In case you haven’t heard, Simon Wren-Lewis tried to kill the money multiplier earlier this week. And if he succeeded, and the money multiplier stays killed, if it has indeed been well and truly buried, I for one shall not mourn its long overdue passing. Over the course of my almost thirteen months of blogging I have argued on a number of occasions that, contrary to the money multiplier, bank deposits are endogenous, that they are not so many hot potatoes that, once created, must be held, never to be destroyed. This view has brought me into sharp, but friendly, disagreement with some pretty smart guys whom I usually agree with, like Nick Rowe and Bill Wolsey, but I’m not backing down.
My view of bank deposits has also put me in the same camp — or at least created the appearance that I am in the same camp — with the endogenous money group, Post-Keynesians, Modern Monetary Theorists and the like, whose views I only dimly understand. But it seems that they deny that even the monetary base (i.e., currency plus bank reserves) is under the control of the monetary authority. This group seems to think that banks create deposits in the process of lending, lending is undertaken by banks in response to the demands of the public (businesses and households) for bank loans, and reserves are created by the monetary authority to support whatever level of reserves the banks desire, given the amount of lending that they have undertaken. The money multiplier is wrong, in their view, because it implies that reserves are prior to deposits and, indeed, are the raw material from which deposits are created, when in fact reserves are created to support deposits.
So let me try to explain how I view the money multiplier. I agree with the endogenous money people that reserves are not the stuff out of which deposits are created. However, there is a sense in which base money is logically prior to deposits. Every deposit is a promise to pay the bearer something else outside the control of the creator of the deposit. That something is base money. Under a fiat money system, it is a promise to pay currency. Under a gold standard, it was a promise to pay gold, coin or bullion. This distinction is captured by the distinction between inside money (deposits) and outside money (currency).
It is my position that the quantity of inside money produced or created in an economy is endogenously determined by the real demand of the public to hold inside money and the costs banks incur in creating inside money. Because banks legally commit themselves to convert inside money into outside money on demand, arbitrage usually prevents any significant, or even insignificant, deviation between the value of inside and that of outside money. Because inside money and outside money are fairly close substitutes, the value of outside money is determined simultaneously in the markets for inside and outside money, just as the value of butter is determined simultaneously in the markets for butter and margarine. But heuristically, it is convenient to view the value of money as being determined by the supply of and the demand for base money, which then determines the value of inside money via the arbitrage opportunities created by the convertibility of inside into outside money. Given the equality in the values of inside and outside money, we can then view the supply of inside money and the demand for inside money as determining the quantity of deposits and the interest rate paid on deposits. Under competitive conditions, the interest paid on deposits must equal the bank lending rate (the gross revenue from creating a deposit) minus the cost of creating a deposit, so that the net revenue (the lending rate minus the deposit rate) equals the cost of creating deposits.
What determines the value of base money? The monetary authorities (central bank plus the Treasury) jointly determine the amount of currency and reserves made available. The public (banks plus households plus businesses) have demands to hold currency when tax payments are due, demands to hold currency for transactions purposes when taxes are not due, and demands to hold currency as a store of value, those demands depending as well on the expected future value of currency and on the yields of alternative assets including inside money. The total demand for currency versus the total stock in existence determines a value at which the public is just willing to hold the amount currency (base or outside money) in existence.
This theoretical setup is analogous to that which determines the value of money under a gold standard. Under a gold standard the amount of gold in existence is endogenously determined as the sum of all the gold ever mined from time period 0 until the present. But in the present period the total stock can be treated as an exogenously fixed amount. The total demand is the sum of the monetary plus non-monetary demands for gold. The value of gold is whatever value is just sufficient to induce the public to hold the amount in existence in the current period. Given that all prices are quoted in gold, the price level is determined by the conversion rate of money into gold times the gold value of every commodity corresponding to the equilibrium real value of gold. The amount of inside money in existence is whatever amount of convertible claims into gold the public wishes to hold given the yields on alternative assets and expectations of the future value of gold.
