Fractional reserves, capital, communism, and the optimum quantity of money

Just trying to get my head clearer on some related stuff.

I have a weird thought-experiment, that I think helps us understand fractional reserve banking better. Even though, paradoxically, there are no commercial banks in my thought-experiment. There is just One Big Bank, owned and controlled by the government, that issues the only form of money, that is used as the only medium of exchange and unit of account.

There are two parallel worlds:

In one world the Bank holds assets equal in value to its monetary liabilities.

In the second world, the Bank holds no assets at all. It has M on the liability side of its balance sheet, and absolutely nothing on the asset side. So if the Bank wants to expand or contract the money supply, it cannot use Open Market Operations, but can only use helicopter (lump sum transfers) and vacuum cleaner (lump sum taxes) operations.

I'm going to ask what happens, in both of those parallel worlds, in an extreme case - when we go to Milton Friedman's Optimum Quantity of Money (aka ultra-liquidity).

To keep it simple, so I don't have to differentiate between real and nominal interest rates, assume the Bank successfully targets 0% inflation. Assume that money pays a rate of interest Rm, that is set by the Bank. And it adjusts the quantity of money to keep aggregate demand at the right level to keep inflation at 0% and the price level constant.

People willingly hold some money (there is a demand for money), even if the rate of return on other assets, R, exceeds Rm, because those other assets are not used as media of exchange, and it is very inconvenient to buy and sell things unless you hold a positive average stock of money. And the Bank adjusts the stock of money, using purchases/sales of assets (world one), or helicopter/vacuum cleaner operations (world two), until it is just willingly held at the target price level, and there is neither upward or downward pressure on that price level. [Previous sentence edited for clarity.] (It adjusts M to adjust Aggregate Demand to ensure the price level target is hit).

The cost to people of holding the liquid asset M, rather than less liquid assets, is the interest rate differential R-Rm. Suppose we start out with Rm a long way below R. Then suppose the Bank decides to reduce that interest rate differential, to reduce the price of liquidity. So the Bank decides to increase Rm.

[If paying interest on currency is impractical, then reducing the inflation target below 0% is an alternative policy that is equivalent to increasing Rm above 0%.]

But if the Bank sets a higher Rm, while holding M constant, the demand for money (the stock of money people want to hold) will increase and exceed the supply of money. This excess demand for money will cause a fall in aggregate demand, which in turn will cause the inflation rate to fall below target. So when it increases Rm, the Bank must also increase the supply of money to match the increased demand for money, to prevent the price level falling.

In the first parallel world, the Bank would use Open Market Operations to buy assets to increase the supply of money. In the second parallel world the Bank would use helicopters to increase the supply of money. What is the economic difference between these two different ways of increasing the supply of money to match the increased demand for money when the Bank increases Rm?

Sometimes it is easier to answer a question if we take an extreme case. Let's do that here. Let's suppose the Bank increases Rm all the way up, until Rm equals R. The Bank eliminates the interest rate differential between money and all other assets. It makes the price of liquidity zero. (This is the "Friedman Rule", for the optimum quantity of money, if the marginal cost to the Bank of providing liquidity is zero. The government-owned monopolist should set price = marginal cost. [And if it impractical to pay interest on currency, reducing the inflation target until nominal interest rates on other assets equals 0% is equivalent to increasing Rm until it equals R.])

If we assume that people are never satiated in liquidity, because there is always the possibility, however remote, that an individual will want to spend all his wealth immediately, we get some very extreme conclusions:

1. In the first parallel world, the Bank would own all the non-money assets. People prefer holding money to other assets, because it's more liquid, so would sell all the non-money assets to the Bank, if R=Rm.

2. In the second parallel world, money would be the only asset. People prefer holding money to other assets, because it's more liquid, so nobody would want to hold any other assets, if R=Rm. Physical capital would disappear, because it would not be replaced when it depreciates. But land cannot disappear. And if land pays positive rents, but people always prefer holding money to owning land, the price of land will drop to zero, which means R and Rm will rise to infinity.

Weird, huh?

"But Nick," I hear you ask, "what does this have to do with fractional reserve banking? You don't even have any commercial banks in your "model"!"

My answer:

My first parallel world is like a world in which commercial banks hold 0% reserves, and the central bank is very small relative to the size of the commercial banking system. Because (solvent) commercial banks do hold assets equal in value to their monetary liabilities. The only difference between my first world with One Big Bank is that the central bank has contracted out the management of its assets and liabilities to the private sector.

My second parallel world is like a world in which commercial banks are required to hold 100% reserves, and the central bank only holds government bonds. Because if the government owns the central bank, then the central bank owning government bonds is like my left pocket having a debt to my right pocket. It's a wash. The whole banking system only holds intrinsically worthless bits of paper as assets, so really holds no real assets at all.

