Wicksell and the hot potato

There is no monetary hot potato in standard Keynesian and New Keynesian models. That is because those models make wildly implausible assumptions about people's knowledge. They assume people have perfect knowledge about how much money everybody else is borrowing from the banking system, and how much they are planning to spend from what they borrow.

People borrow money for two reasons:

1. Because their planned expenditures of money exceed their expected receipts of money. They "borrow to spend".

2. Because their desired stock of money exceeds their current stock of money. They "borrow to hold".

In aggregate, actual expenditures of money will always equal actual receipts of money. That is an accounting identity. But this does not mean that aggregate planned expenditures of money will always equal aggregate expected receipts of money. In aggregate, borrowing for the first reason ("borrowing to spend") will necessarily turn out to have been a mistake. Because actual spending must always equal actual receipts. But that mistake creates a monetary hot potato. It creates money that people hold, but did not plan to hold.

Let's consider an extremely simple monetary exchange economy. There are no commercial banks. A central bank chooses a rate of interest at which individuals can either borrow money from the central bank or lend money to the central bank, as they wish. A Wicksellian central bank with a horizontal LM curve. Most economists say that the stock of money is demand-determined under that assumption. I think they are wrong. There can be an excess supply of the stock of money. There can be a hot potato. The Law of Reflux, which says an excess supply of money must flow back to the central bank, is invalid, even in this case.

Start in equilibrium in a stationary economy with no borrowing from the central bank. The stock of currency is constant over time, and equals the desired stock.

Now let's ask what happens when the central bank reduces the rate of interest from 5% to 4%.

Two things happen:

1. The representative individual plans to spend (say) $100 per month more than he expects to receive per month. (The exact amount depends on the interest-elasticity of consumption and investment demand).

2. The representative individual plans to hold an extra (say) $10 stock of money. (The exact amount depends the interest-elasticity of the demand for money).

So in the first month, the representative individual borrows $110 from the central bank. He plans to borrow another $100 in the second month, and $100 again in the third month, etc.. But his expectations will be falsified by events, and his plans may change as a result.

At the end of the first month, the representative individual will be surprised to find that his receipts of money are $100 higher than expected. Because every other individual did the same thing as he did. He holds an extra $110 in his pocket, not the extra $10 that he expected to hold.

What happens next depends on whether he revises his expectations about future monetary receipts.

Suppose he doesn't revise his expectations. He thinks his extra monetary receipts were a temporary fluke, unlikely to be repeated. He now has $100 more in his pocket than he wanted to hold. He was planning to borrow $100 from the central bank in the second month. He now borrows nothing. He again plans to spend $100 more than he expects to receive in the second month.

At the end of the second month the representative individual is again surprised to find his monetary receipts are $100 bigger than he expected, and that he holds $100 more money in his pocket than he wanted to hold.

If he does not revise his expectations, or revise his planned spending, or revise his stock demand for money, this $100 hot potato of excess supply of money will continue to circulate forever, month after month.

Suppose eventually, at the end of the third month, the representative individual revises his expectations. He expects the $100 increase in monthly receipts to be permanent. He revises his planned flow of expenditure, and he revises his desired stock of money.

In the fourth month he plans to increase his spending by an additional $100 per month, which is again $100 more than he expects to receive. And his desired stock of money rises by (say) $20. He now holds $80 more money in his pocket than he desires, so he borrows another $20 from the central bank.

Once again he is surprised. At the end of the fourth month his receipts turn out to be $100 bigger than expected, and there is $100 more in his pocket than he planned and desired. And until he revises his expectations again, this $100 excess supply of money will continue to hot potato around the economy, even with no more borrowing from the central bank.

And so on.

The hot potato process continues until the central bank raises the rate of interest again. [Update: or people stop borrowing to spend for some other reason.]

Any money that people in aggregate borrow for the first reason, "borrowing to spend", will create a permanent hot potato that falsifies their expectations. Any money that people in aggregate borrow for the second reason, "borrowing to hold", will not create a hot potato, and will not falsify their expectations.

Standard Keynesian and New Keynesian models do not allow what I have just described above to happen. They assume an equilibrium in which aggregate planned expenditure is always equal to aggregate expected income for the current period. If the central bank cuts the rate of interest, both planned expenditure and expected income rise by the same amount. In aggregate, people never borrow money to spend. They only borrow money because they want to hold more money. In those Keynesian models, people are never surprised in aggregate to find themselves holding more money than they desire to hold. There is no hot potato in keynesian models

Does the standard Keynesian assumption of continuous equilibrium between aggregate planned expenditure and aggregate expected receipts make sense? Is what I have just described a rational expectations equilibrium? It might be. Even if every individual is fully rational, he does not know that a cut in the interest rate from 5% to 4% will lead to aggregate planned spending in excess of expected receipts, and falsify his expectation. For all he knows, the central bank might have cut the interest rate because everyone else planned to spend less, and the central bank was adjusting the actual interest rate down to match the lower natural rate of interest. For all he knows, aggregate planned spending might equal aggregate planned receipts at 4%.

The standard Keynesian and New Keynesian model assumes that aggregate planned expenditure always equals aggregate expected receipts. People in aggregate never borrow money to spend. They only ever borrow money to hold. It therefore makes totally implausible assumptions about individual agents' knowledge. It assumes a rational expectations equilibrium in which each individual knows the current plans and expectations of all agents. It is that wildly implausible assumption that ensures there is no monetary hot potato in standard Keynesian and New Keynesian models.

If agents in aggregate "borrow to spend", actual income will not equal what agents had expected when they planned their expenditure, and actual money balances will not equal desired money balances. The economy will be "off" the IS curve, and also "off" the LM curve.

Update: basically, in Keynesian terms, the hot potato story is a story about the process by which the economy moves from one ISLM equilibrium to another. It is a story of "false trading" (or "false borrowing" in this case) -- because people's expectations and plans do not adjust instantly to the new Hicksian temporary equilibrium where those plans and expectations are mutually consistent, so they make trades they would not make in equilibrium. And when false trading happens, and stocks change as a result, there is always the chance that the economy may move to a different equilibrium, or even away from equilibrium. People may not always succeed in learning the new equilibrium. And their learning may itself change that equilibrium.

(I think this is related to what the interwar pre-General Theory monetary economists were on about. Robertson, Hayek, etc.)

(And I thank the commenters on my last couple of posts, especially the critical ones, for forcing me to try to think this through. It was hard.)

Comments

[Scott Sumner]

I'm confused by this. Tell me how it relates to what I know:

1. It's generally accepted by monetary economists that if the central bank pegs the interest rate, the money supply is endogenous. In most cases (unless done perfectly) the price level shoots off to zero or infinity. I.e., interest rate pegging leave the price level indeterminate. That seems like disequilibrium to me.

2. To avoid this price level indeterminacy, NKs recommend adjusting the interest rate peg on the basis of deviations of inflation and output from the target. (The Taylor Rule)

I'm not questioning anything you wrote, just wondering how it links up with what I know. Are the NKs getting the same policy implications without the hot potato effect, or does their model have different policy implications? And if so, what are the differences?

I also don't follow the problem with ratex. If I know the government is pouring too much money into the economy, I will try to get some and spend it before it loses value. So how would ratex prevent the hot potato effect?

[Nick Rowe]

Scott: "1. It's generally accepted by monetary economists that if the central bank pegs the interest rate, the money supply is endogenous."

Let me re-phrase what you just said: 'It's generally accepted by monetary economists that if the central bank pegs the interest rate, the money stock is determined by and equal to the stock of money demanded at that rate of interest'.

Yep. Nearly all monetary economists would say that. And I am saying they are wrong. Bill Woolsey, Leland Yeager, and David Laidler will, I think, agree with me. I can't think of anyone else who would agree with me.