The operation of a gold standard requires no legal reserves of gold to be held. Legal reserve requirements were an add-on to the gold standard – in my view an unnecessary and dysfunctional add-on – imposed by legislation enacted by various national governments for their own, often misguided, reasons. That is not to say that it would not be prudent for monetary authorities to hold some reserves of gold, but the decision how much reserves to hold has no intrinsic connection to the operation of the gold standard.
Thus, the notion that there is any fixed relationship between the quantity of gold and the amount of convertible banknotes or bank deposits created by the banking system under the gold standard is a logical fallacy. The amount of banknotes and deposits created corresponded to the amount of banknotes and deposits the public wanted to hold, and was in no way logically connected to the amount of gold in existence. Similarly, under a fiat money system, there is no logical connection between the amount of base money and the amount of inside money. The money multiplier is simply a reduced-form, not a structural, equation. Treating it as a structural equation in which the total stock of money (currency plus demand deposits) in existence could be juxtaposed with the total demand to hold money is logically incoherent, because the money multiplier (as a reduced form) is itself determined in part by the demand to hold currency and the demand to hold deposits.
So it’s about time that we got rid of the money multiplier, and I wish Simon Wren-Lewis all the luck in the world in trying to drive a stake into its heart, but somehow I am not all that confident that we have yet seen the last of that pesky creature.
PS I hope, circumstances permitting, tomorrow to continue with my series on Earl Thompson’s reformulation of macroeconomics. This post can perhaps serve as introduction to a future post in the series on alternative versions of the LM curve corresponding to different monetary regimes.
Uneasy Money 
David:
I’d join you in dancing on the grave of the multiplier, but when you say “The total demand for currency versus the total stock in existence determines a value at which the public is just willing to hold the amount currency (base or outside money) in existence.” you get into hot water. The demand to hold base money depends on the quantity of derivative moneys, so when credit cards are invented, the demand for paper dollars falls, and inflation results. The credit card companies thus would have the same effect on the value of the base money as counterfeiters. That’s crazy. It would be like saying that the issuance of call options on GM stock reduces the demand for GM stock and thereby reduces its value (also a crazy statement, BTW).
Much better to say that the value of the base dollar is determined by the Fed’s assets, just like the value of GM stock is determined by GM’s assets. Then it becomes clear that the issuance of derivative dollars (which are call options on base dollars) does not affect the value of the base dollars, just like the issuance of calls on GM stock does not affect the value of GM stock.
A quibble: Nothing says that banks must convert derivative money into base money on demand. I’d be content with a bank that promised to convert my derivative dollars into a dollar’s worth of something, as opposed to dollars themselves.
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Didn’t it die twenty years ago in Japan?
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Mike Sproul: Much better to say that the value of the base dollar is determined by the Fed’s assets, just like the value of GM stock is determined by GM’s assets. What happens in hyperinflation?
And what determines the value of the Fed’s assets? The value of GM stock is a function of expected income. The value of the Fed’s assets is a function of … ?
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David Glasner,
Where do demand deposits (or “sight deposits”, as Hawtrey and I know them) come into this picture? It seems rather odd to have different demand functions for demand deposits and notes/coin, so does “inside money” include these accounts?
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How do you reconcile the belief in inexitence of the MM with opposing IOR?
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PeterP,
Banks still presumably have a demand function for holding reserves in this model. IOR is significant in the same way that a subsidy for banks holding bonds (as opposed to loans) would be significant, i.e. it affects banks’ portfolio preferences, just like any other subsidy of an asset.
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Lorenzo:
In a hyperinflation there is less backing per dollar, either because the central bank lost assets, or because the central bank issued new money without getting new assets.
The fed’s assets consist of its gold and its bonds, both of which have value. In some countries, the central bank’s assets have a chance of being augmented by from some outside source (the government, the European Union). In other countries (Weimar Germany) the government has its hands in the pocket of the central bank, so central bank assets are less than they might appear.
