Negative money

There are two parallel worlds. Both worlds use bits of coloured paper as money, because barter is very difficult. The green world uses green paper as money, and the red world uses red paper as money. The green paper money has a positive value. The red paper money has a negative value.

In the green world, if I sell you apples, you agree to give me your green money in exchange. Goods and money flow in opposite directions around the economy. In the red world, if I sell you apples, you agree to take my red money in exchange. Goods and money flow in the same direction around the economy.

In the green world, it is illegal for anyone except the central bank to create money. And only the government is allowed to take your money without your consent.

In the red world, it is illegal for anyone except the central bank to destroy money. And only the government is allowed to give you money without your consent.

These laws are much harder to enforce in the red world than in the green world.

In the green world, people will sometimes lend money, in return for a promise to give back that money, plus interest, at some future date.

In the red world, people will sometimes borrow money, in return for a promise to take back that money, plus interest, at some future date.

In both worlds, people are not allowed to have negative net wealth, in case they die leaving a negative bequest to their heirs.

This law is much harder to enforce in the red world than in the green world.

In both worlds, the central bank, which issued the paper money, may decide to pay positive (or negative) interest to people who hold that paper money, by giving them more money (or taking money away).

Negative interest rates are hard to enforce in the green world, and positive interest rates are hard to enforce in the red world.

MV = PY works fine in both worlds, except both M and P are negative in the red world.

But slightly different things happen if M halves, so there is a shortage of money at existing prices.

If there is a shortage of money in the green world, there is a fall in trade, and an excess supply of goods, because people stop buying goods. This causes sellers of goods to cut their prices (prices halve), so less money is needed to buy the same volume of goods, so the shortage of money is eliminated.

If there is a shortage of money in the red world, there is a fall in trade, and an excess demand for goods, because people stop selling goods. This causes sellers of goods to raise their negative prices (prices halve), so less money is needed to sell the same volume of goods, so the shortage of money is eliminated.

Then, in both worlds, the central bank decides that it is too much of a hassle enforcing all the laws. So it insists that all money be deposited in the central bank to make it easier for the central bank to monitor who owns what money, to prevent unauthorised creation, destruction, and transfer of money, and to make it easier to pay interest. The central bank creates a box for each person, puts their money in that box, and transfers money between those boxes when it gets their consent to make those transfers.

In both worlds, a rumour spreads that the central bank has actually destroyed all the money, and is simply keeping a record on a ledger about how much money is supposed to be in each person's box. But economists say that rumour has no empirical content; it doesn't matter if it is true or false.

Then the two parallel worlds merged into one world. The combined world used both green notes and red notes as money.

If the combined central bank finds a person has 6 green notes and 2 red notes in his box, it tears up 2 green and 2 red notes, leaving 4 green notes. If the combined central bank finds a person has 2 green notes and 6 red notes in his box, it tears up 2 green and 2 red notes, leaving 4 red notes. And when it adds up all the notes across all the people, it finds the total number of green notes is exactly the same as the total number of red notes.

And then some New Keynesian macroeconomists said that money didn't exist in the new combined world. They said there was no "cash", only "credit".

They were wrong.

[I think I've got this right. But the bit about halving the money supply was hard to get my head around.]

Comments

[Anon]

But Nick, so what? I don't see how it matters whether we call it money or not. The question is whether there is some measure of its quantity that has any real macroeconomic relevance. If M=0 that only goes to show you that there is no meaning at all in MV=PY.

No matter how much net M you put in your economy you end with the same effective model, as I described this morning:

"if you have agents with loans between them who must transact goods by changing their loan balances and you change the interest rate on those loans, then the best available intertemporal consumption allocation will be suboptimal. I can write down that model and solve it. I can also simulate it with many rational agents making rational optimizing choices on a computer and get the same result."

The total quantity of M doesn't change the equilibrium allocation at all, given the level of Rb.

[Anon]

I'm assuming that anybody in your final world can create green and red notes so long as they create them in equal quantities, is that correct? Also, was I correct that you intended for M to be zero in that final world?

[RPLong]

With the right kind of compounding interest, the green world will become the red world.

[Nick Rowe]

Anon: "I'm assuming that anybody in your final world can create green and red notes so long as they create them in equal quantities, is that correct?"

No. Only the central bank can create green or red notes.

"Also, was I correct that you intended for M to be zero in that final world?"

Hmmm. The total net value of red and green notes is zero. The total gross value is not zero. Both can be used as media of exchange. Which is M?

But I don't think it really matters much if they net to zero in the combined world.

