constraints where there are none, and then wave them away when they do exist! You discussing lending without mentioning the words debt or capital! The intellectual path dependence is remarkable.

  15. TheMoneyDemand blog's avatar

    Winterspeak,
    if you want a money multiplier model that is more useful to you, replace obsolete textbook term “reserves” with “liquid assets”. And yes, central banks are always adjusting the price of liquidity. That’s why monetary policy works. And yes, capital constraints are really important, they have a huge impact on the parameters of money multiplier model. When Fed forgot that in September 2008, we had a huge problem.

  16. TheMoneyDemand blog's avatar

    Winterspeak said:
    “You discussing lending without mentioning the words debt or capital! ”
    This contradicts your earlier assertion “I find your distinction between bank loans and bank deposits trivial.” Look, assets = liabilities, so if Nick wants to focus on the asset side there is no harm.

  17. winterspeak's avatar

    TheMoneyDemand:
    I do not want a money multiplier model that is useful. I simply want to describe reality, and in reality, there is no “money multiplier” as is plain as day to everyone (except Monetarists) right now. “Liquid assets” is uselessly vague–you are welcome to it.
    As for Nick, well, he made a (bogus) statement about bank deposits. Those are liabilities, not assets as you claim. But I have found that Monetarists are clueless around balance sheets, and proud of it.

  18. Winslow R.'s avatar
    Winslow R. · · Reply

    “Short version: Winslow: basically, I want to keep the Bank of Canada as a Crown Corporation acting (or trying to, as best it can) in the public interest. But if a bunch of hippies (or whoever) want to set up their own private money on the side, as long as they don’t infringe in ANY way on the Bank of Canada’s brand name “the Canadian Dollar”, then I think that’s probably OK too.”
    …and you believe the printing press (the one capable of printing the dollars acceptable for paying taxes) should reside in the Bank of Canada and the commercial banks or in government?

  19. Jon's avatar

    “The idea that bank lending is capital constrained is interesting and important. How important it is will depend on the supply curve of new capital (people’s willingness to buy newly-issued bank shares, and at what P/E ratio. But that’s more relevant to the supply of bank loans. As I said in the post, the textbook model is not a theory of the supply of bank loans, it’s a theory of the supply of bank deposits, i.e. money.”
    There is plenty of evidence that banks are not capital constrained. Bank capital is effectively endogenous in the context of monetary policy. The reason for this is that monetary theory is really about the Price Level. Bank Credit expands => demands more capital, inflation => bank credit expands. Whereas being capital constrained has something to do with the slope of the yield curve. A yield curve steeper than equilibrium attracts capital, shallower than equilibrium causes capital attrition.
    Bank capital does not moor the price-level. Any inflationary process will generate an equivalent increase in capital provisioned by the market.
    Nick: I must say you are wrong vis-a-vis money vs credit. “Credit” is broad money. And monetarists have always focused on broad money not narrow money. I consider your rejoinder about money vs. credit as entirely specious.
    This is something I think Mises nailed hard:

    Claims to a definite amount of money, payable and redeemable on demand, against a debtor about whose solvency and willingness to pay there does not prevail the slightest doubt, render to the individual all the services money can render, provided that all parties with whom he could possibly transact business are perfectly familiar with these essential qualities of the claims concerned: daily maturity and undoubted solvency and willingness to pay on the part of the debtor.
    We may call such claims money-substitutes, as they can fully replace money in an individual’s or a firm’s cash holding. The technical and legal features of the money-substitutes do not concern catallactics. A money-substitute can be embodied either in a banknote or in a demand deposit with a bank subject to check (“checkbook money” or deposit currency), provided the bank is prepared to exchange the note or the deposit daily free of charge against money proper.

    If the money reserve kept by the debtor against the money-substitutes issued is less than the total amount of such substitutes, we call that amount of substitutes which exceeds the reserve fiduciary media.

    The issue of money-certificates does not increase the funds which the bank can employ in the conduct of its lending business. A bank which does not issue fiduciary media can only grant commodity credit, i.e., it can only lend its own funds and the amount of money which its customers have entrusted to it. The issue of fiduciary media enlarges the bank’s funds available for lending beyond these limits. It can now not only grant commodity credit, but also circulation credit, i.e., credit granted out of the issue of fiduciary media.
    While the quantity of money-certificates is indifferent, the quantity of fiduciary media is not. The fiduciary media affect the market phenomena in the same way as money does. Changes in their quantity influence the determination of money’s purchasing power and of prices and — temporarily — also of the rate of interest.