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David: “Thus, the notion that there is any fixed relationship between the quantity of gold and the amount of convertible banknotes or bank deposits created by the banking system under the gold standard is a logical fallacy. The amount of banknotes and deposits created corresponded to the amount of banknotes and deposits the public wanted to hold, and was in no way logically connected to the amount of gold in existence.”
Did you mean to say that? Suppose the worldwide stock of gold doubles. In equilibrium the value of gold may (say) halve (roughly, it won’t exactly), the real stocks of convertible banknotes and bank deposits stays the same, but their nominal quantities double.
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“But it seems that they deny that even the monetary base (i.e., currency plus bank reserves) is under the control of the monetary authority.”
I don’t think this is completely true. What we do say is that the CB controls M0, but if it doesn’t want to destroy the economy it largely has to follow the whims of the banking sector. It can increase M0 above what the sector demands as much as it cares to, though it will have little to no effect.
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Unlearningecon,
The central bank can act as lender-of-last-resort and when doing so it cannot fix definitely the quantity of M0 (a monopolist cannot fix both price and quantity) but it can only be the lender-of-last-resort BECAUSE the monetary base is under its control.
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W. Peden,
I think what Unlearningecon was trying to get at is the CB must provide the necessary reserves in order to maintain its interest rate target. So the CB does control MB but largely follows the banking sector (typically increasing MB) because it chooses to control interest rates.
David,
Great post. One thing, the above point is an important difference (IMO) between the gold standard and current fiat system. Under the gold standard the supply was constrained by physical resources and costs of extraction. Under the current system, there are no real constraints on the MB, which can be increased at will to meet the desires of private banks.
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Woj,
Fair point, I misunderstood his first sentence. I’m not aware of the factual basis for the claim that the LOLR function is necessary to avoid destroying the economy, given that LOLR is a recent invention in human history yet economies have been around for some time. One might argue that it’s OPTIMAL for a central bank to perform LOLR (good arguments for or against this proposition seem to be rather rare) but even then central banks often set interest rates that cannot realistically be described as the whims of the banking sector. I refuse to believe that it was the “whims of the banking sector” that led the Bank of England to set bank rate at 17-16% in 1979-1981 or 15% in 1989-1990. I’ll believe that after I believe Kaldor’s claim that the money supply adjusts to the “needs of trade”, after I believe the strong efficient market hypothesis, and after I’ve had a full lobotomy.
I only really started to get the idea behind the gold standard’s dynamics once I heard about the Somalian currency, which increases until it meets the cost of printing and importing it. The gold standard seemed like an incredibly stupid system and its stability mystified me, until I realised that it operated on a similar principle of the cost of extraction setting limits on the expansion and contraction of the money supply. Hence Romer’s work, which shows that since the 1930s we’ve never found a way of replicating the gold standard’s stability.
Nick Rowe has convinced me that most modern fiat currencies are pseudo-gold standard systems: a CPI target, for example, is like a gold peg, since the monetary base adjusts over the long-term to keep the CPI index on target. You could conceivably have a similar system with gold; in practice, exchange pegs like the ERM (but NOT currency boards or the gold standard) operate on the same principle.
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Seems to me that the following is self evident:
1) central banks can add or subtract reserves at will by open market operations.
2) central banks cannot force the public to hold demand deposits instead of currency.
3) central banks are monopolists that target the price (the interest rate), and not the quantity of reserves. Discount reserves from the CB are generally just 1% more than interbank reserves.
4) commercial banks have an implied break even rate of interest at which they are indifferent between lending and not lending. This is a function of the credit risk of the borrower and the cost of reserves.
Thus we can conclude the central bank sets a floor on interest rates at which banks are willing to lend by targeting the price of reserves. For a given interest rate target, however, the CB does *not* restrict the quantity of reserves. Therefore bank credit quantity is endogenous – set by commercial bank’s information and efficiency (supply), lenders’ creditworthiness (demand), and the public’s willingness to hold bank deposits instead of currency (supply).