"In most cases (unless done perfectly) the price level shoots off to zero or infinity. I.e., interest rate pegging leave the price level indeterminate. That seems like disequilibrium to me."

Yep. I'm ignoring that, by (implicitly) assuming sticky prices, or sticky price expectations, so the excess demand for goods doesn't immediately cause the price level to explode. You can hold P fixed in my example, if you like, for simplicity.

"2. To avoid this price level indeterminacy, NKs recommend adjusting the interest rate peg on the basis of deviations of inflation and output from the target. (The Taylor Rule)"

In my example, the central bank would eventually have to raise the interest rate again to prevent the hot potato slowly causing inflation. Notice how planned expenditure slowly rises in my example, as expectations of receipts adjust upwards. But maybe the desire to borrow to spend would fall to zero when income reached a higher level (if the IS curve sloped down).

"I'm not questioning anything you wrote, just wondering how it links up with what I know. Are the NKs getting the same policy implications without the hot potato effect, or does their model have different policy implications? And if so, what are the differences?"

My brain isn't ready to handle questions like that yet. This stuff is too hard for me. All I can figure out so far is that the economy can be off the IS and LM curves, so there must be some policy implications. I *think* it means that something like QE can create an excess supply of money, even at a given interest rate. But I'm not sure yet.

[Nick Rowe]

Yep. I'm way out alone on a limb here Scott. But remember Dennis Robertson on those horrible concepts like "automatic stinting, induced lacking, etc., etc.", ? Or all that confusing Hayekian stuff about I-S = delta M? I reckon this is sort of what they might have been rabbiting on about. See what Greg Ransom says.

[Mike Sproul]

Nick:
"The Law of Reflux, which says an excess supply of money must flow back to the central bank, is invalid"

Let's work through a few cases:

1. Money is silver coins, issued by a mint. If the mint stamps out more coins than people want to hold, then someone will find it profitable to melt those coins. The coins reflux back to bullion. I don't see how you could deny the validity of the Law of Reflux in this case.

2. The mint makes one change: Rather than coining any silver it receives into coins, it puts those coins in its vault and issues circulating paper or credit money, each unit redeemable into a silver coin or equivalent bullion. If the mint issues more money than people want to hold, someone will find it profitable to return that money to the bank for silver, which they melt. If you can't deny the validity of case 1, I don't see how you can deny this case.

3. The mint makes another change: Rather than only issuing money to people who bring in a unit of silver, they issue money to anyone who brings in goods of (at least) equal value to the unit of silver. The mint keeps those goods in its vault, next to the silver. These goods might include deeds to land, so the land still gets farmed even though it is backing units of money. If the mint issues more money than people want to hold, the money will be returned to the bank in exchange for silver or other goods. The Law of Reflux still seems above reproach.

4. The mint stops redeeming money for silver, but still redeems it for other goods. As long as the quantity of refluxing money does not exceed the quantity of non-silver goods the mint has, people won't care that they don't get silver.

At which of these steps do you think the Law of Reflux loses its validity?

[Too Much Fed]

Is the representative individual making interest and principal payments to the central bank?

[JW Mason]

I'm not sure what the implicit Keynesian model is, but I'm not really seeing Keynes here. Certainly not Minsky or Mehrling.

In general, the decision to borrow and the decision to change your holdings of outside money are entirely distinct. When I borrow from a bank, two offsetting liabilities are created, one from me to the bank (the loan) and one from the bank to me (a deposit). I can then make payments by transferring the bank's liability to me to some third party. I might also decide to convert some of the new deposit into cash, either to hold it or to make payments with it, but that's likely to be quantitatively very small and is logically independent of the creation of the deposit.

It *may* be that the bank's willingness to create the two offsetting liabilities will depend on its holdings of outside money in the form of reserves. but this is highly dependent on the institutional and regulatory context.

I realize this isn't how your model works. But I don't think a model where all money is outside money is a useful way to think about money in modern capitalist economies, which are fundamentally credit economies and not simply money economies.

I definitely do agree that this stuff is hard, tho.

[Ralph Musgrave]

Nick, Why bother with the unrealistic scenario where people borrow from the central bank? In the REAL world, private sector non bank entities borrow from COMMERCIAL banks. And for every dollar that the latter creates, a dollar of “negative money” i.e. debt is also created. I.e. commercial bank money nets to nothing.

That invalidates your claim that “Any money that people in aggregate borrow for the first reason, "borrowing to spend", will create a permanent hot potato..” (if the latter claim was supposed to apply to the real world). I.e. the commercial bank system cannot create hot potatoes. In contrast, the government / central bank machine CAN. That is, when government borrows and spend $X, private sector net financial assets rise (by $X worth of bonds). And if and when those bonds are bought back by the central bank, the $X of bonds are converted to $X of cash. The hot potato effect occurs before the bonds are bought, but more particularly, AFTER they are bought.

[Min]

@Nick Rowe:

Now, I'm sorry I did not write that long note some days ago questioning the hot potato idea. {sigh} Suffice it to say that a fair amount of web searching only turned up something about hyperinflation, which is not what you are talking about. But down to the current discussion:

Nick Rowe: "People borrow money for two reasons:
1. Because their planned expenditures of money exceed their expected receipts of money. They "borrow to spend".

"2. Because their desired stock of money exceeds their current stock of money. They "borrow to hold".

Reason #2 is a losing proposition, per se. There has to be something else going on, right?

Nick Rowe: "In aggregate, actual expenditures of money will always equal actual receipts of money. That is an accounting identity. But this does not mean that aggregate planned expenditures of money will always equal aggregate expected receipts of money. In aggregate, borrowing for the first reason ("borrowing to spend") will necessarily turn out to have been a mistake."

We could just as well say that not borrowing at all will necessarily turn out to have been a mistake. Damned if you do, damned if you don't.

Nick Rowe: "Because actual spending must always equal actual receipts. But that mistake creates a monetary hot potato. It creates money that people hold, but did not plan to hold."

Since that also arises from not borrowing, we have the immaculate conception of the hot potato. Right so far?

At this point I would like to see some evidence. We have the saying about money burning a hole in your pocket. Is that what you are talking about?

Thanks. :)

[Bill Woolsey]

Black's paper, "Banking in a World Without Money," covers the monopoly bank scenario which is a bit like what you describe here. If I recollect correctly, he has bank set two interest rates (like the cooridor.) Everyone has a debit/credit card, and the bank charges interest on positive balances and charges interest on negative balances. Black said there is no money in the system, but it is clear to me that the quantity of money is the positive balances. The positive balances match desired negative balances at the interest rate charged. Desired positive balances depend on the interest rate paid. If they are both too low, there is an excess supply of money which is like a hot potato. (Too high, we get excess demand and deflation.) If they are just right, the quantity of money determined by those desiring to borrow matches the amount demanded by those wanting to hold money. Bring the rates together, the quantity is higher. Spread them apart, the quantity is lower.

I found it a very instructive model.

Do you realy think that Keynesians or new Keynesians believe that people borrow money to hold it? It seems pretty unrealistic to me. I would lean towards, "they can't mean that," let's try another explanation of what they must mean.

I agree, of course, that they say that people want to hold the existing quantity of money in equilibrium, which holds continuously.

[Nick Rowe]

Bill: "I agree, of course, that they say that people want to hold the existing quantity of money in equilibrium, which holds continuously."

That's what I meant. In "equilibrium", where Y = Yd, people (in aggregate) only ever borrow money to hold it. We are always "on" the LM curve and IS curve.

My "model" here is like Black's except the corridoor narrows down to zero, and you can think of the central bank as lending currency. I don't think it matters that it's currency, or if the quantity of it is zero or above zero in equilibrium.