    The laws which compelled the banks to keep a reserve in a definite ration of the total amount of deposits and of banknotes issued were effective in so far as they restricted the increase in the amount of fiduciary media and of circulation credit. They were futile as far as they aimed at safeguarding, in the event of a loss of confidence, the prompt redemption of the banknotes and the prompt payment on deposits.

    The second fault of the Currency School was that it failed to recognize that deposits subject to check are money-substitutes and, as far as their amount exceeds the reserve kept, fiduciary media, and consequently no less a vehicle of credit expansion than are banknotes. It was the only merit of the Banking School that it recognized that what is called deposit currency is a money-substitute no less than banknotes. But except for this point, all the doctrines of the Banking School were spurious.

  20. Unknown's avatar

    Jon: “Bank capital does not moor the price-level. Any inflationary process will generate an equivalent increase in [nominal NR] capital provisioned by the market.”
    A very important point. I missed it. It needed saying. I have added one word to clarify what you meant against possible objections. And the standard nautical metaphor is “anchor”, not “moor”! 😉
    But I think you are misinterpreting either me or Mises there (probably me). Some credit is a medium of exchange (bank’s demand deposits for example). But not all credit is medium of exchange. That’s what Mises is saying, and I agree. But I would call those media of exchange “money” too. What I meant was that I am not interested (in this context) in credit per se; only in that subset of credit that is media of exchange.
    Yes, many (most) monetarists focus on broader money. I don’t. (Maybe I’m not a “true” monetarist, OK). On this point I am closer to Yeager and Clower. And I can never tell if they are monetarists, Keynesians, or what. (And I’m not sure it really matters what we call them.)

  21. Unknown's avatar

    Winterspeak: “As for Nick, well, he made a (bogus) statement about bank deposits. Those are liabilities, not assets as you claim.” ?!!!
    Not sure who the “you” refers to there: me or TheMoneyDemandblog. But I know (and I’m 99.9% sure that TMDb knows this too, since he obviously knows his stuff very well) that my deposit at the Bank of Montreal is a liability of the Band of Montreal. (On the other hand, the Bank of Montreal’s deposit at the Bank of Canada is an asset of the Bank of Montreal).
    “I do not want a money multiplier model that is useful. I simply want to describe reality, and in reality, there is no “money multiplier” as is plain as day to everyone (except Monetarists) right now.”
    Now that is (unless I am misinterpreting it) a very revealing statement. If you merely want to describe what is, in the sense of a photograph, or picture (or even a movie), then yep, a set of accounting statements (balance sheet(s), and income statement(s)), is all you need. Forget about the money multiplier, or any alternative theory of the money supply. Theories are trying to do more than just describe reality; they are trying to explain it. And accounting pictures do not do that.
    In this context, I think my analogy between the simple Income Expenditure multiplier model and the simple money supply multiplier model is very instructive (I’m wondering whether to do a post on this). Those two models are formally identical (in a mathematical, and game-theoretic sense). They contain exactly the same insight: there’s a difference between the individual household/bank and all households/banks. But if you look at the simple Keynesian income-expenditure model from a purely accountant’s perspective, you miss the crucial distinction between actual and desired savings, and can end up in fallacies like Say’s Law if you mistake accounting pictures for a theory of what determines savings. Same with the money multiplier.
    (Also, both those models are flawed in the same way: they ignore interest rates. That is indeed a flaw, but it does not prevent them containing an important insight).

  22. TheMoneyDemand blog's avatar

    Jon said:
    “There is plenty of evidence that banks are not capital constrained. Bank capital is effectively endogenous in the context of monetary policy. ”
    You should have told this to Lehman Brothers in September 2008 or to Citi in February 2009.
    Winterspeak said:
    “I simply want to describe reality, and in reality, there is no “money multiplier” as is plain as day to everyone (except Monetarists) right now. “Liquid assets” is uselessly vague–you are welcome to it.”
    It is quite obvious that banks actively manage their liquidity position on the asset side of the balance sheet. Banks have a desired mix of liquidity on their balance sheet, this creates money multiplier effect. All the things you mentioned – cost of capital, etc. are very important inputs that change the parameters of the money multiplier model.