Dunno. I'm still getting my head around all this.

(Arguing with you was a large part of my inspiration, of course. Thanks!)

[Anon]

You're welcome. Thank you!

"No. Only the central bank can create green or red notes."

OK. Then it's not the real world. In the real world the banking system just intermediates credit. Debits and credits are not independently conserved or controlled by the central bank (only the net). Private agents can create as much of each as they want, so long as they do so in equal amounts. In order to preserve your monetarist logic that the central bank could still halve the quantity of money by halving each of the red and green notes (just like before you put the worlds together) you broke reality.

[Ralph Musgrave]

Negative interest rates (popular in the economics profession at the moment) are a great idea. When the rate is minus 4%, I’ll borrow enough to buy up 100 houses a year, knock down 2 of them, then sell the remaining 98. That leaves me with a profit, doesn’t it? Alternatively I might buy an office block and leave it empty. As long as the depreciation etc is less than the interest rate I’d make a profit while actually destroying wealth: the opposite of the basic purpose of economic activity.

[Alex Godofsky]

Nick:

No. Only the central bank can create green or red notes.

But... when I give someone a green note (through my central bank account) if that person's account holds red notes then both a green and a red note are annihilated. Eventually wouldn't this lead to the complete annihilation of the stocks of both notes?

Maybe I'm not understanding something. Is there a real-world object I'm supposed to understand the red notes as an analog of?

[Frank Restly]

Nick,

"In the green world, it is illegal for anyone except the central bank to create money. And only the government is allowed to take your money without your consent.
In the red world, it is illegal for anyone except the central bank to destroy money. And only the government is allowed to give you money without your consent.
In both worlds, people are not allowed to have negative net wealth, in case they die leaving a negative bequest to their heirs.

I think you need to modify something here. In the green world the government is allowed to take from you a portion of your income without your consent. Governments typically tax income (a flow) rather than wealth (a level). A government can't take more income from you that what you obtained. In the red world the government is allowed to give to you a portion of your income without your consent. A government could conceivably give you more income than what you obtained or could give you an income even if you did not have one.

"If the combined central bank finds a person has 6 green notes and 2 red notes in his box, it tears up 2 green and 2 red notes, leaving 4 green notes."

How does the central bank always destroy 1 green note for every 1 red note (maintain green note / red note parity) when a government may give out more red notes than they take in green notes?

[Nick Rowe]

Alex: what I meant was you cannot have counterfeit red and green notes. The central bank can create them.

Ralph: real interest rates on currency are currently negative. Because they are 0% nominal and inflation has been positive. They were even more negative a few years back.

[Lord]

The borrower would instruct the bank to give a number of red notes (IOUs) to the creditor in exchange for that number of green notes and the bank would create the red notes as needed, but they would only create the green notes if the creditor was borrowing from them. Red notes probably preceded the origination of green notes historically and people developed color blindness/negatives, thinking of red notes as green ones.

[Lord]

It's trickier than that since IOUs would still flow in the opposite direction as the goods. It would have to be more along the lines of a charter/stamp tax identifying the goods as legally tradeable. The borrower would receive the red notes along with the green?

[Peter N]

Ralph,

You have to satisfy a no arbitrage condition, so real interest rates have to so negative that you make no money. You'll get on average less than $0.96 on the dollar for your houses. This, of course, ignores any risk and liquidity premiums.

[Marko]

RM said :

"...I’d make a profit while actually destroying wealth: the opposite of the basic purpose of economic activity. "

Lots of people have been practicing for this , and they're getting pretty good at it.

If we want to see moral hazard on steroids , all we have to do is continue with ever more negative real interest rates. It's insane.

On the other hand , I might be well-suited for a world that rewards you for negative productivity growth , so maybe there's something to this after all......

[Squeeky Wheel]

I think that prices are less sticky in the red world. In the green world a shortage of money means that at t=0 consumers see they can't buy as many goods and reduce purchases. At t=+1epsilon, sellers see that they have sold fewer goods and reduces prices. In the red world, the seller sees at t=0 that he lacks the money to make sales. He can adjust at t=0. In the red world the information about shortage of money gets to the price setters faster. (I think)

If buyers set prices (ala Priceline) perhaps the green world would adjust faster?

In a purely double auction world, perhaps they are the same?