Yep, Black's world is not a world without money. I would say the stock of money in his model is the sum of people's unused credit limits at the central bank. Not sure about that though.

[Ashwin]

Nick - interesting post. Couple of points:

1. I second JW Mason's point about modern capitalist economies being credit economies. I wrote a post on this couple of weeks back http://www.macroresilience.com/2011/09/22/operation-twist-and-the-limits-of-monetary-policy-in-a-credit-economy/

2. Nevertheless, obviously you're trying to clarify something via a thought exercise. Another point which I made in the above post is the following:

a. Reduction in interest rates may not stimulate investment demand at all in certain circumstances. This is similar to the point made by Chapter 12 Keynes/Minsky/Shackle etc.
b. Reduction in interest rates may induce a fall in consumption and an increase in savings as households cut down expenditure in order to meet fixed real savings goals in the future.

Th effectiveness of these transmission channels is an empirical and contextual matter rather than a theoretical one.

[Nick Rowe]

Mike: I'm not sure I know the answers to your questions. But think of it this way: If I borrow $2,000 to buy a car, I am temporarily holding $2,000 more than I plan to hold. When I buy the car, one day later, I expect to be back holding my planned amount of money. But if everyone else does the same thing, I am surprised to discover that $2,000 back in my wallet. The whole point of holding a buffer stock is that you can temporarily depart from your desired stock. It's only when you revise your expectation of your flow in, without at the same time revising your planned flow out by the same amount, that you see a permanent discrepancy between your buffer stock and its desired level. Only then might you get reflux.

TMF: yes, or just letting it accumulate temporarily. It doesn't matter for this point.

JW: I needed to keep it simple, so scrapped commercial banks. Or rather, I merged the commercial banks into the central bank. My hunch is that it wouldn't matter much if I introduced commercial banks.

Ralph: "And for every dollar that the latter creates, a dollar of “negative money” i.e. debt is also created. I.e. commercial bank money nets to nothing."

Nope. You cannot use the words "debt" and "money" as if they are synonyms. An IOU signed by me is debt, but it is not money. My IOUs do not circulate as a medium of exchange. Only my bank, and close friends, will accept my IOUs. My friends cannot spend my IOUs with people who don't know me.

Min: "Reason #2 is a losing proposition, per se. There has to be something else going on, right?"

Suppose I hold an average $100 in my account, that I spend down once a week. I might decide to borrow an additional $100, so I hold and average $200 in my account, that I spend down once a fortnight, by shopping at only half the frequency but buying twice as much per shopping trip.

"We could just as well say that not borrowing at all will necessarily turn out to have been a mistake."

If, in aggregate, people borrow money planning to spend it, that will ex post turn out to have been a mistake, in aggregate.

"We have the saying about money burning a hole in your pocket. Is that what you are talking about?"

Yep. That's another metaphor just like the hot potato metaphor.

[Ralph Musgrave]

When representative individuals find they’ve got too much money, they’ll pay off enough of their loans to their banks to leave them with the stock of money they want. Now where have I gone wrong?

[Jeff]

@Ralph Musgrave,

Congratulations. I think you've just rediscovered the Real Bills Doctrine.

[Mike Sproul]

Nick:
" If I borrow $2,000 to buy a car, I am temporarily holding $2,000 more than I plan to hold. When I buy the car, one day later, I expect to be back holding my planned amount of money. But if everyone else does the same thing, I am surprised to discover that $2,000 back in my wallet."

Except that the car seller's actions offset yours. He gets your $2000 and either puts it into his bank (Let's say the same bank you just took it out of.) or repays some previous loan from his bank. Either way it refluxes.

At the very least, you do agree that the Law of Reflux is valid in my case #1 don't you?

[Min]

Moi: "We could just as well say that not borrowing at all will necessarily turn out to have been a mistake."

Nick Rowe: "If, in aggregate, people borrow money planning to spend it, that will ex post turn out to have been a mistake, in aggregate."

That does not deny what I said that not borrowing at all will turn out to have been a mistake (in aggregate). If you admit that, then it is not clear that the word, "mistake", adds to the discussion.

Moi: "We have the saying about money burning a hole in your pocket. Is that what you are talking about?"

Nick Rowe: "Yep. That's another metaphor just like the hot potato metaphor."

Well, I do not see how the saying will bear the weight of the argument. It is too iffy.

[Mike Sproul]

Ralph and Jeff:

Actually, Ralph is stating the Law of Reflux, which is closely related to the real bills doctrine. Note that reflux does not preserve the value of money by limiting its quantity. Rather, the issuer of money provides various channels through which its money can reflux to the issuer. (e.g., through redemption in base money, through repayment of loans, through purchases of the issuer's assets, etc.) Thus reflux preserves the value of money by providing customers with various ways to access the assets that back their money.

[Dan Kervick]

In aggregate, borrowing for the first reason ("borrowing to spend") will necessarily turn out to have been a mistake. Because actual spending must always equal actual receipts.

I don't get this part. Suppose there are only ten people. Suppose five of them desire to spend $1000 more over the next year than the income they expect over the next year, and none of the five desires to increase or deplete personal money stocks over the next year. The first five thus desire to borrow the additional $1000 each from the bank in order to meet their spending desires. Suppose the other five desire to spend $1000 less over the next year than the income they expect over the next year, and again none of the five desires to increase or deplete personal money stocks over the next year. The second five thus do not desire any borrowings, but desire to lend the additional $1000 each to the bank in order to keep their holdings constant.

Suppose the bank does not expect a net increase or decrease in their holdings over the upcoming year. Finally, suppose each of the ten people expects exactly the same amount of personal income, which we denote X.

Now suppose, by hypothesis, that they are all exactly correct in their income expectations and spending projections. The total income for the group is 10X. The total spending for the first 5 is 5X + 5000, while the total spending for the second group is 5X - 5000. Total spending for the whole group of 10 is thus (5X + 5000) + (5X - 5000) = 10X. So total income = total spending. The total borrowing for the group is 5000 and the total lending for the group is 5000. It all adds up. Where is the aggregate inconsistency?

Certainly you can tell other stories in which the individual expectations of a group of people are necessarily frustrated. That would happen if you posit a group of people who are not just each representative but are in fact each identical, and if you assume each of these identical people expects income to differ from spending in any way. But why assume such a model? Only if you use such a model does it turn out that borrowing to spend necessarily turns out to be a mistake, and that people necessarily end up holding either more or less money than they either expected or desired.

But to return to the who issue of monetary hot potatoes, I find the very concept extremely puzzling. For a given level of income during some period, I might have certain expectations of the prices that will obtain for the goods I want, and certain preferences, based on those prices, for the proportion of that income I will spend and the proportion I will end up holding. If I find less of a market for my money than I expect, and end up at the end of the period with fewer goods and holding more money than I would have preferred, I might then accept a new round of exchanges at higher prices, so I end up with all the goods I expected and less money holdings I expected. (Or I might accept something something in between depending on the exact nature of my preference rankings).

But suppose I simply receive more income than I expected, but receive all the goods I expected at the prices I expected. Then I end up with more money holdings than I expected. But these holdings are in no sense a hot potato. Extra money stocks are only a hot potato when they represent an undesired tradeoff for desired goods. If the extra holdings are, however, pure bonus money, then great. I will be perfectly willing to hold the extra money. It's not a hot potato - just a nice, comfortable cool potato to stick in my potato stock.

Now suppose the reason I end up with extra, unanticipated money stocks at the end of the period in question because, after purchasing exactly the goods I wanted at exactly the price I anticipated, someone comes along and offers me money for some of my goods, and at a price that makes the deal a good one for me. I end up, then, with fewer foods than I anticipated, and more money stocks than I anticipated; but not because I have been forced into an undesired tradeoff, but again because I receive more income than expected, and have made different exchanges than I anticipated in accordance with my preferences.

