Money, banks, loans, reserves, capital, and loan officers

Anyone who has taken ECON1000 has probably seen the simple model of how banks create money in a fractional-reserve banking system, and how an increase in reserves creates a multiple expansion of loans and the money supply. An alternative approach, cogently argued in comments here by JKH, says that it is bank capital, not reserves, that plays the crucial role. I think there may be some truth in what JKH says, especially at present, but it is not the whole truth. I'm going to lay out what i believe. Others can either learn from what I say, or try to help me learn where I might be wrong (or maybe even both).

Let's start with the simplest textbook story.

Bank deposits are money, by assumption. Each bank desires to keep (say) 10% reserves against deposits, either to cover liquidity risks, or because it is required to by law, or a bit of both. Bank capital is irrelevant. Start in equilibrium, where reserves are 10% of deposits at every bank. Now assume the central bank does something that causes each bank's reserves to increase by $10. Each bank now has $10 excess (undesired) reserves. In the first round, each bank increases the supply of loans and deposits by $10. It does not increase loans and deposits by $100 immediately, because it anticipates that when the deposit is spent, it will be re-deposited in another bank, so it will lose $10 in reserves. (The textbook story implicitly assumes that each bank is small relative to the whole banking system, and is looking for the Nash equilibrium.) But in aggregate, of course, there is no loss of reserves. If all banks are doing the same thing, each bank finds it gains as many reserves and deposits as it loses (absent a currency drain, of course). So with deposits and reserves both $10 higher than in the original equilibrium, each bank now has $9 excess desired reserves, so it increases loans and deposits again...

In the new equilibrium, deposits (the money supply) expands by 10 times (1/10%) the increase in reserves. That's the simplest textbook story. (OK, I've told it slightly differently from the textbook, by assuming all banks get the extra $10 reserves, rather than just one bank. That helps me think about the symmetric Nash equilibrium.)

Now let me give a totally different theory. It's one I just thought up this morning. Initially it was just a thought-experiment to help get my head clear. But then I wondered if there might be some truth to it after all. I call it the "Loan Officer Theory of Money Supply".

Forget reserves. Banks don't need reserves to make loans; they need loan officers to manage those loans. The desired reserve ratio is probably zero anyway, and doesn't matter. What matters is the ratio of loans to the loan officers who are needed to manage those loans. Assume, given an average turnover and complexity of loans, that one loan officer can manage a $10 million loan portfolio.

Start in equilibrium, with the desired ratio of loans to loan officers. If the central bank increases the supply of reserves, that does nothing to the money supply. The extra reserves just sit there. Banks won't increase loans with the same number of loan officers. But an increase in the number of loan officers, one per bank, would increase loans by $10 million per bank, and would also increase the money supply by $10 million per bank.

It's the supply of loan officers, and the desired ratio of loans to loan officers, that determine the supply of loans and money.

What's wrong with the loan officer theory? Absolutely nothing, provided we make explicit some assumptions. The first assumption is that the banking technology has fixed proportions between loans (the output good) and loan officers (one of the inputs). There is zero substitution between loan officers and other inputs. This means that banks' demand curves for composite other inputs, holding the quantity of loan officers fixed, is perfectly inelastic when loan officers are fully employed. The second assumption is that the market supply curve of loan officers is perfectly inelastic. Given these two assumptions, and change in the price or availability of any other input (like reserves, or capital) will have no effect on the quantity of loans, and so no effect on the money supply.

But if we relax either of those two assumptions, the supply of loan officers to the industry will no longer be the sole determinant  of the supply of loans and money. A fall in the price (or increased availability) of other inputs will cause banks to expand loans by using more other inputs per loan officer, or hire more loan officers (pushing up wages along their supply curve) to make more loans.

You can see where I'm going with this. Here's the Bank Capital Theory of Money Supply.

Forget reserves and loan officers. What matters is the ratio of capital to loans. Assume banks desire (or are required by law, or both) to have capital equal to 10% of their loans. Then the money supply is 10 times bank capital. A fall in the price, or increased availability, of reserves (or loan officers) will have no effect on the money supply. But an increase in banks' capital will cause a tenfold increase in loans and the money supply.