It seems really hard to enforce limits on how much red money someone can hold. Wealth would be determined by a) capacity to hold red money (more red money = I have acquired more goods) - credit - and b) rate of getting rid of red money (my employer takes red money from me). In the red world credit capacity is a global property - everyone who 'sells' me something is increasing my 'debt' level but it's unlikely we could get the red money back to them if there is a 'default'. Finally, how does one save? Savings in the red world would be negative money? My brain hurts.

[Nick Edmonds]

Nick,

Very nice to see a post on negative money - I think it's a good way of highlighting some of the problems with interpreting velocity. A few points:

1. There should be no reason why you need to assume they net to zero. They don't net to zero in the real world.

2. If you want to add commercial banks into the picture, I think it works best to replace "the central bank" in your story with "the banking sector" with this taken to include the central bank. In addition to positive and negative checking account positions, the sector will also have other financial assets and non-money liabilities.

3. Negative P? I think you will tie yourself in all sorts of knots with that, especially in your final world with both types of money.

4. I don't think I agree with your description of what happens with a shortage of money in the red world. Let's say this comes about because people spontaneously decide they want to hold greater (negative) balances. To do this they have to spend more on goods (or other financial assets). This will push up prices, which will reduce the value of their existing negative balances. So in isolation, this will not restore equilibrium.

However rising prices will deflate the real value of other financial assets. Even with negative money, we would normally expect net outside financial assets to be positive, so this would tend to counter the effect. In practice, what we would expect to see would be people meeting their requirement for more negative money by placing more into bank time deposits (thereby reducing - making more negative - their checking account balances).

[Ludovic Coval]

Pr Rowe

"If there is a shortage of money in the red world, there is a fall in trade, and an excess demand for goods, because people stop selling goods. This causes sellers of goods to raise their negative prices (prices halve), so less money is needed to sell the same volume of goods, so the shortage of money is eliminated."

I'm bit perplexed by this one. In green world increasing money is an objective, in red world it is the opposite : lowering money is an objective (since government give money without consent).

Now in case of money shortage would not sellers try to lower their stock of red money by lowering negative price thus doubling price ?

[Nick Rowe]

Dear all: I'm still trying to get my head around this. It *seemed* to make some sort of weird sense at the time, but I really don't know.

A negatively priced real commodity (i.e. a "bad", like garbage that you want to get rid of, and would pay someone to take off your hands) seems to be able to work as a medium of exchange. And there would seem to be a well-defined demand function for such a money. If you hold too little money, you can't sell things, so you would try to buy more than you sell in order to increase your stock of garbage money.

Now replace that real garbage money with a convertible red paper money, which is an obligation to accept a fixed quantity of garbage. That red paper would have a negative value, just like the garbage that backs it, and would also work as a medium of exchange. Now suspend convertibility (just like in the real world). Could not that red paper continue to have a negative value? If you are not allowed to throw it away? Damn. I don't know.

[Anon]

Nick,

"It *seemed* to make some sort of weird sense at the time"

I followed it the whole way along. You were trying to demonstrate that credit money is equivalent to outside money because it is a combination of two outside money systems: one positive money and one negative money system. I think your negative money works fine, and the two also work in combination. (Depending how you model exchange, you might want to do green as cash in advance, and red as cash in arrears, but whatever.) And if the quantity of each mattered before we combined them, it should still matter after. It was pretty clever, but you did some strange stuff towards the end.

First you cancelled some green money with some red, thus reducing the quantity of both. That seems to be contractionary in a constant velocity economy.

Second, you don't allow private agents to create red and green notes in combination. This, I guessed, is because that would break the monetarist argument that the CB can control PV by raising M at constant V. But it also means that your economy is nothing like the real economy in which debits and credits can be created arbitrarily as transactions occur, and private agents have no need for the banking system to create any net money at all. They just need to provide a central booking system for debits and credits created in the process of transactioning goods.

[Anon]

Actually, they are both cash in advance, so scratch that parenthetical comment.

[Enonymous]

Excellent post! Very thought provoking.

I didn't understand the last part about why the New Keynesians were wrong. Could you elaborate?

It seems to me that that the main differences between cash and credit are:

1. Credit has a default risk while cash does not: if I own claims on others (i.e., credit) there is some uncertainty about whether it is convertible into cash.
2. Only the central bank can create or destroy cash while anyone can create or destroy credit.

You seem to imply that just because the central bank tears up all the paper then cash becomes credit. This seems confusing to me since I always interpreted credit as something which anyone can create.

Finally, I think there is an important asymmetry in the red and green worlds. In the green world, if you have no cash then the government can not take it away. You are bankrupt. The government can create a claim on your future cash earnings but that isn't the same as taking your cash because you may never pay. In the red world, the government can give you all the red money in the world if it wants to. Note that in the green world, you basically have no consumption (except perhaps barter) while in the red world you can continue consuming by accepting more and more red money.