Compare now the kinds of central bank operations we have debated before. If a central bank simply gives a member bank some free reserves, the situation is like the former of the two situations I just described. The member bank might end up with more reserves than it desired at the beginning of the year. But those reserves aren't a hot potato, because the bank has not been forced into any undesired tradeoffs. They just received more "income" than they expected. Great - free money. Keep it on the shelf with the other nice cold potatoes.

Suppose on the other hand the central bank offers money reserves in exchange for securities, and the member bank freely accepts the offer because they believe the offer is a good deal for them. Then again, even though they have fewer securities and more reserves than they expected to have at the start of the period, they have not been forced into any undesired tradeoffs. They have just received more income than expected, and have made different exchanges anticipated in accordance with their preferences. No hot potatoes.

So I'm still having trouble seeing how central bank operations can force member banks into lending or spending that they would otherwise prefer not to engage in, due to a hot potato effect.

[Nick Rowe]

Dan: "Now suppose, by hypothesis, that they are all exactly correct in their income expectations and spending projections."

Then we jump straight to the new equilibrium, where people in aggregate do not borrow to spend. But the amount of knowledge it would take to jump straight to that new equilibrium makes it totally implausible. I tend to believe in rational expectations, but there are limits. It is totally implausible to assume that each individual knows whether all other individuals are borrowing to spend, borrowing to hold, or not borrowing at all. Sure, if all individuals were literally identical, then it *might* work. "Let's see, I'm planning to borrow to spend, therefore everyone else must be too, therefore my expectations must be wrong, and what would I have to believe before I would stop borrowing to spend? Hmmm, that must be what will happen, because everyone else is running that same thought-experiment through their heads like I am."

We have markets because normal people can't figure that sort of thing out.

Sure, you are happily surprised to get the hot potato. (Though in reverse, when it's musical chairs, rather than hot potato, you are unhappily surprised). But you are still surprised, and wish you hadn't borrowed that money, because it turns out you didn't need it. In aggregate, if all are identical, each can spend whatever he feels like, because he knows it will come straight back to him, when others do the same.

[Nick Rowe]

Min: "We could just as well say that not borrowing at all will necessarily turn out to have been a mistake."

Not borrowing (to spend) at all, *in aggregate* will never turn out to be a mistake. It is always the rational thing to do, in aggregate. The full information rational response to the central banks' cutting from 5% to 4% will be to borrow *only to hold* (in aggregate), and to revise upward your expectations of receipts of money, and planned spending.

[Nick Rowe]

Mike: "Except that the car seller's actions offset yours. He gets your $2000 and either puts it into his bank (Let's say the same bank you just took it out of.) or repays some previous loan from his bank. Either way it refluxes."

Why would the car seller want to repay loans, if the interest rate has dropped from 5% to 4%? He's like you -- he wants to borrow to spend. He spends my $2,000 on a new car to replace the one he sold to me, and borrows some more from the bank, because loans are cheaper.

[Mike Sproul]

Nick:

That's cheating! You can't go around making the interest rate drop, just in time to save your argument.

Assuming that you and the car seller are too small to affect the interest rate, the seller would put the $2000 in the bank as soon as he got it. No hot potatoes.

Assuming the bank is big enough to influence the interest rate, its easy lending policy would leave the bank issuing $100 but getting IOU's worth only about $99 in exchange. Backing per unit of money falls, inflation results, and people will hold about 1% more nominal cash than they used to (real cash balances unaffected). Once that new equilibrium is reached, reflux goes back to operating as before.

[Nick Rowe]

Mike: start in equilibrium. *Something* must have changed to cause aggregate borrowing to spend to increase. I'm assuming it was a cut in the rate of interest. Could also be an increased demand for loans. In your case, could be more silver mined?

[Nick Rowe]

"Assuming the bank is big enough to influence the interest rate, its easy lending policy would leave the bank issuing $100 but getting IOU's worth only about $99 in exchange. Backing per unit of money falls, inflation results, and people will hold about 1% more nominal cash than they used to (real cash balances unaffected). Once that new equilibrium is reached, reflux goes back to operating as before."

OK. I can live with that. The hot potato is what is getting us from one equilibrium to the second. The hot potato is a disequilibrium process story. It's the hot potato that causes the inflation.

[Dan Kervick]

Then we jump straight to the new equilibrium, where people in aggregate do not borrow to spend.

Why, Nick? The hypothesis is that everybody is exactly correct in their income and spending expectations, and those expectations were stipulated to include, for five of the people, income levels below spending levels. Even with perfect information, people would still borrow.

I don't believe in perfect information either. I think it's pretty rare. But I think that consideration of the hypothetical situation of perfect information just makes it easier to see that borrowing to spend need not necessarily turn out to be a mistake.

[Mike Sproul]

Nick:

In my silver coin example, an increased demand for loans doesn't have to mean an increased desire to hold silver. But if it did, more bullion would be minted, and if the effect was strong enough to increase the price of silver, more would be mined.

We are still far apart on the hot potato issue. I think of a stock analogy: People have an increased desire to hold GM stock, to the company issues more shares in exchange for equal-valued assets. Share price doesn't change. No hot potatoes anywhere.

But maybe GM issues new shares without getting enough assets in return. Share price drops because of reduced backing per share, but that's not a hot potato process. People just see less backing per share and adjust their valuation accordingly.

[Min]

Nick Rowe: "In aggregate, actual expenditures of money will always equal actual receipts of money. That is an accounting identity. But this does not mean that aggregate planned expenditures of money will always equal aggregate expected receipts of money. In aggregate, borrowing for the first reason ("borrowing to spend") will necessarily turn out to have been a mistake."

Moi: "We could just as well say that not borrowing at all will necessarily turn out to have been a mistake."

Nick Rowe: "Not borrowing (to spend) at all, *in aggregate* will never turn out to be a mistake. It is always the rational thing to do, in aggregate. The full information rational response to the central banks' cutting from 5% to 4% will be to borrow *only to hold* (in aggregate), and to revise upward your expectations of receipts of money, and planned spending."

I do not see how you current response relates to what you said earlier. Aggregate planned expenditure and expected receipts need not be the same in any event, no?

As for not borrowing to spend in aggregate being rational, you gotta spell that out more. Suppose that everybody but me does not borrow to spend. Does that mean that I should not, either?

Thanks. :)

[Nick Rowe]

Dan: "Why, Nick? The hypothesis is that everybody is exactly correct in their income and spending expectations, and those expectations were stipulated to include, for five of the people, income levels below spending levels. Even with perfect information, people would still borrow."

Unless I misunderstand you, that is logically impossible. It violates the accounting identity that aggregate spending of money equals aggregate receipts of money. If half the people expect to spend more than they receive, and the other half expect to spend an amount equal to what they receive, at least one person must turn out to be wrong.

Min: and unless I misunderstand you, it's the same response. If 99 people out of 100 are planning and expecting to spend exactly what they receive, and 1 out of the 100 is planning and expecting to spend more than he receives, then at least one person will turn out to be wrong. Their plans and expectations violate the accounting identity.

Suppose the only thing they buy and sell is apples. Total number of apples bought must equal total number of apples sold.

Mike: "We are still far apart on the hot potato issue. I think of a stock analogy: People have an increased desire to hold GM stock, [s]o the company issues more shares in exchange for equal-valued assets. Share price doesn't change. No hot potatoes anywhere."