What my weird thought-experiment shows is that there are trade-offs. If you want 100% reserves you can have it. But you must give up something else in exchange. Either:

1. Moving away from the Optimum Quantity of Money, so that liquidity is priced above the marginal cost of producing liquidity.

2. Moving towards communism, where the government-owned central bank owns all the assets.

3. Moving towards a world where real interest rates are infinite, capital disappears and money is the only valuable asset.

Your call.

(I have ducked the question of the optimum mix of two different types of money: chequing account money (normally provided by commercial banks), and currency (normally provided by central banks). Because it is too hard for me to get my head around that question too.)

[Update: OK, maybe it's clearer this way. If the marginal cost of producing producing money/liquidity is zero, then Friedman says we should price liquidity at zero, so that people are satiated in liquidity. But it is reasonable to assume that people never are satiated in liquidity, and will always prefer a more liquid to a less liquid asset, if they have the same rate of return. So people will hold only money, and no other assets. But if people hold only money, who is holding all the real assets like capital and land? Under 0% reserve banking, banks will hold those real assets. But under 100% reserve banking, commercial banks only hold central bank money. If the government-owned central bank holds all the real assets, we have communism. And if the central bank doesn't hold any real assets, then either there are no real assets, or those real assets are worthless. But land always exists. Therefore land must be worthless. But if worthless land pays positive rents, the real interest rate must be infinite. Which means money must pay an infinite real interest rate too.]

Comments

[Majromax]

A bit of commentary from a hopefully not too-ignorant observer:

> Then suppose the Bank decides to reduce that interest rate differential, to reduce the price of liquidity. So the Bank decides to increase Rm.

> This excess demand for money will cause a fall in aggregate demand, which in turn will cause the inflation rate to fall below target. So when it increases Rm, the Bank must also increase the supply of money to match the increased demand for money, to prevent the price level falling.

How can the Central Bank do this? You've made a very Big Deal that a CB with a single policy instrument can only target a single quantity with dollars in the numerator. But here, you've supposed that the CB targets both an interest rate *and* a price level.

That this causes blow-up in the money system isn't too surprising, since the same happens if the CB tries to target both unemployment/output and inflation (rather than a weighted mix, as NGDP targeting)

> If we assume that people are never satiated in liquidity, because there is always the possibility, however remote, that an individual will want to spend all his wealth immediately, we get some very extreme conclusions

Why is this assumption reasonable?

It seems to me that if we're to assume no satiation of liquidity, then we have to assume that *every* individual (rather than just *an* individual) will wish to spend all of their wealth immediately.

In a population, some agents may wish to spend their wealth immediately, but others have just settled down for their afternoon naps and do not. So it makes sense for the napping agents to lend their cash reserves at a rate slightly higher than Rm. This might take the form of an optional repurchase agreement.

Limitless demand for liquidity by a single agent with finite wealth does not seem to require that the system provide truly unlimited liquidity, just enough to satisfy the finite wealth.

> Because (solvent) commercial banks do hold assets equal in value to their monetary liabilities.

But solvent commercial banks don't own hard assets equal in value to their monetary liabilities; many of their assets are nominal in nature and take the form of loans.

If our hypothetical OMO central bank did the same, then the "assets" it purchases could themselves be debt. That is to say, it could freely issue a loan at interest Rm. If it does so, then the amount of money in circulation can grow indefinitely without the CB owning more real assets -- its profile is just leveraged.

Of course, this effectively breaks the "Rm = R" target, since while all CB money would pay interest, some fraction of that would promptly have to be returned as a loan payment. If we mix the money and loans throughout the system, then we'll find that the mix of money that actually trades pays effective interest less than R.

[Mike Sproul]

Confused about this:

"My second parallel world is like a world in which commercial banks are required to hold 100% reserves, and the central bank only holds government bonds. Because if the government owns the central bank, then the central bank owning government bonds is like my left pocket having a debt to my right pocket. It's a wash. The whole banking system only holds intrinsically worthless bits of paper as assets, so really holds no real assets at all."

In your first world, the bank's balance sheet shows $100 of money on the liability side, and $100 of government bonds on the asset side. In your second world, the bank's balance sheet shows $100 on the liability side, and $100 of "taxes receivable" on the asset side. That's not "no assets at all".

As you say, it's a left pocket/right pocket thing. But how does that relate to private banks having to hold 100% reserves? In either of your worlds, private banks could operate on either fractional or 100% reserves.

[Majromax]

@Me:

> You've made a very Big Deal that a CB with a single policy instrument can only target a single quantity with dollars in the numerator. But here, you've supposed that the CB targets both an interest rate *and* a price level.