You address this by saying that nobody is allowed to have negative wealth and this is hard to enforce. I think this is the key difference between red and green worlds, why most money systems are "green", why credit and cash are different, and so on. You could even go so far as to say that a credit crisis occurs when you can no longer enforce this condition (no negative net wealth) on a significant fraction of the population in the green world.

Thanks again. I look forward to any clarifications you may have to my understanding,
-E

[J.V. Dubois]

Nick: "If you hold too little money, you can't sell things, so you would try to buy more than you sell in order to increase your stock of garbage money."

If garbage is money then this sentence does not make much sense to me. Imagine that everyone can hold up to 100 Kg of garbage and then they have to get rid of it or they get sick and die. So the garbage is traded in the same direction as goods (as you wrote in your post) . You give somebody an apple AND 1 kg of garbage so that you can then accept 1kg of garbage from somebody else along with some other good.

The main problem with negative money is that there should be some cap to how much you may hold, otherwise you can accept infinite ammount of negative money which is the same thing as having ability to print money in green world. Morover, this cap has to be real in some way. If you for instance say that negative money makes you pay interest - in terms of negative money - then you can just pay interest by accumulatine ever more negative money until infinity. One way to solve this conundrum is to say that you can absorb negative money as long as it is backed by real assets. You need to pay collateral so you may have debt backed as collateral as negative money.

Now I am kind of in your position - how to make all this work with medium of exchage stuff? I think there are two possible ways to reconcile these two consepts:

1) Invoke medium of account function of money. Green money is medium of account. Stock of positive "green" money determines value of assets. Red money is pegged 1:1 to green money, and backed by collateral. Other assets that are all potential collateral are another step farther from red/green money.

1) Retain medium of exchange view of money and treat the whole "red money/green money/collateral/assets" dichotomy in the same way you now answer "gold/green papers with pictures of dead presidents" or "depreciating basket of goods/green papers with pictures of dead presidents" question

[Nick Rowe]

Anon: "First you cancelled some green money with some red, thus reducing the quantity of both. That seems to be contractionary in a constant velocity economy."

Yep. That is one of the things I'm unsure about.

"Second, you don't allow private agents to create red and green notes in combination."

I wanted to keep it simple, so that the central bank is the only bank, and central bank money is the only money. But I also wanted to keep it like the simplest NK model, which makes the same assumption, so each agent has an account at the central bank, so we can focus on the most important question: "Is what is in that account 'money' (medium of exchange)?"

Arguing for "monetarism" is a secondary concern. My primary concern is to argue that NK models really do (at least implicitly) have money in them, and that they are models of monetary exchange economies. I am arguing for Clower, rather than Friedman. Old-school disequilibrium macro (Clower, Leijonhufvud, Benassy, Barro-Grossman) rather than old school monetarism.

[Nick Rowe]

Above all, I wanted to attack the Woodfordian distinction between cash and credit. To me, the important distinction is between things that are and are not used as media of exchange.

[Enonymous]

I like your point about red money backed by garbage.

I think this is on the right track but still not quite right. What if I was willing to accept an infinite amount of garbage?

I think better is something more Draconian like assuming that each agent has a known, finite life (say N=100 years) and each unit of red money is convertible by reducing your life span by 1 year. Provided the government enforces convertibility when your amount of red money exceeds your remaining life span, enforceability of the no negative wealth condition is solved. I think this solves a lot of issues between the asymmetry of red and green money. It doesn't have to be years of life, you just need to have some finite resource backing the red money.

One generalization you could apply is to allow people to be created at a fixed or random rate. I think this would be analogous to gold backing green money being discovered and mined at a fixed or random rate in the sense that both allow the stock of green or red money to increase in an asset backed as opposed to fiat money system.

If you want to generalize further and get away from the finite limit, you could have the red money backed by some commodity that increases your chance of death scholastically (e.g., radioactive garbage). This still means that enforceability is tough in the red money world but still ensures that there is negative utility to owning the red money.

[Nick Edmonds]

"It *seemed* to make some sort of weird sense at the time"

It should make sense, because it's the real world isn't it (at least once you've made it book entry)? If you and I are both already overdrawn and I buy goods from you, isn't that you transferring negative money to me?