However, bank credit’s price has a floor set by the cost of reserves, which is an monotonic function of the central bank’s target rate.
Thus credit easing may only lower the interest rate of bank credit without stimulating borrowing. Existing borrowers get a windfall at the expense of existing savers, but no new borrowers are created.
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W Peden,
Imagine you introduce large negative IOR, then the interest rate will drop to that (that is why the Fed introduced *positive* IOR – to put the floor under rates, not to slow down loans), and then what? Do you imagine that just because the return on capital if stored in reserves/bonds is negative, banks will start making loans at a loss? “What do we care, we lose our money when storing it in bonds/reserves, let’s lose it instead by making bad loans!
No, what will happen is that capital will flow out of banks because they now have expected negative RoC. Banking will be killed.
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PeterP,
(1) There is a difference between the possibility of a loss and a certainty of a loss.
(2) There is a difference between a big loss and a small loss.
I expect professional bankers to be aware of both sorts of difference and act accordingly. I also do not expect the banking system to implode the moment banks start making losses.
I am surprised at your confident prediction that “Banking will be killed”. Is banking dead in Sweden? Is there a lag effect? I know that Bill Mitchell predicted it would do nothing to help Sweden (http://bilbo.economicoutlook.net/blog/?p=4763) but at the very least, I would be surprised if the Swedish economic performance could have been much better since 2009.
The assertion that negative IOR is ineffective has not been empirically falsified (yet). The assertion that it would “kill banking” seems very dubious to me, based on the Swedish experience. Is there some institutional difference that would make all the difference?
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W Peden.
Sweden had tiny negative IOR, so it is a small step in the wrong direction, a tax on banks. Take it to the extreme to see if it is expansionary or contractionary: a negative IOR of -90% is simply a huge tax. No business will choose another money losing activity (like giving bad loans) just because you tax it more, it will just shut down or change what it does (invest in commodities – hence bubbles there despite weak economy). Similarly Walmart will not lower prices just because you slap a tax on it, it already is making all the money it can. So Bill Mitchell was right. Sweden did OK because it had a fiscal stimulus, it is a small country that can devalue, plus the state guaranteed some bank loans which is also a (hidden) fiscal stimulus: bank makes a bad loan but is not left holding the bag, instead the state effectively transfers money to the borrower because if he defaults it makes the bank whole. It is encouraging banks to extend fiscal stimulus on behalf of the government, so of course it worked.
Mitchell was also right that a fiscal contraction cannot be offset by monetary policy, especially if there is no demand for loans (like now), something Scott Sumner believed. Sumner predicted in Dec 2010 that austerity program in Britain will turn out ok, because “fiscal multiplier is zero”. Tell it now to the new British unemployed. The economy is devastated there with unnecessary austerity.
So again: banking was not killed in Sweden because the IOR was small. Make it big and the capital will go somewhere else. Make a fiscal stimulus big and you will get debt deleveraging, repaired private balance sheets, full employment and finally inflation. Fiscal stimulus is expansionary in the limit, negative IOR is contractionary in the limit.
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PeterP,
“No business will choose another money losing activity (like giving bad loans) just because you tax it more, it will just shut down or change what it does (invest in commodities – hence bubbles there despite weak economy). Similarly Walmart will not lower prices just because you slap a tax on it, it already is making all the money it can.”
1. So we agree that banks will go for those activities that minimise their losses (loss-aversion is important) and that businesses do not shut down simply because one line of business (in this case, holding reserves) is being taxed.
2. Why shouldn’t banks minimise losses? It’s not as if people will sell their shares into oblivion the moment a bank makes a loss. RBS has been making losses for years and still has shareholders- they have more shareholders, the smaller a loss they make. So, at the margin, a dubious loan (which MAY turn out well) is better than holding an asset which will certainty make a greater loss.