Re-reading what I quoted, I think I erred in considering the CB as having only a single policy instrument. It appears that Rm is set independently of the quantity of money, which means that our hypothetical CB indeed has two separate policy instruments.

On the other hand, I'm not sure how independent these policy instruments would be for CB#2 (Helicopter). If money is helicoptered in, how does that look different than an irregular interest payment?

[Nick Rowe]

Mike: Suppose you have One Big Bank with zero assets. Then it allows commercial banks to set up, with 100% required reserves, and take some of its business away. Nothing changes. Total M stays the same, and total K stays the same. We have privatised part of the One Big Bank.

Now suppose you have One Big Bank with 100% assets. Then it allows commercial banks to set up, with 0% reserves, and take some of its business away. Total M stays the same, and total K stays the same. We have privatised part of the One Big Bank.

[Nick Rowe]

Majromax: a central bank that can control both the quantity of base money and the interest paid on base money Rm has two instruments. One affects the supply of money, and the other affects the demand for money. But both instruments affect the rest of the economy through the same single channel -- through affecting the excess demand for money. Two different ways of shifting the same AD curve. So you can't target (say) both inflation and unemployment at the same time.

"If money is helicoptered in, how does that look different than an irregular interest payment?"

If you knew that the amount of new money the helicopter dropped on each individual would always be proportional to the amount of money that individual currently held, it would be interest on money. Because it creates an incentive to hold more money.

Suppose that every individual had a very small but still positive probability that in the next minute he would see an opportunity to buy something he really wanted to buy, but that would take all his wealth to buy, and that opportunity would vanish a minute later. Then no individual would ever be satiated in liquidity.

[Majromax]

> Suppose that every individual had a very small but still positive probability that in the next minute he would see an opportunity to buy something he really wanted to buy, but that would take all his wealth to buy, and that opportunity would vanish a minute later. Then no individual would ever be satiated in liquidity.

Okay, I can buy that. At any given moment, a genie can fly in and transport a person to paradise -- if they can remit their entire net worth, in cash, at that moment (and otherwise they go straight the other way). Since consumption reduces net worth, that isn't affected by the genie, just the desire to own assets.

With that in mind, we can reach your conclusion without needing to reason about money or liquidity. The genie establishes that nobody wants to own capital, but the offer doesn't apply to the central bank. So therefore, the central bank (or government) is the only agency who *could* wish to hold capital.

In scenario #1, the CB is permitted to purchase capital and so naturally acquires all of it. In scenario #2, the CB is not permitted to purchase capital, and so like any other good with zero (infinitesimal) utility, the equilibrium price is also zero.

[Nick Rowe]

Majromax. you're not getting it. People want to own assets. But they also want the *option* to sell them very quickly, without taking a loss in a firesale. They like liquidity. If a genie offered to make all your assets more liquid, you would accept, even if you didn't want to sell all your assets right now. you never know when you will want to sell them.

[Ralph Musgrave]

Nick,

You say “Assume that money pays a rate of interest Rm..”. What on Earth is the point of paying interest on base money? No one is paid interest for holding dollar bills and quite right. For most of the time since WWII central banks paid zero interest on base money. Quite right. Warren Mosler, and Milton Friedman in his 1948 paper advocated no interest on base money or “reserves”. Quite right.

Re point No.1 near the end, you say “liquidity is priced above the marginal cost of producing liquidity.” What marginal cost? There IS NO COST to creating base money. It’s produced by pressing buttons on a computer keyboard. Alistair Darling, the UK’s finance minister at the height of the crisis produced £60bn at the press of computer key for the benefit of two banks in trouble.

Finally, if you are suggesting that 100% reserve banking is a system under which commercial banks’ only assets are reserves, that is not true. 100% reserve banking is a system under which the banking industry is split in two. One half, the safe half, holds only reserves (and/ or short term government debt). The other half lends to mortgagors, businesses, etc, but it is funded only by shares. For more on that, see section 1.1 here:

http://mpra.ub.uni-muenchen.de/57955/1/MPRA_paper_57955.pdf

[Nick Rowe]

Ralph: you really need to read Milton Friedman's "Optimum quantity of Money". And no, this is not the same Milton Friedman who advocated making m grow at a steady 4% per year. That was a totally different paper. I tried to find an online source but couldn't. Wiki on the Friedman rule is maybe a good start. But if you don't understand the Friedman rule/Optimum Quantity of Money you won't understand this post.

"What marginal cost? There IS NO COST to creating base money."

Jeez! I am ASSUMING that marginal cost is zero! I am ASSUMING there is no cost to printing money! (Actually there is a cost, but I am assuming it away, for simplicity.)