[Anon]

"But I also wanted to keep it like the simplest NK model, which makes the same assumption"

This is just not true, Nick. Here's Eggertsson and Woodford 2003: "For simplicity we shall assume complete financial markets and no limits on borrowing against future income." No limits! Private agents decide how much they want their credit balance to be. In your world if you want to sell me a $2 banana, either

1) I must have two greens;
2) you must have two reds;
3) I must have one green and you must have one red.

Otherwise we can't transact. In Woodford's world my account is debited by $2 and your's is credited with $2. There is no limit, whatsoever, to the total quantity of red and green credits as private agents are creating them at will. Therefore we can always carry out any intertemporally pareto improving transaction. In Woodford's world the only consequential "monetary" consideration is the real rate. In yours, we need to understand how the mechanism of exchange limits the possibilities of exchange (independently of its effect on the real rate).

[Nick Edmonds]

Anon,

I think that's because in Nick's version, the central bank is always cancelling out reds and greens, but not doing the reverse. If it was allowed to sometimes do the opposite - say simultaneously adding two reds and two greens to someone's account, then your transaction would be possible.

[Nick Rowe]

Enonymous: I was thinking about garbage that gave disutility to the owner, by being smelly, or ugly or something. The opposite of gold, or shells, which give utility because they are pretty. Then having convertible paper money. Green money is convertible into shells (a call option for shells), and red convertible into garbage (the issuer has a put option).

Nick E: I think that's right.

Anon: I was worried about the transversality condition in the red world (why wouldn't someone just keep on buying goods and holding more and more red money?). There's the cash in advance condition, and the transversality condition.

Yep, in NK models, the amount of money created by the central bank is unlimited, given Rm and the demand for money. I would need to make my model like that, to make it an exact replica.

[Anon]

Nick Edmonds,

"If it was allowed to sometimes do the opposite - say simultaneously adding two reds and two greens to someone's account, then your transaction would be possible."

Not "allowed" to. *Required* to, at the demand of the account holder. Now it's the NK model.

Nick,

"I would need to make my model like that, to make it an exact replica."

Right. And then your statements about halving the money supply no longer make sense.

[Nick Rowe]

Enonymous: "It seems to me that that the main differences between cash and credit are:

1. Credit has a default risk while cash does not: if I own claims on others (i.e., credit) there is some uncertainty about whether it is convertible into cash.
2. Only the central bank can create or destroy cash while anyone can create or destroy credit."

I find the concepts "credit" and "cash" unhelpful. I prefer "IOU's" and "money".

An IOU is a promise to pay something. That something might be money or it might not. So there is a default risk. That IOU might be used as money, or it might not.

"Money" means medium of exchange/unit of account. The good that is used as money might be an IOU (convertible money); it might be intrinsically valuable (commodity money), or it might not (Bitcoin).

"You address this by saying that nobody is allowed to have negative wealth and this is hard to enforce. I think this is the key difference between red and green worlds, why most money systems are "green",..."

I agree. The laws in the red world would be impossibly hard to enforce. It is much easier to destroy or throw away red money than to create or steal green money. And it would be impossible to prevent people having a massive stash of red money when they die.

But note that NK models assume this problem away too. Why can't people spend like crazy, run up a massive obligation to the central bank, then die or disappear? In the green world, you just have to deter counterfeiters and thieves. That is why the real world is more like the green world than the NK (red/green) world. The only red is where you really know the person who is in the red to you.

[Nick Rowe]

JV: "You give somebody an apple AND 1 kg of garbage so that you can then accept 1kg of garbage from somebody else along with some other good."

Yes, but if you don't have 1 kg of garbage, you can't sell your apple.

In the green world, if you have no money, you must sell goods before you can buy goods.

In the red world, if you have no money, you must buy goods before you can sell goods.

In both worlds, if buying and selling opportunities are scarce, and arrive at random, you will be unable to realise some of those opportunities if you don't have a big enough stock of money.

[Nick Rowe]

If money pays positive interest Rm, and if you can borrow or lend money at Rb, then Rb-Rm is the opportunity cost of holding money in the green world.

What is the opportunity cost of holding money in the red world? My brain is fried, with all the negatives!

[Nick Rowe]

If money is more liquid than bonds, and if people value liquidity at the margin, then:

In the green world, Rb > Rm.

In the red world, Rm > Rb.

If so, then in the red/green combined world, Rm(red) > Rb > Rm(green).

Yep, I think that's right. That's what the Bank of Canada does, provided you are a commercial bank. And that's what commercial banks do, provided they can track you down so you can't destroy your red money.