Agreed. But GM stock is not a medium of exchange. GM stock is like a refrigerator. People do not buy more GM stock because they want to buy more refrigerators. People do not buy more refrigerators because they want to buy more GM stock. People *do* buy more money because they want to buy more GM stock. People *do* buy more money because they want to buy more refrigerators.

[Nick Rowe]

Mike: I should have said: "Agreed on the 'no hot potatoes anywhere', but not agreed on 'share price doesn't change'" (because the price of the underlying assets that GM buys may get bid up). But that's not central to what we are arguing over.

[Dan Kervick]

Nick: "Unless I misunderstand you, that is logically impossible. It violates the accounting identity that aggregate spending of money equals aggregate receipts of money. If half the people expect to spend more than they receive, and the other half expect to spend an amount equal to what they receive, at least one person must turn out to be wrong."

In my example, five people desire to spend less than they receive and five desire to spend more than they receive. Their expectations are all correct, and the accounting identity is not violated. Five of the people desire to borrow to spend, and their borrowing doesn't turn out to have been a mistake.

[Scott Sumner]

Nick, Sorry for the slow response. So let me see if I have this right:

1. You agree that the stock of money supplied equals the demand as a function of the interest rate.

2. You point out that the stock of money doesn't, in general, equal the demand as a function of the price level.

The second disequilibrium is what matters, hence the money market is in disequilibrium.

[Nick Rowe]

Scott: No worries. You have been blogging up a storm, of good stuff.

"1. You agree that the stock of money supplied equals the demand as a function of the interest rate."

Nope. I don't agree with that. That will only be true if we assume that aggregate planned expenditure equals aggregate expected receipts. And that is an implausible assumption if something changes unexpectedly.

Dan: sorry. I did misunderstand you. Assuming the first 5 want to borrow and spend the same amount as the second 5 want to lend and not spend, there is no net borrowing from the bank, and no hot potato.

[Mike Sproul]

Nick:

Reflux works for both GM stock and for money. As long as a dollar is redeemable by its issuer for 1 oz. of silver, or an equivalent value of bonds or bikes, then if dollars were over-issued and started trading on the street for .99 oz., then the dollars would immediately reflux to the bank in exchange for 1 oz. worth of silver, bonds, or bikes. It's no different from the case where all money is silver coins. The silver coin example just makes it easier to see the impossibility of over-issue in a world where new money is issued in exchange for equal-valued assets.

[Nick Rowe]

Mike: it's not going to be immediate, if money is used as a medium of exchange. It takes time for people's expectations of monetary receipts to adjust. And their plans may change as a result of changing expectations, which will, in aggregate, falsify those expectations again. It's an interactive learning process, where the truth changes as a result of your learning it. You are assuming an immediate jump to the new RE equilibrium.

[Nick Rowe]

So it won't trade on the street for .99oz, because people will falsely think they need the money they hold as a medium of exchange. They keep getting surprised at how much is in their wallet, but think it's temporary. That's the thing about buffer stocks. We sometimes temporarily hold more than we want because we think they will be going down soon. But if what leaves my buffer stock simply goes into yours, and vice versa, we will be mistaken in aggregate. And money, unlike other buffer stocks, does just that. Because everyone accepts it for everything.

[anon]

"So it won't trade on the street for .99oz, because people will falsely think they need the money they hold as a medium of exchange. They keep getting surprised at how much is in their wallet, but think it's temporary."

Nick, can this story be rephrased in a way that's consistent with ratexp equilbrium? Like, perhaps a fraction of the population have to keep money in their pocket because of liquidity constraints, but we don't know how large that fraction is, and your "adjustment" process is agents Bayes-learning that fraction?

Another issue: if agents know the model, why don't some of them "speculate" and spend more money than they otherwise would, hoping that an increase in spending will restore their money balances? Surely this must occur in any proper equilibrium solution?

[Mike Sproul]

Nick:

But aren't you saying that eventually, a new equilibrium will be reached where the dollar will trade for .99 oz? Then we are right back in the world where people see that they can get 1 oz worth of stuff by refluxing their money to the bank, so back it goes.

[Min]

Nick Rowe: "Min: and unless I misunderstand you, it's the same response. If 99 people out of 100 are planning and expecting to spend exactly what they receive, and 1 out of the 100 is planning and expecting to spend more than he receives, then at least one person will turn out to be wrong. Their plans and expectations violate the accounting identity."

Nick, I have been cogitating a bit on this, and I think that I may have a better understanding of one place that we differ. What you say here is clear and true. Where I think that we differed is that you appear to say (earlier) that someone's borrowing to spend is a mistake. In the case that I brought up, since I would be the only borrower to spend, that would be me. Now you say only that someone has made a mistake. (Possibly somebody else has, possibly everyone has.) Perhaps that is what you meant by a "mistake in aggregate". (I have trouble making sense out of that phrase.)

Perhaps I have misunderstood you, but it seems to me that you put the entire onus of the mistake on behavior, on borrowing to spend or not, and on how much is borrowed. But what about plans and expectations? Maybe there is where the mistakes lie. (BTW, even without borrowing to spend, expectations are often dashed, and we can expect that someone's expectations will not be met. As the general semanticists might say, "Expect-2 the unexpected-1.")

Also, just because events do or do not meet expectations does not mean that a mistake has been made. For instance, suppose that the total of fire insurance premiums in a small town is $5,000,000 one year, but nobody's house catches fire. Did somebody make a mistake? That is hard to argue. Suppose that I, like that man in Tennessee a while back, live outside of city limits, but do not pay the city to get protection from the city fire department. If, unlike the case with the Tennessee man, my house does not burn down, should I pat myself on the back for making the right decision? (For those who do not know the story, the fire department came out to the fire, ready in case the paid-up neighbor's house caught fire. Despite the desperate entreaties of the man, who offered to pay the fee (and more, I think) for the fire dept. to put out the fire, they let his house burn to the ground.)

Still, in the case where you can guarantee that expectations will be violated, it is hard not to think that somebody has made a mistake somewhere. ;) However, it is not at all clear to me that the error must lie, as I believe that you claim, in borrowing or in the amount to borrow. Why is it not in the estimations of expenditures and receipts? I see no a priori reason that those estimations cannot be accurate. If your assumptions tell you that they must be wrong, then perhaps the fault lies in those assumptions.

Now, even if such estimations can be accurate, that does not mean that we can make them rationally. More on this next. :)

Nick Rowe: "There is no monetary hot potato in standard Keynesian and New Keynesian models. That is because those models make wildly implausible assumptions about people's knowledge. They assume people have perfect knowledge about how much money everybody else is borrowing from the banking system, and how much they are planning to spend from what they borrow."

Well, I do not know about the standard Keynesian model. However, I sincerely doubt that Keynes would have endorsed the idea of perfect knowledge about how much everybody else s borrowing and how much they are planning to spend. Keynes addresses this sort of thing in his "Treatise on Probability" (1921). :)

In Chapter 3, on the measurement of probabilities, he argues at length that probabilities are not necessarily single numbers, that they are only partially ordered, and that they may not even exist for certain cases. I cannot do justice to his argument in a line or two.

He refutes the claim that the practice of insurance underwriting implies numerical probabilities. He states:

"Underwriters are actually willing, it might be urged, to name a numerical measure in every case, and to back their opinion with money. But this practice shows no more than that many probabilities are greater or less than some numerical measure, not that they themselves are numerically definite. It is sufficient for the underwriter if the premium he names exceeds the probable risk. But, apart from this, I doubt whether in extreme cases the process of thought, through which he goes before naming a premium, is wholly rational and determinate ; or that two equally intelligent brokers acting on the same evidence would always arrive at the same result. In the case, for instance, of insurances effected before a Budget, the figures quoted must be partly arbitrary. There is in them an element of caprice, and the broker's state of mind, when he quotes a figure, is like a bookmaker's when he names odds. Whilst he may be able to make sure of a profit, on the principles of the bookmaker, yet the individual figures that make up the book are, within certain limits, arbitrary." (p. 22). He continues, "That the transaction is in principle one of bookmaking is shown by the fact that, if there is a specially large demand for insurance against one of the possibilities, the rate rises ; the probability has not changed, but the "book" is in danger of being upset." (p. 23).