3. You’ve moved quite some way from “banking will be killed” (if large negative IOR is introduced) and at no point have you argued that small negative IOR, which is all that anyone has proposed, would be contractionary (let alone argued that eliminating positive IOR would be a bad idea*). Now, negative IOR is contractionary “in the limit”, presumably like effluent taxes. I am unconvinced, either in the case of negative IOR or in the case of effluent taxes, that these cannot shift business behaviour. In the case of banks, this means changing their asset portfolios from excess reserves at the central bank to other assets.
I’m curious as to why you extend a charitable approach to Bill Mitchell’s prediction (extraneous factors explain the fact that negative IOR did not sink the Swedish economy and the Swedish economy had a strong recovery) but a much less charitable approach to Scott Sumner’s prediction (ignoring Market Monetarist caveats about monetary policy). I would have thought that it would make sense to be as charitable or uncharitable to both predictions.
* The original point at issue was POSITIVE IOR. This stuff about negative IOR is an interesting diversion, but you haven’t yet provided a reason for thinking that one should oppose positive IOR under present circumstances, even if one rejects- as Glasner and I do- the concept of the money multiplier.)
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“Because inside money and outside money are fairly close substitutes, the value of outside money is determined simultaneously in the markets for inside and outside money, just as the value of butter is determined simultaneously in the markets for butter and margarine.”
Say the quantity of inside money increases beyond demand, causing inside money to trade at a discount to outside money. You’ve pointed out before that arbitrage should cause this excess inside money to reflux back to the issuer, thereby restoring equilibrium. But as you point out, inside and outside money are to each other like margarine is to butter. After all, you can pay taxes or buy stuff with either inside or outside money, just like you can spread either butter or margarine on toast. Who is to say then that the excess won’t be fixed by the value of outside money falling (and as a corollary the value of inside money falling too via arbitrage)? Wouldn’t this mean that changes in the quantity of insi de money can affect the price level?
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Mike, The invention of banknotes and deposits reduced the monetary demand for gold, thereby reducing the value of gold thereby causing inflation. Monetary and financial innovations like credit cards that reduce the demand for base money do have the same (at least directionally) effect on the value of base money as counterfeiters. I don’t think I disagree with your quibble, but in most cases it seems most convenient to make the derivative money directly convertible into the base money.
Ryan, Good point, but I am talking about the idea of a money multiplier, not a particular instance.
W. Peden, Demand (sight) deposits are the main component of inside money. Whether you want to lump the demand for sight deposits together with the demand for banknotes is a matter of convenience. I would assume that you are not indifferent between holding 98% of your cash in the form of banknotes and 2% in the form of sight deposits on the one hand with holding 98% of your cash in the form sight deposits and 2% in the form of banknotes. This would be especially the case when the nominal yield banks pay on demand deposits is significantly greater than the 0 nominal yield on banknotes. But there are certain types of transactions for which you want to use demand deposits and certain types that you prefer to use banknotes, so the two types of instruments are not perfect substitutes even when there is no difference in their nominal yields.
PeterP, I’m sorry, I don’t see why you think there is any inconsistency between the two.
Nick, Yes, I meant to say exactly that, even though for purposes of this argument I accept that your example is valid. The reason that the quantity of deposits doubles after the quantity of gold doubles is because the public demands twice as many deposits in nominal terms after the doubling of the quantity of gold doubles the price level. You are focusing on the reduced-form equation, I am focused on the underlying structural equations.
Unlearningecon, Fair point, though I think you greatly(?) exaggerate the discontinuity associated with supply too little as opposed to too much reserves.
W. Peden. Agreed.
Woj, It chooses to control interest rates, but it can change the interest rate at which it makes reserves available. When it alters the terms on which it makes reserves available, there is a corresponding effect on the value of the monetary base.
Thanks. Although I was trying to highlight the analytical similarity between the determination of the price level under a gold standard and under a fiat money system, I certainly agree with you that the ability of the monetary authority under a fiat money system to alter the quantity of the money that it issues at will is a major difference between the two systems, but that difference can be encompassed by a single analytical framework.