Again, this assumes that there are fixed proportions between loans and capital. And it assumes the supply curve of bank capital is perfectly inelastic. Relax either of those two assumptions, and a fall in price or increased availability of other inputs will cause an increase in the supply of loans and money. If banks can vary the loan/capital ratio, by varying the average riskiness of their loan portfolio (at the expense of lower returns or greater loan management costs of course) then the model fails. Or, if banks can all raise more capital, perhaps at a higher price, the model fails.

The Loan Officer and Bank Capital models fail except under extreme assumptions. But that's not surprising. All simple models fail. That doesn't mean they contain no truth. The supply of bank capital, and the supply of loan officers, will affect the supply of loans and the supply of money, other things equal. And perhaps their effect is more important in the current recession than normally. Bank capital is certainly important now, but has been discussed by others. But maybe, just maybe, my Loan Officer model contains more truth than normal as well. If there have been large structural changes in the demand for loans, so that loan management is now much harder to do, and in greater demand than normal, then perhaps the supply of experiences loan officers does matter much more than normal. (Sound plausible, bankers?)

But, but, but. Why all the emphasis on the supply of reserves, if reserves are just one of many inputs? And more importantly, are reserves really an input? 

Let me tackle the second question first. Are reserves really an input in the production by banks of loans and money?

Yes, and no. At the level of the individual bank, reserves are certainly an input at the margin; and rational individuals and banks make choices at the margin. At the level of the banking system as a whole, reserves aren't an input (or, are only r% of an input with an r% desired reserve ratio, and I am quite happy to let r go to zero).

Suppose the desired reserve ratio is zero, for simplicity. An individual bank that makes a new $100 loan, by crediting the borrower's chequing account $100, knows that the borrower will spend the loan, and if his cheque is cashed at another bank, the first bank will lose $100 reserves. If it doesn't have $100, it will need to borrow $100 reserves. That's a required input, and that input has a cost. The cost is the interest rate at which it could borrow reserves, or, in an opportunity cost sense, the interest rate at which it could have lent its own reserves. So the interest rate on reserves is a marginal cost of an input to the individual bank, and affects its supply of loans in exactly the same way that the marginal cost of capital and the marginal cost of loan officers affects its supply of loans.

It simply does not matter to the individual bank's decision, in Nash equilibrium, where it chooses its own quantity of loans taking other banks' quantities of loans as given, that there is no loss of reserves to the banking system as a whole. It's maximising its own profits, not those of the whole banking system. It does not internalise the externality of the fact that its reserve loss is another bank's reserve gain.

So the price and availability of reserves matters, at the margin, for an individual bank's decision, in exactly the same way that the cost of loan officers and bank capital matters.

So why do economists concentrate so much on reserves, and downplay or ignore other inputs in the money supply process?

Because reserves can be influenced by policymakers. Other things equal, the price and availability of reserves, capital, loan officers, etc., all influence the money supply and loan supply process. But a central bank's job, when it determines the price and availability of reserves, is to make sure those other things aren't equal. The slope and position of the market supply curves of bank capital and loan officers are what they are. The slope and position of the market supply curve of reserves is whatever the central bank wants it to be. It can make it horizontal, or vertical, or anything in between. It can make it shift left, right, up, down, back and forth, to try to attain whatever objective it wants to attain.

Comments

[Scott Fullwiler]

I needed to laugh today . . .thanks, Winterspeak!

[Winslow R.]

Hope to see Nick accept the horizontal supply of reserves.

Nick wrote: My (eventual) post won't be on this topic. Probably on "Why bad banks are a problem"

Try, "Why the government/bank partnership is a problem."

Mosler would problaby not agree but I find the corporate cloak to be the root problem when reserves are borrowed in 'unconstrained' quantities allowing near unlimited quantities of FDIC insured deposits to be created.

[winterspeak]

Winslow: That's what capital requirements are for, and they actually work when the Govt bothers to enforce them.

[Winslow R.]

Winterspeak: "That's what capital requirements are for, and they actually work when the Govt bothers to enforce them."

Right, so why does the Govt not bother to enforce them?

[winterspeak]

Winslow: They always come up with some reason. When things are going well, it seems like banks should not be hindered by them. When things are going badly, capital requirements would mean shutting the bank down.