No perfect knowledge here. Far from it. :) Note the subjective elements, caprice and state of mind. Not the stuff of rational calculation. Keynes goes on to speak of the practice of determining damages in a court of law, which in some cases are held to be imponderable. He also discusses ordinary questions, such as the probability of returning home alive from a walk.

Keynes concludes: "Some cases, therefore, there certainly are in which no rational basis has been discovered for numerical comparison. It is not the case here that the method of calculation, prescribed by theory, is beyond our powers or too laborious for actual application. No method of calculation, however impracticable, has been suggested. Nor have we any prima facie indications of the existence of a common unit to which the magnitudes of all probabilities are naturally referable. A degree of probability is not composed of some homogeneous material, and is not apparently divisible into parts of like character with one another." (p. 30).

We are, after all, talking of an n-person game with incomplete information. Such terms were not available to Keynes in 1921, but I suspect that he would deny the possibility of the rational numerical estimation of expenditures and receipts in this case. Far from assuming perfect knowledge, he would assume no knowledge of any precision. (Roubini might agree, I don't know. :)) Under such conditions, the mistake would lie in making precise estimates at all.

[Nick Rowe]

Min: "Now you say only that someone has made a mistake. (Possibly somebody else has, possibly everyone has.) Perhaps that is what you meant by a "mistake in aggregate". (I have trouble making sense out of that phrase.)"

Yes, that's what I meant, or should have said. If we assume that only 1 person borrows to spend, and output is demand-determined, and everything is symettric otherwise, then somewhere between 99% and 100% of the total mistake will be made by the other 99 people. They didn't know that the 1 guy was going to buy more from all of them. And in fact, only if the 99 turn immediately around and spend more from the 1 in response to their higher recepits does he make a mistake. If they are slow to adjust their planned spending, your 1 guy makes all the other 99 make a mistake, while he makes no mistake.

(The problem is that I kept talking about the representative agent. If he borrows to spend, then he necessarily makes a mistake.)

Keynes never wrote down an ISLM. And he was very fuzzy on the distinction between I=S as an accounting identity and I=S in terms of plans and expectations, which is what this is all about. It had to be explained to him, AFAIK. So while I think he would have been sympathetic in principle, about uncertainty and stuff, he didn't really get this.

Hayek would have been closer, I think. My language here, in talking about mutual consistency of plans, is borrowed straight from Hayek.

[Min]

@Nick Rowe: Thanks for taking the time to explain things more. :)

Nick Rowe: "Keynes never wrote down an ISLM. And he was very fuzzy on the distinction between I=S as an accounting identity and I=S in terms of plans and expectations, which is what this is all about. It had to be explained to him, AFAIK. So while I think he would have been sympathetic in principle, about uncertainty and stuff, he didn't really get this."

I am certainly not one to judge, but maybe it is not that Keynes did not get it, maybe he just didn't buy the assumptions.

[dlr]

I know I'm late, but I am not sure I get your point as it applies to the NK model. Well, I do get your observation that NK, like IS/LM, tries to describe an only equilibrium. But aren't you oversimplifying the equilibrium here? Isn't the whole point of the NK model to show that determinate equilibria can emerge under ratex via a learning game between agents and the central bank? You describe a plausible scenario in a simple world where a cut in interest rates might lead a ratex agent unsure whether aggregate planned spending now exceeded planned receipts or the bank was just finding the new rate where planned spending actually equaled receipts. But does that ratex assumption survive under a rigorous learning model where the central bank has an entire reaction function (not just a single interest rate cut) that agents can observe? I don't think NK requires perfect foresight as to planned spending and planned receipts, I think it shows that under ratex, a certain policy rule and certain other conditions a determinate equilibrium can be expected. And if agents even begin to make an "aggregate mistake" and hot potato the price level up there is a whole reaction function, and expectation of a reaction function, in place to police that mistake back in equilibrium. Under ISLM, the "off equilibrium story" can trump whole shebang because "equilibrium" really means partial equilibrium using only a few variables and without expectations (or maybe with perfect foresight). But I don't see how that's also the case under the NK model, which seems to say, we can imagine an entire equilibrium where hot potato mistakes are unlikely to be important because agents and a CB with an understood reaction function will begin to notice the aggregate mistake quickly and react to it.

[Nick Rowe]

dlr: my hunch is that in "normal times" you are basically right, or at least approximately so. I'm quite happy with ratex if the world seems to carry on as normal. People don't even need to understand the model; they just spot patterns, and know roughly what's coming next, even if they don't understand *why* it's going to happen. More or less accurate rules of thumb will evolve. And central banks don't just adjust monetary policy for no reason, so people know how to interpret the central bank's actions.

But in abnormal times, when something new happens, and people just don't know what will happen next, and why the central bank is doing what it's doing, I'm less comfortable with the ratex equilibrium assumption.

[Too Much Fed]

"He now borrows nothing. He again plans to spend $100 more than he expects to receive in the second month.

At the end of the second month the representative individual is again surprised to find his monetary receipts are $100 bigger than he expected, and that he holds $100 more money in his pocket than he wanted to hold.

If he does not revise his expectations, or revise his planned spending, or revise his stock demand for money, this $100 hot potato of excess supply of money will continue to circulate forever, month after month."

And, "Is the representative individual making interest and principal payments to the central bank?"

And, "TMF: yes, or just letting it accumulate temporarily. It doesn't matter for this point."

The way the accounting people have explained to me is that if interest and principal payments are being made then the original amount of $100 in medium of exchange will go down and become zero(0) when the loan is paid off.

[Oliver]

Your two examples seem very unrealistic to me. Could you give examples of real world situations where these take place? Imo people borrow money mainly for the following reasons:

1. Investment. They borrow because their expected receipts of money with borrowing exceed their expected receipts of money without borrowing. They "borrow to spend" on an investment that will hopefully create an income stream larger than that needed to service the loan.

2. Acquisition of assets for end use. They borrow because their desired stock of assets exceeds that which their current stock of money can buy. They "borrow to spend" on an asset that they believe will give them more satisfaction / utility than living without the incurred liability and the asset and in the belief that their future income will suffice to service the loan, e.g. mortgage or car lease.

In example 1, there is a producer of capital goods who will have done the same as our investor and thus fully expects, indeed needs, the money received to service his own debts and hopefully buy a house or car.

In example 2 there is a previous home owner or developer who will also have done the same as our investor 1 and thus is also expecting the money.

It is only when the amount of money on offer can not be met by goods delivered, or when asset values fall below those calculated at the time of the loan at the desired time of sale, that disequilibria arise which, causes prices to fluctuate. This has nothing to do with the amount of money loaned into existence, but with the congruence of the rise in value of assets and the capability of the real economy to produce goods with aggregate growth in loans / money. My reading of your post is that you're searching for some inter-monetary disequilibrium while imo it's always a disequilibrium between the financial and the real worlds that causes problems.

But I may just be too dim or hopelessly out of your paradigm to even know what you're on about, let alone criticize it meaningfully.

[Nick Rowe]

Oliver: Both your examples, I think, are examples of what I mean by "borrowing to spend".