  23. winterspeak's avatar

    Nick: TMDB said you wanted to focus on assets, when in fact you were focusing on liabilities. I don’t know who got confused, or whether there was a typo somewhere, but I guess it’s good enough for Government work in Monetarist quarters.
    Call me old fashioned, but I think accurately describing reality is a necessary first step to explaining it. This post is on a very basic point: whether bank lending is at an individual, or system level, reserve constrained. You say it is, I say it is not. You argue that, at an individual bank level, needing 100% reserves makes it so, and I point out that it’s just managing a reconciling flows between banks, something that happens as part of payment settlement, and immaterial to credit extension. A bank doesn’t check its reserve balance before it clears a check, and a bank doesn’t check its reserve balance before it extends a loan. It does not need to.
    I think it’s revealing that you don’t believe accurately describing reality is a necessary prelude to trying to explain it. You are trying to explain fire via phlogiston.
    TMDB: No. Liquidity management, neither on the asset side nor on the risk of needing the ON market or discount window, creates the multiplier effect. In fact, the latter eliminates it. And the things that I mention do not change the parameters of the money multiplier model as reserves are simply not multiplied out into money supply.

  24. Winslow R.'s avatar
    Winslow R. · · Reply

    In Nick’s case I find theory isn’t guided by actual reality but rather a preferred reality.
    Nick, at the risk of provoking an angry backlash, I’ll continue to infer you prefer the printing press to be controlled by a crown corporation or ultimately the monarch (who will work in the public interest or try to, as best it can)
    http://en.wikipedia.org/wiki/Crown_corporations_of_Canada
    Wow! Your preferred reality pushes us into a monetary structure more feeble than the gold standard.
    At least the gold standard had some fig-leaf of democracy as it allowed anyone to dig up gold out of the ground to pay their taxes. In your reality, the ability to pay taxes is limited by an unelected monarch. I thought this war was fought a long time ago but I guess there are a still more than a few monetarist monarchists hiding in closets.
    Bill, Larry, Bob meet Nick.

  25. Scott Sumner's avatar
    Scott Sumner · · Reply

    Nick, I must have missed something in the C/D and R/D going to zero example. In the US the base is normally $800 billion. If the numerator of a fraction is $800 billion, how big does the denominator have to be before the fraction goes to zero? That’s why I assumed the price level went to infinity.
    Here’s how I view banking: I see the money multiplier as like the toaster multiplier. If the base rises 20%, then the nominal size of NGDP rises 20%. If the toaster industry is typlical, the nominal size of the toaster industry also rises 20%, and for the same reason. And if the banking industry is typical, the nominal size of the banking industry rises 20%. Loans, securities, deposits, capital, reserves, everything rise 20%. The textbook approach to the money multiplier makes things seems magical, the mysterious fact that deposits rise more than reserves. Everything rises more than reserves, but they all rise in the same proportion. Nothing mystical at all. I still want to stick to a consolidated balance sheet.
    No need to respond to this tirade, I see you are off to the next step, I’ll pick up there.

  26. Jon's avatar

    TMDb writes:

    “There is plenty of evidence that banks are not capital constrained. Bank capital is effectively endogenous in the context of monetary policy. ”
    You should have told this to Lehman Brothers in September 2008 or to Citi in February 2009.

    Please. First, you truncate the quote when I define what it means to be in the context of monetary policy.
    Second, what happens in the aggregate is different from what happens to an individual firm. The ‘market’ withdraws capital from particular firms or prefers to provision capital to different firms differently on a daily basis, and indeed, the firms so discriminated against do feel the effects, but so? The capital went elsewhere. And special-pleading about this firm or that firm does not really describe what happens in the aggregate.
    If capital markets don’t want to be entangled with bad banking, they’ll invest in ‘good’ banks or start new entities.

  27. TheMoneyDemand blog's avatar

    Nick, Scott,
    I tentatively agree with Scott here. One big commercial bank may have a desired reserve ratio equal to zero, but it will need to have another kind of liquidity buffer, for example T-bills. Let’s say that one big commercial bank has a desired T-bill/deposit ratio of X. Then central bank can control the commercial bank by buying/selling T-bills, and making other changes to the size and composition of the central bank’s balance sheet. The only change is that one big commercial bank will earn excessive monopoly profits, but the central bank will still be able to control monetary policy by manipulating various interest rates.