Making loans that get paid back, and staying within their capital requirements, is the very core of what banking is the reason the Govt gives them reserve accounts. There facts are completely over the heads of the politicians and regulators who govern banks, and the academics who advise them.

[tjfxh]

Winslow R: "I find the corporate cloak to be the root problem..."

Eisenhower warned in his farewell speech about the the military-industrial complex. What many do not know is that Ike seems to have originally written "military-industrial-congressional complex." What he meant was the influence of corporate donations and the revolving door between business and government. That has only expanded since the Fifties. Presently, the top echelon has taken over corporations from the shareholders through cozy relationships among the boards, and large corporations have essentially captured the apparatus of the state through their influence on policy. Academia and the media have largely been intellectually captured by ideas that favor expansion of the status quo, so competing views are marginalized.

Professor William K. Black has been arguing for some time that the present crisis is more a forensic issue than an economic one, in that laws and regulations already on the books were not enforced because oversight was intentionally relaxed. No Pecora Commisision in the works through, and reform proposals put forward in Congress are being quickly and quietly gutted. Practically the only whistleblower on the inside of the administration is Elizabeth Warren, and he is being marginalized as much as possible by the forces that are working hard to get rid of her.

Until the people of the US rise up in anger and demand that legalized bribery be ended and the revolving door locked permanently, this situation will not only continue but expand. For example, the crisis has so far resulted in further bank consolidation and an expansion of the "To Big To Fail, Break Up, Nationalize, Or Put Into Resolution" doctrine. Consequently, the US is headed for a bigger crisis down the road. Unfortunately, most people aren't sophisticated enough to correctly analyze the problem, so even if public disfavor does result in action, it is likely to be easily deflected by the powers that be.

In the popular uprisings of the Sixties and Seventies, it was the "free" or alternative press that kept people informed. This was pretty inefficient, but it worked to a degree. However, the net has changed things now, and hopefully, enough people can be awakened before the next disaster takes place. Given the speed of developing events, the number and scale of the challenges, and the powerful forces aligned with the status quo, I am not optimistic for anything significant happening either soon or easily.

[Winslow R.]

Tend to agree.

Even though an 'optimal' system may be decades if not centuries off, it would be good to a least have a replacement framework to compete with the 'gold bugs'.

Some believe in doing away with money altogether.

Some believe in shifting money creation from international corporations to a nation's citizens.

Seems reasonable to me.

[tjfxh]

Winslow R., as I understand the MMT position, it would be to recognize that the Treasury and CB are in effect on entity operationally, and they should be using an updated version of Lerner's principles of functional finance to manage a monetary system that recognizes the vertical relationship of government and non-government, wherein the sovereign government is not revenue constrained as currency issuer, while currency users are revenue constrained.

On the horizontal level, it is government's responsibility to provide the legislation, regulation, oversight, and strict accountability that insures that banking is conducted on fiduciary principles that preclude imprudent extension of credit, as well as to separate banking as fiduciary from other financial operations.

The financial crisis arose largely due to the horizontal non-government financial sector acting irresponsibly, with government turning a blind eye and later refusing to impose accountability. Now that the financial crisis has spread to the real economy, it is imperative for the government to recognize the implications of the vertical-horizontal MMT position with respect to deficit spending without the need to tax or borrow in order to alleviate the human cost and right the ship as quickly as possible — and keep it upright.

[Winslow R.]

I really respect the MMT guys and their robust framework.

Vertical
The ELR (employer of last resort) used to set a self-correcting level of deficit spending is an important insight.

Horizontal
The problem is they look at the system from a banking perspective as some are bankers and other supported by bankers (all good guys!).

I'd just like to see a horizontal component added to their framework. Allow citizens the choice between a job of last resort or a loan (think $10,000/yr student/small business loan at age 18 for 4 years) for the entrepreneurial types, bypassing the banks (sorry guys!..... not really).