[Mike Sproul]

Nick:

Maybe my problem is that you assume one big bank with zero assets, and then you say the government stands ready to vacuum with taxes. But that means the big bank does have assets, namely, the "taxes receivable" of the government. So your two types of banks are actually identical in every respect.

[Majromax]

@Nick:

> Majromax. you're not getting it. People want to own assets. But they also want the *option* to sell them very quickly, without taking a loss in a firesale.

Okay, I think I see this. I could still quibble with the setup of the thought experiment, but that's not relevant to the main point. If I understand you correctly:

*) Money pays interest. Real goods have an initially higher rate of return.
*) The Central Bank reads Friedman and decides to set the money interest rate equal to the rate of return on real assets.
*) Seeing the liquidity advantage, people decide to hold all of their net worth in money rather than less-liquid goods.
*) To satisfy this demand for money, the CB is forced to either buy all assets (case 1) or print so much money that assets are worthless (Case 2).

I'm not sure that the parallel between CB1 and the real world (low reserve ratios, small-ish CB) holds, however. Commercial banks tend to hold nominal assets against their liabilities, consisting mostly of bonds and loan portfolios. If that is what CB1 holds in the thought experiment, then it can satisfy the demand for money not only by purchasing real assets but also by loaning funds.

But loans in turn muck things up a lot, since we start getting into intertemporal preferences. (On the other hand, doesn't liquidity do just that? Payroll loans and credit cards and such?)

[Too Much Fed]

What is your capital requirement(s) here?

[Too Much Fed]

"In the second world, the Bank holds no assets at all."

Does that mean no loans are made by this bank?

[Nick Rowe]

Mike: Consolidate the government and government-owned One Big Bank. In both cases the government has the power to tax. But in the first case the Bank owns some real, productive assets too, like capital goods, as well as the power to tax. And those capital goods are equal in value to its monetary liabilities. In the second case the Bank owns nothing, except the power to tax. Now maybe under Ricardian Equivalence it wouldn't matter, because infinitely-lived agents own the government. But consider an OLG model, where RE doesn't hold.

Majromax:

"*) Money pays interest. Real goods have an initially higher rate of return.
*) The Central Bank reads Friedman and decides to set the money interest rate equal to the rate of return on real assets.
*) Seeing the liquidity advantage, people decide to hold all of their net worth in money rather than less-liquid goods.
*) To satisfy this demand for money, the CB is forced to either buy all assets (case 1) or print so much money that assets are worthless (Case 2)."

You got it. Nice and clear.

"If that is what CB1 holds in the thought experiment, then it can satisfy the demand for money not only by purchasing real assets but also by loaning funds."

But in my thought-experiment, if those loaned funds are used to buy real assets, it is as if the Bank owns those real assets (or a share in those real assets). If I get a mortgage of $50,000 to help me buy a $100,000 house, it is as if the Bank owns 50% of my house. If I get a $100,000 mortgage to buy a $100,000 house, it is as if the Bank owns 100% of my house, and I am the tenant, paying rent. (I am ignoring the distinction between debt/bonds and equity/shares).

TMF: Yes.

[anon]

> If the marginal cost of producing producing money/liquidity is zero, then Friedman says we should price liquidity at zero, so that people are satiated in liquidity. ...

ISTM that you're misinterpreting Friedman's original point. In a world where the central bank can hold no assets, the marginal cost of producing money is clearly not zero. If the central bank is restricted to holding government bonds, producing liquidity may or may not be costly depending on the government's preferred fiscal stance (due to, e.g. dynamic inefficiency). If the central bank needs to incur more money-like liabilities than the government otherwise would, that matters as a cost. By creating money beyond that point, the government is essentially crowding out all private investment ability, and this is why capital disappears.

[Nick Rowe]

anon: "In a world where the central bank can hold no assets, the marginal cost of producing money is clearly not zero."

Good point. Especially if there are no lump-sum taxes, because if distorting taxes are used to pay interest on money, that has a social cost.

But whether that is *misinterpreting* Friedman's original point, or instead pointing to a new marginal cost of producing money that wasn't in Friedman's original paper (was it?) as a critique of Friedman, could be argued.

But it might depend on the growth rate. If Rm=g, the central bank would be printing money to pay the interest on money, in steady state. If Rm > g, the central bank would need taxes to finance the payment of interest on money.

I'm still thinking this one through. My head isn't clear yet. Good comments like yours help.

[Ivan]

I like the thought experiment. But I think the conclusion involving capital going to zero or rates of return to infinity does not follow, at least not from standard models that I think do fit your post description. I am talking about the case when the bank holds no assets and introduces money by way of helicopter drops.