  28. Unknown's avatar

    Just catching up after a visit to Toronto. Some interesting arguments in my absence!
    My view (I think Bill Woolsey said it somewhere in the last week on his blog) http://monetaryfreedom-billwoolsey.blogspot.com/ , is that reserves are the medium of exchange to banks in the same way that deposits at the commercial banks are the medium of exchange for the rest of us.
    If you think (as I do, and Bill does) that the medium of exchange is crucially important (and quite over and above the fact that the medium of exchange usually also serves as the unit of account), then the demand for and supply of the quantity of money (medium of exchange) matters far more than the demand and supply of other assets that people hold. And the demand and supply of the quantity of reserves matters far more than the demand and supply of the other assets that banks hold.
    I think this is the underlying reason why I would disagree with TheMoneyDemandblog. I have already argued (in earlier posts) why an excess demand for the medium of exchange can cause Say’s Law to be false, and create a general glut, but that an excess demand for antique furniture cannot do that. Clearly, I need to make a similar argument for bank reserves. But yes, if you don’t see that the medium of exchange should be in such a “privileged” position in macroeconomics, you won’t see that reserves should occupy an equally privileged position in monetary theory.
    This debate is helping me clarify my thought (always the selfish reason for blogging)!
    Apropos of the above: Scott: toasters! This reminds me of Arnold Kling’s post on Mackerel! (And at least mackerel begin with ‘M’!) An excess demand for toasters or mackerel cannot cause a violation of Say’s Law and a general glut.

  29. Unknown's avatar

    Winslow: You Republicans (ooops! I meant republicans) are going to re-start the War of 1812! And a parliamentary system under a constitutional monarchy seems to work no worse than the system south of the border!

  30. Winslow R.'s avatar
    Winslow R. · · Reply

    Nick “And a parliamentary system under a constitutional monarchy seems to work no worse than the system south of the border!”
    True we both operate under an elite, though Canadians seem to relish the situation. South of the border we are in denial and we post-keynesians deny it the most.
    Amazing to commit one’s life to serving that elite unless somehow you are part of it? Moving the system towards ‘independence’ from the huddled masses is the life work of most central bankers and is understandable given their situation.
    As a professor, I’d think you’d have other goals. ‘Independence’ has failed, and bankers have been shown to be very dependent. Why try to design a system that just once again hides that dependency? Does the economic system really work best with a monarch (amorphous elite) picking winners and losers?

  31. Winslow R.'s avatar
    Winslow R. · · Reply

    Nick wrote: “My view (I think Bill Woolsey said it somewhere in the last week on his blog) http://monetaryfreedom-billwoolsey.blogspot.com/ , is that reserves are the medium of exchange to banks in the same way that deposits at the commercial banks are the medium of exchange for the rest of us. ”
    I think there is something to be desired here. Though I’ve tried to get the idea across several times, I’ll try again.
    Reserves are the currency (medium of exchange) that the Federal government uses when it spends and taxes. Banks use deposits/loans just like the rest of us and call it interbank lending. BofA will have an account at Wells Fargo etc.
    Only if BofA refuses to give Wells Fargo a loan, due to credit concerns, will Wells Fargo then go to the Fed for a loan of reserves, as reserves are ‘legal tender for all debts public and private’.
    Reserves matter when we go to BofA and demand that our deposits be converted to pay for our taxes. BofA can’t just ‘print’ money to pay off a federal tax bill. The printing press doesn’t reside in the commercial banks for good reason as we don’t want an amorphous elite picking winners and losers. BofA deposits are not acceptable as payment for federal taxes.

  32. TheMoneyDemand blog's avatar

    Nick said:
    “But yes, if you don’t see that the medium of exchange should be in such a “privileged” position in macroeconomics, you won’t see that reserves should occupy an equally privileged position in monetary theory.”
    No, I agree that the medium of exchange should occupy a privileged position. Where I disagree is that only reserves are a medium of exchange for banks. The existence of repo markets means that other assets can serve as media of exchange.

  33. TheMoneyDemand blog's avatar

    Jon said:
    “Second, what happens in the aggregate is different from what happens to an individual firm. The ‘market’ withdraws capital from particular firms or prefers to provision capital to different firms differently on a daily basis, and indeed, the firms so discriminated against do feel the effects, but so? The capital went elsewhere. And special-pleading about this firm or that firm does not really describe what happens in the aggregate.
    If capital markets don’t want to be entangled with bad banking, they’ll invest in ‘good’ banks or start new entities.”
    During the crisis markets didn’t want to invest in banks, but I agree that many new entities such as distressed debt vulture funds were started. But such new entities are no help for monetary policy.

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