[RebelEconomist]

If you are still reading Nick, I would be grateful if you would either sketch out Wicksell's argument (I had hoped it might get included in a post on "money and loans"), or refer me to a good account of it. I don't see why it matters whether the asset that the central bank monetises is denominated in dollars (and hence has a price that can be expressed as a percentage of a money unit today) or not. For prices to be indeterminate/ever-accelerating it seems necessary for there to be a never-ending supply of borrowers at the rate set by the central bank, and I would have thought that, at some point, this supply is exhausted. Perhaps it is assumed that there would be a never-ending supply of investment projects that would yield the natural rate?

[tjfxh]

Winslow R.,

The adoption of MMT would permit the government to fund many programs conducive to the public purpose directly, such as education and health care, infrastructure, instead of providing guarantees to banks and other institutes that profit enormously essentially without risk-taking. For example, the US government funds a great deal of public education and states act as the contractors. The US government funds Medicare while mostly private contractors provide the services at a competitive rate. Plus, there is a real question of priorities when programs involving the public purpose and vital national interests are managed chiefly for profit. The incentive here is misplaced.

The federal government funds these programs but doesn't actually run them, so there's little incursion on the private sector other than in funding. In fact, the private sector would grow with increased funding for programs that serve the public purpose that the private sector would never undertake otherwise because many of these activities are not profitable. There are an enormous number of projects furthering the public purpose that could rather easily be provided for, if the illusion that the sovereign government as monopoly currency issuer would be overcome and the myths surrounding it exposed.

Taking your banking example, Fannie Mae now operates explicitly as a government agency instead of a private company with an implicit government guarantee, thereby breaking the illusion. Without government's involvement the housing industry would be a lot smaller and the US would be nation of renters. Similar institutions could easily be set up to deal with matters like student loans instead of the façade that is now in place that gives the private sector a needless cut at little to no risk. What's the point of that other than to transfer funds to corporate interests?

[tjfxh]

Oops. " the illusion that the sovereign government as monopoly currency issuer would be overcome" is truncated. I meant to say, if the myth that the government as monopoly currency issuer is revenue-constrained would be overcome....

[Nick Rowe]

Rebel: suppose there is some interest rate at which there is neither upward nor downward pressure on prices. And suppose the central bank keeps the interest rate precisely at that rate. Now suppose there is some temporary shock, that pushes the price level upwards. The price level rises, the money supply and reserves rise too. There is nothing to bring the price level back down again. It's like a perfectly smooth round ball on a perfectly smooth flat table. Anything is an equilibrium.

Now suppose the central bank sets the nominal interest rate just slightly too low. There is a tiny bit of upward pressure on prices. Inflation slowly begins. As it begins, people slowly adjust their expectations of inflation. This lowers the real interest rate, and increases demand for goods, so inflation increases still further, and so on.

Pegging the real interest rate, even if you peg it at exactly the right rate, leaves the price level like a ball on a flat table. Pegging just a little too high or low is like a ball on a tilted table.

Pegging the nominal rate is like a ball on a curved table, that slopes away from the centre.

Simplest metaphor I can do, Rebel.

[RebelEconomist]

Thanks Nick. An explanation of why prices accelerate which says that that an initial rise in prices generate expectations of future rising prices sounds a bit circular though. I will think about it by way of putting myself to sleep!

[Adam P]

Rebel, this "an initial rise in prices generate expectations of future rising prices" is NOT what Nick said.

The arguement goes like this:

1) Fix an initial value for expected inflation. Now suppose that the NOMINAL interest rate is set less than the sum of the natural (real) rate plus that expected infaltion (perhaps it was right for a few periods but now a shock has changed the value of the natural rate).

2) Now the REAL rate that prevails is too low and so AD TODAY is too high to be consisent with those inflation expectations. This puts upward pressure on prices today. However, some sort of friction in the price setting process (menu costs, staggered contracts, calvo pricing, take your pick) has delayed some of the actual price changes.

3) Rational forward looking agents see that at the current NOMINAL interest rate inflation will be higher than previously expected.

4) Now the crux, in this thought expiriment the CB is assumed to try to keep the nominal rate fixed for all time, thus (3) implies that the REAL rate that agents perceive is even lower and thus AD even higher.

5) The expectational explosion is in progress, it is slow in terms of actual prices because of the friction but expected inflation is now always above the level at which the (fixed) nominal rate is consistent with the real rate being equal to the natural rate, so the inflation keeps accelerating.