[Tom Brown]

Nick, I usually come here to read about apples, bananas, cows and the occasional haircut or painting, but I'm liking these new additions to your cast of characters (red & green money). I especially like the idea that the red money might be "backed by garbage." I hope Mike Sproul chimes in.

[Nick Rowe]

Thanks Tom! (And thanks for your comment on the other Mike's blog.)

Anon: "Right. And then your statements about halving the money supply no longer make sense."

Start in equilibrium where Rm(red) > Rb > Rm(green). Some people have only green notes in their box at the central bank, and some people have only red notes. (No individual would have both green and red).

Let G be total number of green notes, and let R be total number of red notes. Define M=G+R.

1. Assume G=R. Now let the central bank double both G and R. (If I have one red in my box, I now have two reds). Hold Rm(red) and Rm(green) constant. Under perfectly flexible prices, P doubles, and we are back in the original equilibrium. The Quantity Theory rides again!

2. Assume G=/=R. Again, double both G and R, for each individual. Same result.

3. Double M by increasing G and holding R constant. (And if any individual cancels a red and green, increase G so that M stays doubled. Same result, except for wealth transfers, that can be offset by doing it through an OMO.

[Frank Restly]

Nick,

"Both worlds use bits of coloured paper as money, because barter is very difficult. The green world uses green paper as money, and the red world uses red paper as money. The green paper money has a positive value. The red paper money has a negative value."

With red money, the purchaser of the good has all the physical evidence that a transaction has taken place. And so the purchaser can seek legal recourse without cause.

Judge: Mr. Purchaser state your case
Mr. Purchaser: I agreed to take a car and 40 red notes. Instead I got a car and 60 red notes
Judge: Mr. Purchaser present your evidence
Mr. Purchaser: The car is sitting in the lot and here are 60 red notes
Judge: Mr. Seller state your case
Mr. Seller: I agreed to sell a car and 40 red notes.
Judge: Mr. Seller present your evidence
Mr. Seller: The purchaser has the car sitting in the lot and 40 red notes

[Too Much Fed]

Anon's post said: "You're welcome. Thank you!

"No. Only the central bank can create green or red notes."

OK. Then it's not the real world. In the real world the banking system just intermediates credit. Debits and credits are not independently conserved or controlled by the central bank (only the net)."

Agreed.

In the real world, demand deposits of commercial banks and currency are 1 to 1 convertible. That makes the DD's medium of account (MOA). They are also medium of exchange (MOE).

Also, the reserve requirement is not 100%, and the capital requirement is not 100%.

The central bank is not in total control of "money".

[Tom Brown]

Nick, did you ever think about writing a children's book about monetary economics? I could illustrate it for you. I can't imagine there's much competition for that niche.

[Squeeky Wheel]

Nick: "1. Credit has a default risk while cash does not: if I own claims on others (i.e., credit) there is some uncertainty about whether it is convertible into cash."

In Myanmar "the old government also used to screw with the money all the time. Officials would suddenly announce that certain denominations of the local currency were worthless." (http://www.npr.org/blogs/money/2013/05/10/182309623/why-almost-no-one-in-myanmar-wanted-my-money)

Cash is a liability of the government/central bank. There is default risk if the government chooses to default on cash (Myanmar) or effectively defaults by making it worthless (Zimbabwe). There's lots and lots of (old) cash in the world which is now worthless. All fiat money is credit / willingness to accept. Some credit is just better (and thus more liquid) than others. Commodity backed money is the same - it's still a promise to convert, and thus based on the good faith of the issuer of the currency. Real goods don't have this issue, but they tend to be lousy mediums of exchange.

[Tom Brown]

... I'm thinking about how to draw the "New Keynesian macroeconomists" though, whose "wrongness" in this tale makes for a happy ending of sorts. Any ideas? Something like:

http://media.economist.com/images/20081108/D4508BB1.jpg

[Nick Edmonds]

"If so, then in the red/green combined world, Rm(red) > Rb > Rm(green)."

In the green world, if I use my liquidity, it reduces the balance of my green money. The amount of liquidity I have is therefore based on the amount of green money I hold. The cost of holding that amount is therefore what matters.

In the red world, if I use my liquidity, it increases the balance of my red money. The amount of liquidity I have is the maximum amount of red money others will allow me to have, less what I already have. The cost of holding my existing red money is therefore not the right measure.

I could, however, calculate a cost of liquidity as the difference between the amount I pay for a term borrowing less the amount I receive on ready (green) money. This would probably be Rb-Rm again. We could interpret red money as term borrowing, but I don't think that's consistent with the general approach here. Borrowing through overdraft for example is usually repayable on demand.