I understand the conclusion you wrote about is tempting because of the instinct to think of private wealth as fixed, and allocated between money and capital. Ergo, as money rises and capital must be driven out. Alternatively, from a more partial equilibrium perspective, if money comes to dominate capital, nobody will hold capital, so capital must be zero.

Part of the problem (especially with the latter argument) is that literately setting Rm=R is problematic mathematically, one cannot think of money already being "at infinity". This nuisance is best avoided, so let us take the limit as Rm approaches R from below. This seems to still capture your "Let's suppose the Bank increases Rm all the way up, until Rm equals R." Or, more to the ultimate point, if we can show that we can be arbitrarily close to the Friedman rule, then there is no real tradeoff (we can make it vanish).

So imagine Rm is very close to R, but just below. This requires huge but finite amount of cash. How does this work? The bank issues the cash, the agents hold it. Consulting a standard money demand we have (informally, this can be formalized in various ways)
L(R-Rm)=M / P
Let us suppose M is held fixed so that P is fixed; normalize the latter to 1. All is consistent. As Rm approaches R we have M going to infinity.

On the budgetary side, what is going on? The agent has wealth from capital but also this helicopter wealth (which is very very large for Rm close to R). So the agent feels very wealthy indeed. However, he/she needs this high wealth to replicate his portfolio (i.e. choosing to hold large money again) and he/she must also pay a tax to the government with all the interest earned on money. This tax is required for the government budget balance, since it pays interest on money and has no assets. Thus, although wealth is very large, this is compatible with standard consumption and capital/saving outcomes.

Of course, we can take the limit now and everything goes off to infinity nicely, and we know that along this limit each of these equilibria are well behaved.

Indeed, to make the point for an important example: with money in the utility function, if preferences are separable u(c,n) + v(m) for some v utility from real money balances, it is well known that we get a complete dichotomy and none of the monetary stuff affects the real allocation (assuming a flexible price competitive equilibrium here). An out of steady state Sidrauski type neutrality result. Thus, in this case it is quite ironclad that one cannot drive capital to zero by way of monetary policy.

[Nick Rowe]

Ivan: thanks very much for your very good comment.

My brain is not yet fully clear on this.

Taking the limit as Rm approaches R from below sounds fine to me. I jumped to the "at the limit where Rm=R" case because it looked easier.

In a Sidrauski like model, with infinitely-lived agents, I think you are right. The steady state R is bolted down by the rate of time preference proper. So that bolts down K too. So M/P can approach infinity as Rm approaches R, with nothing much else changing. The central bank imposes very large lump sum taxes, and pays them out as very large interest payments on money Rm.M/P

But if we had finite-lived agents I think we would get a result more like mine. Because an agent with a finite life will not want to hold infinite wealth K+M/P when R is finite. So if K does not approach zero, then as M/P approaches infinity, we know that K+M/P approaches infinity. But finite-lived agents will not wish to hold arbitrarily large stocks of wealth, unless R is arbitrarily high too.

[Frank Restly]

Nick,

"What my weird thought-experiment shows is that there are trade-offs. If you want 100% reserves you can have it. But you must give up something else in exchange. Either:

1. Moving away from the Optimum Quantity of Money, so that liquidity is priced above the marginal cost of producing liquidity.
2. Moving towards communism, where the government-owned central bank owns all the assets.
3. Moving towards a world where real interest rates are infinite, capital disappears and money is the only valuable asset."

If you separate the monetary authority from the government (independent central bank) by having the government create an asset that the central bank cannot buy, then you can get 100% reserves and the optimum quantity of money.

Government buys / sells an asset that it creates to the general public to change the supply of liquidity.
Central bank eliminates the interest rate differential between money and all other assets. It makes the price of liquidity zero.

[Nick Rowe]

Frank: and who owns all the capital and land?

[Market Fiscalist]

"Suppose you have One Big Bank with zero assets. Then it allows commercial banks to set up, with 100% required reserves, and take some of its business away."

I'm not getting the reason why its relevant that in this case you need 100% reserves and the other 0%. Is there a simple explanation ?

[Majromax]

@Nick:

> But finite-lived agents will not wish to hold arbitrarily large stocks of wealth, unless R is arbitrarily high too.

Maybe this just says that R loses its meaning if the price of capital is fully flexible?

Holding R fixed, replacing the output of 1 unit of capital requires R/Rm money. If R=Rm (or arbitrarily close) but money provides finite additional utility, then the equilibrium market price of 1 unit of capital will be strictly less than 1. So we have a contradiction: R=Rm implies that 1 acre = $1, but the additional utility implies that 1 acre < $1.