Notice though the big caveat at 4, everything stays stable if agents believe that at some future date when the inflation is in progress the CB will make a BIG tightening, an over reaciton so to speak. This belief can put a damper on the explosion today.

Which brings up the most important point, price level determinacy depends on the ENTIRE CB REACTION FUNCTION, not just on what it actually does. Whether or not the price level today is determined depends on what agents think the CB will do in all states of the world, both states that may occur and states that may never occur. Put another way, private agent behaviour in equilibrium is controlled by beliefs about what the CB will do out of equilibrium even though that may (and we hope won't) ever happen.

[Nick Rowe]

What Adam P said above! Just add to it the definition of the natural rate as the rate which would not put upward or downward pressure on prices.

Thanks Adam. You said it much more clearly.

And I really wish that everyone fully understood what Adam said above. Even though what Adam says reflects a more sophisticated and modern understanding, at root, in a simpler form, it's really a very old point.

[Nick Rowe]

Adam P.: "Which brings up the most important point, price level determinacy depends on the ENTIRE CB REACTION FUNCTION, not just on what it actually does."

And that point REALLY needs emphasising.

[Nick Rowe]

Adam again: "Put another way, private agent behaviour in equilibrium is controlled by [private agents'] beliefs about what the CB will do OUT OF EQUILIBRIUM..." (emphasis and [.] added).

And one very simple way to model that out of equilibrium behaviour of the CB is to draw an upward-sloping (or even vertical) supply curve of reserves. It's horribly crude, of course, but it does resolve the indeterminacy problem.

[RebelEconomist]

Thanks Adam and Nick, but, having thought about your answer, it seems to me to assume away the dynamics that motivated my question. When the (real) interest rate set by the central bank is less than the natural rate, aggregate demand rises (partly) because desired investment demand rises, but as desired investment rises, the return on the marginal available additional project can be expected to fall, so that even if the additional demand does start to raise prices (the knowledge of which process, by the way, I would have thought could be described as expectations of future rising prices) it is not necessarily true that the resulting fall in ex-ante real interest rates does increase aggregate demand further. The process might well be convergent rather than ever-accelerating. I suppose what I am saying is that the natural rate should not be assumed to be fixed (with respect to investment demand).

[Adam P]

Rebel no, you're not correct here. The inflation is coming from the supply side, because we are pushing up against capacity constraints. Remember, the natural rate was DEFINED as the real rate at which we have full-employment with no-inflationary pressure, basically the natural rate is one that gives the economy an output gap of zero. (The natural rate defines a point on the investment demand curve, changing the natural rate means shifting the whole curve. When you speak of increased investment lowering the marginal investment return until it equals the prevailing real rate you are talking about movements along the curve.)

To take a simple example suppose the economy has a hard capacity constraint, a maximum output at which it is physically impossible to produce more. By definition, a zero output gap means the economy is operating exactly at this bound, not above or below. Thus, when the CB tries to impose a lower real rate output can't increase so price will. If the economy does shift some resources to the capital goods sector and thus increase investment to re-establish the equality of the real rate and marginal product of capial then his just starves the conumption sector of resources and increases the inflationary pressure there.

Now, we usually think of the zero output gap point as still allowing the possibility to increase output but only at the cost of paying overtime or higher real wages to induce more labour input. Zero output gap is always taken to mean full employment after all. So, while what you say is true, higher investment comes about until the marginal investment return has been reduced to equal the prevailing real rate, there is no way to increase investment at all without causing inflation. It all comes from how the natural rate was defined in the first place.

And we now arrive at step (1).

[Adam P]

Rebel, let me give you the argument again with another level of detail added:

1) Fix an initial value for expected inflation. Now suppose that the NOMINAL interest rate is set less than the sum of the natural (real) rate plus that expected inflation (perhaps it was right for a few periods but now a shock has changed the value of the natural rate).

-- Denote by M the money supply that was set to obtain the given nominal rate at the initial level of expected inflation.

2) Now the REAL rate that prevails is too low and so AD TODAY is too high to be consistent with those inflation expectations. This puts upward pressure on prices today. However, some sort of friction in the price setting process (menu costs, staggered contracts, calvo pricing, take your pick) has delayed some of the actual price changes.