Alternatively, an obvious measure of the cost of liquidity would be the amount paid as commitment fees on undrawn liquidity facilities. Having a committed undrawn facility is similar to having a term borrowing and ready cash.

If we do take red money as representing overdraft, repayable on demand, then in theory Rm (red) should be less than Rb for the same party (i.e. the party that is holder of red money or borrower of green money), because Rb represents a longer commitment for the lender and therefore greater liquidity transfer. In practice, it may not, because various complicating factors come into play.

My own latest post was prompted by yours here: http://monetaryreflections.blogspot.co.uk/2014/02/velocity-and-negative-money.html

[Alex Godofsky]

Nick:

In the green world, if you have no money, you must sell goods before you can buy goods.

In the red world, if you have no money, you must buy goods before you can sell goods.

In the red world, if you can't sell your goods for lack of money that's just fine! In the red world, the only purpose of selling goods is to get rid of money; if you have no money you have achieved your goal.

[Nick Rowe]

Alex: In both worlds, value of goods you sell must equal value of goods you buy, over your lifetime. In the red world, if you miss a good selling opportunity, because you don't have enough red money, that means you can't buy as much in future.

Think of people buying and selling services, meeting at random in the forest. You are unemployed unless you meet someone who wants to buy the service you want to sell. But, in the green world, unless the person who wants to buy has enough green money, there is no trade. And in the red world, unless the person who wants to sell has enough red money, there is no trade.

[Peter N]

In the red world, if you miss a good selling opportunity, because you don't have enough red money, that means you haven't bought enough in the past.

In the red world, I have to pay to work. Without some disincentive to holding red money and/or limit on the amount that can be held, nobody would work without some other utility (status, enjoyment, fringe benefits...). In fact the only reason to sell with red money instead of barter is the need to get rid of red money. This is fiat money with a vengeance.

Someone with bad debit would have to buy in small amounts and then immediately work to get rid of it. In bankruptcy, there would be no creditors. Instead there would be debitors - people who agreed to supply consideration now for promises to accept red money in the future.

Of course debitors would expect to be able to pay interest on the credit, so credit service would involve receiving red money.

Credit securities would involve the issuer receiving interest payment during the term and a principal payment at maturity.

Now imagine running the movie backwards.

[Nick Rowe]

peter N: "In fact the only reason to sell with red money instead of barter is the need to get rid of red money."

That's not quite right. Barter is very difficult. Coincidence of wants and all that.

It's like saying: "the only reason to sell for green money instead of barter is the need to get some green money."

Yep. People who own red money have bought more than they sold. There needs to be some limit on people doing that, just like in the real world. Otherwise they die with negative wealth.

[Min]

"Both worlds use bits of coloured paper as money, because barter is very difficult. The green world uses green paper as money, and the red world uses red paper as money. The green paper money has a positive value. The red paper money has a negative value."

Frank Restly: "With red money, the purchaser of the good has all the physical evidence that a transaction has taken place. And so the purchaser can seek legal recourse without cause.

"Judge: Mr. Purchaser state your case
Mr. Purchaser: I agreed to take a car and 40 red notes. Instead I got a car and 60 red notes
Judge: Mr. Purchaser present your evidence
Mr. Purchaser: The car is sitting in the lot and here are 60 red notes
Judge: Mr. Seller state your case
Mr. Seller: I agreed to sell a car and 40 red notes.
Judge: Mr. Seller present your evidence
Mr. Seller: The purchaser has the car sitting in the lot and 40 red notes"

The evidence would be more like this.

Mr. Seller: Here is my receipt for the sale of the car with 40 red notes, signed by the purchaser.

[Frank Restly]

Min,

In the red world, why wouldn't both receipts go to the purchaser of a the car? Purchaser of car receives car, red notes, receipt for car received, and receipt for red notes received. And you are assuming that the red world operates such that a receipt is recognized by the courts as evidence. Having no means to prevent forgery of receipts (central bank / government prevents forgery of red notes), the courts in the red world could rule them invalid.

[JKH]

Nick,

My version:

http://monetaryrealism.com/negative-money/

I think it should amount to about the same thing as a platform for discussing some of the issues of interest, but I've described it quite differently.

[Nick Rowe]

Good post JKH! Is it monetary unrealism, or just a different way of looking at monetary realism? Welcome to the Dark Side!

[JKH]

Thanks Nick.

It may be both.