When people in aggregate borrow to spend, all sorts of disequilibria can arise. It depends what they plan to spend it on. If they plan to spend it on goods with sticky prices that are in excess supply (like newly-produced goods in a recession) then we get an increase in output and employment for those goods. Or, if they plan to spend it on goods that have flexible prices and are not in excess supply, those prices will rise. Lots of people will find their expectations falsified by events.

But the one disequilibrium I was focusing on was the excess supply of money. People in aggregate now hold a bigger stock of money than they had planned to hold. Most economists say that can't happen. I'm saying they are wrong.

[Too Much Fed]

Let's say everyone borrows $100 from the central bank the first month and then no more while making interest payments and principal payments of $11 per month for 10 months ($110 in total). The interest rate is changed to make it easier. The central bank raises the interest rate back to what it originally was at the end.

Asset side of CB:
$100 loan

Liability side of CB:
$100 in demand deposits

At the end of the first month:

Asset side of CB:
$11 in medium of exchange
$90 loan

Liability side of CB:
$100 in demand deposits
$ 1 in CB equity

Take the $11 in medium of exchange to "pay down" the demand deposits.

Asset side of CB:
$90 loan

Liability side of CB:
$89 in demand deposits
$ 1 in CB equity

At the end of 10 months:

Asset side of CB:
$ 0 loan

Liability side of CB:
$ 0 in demand deposits
$10 in CB equity

When the interest rate is raised back to what it was at the beginning, assume everyone goes back to no borrowing and the same desired stock. Oops! Everyone is $10 in medium of exchange short because it is at the CB.

That is basically how it was explained to me.

[Oliver]

Can you name me a realistic example of 'borrow to hold'? I can't think of one except perhaps financial intermediaries which you exempted from your model. Seems people borrow when they want something that is on offer for a defined price but can't (or don't want to) afford it out of current income or savings. Never is there a lag between the act of borrowing and spending that which was borrowed. That only happens with saving out of income.

[Nick Rowe]

On average you have a certain number of dollars in your pocket and chequing account, though it fluctuates day to day. And maybe you have some debt too. If you wanted to, you could get by with less money on average in your pocket and chequing account, and pay down some of your debt. Or, you could hold more money on average in your pocket and bank account, and have higher debt. If you choose the latter, you have "borrowed to hold".

[Oliver]

Are you talking about dollars that sit as saved income in people's pockets but were originally borrowed into existence? Is that your definition of borrowed? Because on an individual level, I cannot imagine anyone borrowing more than what is needed to spend on goods at that very moment. I don't see a car in a lot that costs $1'000 and then go to my bank and ask for a loan of $2'000 and sit on the extra $1'000 until some other investment opportunity comes up. I borrow 1'000, spend it immediately while paying for consumption out of income and saving the residue for later, then rinse and repeat. The savings, no matter how high or low vis a vis debt obligations, do not come from borrowing but from income. For individuals, borrowing and spending go together and saving and paying down debt are somewhat interchangeable, imo. 'Borrow to spend' and 'save to hold' sounds right to me.

[Oliver]

Or maybe the terms 'borrowing with the intention of paying down as quickly as possible' and 'borrowing with no intention of paying down' are what you're trying to distinguish?

[Too Much Fed]

Oliver said: "Are you talking about dollars that sit as saved income in people's pockets but were originally borrowed into existence?"

Good! Now we are talking about medium of exchange and how it can be viewed differently depending on the entity's budget.

I don't see 2. being very realistic either. It seems to me entities want to increase the amount of medium of exchange (stock) that has no interest rate and repayment terms attached, but they might need other entities to do 1. for that to happen.

And, "Or maybe the terms 'borrowing with the intention of paying down as quickly as possible' and 'borrowing with no intention of paying down' are what you're trying to distinguish?"

Let's do some personal finance/budgeting. Someone has a $500 per month mortgage. They are lucky enough to get a real wage increase. They might increase their checking account balance to build up an emergency fund instead of paying down the mortgage faster. I don't consider that borrowing to hold.

[Too Much Fed]

Oliver said: "Your two examples seem very unrealistic to me. Could you give examples of real world situations where these take place? Imo people borrow money mainly for the following reasons:

1. Investment. They borrow because their expected receipts of money with borrowing exceed their expected receipts of money without borrowing. They "borrow to spend" on an investment that will hopefully create an income stream larger than that needed to service the loan.

2. Acquisition of assets for end use. They borrow because their desired stock of assets exceeds that which their current stock of money can buy. They "borrow to spend" on an asset that they believe will give them more satisfaction / utility than living without the incurred liability and the asset and in the belief that their future income will suffice to service the loan, e.g. mortgage or car lease."

It seems to me in both cases the entities are doing budgeting/future budgeting. What happens if future business income and/or future wage income don't meet expectations because the goods/services market is in balance/oversupplied or the labor market is in balance/oversupplied?

Lastly, what about borrowing to speculate in financial assets?

[JKH]

TMF:

I haven’t read the rest of this post or the comments, but regarding your question on the accounting suggested in your comment: | October 14, 2011 at 04:06 PM

Your accounting is basically correct.

Although I’d exclude this step:
........
At the end of the first month:
Asset side of CB:
$11 in medium of exchange
$90 loan
Liability side of CB:
$100 in demand deposits
$ 1 in CB equity
........

The CB doesn’t store the “medium of exchange” as an asset, generally speaking. The CB issues the “medium of exchange” as a liability. The “medium of exchange” in this case is most likely bank reserves (in theory it could be CB notes, but not normally when the CB is involved in the transaction).

The CB conducts transactions in the medium of exchange from this perspective – increasing its liability when it makes a payment, decreasing its liability when it receives a payment. The “medium of exchange” in the form of reserves is used as an asset by banks with reserve accounts at the Fed. You are accurate that the reserve account is essentially a form of demand deposit held by the banks.

Paying down principal of 10 reduces both the CB asset and the CB liability by 10. This is a balance sheet transaction that is not reflected on the income statement of the CB. It is a direct book keeping entry without the step I noted above.

Paying interest of 1 reduces the CB liability and increases CB equity by 1. This is a balance sheet transaction that is also reflected on the income statement of the CB.

“Everyone is $10 in medium of exchange short because it is at the CB.”

That is correct at the margin in your example. The medium of exchange has been converted to CB equity. This increases CB profit. This is also reflected in the fact that the CB remits its profit to Treasury, which reduces the deficit. And that is generally contractionary at the margin.

[Nick Rowe]

JKH: "The CB doesn’t store the “medium of exchange” as an asset, generally speaking."

You are right, of course, but also (in a totally irrelevant sense) wrong. The Bank of Canada has lots of BoC notes in its basement (I think, they never let me behind the armoured doors to check). It's just that if you own an IOU that you yourself signed, it doesn't make any difference to anything if you burned it (except the waste of paper and ink).

This is a pedantic comment, that I only wrote for the fun of it.

[JKH]

Nick,

Quite right.

I was thinking of reserve deposit balances more than notes, avoiding that physical inventory aspect of notes.

[Nick Rowe]

JKH: Yep. Just to continue my pedantry, wouldn't it value those notes at a couple of cents each, on the asset side of its balance sheet, to capture the printing costs (if they were newish notes)?

[JKH]

Haven't looked into that Nick. A wild guess is that the bank expenses the cost of printing at the time it purchases the notes from the printer (instead of capitalizing the cost in the form of an asset on the balance sheet). And it probably allocates additional running expenses for storage, guarding, and inventory management, etc.

I'm sure there's an answer somewhere, probably in the accounting notes to the bank's annual report.

Perhaps I'll have a look there, as soon as I've figured out your vertical LM curves.

On that basis, should be back on this around 2020.

:)

[Too Much Fed]

JKH, first thanks for the verification.