-- Notice that AD is too high today even without changing expected inflation or M. The higher AD puts upward pressure on the nominal rate, notice that a lower real rate means less saving so the extra investment will need to be financed with credit/money creation (see last paragraph). Thus, in order to keep the nominal rate fixed the CB must increase the money supply to M' > M. This is before expected inflation has changed. But the upward pressure on prices now leads to...

3) Rational forward looking agents see that at the current NOMINAL interest rate inflation will be higher than previously expected.

-- This just means that the increases in the money supply have further lowered the real rate below its original value (which was already below the natural rate). The fact that the real rate has been FURTHER lowered means the equality of the real rate with the marginal investment return is again disturbed.

4) Now the crux, in this thought experiment the CB is assumed to try to keep the nominal rate fixed for all time, thus (3) implies that the REAL rate that agents perceive is even lower and thus AD even higher.

-- This basically puts us right back at step (2) and the whole process repeats.

5) The expectational explosion is in progress, it is slow in terms of actual prices because of the friction but expected inflation is now always above the level at which the (fixed) nominal rate is consistent with the real rate being equal to the natural rate, so the inflation keeps accelerating.

-- The loop (2) through (4) continues as long as the CB tries to maintain a fixed nominal rate.

Thus we see that money supply keeps increasing by sufficient amounts to keep lowering the real rate and keep the real rate continually below the marginal investment return.

Each time investment expands to bring down the marginal investment return this puts upward pressure on nominal rates (to fund the investment) which requires an increase in the money supply (to keep the nominal rate fixed) which increases expected inflation which further lowers the real rate.

If you're wondering why does the increased investment demand put upward pressure on nominal rates, why must it be financed with an increase in the money supply? Well, because the real rate being too low means that savings are falling, not rising, so savings won't finance the extra investment. Even at step (1), the real rate being below the natural rate means that the supply of savings will be too low even to fund the investment demand implied by the natural rate, let alone the higher investment demanded at the prevailing real rate.

[Nick Rowe]

I'm glad Adam had a go at answering that one! I basically agree with Adam's answer, but want to try to imagine a world where Adam's answer is wrong.

Here's an alternative take:

Suppose prices are sticky for several periods. Suppose there is imperfect competition, so output and employment will increases past full employment if aggregate demand increases.

Start in equilibrium. The central bank now lowers the rate of interest below the natural rate. Investment and output increases. Because prices are very sticky, this lasts for a long time, and the capital stock expands. This increase in the capital stock both increases full employment output, and lowers the natural rate of interest.

Could this process ever lower the natural rate right down to the level set by the central bank, before prices start to rise?

No. I don't think so. Assume for example that investment is proportional to the gap between the actual and natural rate. Then the capital stock would approach the new equilibrium asymptotically, and the natural rate would also approach the actual rate asymptotically. So it would take forever. So you would have to assume prices are sticky forever. Which doesn't make sense.

Therefore, I agree with Adam.

[Adam P]

It's also worth pointing out that the result in no way relies on the economy having the sort of classical structure implied by my introducing M in the extra level of detail. I did that as an example because it's a familiar model but the only role M plays is to facilitate setting of nominal rate.

The result still applies to a "cashless" society (where say all money is inside) or to the type of world the MMTers are talking about.

[Nick Rowe]

Yep. Time for a post on this subject.

[RebelEconomist]

Thanks Adam - I was alerted by your comment on my blog. You are describing the process clearly, and I can now see that there is a key difference between setting the price of carrots and of short term debt, which is that the real value of short term debt depends on the future price level, which affects the supply response. But I still think you are missing consideration of the sensitivities involved, which is necessary to establish that the process is not convergent. If debt supply is inelastic, say because there are few extra investment projects available at interest rates between the natural rate and the interest rate set by the central bank, then aggregate demand will not increase much, so prices won't increase much, so the real interest rate won't decrease much and so on.

I will write something on the new post so that discussion can continue there if there is more to be said.

I suspect, though, that my point is somewhat theoretical, because a large increase in prices is bad enough, even if it is not a runaway increase in the long run.