This is contradictory, implying one of two things:

1) The additional utility of liquidity is infinitesimal for large enough cash holdings. Then for Rm = R - epsilon, the equation balances out provided the money stock is large. This is, I think, Ivan's point.
2) The central bank cannot set R=Rm. This also makes sense. If the central bank tries to set R=Rm, it is effectively monetizing property by saying that it *must* trade at par for property. However, property by assumption is less liquid, so the good currency tries (and fails) to drive out the bad property.

You see contradiction #2 with "R must go to infinity."

[Andrew_M_Garland]

"2. In the second parallel world, money would be the only asset. People prefer holding money to other assets, because it's more liquid, so nobody would want to hold any other assets, if R=Rm. Physical capital would disappear, because it would not be replaced when it depreciates."

Mr Rowe,

You propose a complicated model, as a conversation, and imply that we can learn something about reality from mentally manipulating its many parts. You notice "physical capital disappears" above.

"Physical capital disappears" is obviously impossible in reality. Something else would change, or break, or be laughed at before that could happen. In mathematics, that is called reduction to the absurd. It is a way of invalidating models by easy inspection, not a gee whiz discovery of an unappreciated part of reality.

So, "physical capital disappears" is a bright red light signaling that the model is bad. There is no point speculating about what it might predict if we are interested in reality. It is theoretical math, not practical economics.

[Nick Rowe]

Andrew: most (all?) machines wear out, break down, rust, or rot over time. Some even get lost, like Franklin's ships. They become unable to help us produce goods, and so become worthless. As valuable capital, they disappear. That is practical economics. Jeez! Gimme a break. Economists are allowed to use metaphors too, dammit!

[Nick Rowe]

MF:

A central bank that holds no real assets, and commercial banks that hold 100% reserves of central bank paper money, is like One Big Bank that holds no assets.

A central bank that holds 100% real assets, and commercial banks that hold 0% reserves and 100% real assets, is like One Big Bank that holds 100% real assets.

A central bank that holds no real assets, and commercial banks that hold 0% reserves and 100% real assets, is like One Big Bank that holds 90% real assets (if the central bank is only 10% of the whole banking system).

Majromax: you lost me.

Suppose land lasts forever, and each acre pays a constant rent Z. Then the price of one acre of land in steady state will be Z/R.

[W. Peden]

""Physical capital disappears" is obviously impossible in reality."

I walked over a disused railway line recently, on which you could JUST make out one of the old railway platforms that, in my father's youth, had been one of the stops along that route. I had no idea that my life had become a living nonsense poem!

[Market Fiscalist]

Won't most people who want 100% reserve banking be only too happy to stay away from the Optimum Quantity of Money?

[Vaidas Urba]

I like the principle of pricing liquidity at the social cost. In my view, liquidity is provided at the social cost when economic profit of central bank is zero. This does not mean that interest on reserves is equal to interest on all other assets. Liquidity is provided at the social cost when R-Rm covers the opportunity cost of central bank capital. When R = Rm, central bank loses money.
It is clear what this R-Rm = cost of capital criteria means in the first world with OMOs. But what does it mean in the second world?

[Nick Rowe]

W P: yep! There is a railway line right beside my house. It was in use until 2 years ago. It is fast disappearing into the weeds. Trees will be next. But on Sunday I drove along the new autoroute 50. There are some big new rock cuttings for that road, that will probably still be there thousands of years hence. Unless they are filled in. But I doubt they will be useful a century from now.

MF: probably. But how big a tax on liquidity do they want?

Vaidas. Yep.

"It is clear what this R-Rm = cost of capital criteria means in the first world with OMOs."

I think you meant "cost of providing *liquidity*"

"But what does it mean in the second world?"

I'm wondering about that too.

[Vaidas Urba]

"I think you meant "cost of providing *liquidity*""
The primary cost of providing liquidity is the opportunity cost of central bank capital. OMOs are tentative, and without sufficient capital you run high risk of being unable to reverse them when needed.

[W. Peden]

Nick Rowe,

So there's definitely depreciation of physical and (even more obviously) human capital, but what about financial capital? Say I have some UK Consols: I take it that their opportunity cost is a function of their real rate-of-return and liquidity vs. the next best asset, but they have no date when they reach maturity. Is there a meaningful sense in which they depreciate?

[Nick Rowe]

Vaidas: Ah! OK.

W Peden: well, we will find out very soon, I expect!

Consols should only depreciate over time if the market rate of interest, or risks of default are rising over time, or their liquidity is falling over time. Could happen.

But I don't think of bonds as capital. You can have a world with consumption loans and no real capital.

[Mike Freimuth]

Nick, methinks you are getting perilously close to my way of thinking! I might be able to add to this but will have to do a careful think.