And, Nick's post at the top said: "Let's consider an extremely simple monetary exchange economy. There are no commercial banks. A central bank chooses a rate of interest at which individuals can either borrow money from the central bank or lend money to the central bank, as they wish."

I'm not sure how central bank reserves would fit in this situation, but I might assume that they are created 1 to 1 with the demand deposit when the loan was created. Assuming that and that people are paying the principal and interest with demand deposits, then I think the central bank reserves are being paid down at the same rate as the demand deposit(s) 1 to 1. I believe marking down both central bank reserves and demand deposits 1 to 1 is the equivalent of destroying currency.

If everyone pays down their debt, then the $100 amount starts going down every month and can "become" negative at the end depending on what happens to the $10 in interest that is transferred to the CB.

[Too Much Fed]

JKH, I add this step because it helps me (and hopefully others) "track" the flow and amount of medium of exchange.

At the end of the first month:

Asset side of CB:
$11 in medium of exchange
$90 loan

Liability side of CB:
$100 in demand deposits
$ 1 in CB equity

[JKH]

TMF,

Sorry, I confused the explanation a bit because I didn’t read the post, as I said.

But there’s an easy fix to adjust to the post.

Because there are no commercial banks, the central bank assumes the functional role of a commercial bank. “Loans create deposits”, just as they do in the existing commercial bank system. The central bank in making a loan also creates a deposit liability, which is a deposit held initially by the borrower with the central bank. Such a deposit could be interpreted as a “reserve” held by the depositor.

The central bank is willing to convert these deposits/reserves into currency on demand, and vice versa (just as banks do now acting as intermediaries between the public and the central bank).

There are no longer any conventional reserves held by commercial banks with the central bank, because there are no longer any commercial banks.

And, in addition to assuming the functional role of a commercial bank, the central bank still retains its monetary policy role of setting the policy interest rate by dint of setting the rates it wishes to set on all deposits – it is still the monopoly issuer of the currency. And it can set rates on deposits the same way in which it sets the policy rate for interest on reserves now.

And what I wrote previously still applies – your accounting for the loan is correct.

[Too Much Fed]

JKH said: "There are no longer any conventional reserves held by commercial banks with the central bank, because there are no longer any commercial banks."

Yep. That is the other way to look at the situation.

Everything else sounds good.

I want to go over one other scenario. Let's say for some reason the $100 needs to be maintained meaning that everyone borrows the principal and interest amount they pay back every month. Eventually, will the CB own all the currency? Thanks again!

[JKH]

“I want to go over one other scenario. Let's say for some reason the $100 needs to be maintained meaning that everyone borrows the principal and interest amount they pay back every month. Eventually, will the CB own all the currency?”

TMF,

That’s an interesting question and puzzle.

Suppose the process starts with a $ 100 loan and $ 100 deposit. Assuming a steady state of repayment and re-borrowing of principal, every month the CB’s equity increases by $ 1 and deposits decrease by $ 1, due to the accounting effect of the $ 1 interest payment. At the same time, the re-borrowing of the principal repayment of $ 10 each month keeps the size of the CB balance sheet constant at $ 100. The equity account grows and deposits in total shrink over time.

At some point, due to the accumulation of interest payments over time, the CB will reach $ 90 in equity and deposits will have declined to $ 10. At the next stage, somebody has to pay $ 11 in combined principal and interest, while re-borrowing $ 10. That’s a problem, because there is no longer enough “medium of exchange” (deposits) to make the combined repayment and interest payment accounting entries by debiting deposits for a total of $ 11. That's even with the simultaneous effect of the $ 10 re-borrowing.

There is a solution to this:

The CB should recognize that it needs to make dividend payments from equity in order to keep the monetary economy moving along. E.g. if it pays out all of its earnings as it goes along, then the money supply (deposits) will stay at $ 100, starting with the original loan. That’s because dividend payments will convert equity to deposits as an accounting entry. Each interest payment of $ 1 will flow back as a dividend payment of $ 1.

Alternatively, the CB could start to pay interest on its deposits, which would post pone the problem. The money supply would still shrink, but at a slower pace than the status quo.

As it stands, the CB is imposing a highly deflationary force on this economy by hoarding its earnings and accumulating equity and shrinking the money supply as a result.

Maybe this also shows how accounting can be useful in supporting Nick Rowe’s views on the importance of the medium of exchange.

[JKH]

TMF,

My example doesn't include borrowing the interest.

If that happens, money supply is maintained without dividend payments from equity, because the total loan grows in tandem with each payment of interest/ each increase in CB equity.

But that is ponzi finance.

[Min]

I know that the discussion has moved on, but I am still bothered by the hot potato metaphor. I think that I can express my disquiet more clearly. What I miss in the hot potato metaphor is a theory of the velocity of money. It is like in the song, "Well, I don't give a damn about a greenback dollar, spend it fast as I can." It is like there is an instantaneous indefinitely bounded increase in the velocity of money. That seems to run counter to the idea of money as a store of value. But we know that people indeed treat money as a store of value. To the extent that they do, how can it be a hot potato?

Of course, there are countervailing forces, as the saying about money burning a hole in one's pocket attests. But then why does one force become suddenly dominant?

That is why I asked for some evidence. :)

[Min]

Oh! One reason that I bring this up is that to a good extent, isn't part of our current predicament the fact that the idea of money as a store of value is dominant?

[Too Much Fed]

JKH said: "That’s an interesting question and puzzle."

Oooo! I like an economic mystery that is about trying to figure out what is really going on with clues all around. The biggest mystery of all is why should all new medium of exchange come from debt.

First, do you agree all new medium of exchange comes from debt the way the system is set up now (might be some debate about that depending on definitions)?

"As it stands, the CB is imposing a highly deflationary force on this economy by hoarding its earnings and accumulating equity and shrinking the money supply as a result.

Maybe this also shows how accounting can be useful in supporting Nick Rowe’s views on the importance of the medium of exchange."

I agree with Nick that the amount of medium of exchange trades relative to the amount of goods/services so that it needs to increase as an economy produces more goods/services.

Let's say productivity growth increased so that the amount of medium of exchange needed to increase by $100. It was $5,000 in currency (type unspecified) originally so that $5,100 is needed. Next, what you describe happens. Even if the CB paid out all its equity as dividends, it seems to me the $100 in demand deposits would get paid down so that there is only the $5,000 in currency left.

If an economy is constantly run so that the amount of medium of exchange is increased with currency denominated debt, will this scenario or something similar happen (I haven't even talked about debt defaults yet causing the amount of medium of exchange to go down)?

Also, I disagree with Nick about for every borrower there is a lender in the strictest sense. If that were true in the strictest sense, then how would the amount of medium of exchange increase? For example, there is $5,000 in currency (medium of exchange) with no savings circulating. Someone saves $100 so the amount in circulation goes down by $100. Next, someone borrows the $100 to spend so the amount rises by $100 back to $5,000. It is not increasing.

[Too Much Fed]

JKH, I'm going to repost this from:

http://worthwhile.typepad.com/worthwhile_canadian_initi/2011/10/the-optimum-size-of-the-central-bank.html

'"It ends when the central bank runs out of things to buy, because it already owns everything, right down to your house, furniture, and toothbrush, which it rents back to you. It ends in communism."

J.V. Dubois said: "If you have a government that promises budget surplus from now on forever, you also end in communism."

What is it called when the very few rich people continuously run surpluses (very high real earnings and real earnings growth) so they own all the "currency" and assets and want to rent them back to everyone else?

It seems to me that the problem is excess savers.'

I'll add rich entities like banks too.

[Too Much Fed]

JKH, one of the "mysteries" that needs to be solved is if an economy needs more medium of exchange how should that happen.

Along the same lines, what do you think of having the central bank have only liabilities (medium of exchange) and no assets (per se)?