:)

[Min]

Frank Restly: "In the red world, why wouldn't both receipts go to the purchaser of a the car?"

The thing speaks for itself.

Frank Restly: "Purchaser of car receives car, red notes, receipt for car received, and receipt for red notes received. And you are assuming that the red world operates such that a receipt is recognized by the courts as evidence. Having no means to prevent forgery of receipts (central bank / government prevents forgery of red notes), the courts in the red world could rule them invalid."

Forgery is a problem in any world. The Chinese used to use fingerprints (thumbprints, IIRC) instead of signatures, or in addition to them. The personal stamp, which is still in use, is also not easy to counterfeit.

[Lord]

If green notes are backed by government debt, then I suppose red notes are backed by government taxes. The government presents everyone with their tax bill in red notes and people sell their goods to pass off their bill to those selling to government.

[Frank Restly]

Min,

"In the red world, why wouldn't both receipts go to the purchaser of a the car? - The thing speaks for itself."

I agree that giving both receipts to the purchaser of the car would be strange / unusual, but it would be no stranger than negative money.

"Forgery is a problem in any world."

Agreed. And so a legal system has to deal with the possibility of forgery. It can rely on government sponsored anti-forgery devices (fingerprint identifiers, personal stamps, etc.) or it can preclude items that are subject to forgery as evidence.

One other thing - suppose in this red world, the government / legal system has an anti-forgery receipt detector - for instance all receipts must be printed on special green paper with special insignias all provided by the government. Are receipts green money in a red money world?

[Majromax]

@Nick:

> In the red world, if you miss a good selling opportunity, because you don't have enough red money, that means you can't buy as much in future.

> Think of people buying and selling services, meeting at random in the forest. You are unemployed unless you meet someone who wants to buy the service you want to sell. But, in the green world, unless the person who wants to buy has enough green money, there is no trade. And in the red world, unless the person who wants to sell has enough red money, there is no trade.

I don't think that follows. If I can mow your lawn and give you 10$Red, but I only have 5$Red at the moment, then I have no fiscal inability to mow your lawn with 5$Red. I might not consider it worth my time, but that's all.

Mowing your lawn with 5$Red does not "mean I can't buy as much in the future" -- I can buy exactly 5$Red more of goods in the future. Not providing the service leaves me "poorer" as then I won't be able to even buy the extra 5$Red worth of future services.

I think the functional difference is that I can accumulate $Green without positive bound, but I cannot go below 0$Red. If the person I wish to trade with does not have enough $Green, then I can rationally not trade now because I expect to get more $Green from someone else later. If I do not have "enough" $Red, then I am in no better position if I wait for the next person to come along.

[Nick Rowe]

Majromax: If you originally had 10 red, you could mow the lawn for 10 red, then go buy a meal for 10 red. You end up with the same 10 red as you started, but a full belly in exchange for mowing the lawn. If you miss an opportunity to mow a lawn, you miss an opportunity to eat a meal, if you keep your beginning and ending stock of red the same.

[Majromax]

@Nick:
> You end up with the same 10 red as you started, but a full belly in exchange for mowing the lawn.

But that's not the shortage. Pretend now I have 5 red but everything else remains the same:

If I mow the lawn for 5 red and buy a meal for 10 red, I end up with a full belly, 10 red, and a lawn-mowing workout. That's the same outcome as if I had 10 red to begin with.

Consider the same situation in green world, where I start with 0 green.

If I mow the lawn in exchange for 10 green and then buy a meal with it, I end up with 0 green, a full belly, and a workout.

If my neighbour only has 5 green, then there's the shortage. If I mow the lawn in exchange for 5 green (lowering prices), I can't buy a meal. I end up with 5 green, an empty belly, and a workout.

The distinction is that a shortage of red means that I may be required to provide services with fewer $Red for exchange, but I can always end up in the same place as if there was no shortage. A shortage of green, on the other hand, constraints my opportunity to purchase.

Whether or not I had 5 or 10 red to start with, I end up with a full belly, 10$Red, and a workout for the exchange of my labour. That means I should be indifferent to the starting situation (at least insofar as I couldn't weed-whack someone else's lawn for a fair price of 5$Red).

Whether or not my neighbour has 5 or 10 green to start with *does* make a difference; the 5 green situation makes it impossible for me to indirectly trade my labour for a meal.

Although the accounting is identical save for the sign in front of the currency, the worlds are different: the no-credit red world has a *cap* on one's wealth (it cannot ever go above 0$Red), but the no-credit green world has a *floor* on one's wealth (it cannot ever go below 0$Green).