[Nick Rowe]

Mike: then you are in terrible danger of getting as muddled as me!

[Mike Freimuth]

I've been muddled for a few years already though, so I'm way ahead of you haha.

[JP Koning]

It seems to me that if the marginal cost of producing liquidity was zero then issuers of stocks, bonds, and other financial instruments would be able to costlessly upgrade the marketability of these instruments to the point that they are just as liquid as central bank liabilities. With every asset equally liquid, people who are assumed to be non-satiated in liquidity would not have a specific preference for central bank liabilities (money) but would hold a broad range of assets.

[Nick Rowe]

JP: I think I would agree that making existing assets more liquid is a substitute for banks.

[Winslow R.]

Okay I haven't been to this site in years, so may be confused but wouldn't

"In one world the Bank holds assets equal in value to its monetary liabilities."

... be better written:

In one world the Bank holds monetary assets equal in value to its monetary liabilities.

....and

"Because (solvent) commercial banks do hold assets equal in value to their monetary liabilities. "

... be better written:

Because (solvent) commercial banks do hold monetary assets equal in value to their monetary liabilities.

...the ownership of real assets remain in the private sector in all cases, even if the private sector wants infinite money?  The only things banks (commercial and central) push around is monetary assets while the government may push around( create and destroy) both real and monetary assets?

Did I miss the post that defines bank (central or commercial) assets being something other than monetary assets?

[Nick Rowe]

Winslow: haven't seen you here in a while!

Canadian banks hold a small amount of currency (Bank of Canada notes). That is (almost) the only *monetary* asset that they own. But yes, most of their assets are *financial* assets, like bonds, and other IOUs that they get when they make loans. They don't hold many real assets, except their own buildings etc.

In the model I have sketched, I am abstracting from those non-money financial assets. If people only hold money, then who holds the real assets?

[Winslow R.]

I check back in every once in a while to see where you stand!

From the link....

"If ultra-liquidity is here to stay, as seems likely, we must either re-unify monetary and fiscal policy or resign ourselves to central bank impotence. There is no longer any justification for even the pretence of separation. Fiscal and monetary authorities together need to find new ways of transmitting policy to a world flooded not only with reserves, but with liquid assets of many kinds."

Current policy transmission is allowing leveraged private sector to purchase real assets (currently education and auto loans) through banks creating financial/monetary assets and then cyclically foreclosing on those assets (which is currently extremely difficult with regards to education and depreciating assets especially compared to land and houses) and then reselling those real assets with the help of government created financial assets in the form of bailouts.

....I try and keep score.

The idea we'd either have independent banks or communism seems to need some work. Perhaps the struggle to understand the driver (transmission mechanism) behind real asset growth still not been settled?

I'd hate to misquote, but wasn't this site suggesting government purchase (indirectly through banks) a broad stock index as the new policy transition tool? Maybe you got your wish!

MMR still wants corporate bonds to be the new policy transmission mechanism? Maybe that's next, though it sounds a lot like fascism?

MMT still wants labor as the policy transmission mechanism. An ELR doesn't require communism or government ownership of real assets! Wasn't labor policy even used in the 1930's to thwart communism and protect capitalism during a time of low interest rates and low return to capital?

[Majromax]

@Nick:

> Suppose land lasts forever, and each acre pays a constant rent Z. Then the price of one acre of land in steady state will be Z/R.

The price of one acre will be Z/R by definition, since that's how R is defined. If the monetary authority pays interest Rm on money and satisfies all demand for liquidity, then R=Rm will mean that holding the cash value of one acre supplies the same return (Z) as holding the acre itself.

The problem is that this is not an equilibrium. If cash and land have the same return, then cash strictly dominates land. This could persist if there was a cash shortage, but we're assuming that the CB provides cash as needed. This gives your spiral-to-infinity you note with CB#2 -- it's a way of saying that there's no solution.

Ultimately, that means that one assumption must go. If we have only finite cash, then we restore an imperfect equilibrium. If Rm only *approaches* R, then we get Ivan's solution. It's not even that poorly behaved if the marginal utility of liquidity is diminishing (like log(cash)). Otherwise, we could dispense with the entire notion of owned property at all (and thus make R meaningless), since nobody is left who wants to own it.

(The last scenario would even look like Moses and the manna from heaven: return is based on walking around and picking it up off the ground. In that scenario, owning bits of sand is pretty meaningless.)

[Nick Edmonds]

Nicely explained.

[W. Peden]

Nick Rowe,

Thanks for the explanation. What would you say would be a classic example of financial capital?

[Nick Rowe]

Nick E: Thanks! I'm very glad you got what i was trying to say.