W. Peden, I think that I agree with Nick Rowe, despite some differences in interpretation, that there is a basic analystical similarity between the way in which the value of money is determined under a fiat money system and the way it is determined under the gold standard. But it depends at what level of abstraction one is doing the analysis.
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David Glasner,
Thanks, that makes a lot of sense. I remember looking at the velocity of US M1 on FRED and seeing how the introduction of interest on demand deposits changed M1 from having the kind of steady upward velocity path you’d expect from a narrow aggregate to being almost hilariously unstable. In fact, I’d venture that the instability of regulatory regimes is the main cause of the instability of monetary aggregates and not one that can be predicted, such that even if there were very stable demand functions (excluding regulatory effects) for various aggregates an Old Monetarist approach would be disastrous.
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How ironic that I learned this stuff in College. Such as M1, M2, or M3 all those have different monetary bases. Whether it includes that or that. This sort of data is hard to remember unless you do this on a regular basis.
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requinb4, Setting the quantity of reserves or setting an interest rate at which reserves are freely available allows the central bank to control the price level and the rate of inflation. The question is which method works better in practice. Clearly setting an interest rate is better than trying to fix the quantity of reserves. But that is simply because the demand for reserves tends to fluctuate. The government could control the domestic price of an imported product either by setting a tariff or by imposing an import quota. In practice, setting a tariff is results in less price volatility than does imposing a quota. But the two methods can in principle lead to the same result if the government can anticipate changes in demand with enough skill.
PeterP, The point of a negative IOR is not to tax banks out of existence but to make holding reserves slightly less attractive than it is now so that their demand to hold reserves is not inexhaustible as it is now. Your limit argument is therefore inappropriate inasmuch as there would clearly be an optimal negative interest rate to charge beyond no one would want to raise the rate.
JP, Inside money cannot trade at a discount relative to outside money because inside money is issued on the condition of its being convertible into outside money, so they always are exchangeable at par. If too much inside money is created (i.e., more than the public desires to hold given the relative attractiveness of holding inside money relative to alternatives including outside money) it refluxes back to the issuing banks. If, however, the quantity of inside money increases because the public wants to hold the additional balances and are induced to hold inside money instead of outside money, then the value of outside money will tend to fall (causing the value of inside money to fall as well) unless the value of outside money is maintained by some form of convertibility or a price rule.
W. Peden, Glad you found it helpful.
Tas, Use it or lose it.
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David,
You wrote: “My view of bank deposits has also put me in the same camp — or at least created the appearance that I am in the same camp — with the endogenous money group, Post-Keynesians, Modern Monetary Theorists and the like, whose views I only dimly understand. But it seems that they deny that even the monetary base (i.e., currency plus bank reserves) is under the control of the monetary authority.”
Just to fill out the list the way I understand it (and perhaps with some redundancy), we’d have:
Post-Keynesians
Modern Monetary Theorists (MMT)
Monetary Realists (MR)
Monetary Circuit Theorists (MCT)
and even at least one Austrian (Mish Shedlock)
It’s interesting to me that you and the MR crowd use “inside” and “outside” rather than the MMT crowd use of “horizontal” and “vertical.”
Also, that last bit you wrote: “But it seems that they deny that even the monetary base (i.e., currency plus bank reserves) is under the control of the monetary authority.” I don’t think is actually true of all these groups. For example, my reading of Scott Fullwiler is that current Fed policy in targeting the overnight rate can mean that inside money causes outside money (reserves or currency) to be created, but I don’t think he’d deny that the Fed is certainly capable of changing its policy.
BTW, Steve Keen has recently added models of government created money to his differential equation models (previously he just had bank created money):
slides:
Click to access UWSPresentation.pdf
paper by some Canadian mathematicians evaluating the models:
Click to access GrasselliCostaLimaMAFEonline.pdf
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