WP: I think it's best to avoid the words "finance capital". Because it easily leads to confusion, like double-counting. People might say the total capital stock is human capital + physical capital + finance capital. But finance capital is really just a lot of IOUs, some of which were sold to finance the purchase of human and physical capital, and some of which were sold to finance consumption. Machines are equally productive, whether or not they were financed by issuing bonds and shares or financed out of the owner's own savings.

However, there is a sense in which the financial sector of an economy (if it is working well) is like "organisational capital". A whole web of networks and institutions and trust that are costly to develop, but which make the economy more productive than it otherwise would be.

Majromax: " This gives your spiral-to-infinity you note with CB#2 -- it's a way of saying that there's no solution."

I have some sympathy with your way of looking at it there. At the very least, if it is a solution, it's a very weird sort of solution. (But the infinite always muddles my brain.)

[W. Peden]

Nick Rowe,

Fascinating stuff. Thanks!

[Bob Murphy]

This post has reminded me: If I couldn't be me, my second choice would be Nick Rowe.

[Frank Restly]

Nick,

"Frank: and who owns all the capital and land?"

Let me try again.

From above:

"But it is reasonable to assume that people never are satiated in liquidity, and will always prefer a more liquid to a less liquid asset, if they have the same rate of return. So people will hold only money, and no other assets. But if people hold only money, who is holding all the real assets like capital and land?"

Just because people prefer a more liquid asset to a less liquid asset, that does not preclude them from accepting capital / land. Just because I hold only money does not mean I will not accept land / capital if it is given to me through inheritance, legal settlement, charity, government bequeath, or even barter. If I don't have to give up money to obtain capital / land, then I am perfectly willing to accept land / capital in other arrangements. I have the option of trying to sell that capital / land for whatever money I can get.

Even if land / capital is never exchanged for money, it can still have a price relative to other goods through the means described above. And so I would dispute that the real interest rate on land / capital would rise to infinity even if people are never satiated with liquidity. People would never give up liquidity for land but that does not mean that they would never accept land under any circumstances.

[Nick Rowe]

Bob: thanks!

Frank: OK. Suppose you inherited land. You would want to sell it, because you prefer holding money, if both assets pay the same rate of return. But who would want to buy it, for any strictly positive price? Nobody. Because everybody else also prefers holding money to holding land.

And who would want to sell their apples for land, if they could sell their apples for money instead? Nobody. And they can sell their apples for money, because, by assumption, the central bank prints enough money to prevent the price of apples in terms of money from falling.

So land will have a price of zero. Unless the commercial banks, or central bank, buys it.

Think general equilibrium!

[Frank Restly]

Nick,

I am thinking more along the lines of non-market value theories (legal value, utilitarian value, etc.).

Central bank / government assesses a tax. Tax can be paid either in money or land. Central bank / government sets relative price of land ($1000 dollars per acre for instance) for settlement of taxes and will accept either. Central bank / government bequeaths land back to all tax payers - both those who pay in dollars and those that pay in land.

"Because everybody else also prefers holding money to holding land."

That is not the same thing as no one wants to hold land. And because people are willing to hold land, and land / money are interchangeable in the settlement of paying taxes, land has a value, just not a market value.

"And who would want to sell their apples for land, if they could sell their apples for money instead?"

Presumably these people that have an insatiable appetite for liquidity also have basic human needs (sustenance / calorie intake, fresh air, water). Your stipulation was that people prefer holding money over all other goods. You did not say that money was the only good required to sustain human life. And so I might sell apples for land if I don't have enough apples to sustain my calorie intake - I need to grow more apples / something else.

[Nick Rowe]

Frank:

1. Then the government ends up holding all the land. Communism.

2. But you could get the same rate of return by swapping your current apples for money, and then using that money again later to buy more apples in future.

Stop.

[Frank Restly]

Nick,

The rate of return I would get by swapping apples for money or money for apples is 0% per the 0% inflation successfully targeted by the central bank (This is one of your assumptions above). When I trade apples for land, and use that land to grow more apples than I paid for the land, my real returns are a positive % though they may not be infinite.

Stop changing the rules.

Just because people prefer a more liquid asset to a less liquid asset (money preference over other goods) does not mean that people have no preference order for other goods (land preference with a positive real return over apple preference with no real return).

[Nick Rowe]

Frank: If it costs 100 apples to buy an orchard, and an orchard yields a profit of 10 apples per year (after paying wages etc.) then owning an orchard yields a 10% rate of return. But, by assumption, the central bank gives you a 10% rate of return for holding money, if orchards pay a 10% rate of return. And money is more liquid than orchards, and people prefer a more liquid asset to a less liquid asset, by assumption. So nobody will want to own the orchard.

Stop commenting on this post.