Monetary policy in New Keynesian models is Gesellian

In one important respect, what we call "New Keynesian" macroeconomic models are in fact New Gesellian macroeconomic models. That's only in one respect, but it is important.

Silvio Gesell proposed a tax on currency. The higher the tax rate, the faster people would spend that currency. A tax is a negative subsidy. The higher the subsidy rate, the slower people would spend that currency.

Another name for a subsidy on currency is paying interest on currency. If that interest rate is 5%, for every $100 currency you hold, the bank that issued that currency pays you $5 currency per year.

If I hold a $20 banknote, issued by the Bank of Canada, it is as if I have a chequing account at the Bank of Canada with $20 in it. If I buy something from you, and give you that $20 banknote, it is as if I wrote you a cheque for $20, instructing the Bank of Canada to transfer $20 from my account at the Bank of Canada to your account at the Bank of Canada. It is as if we keep our $20 banknotes in little boxes at the Bank of Canada instead of in our pockets, and when I buy something from you the Bank of Canada switches one $20 banknote from my box to your box. These are just different ways of keeping a record of payments.

Imagine a world where every individual has a chequing account at the central bank. There are no other banks, and no other forms of money. People use cheques drawn on their accounts at the central bank to buy everything. The balance in any individual's chequing account can be either positive or negative. But the central bank puts a limit on how big your overdraft can be, to ensure the no-Ponzi condition is satisfied. You can't have an overdraft bigger than your total human and non-human wealth.

The central bank in that world can choose to pay whatever rate of interest it wants on positive balances, and charge whatever rate of interest it wants on negative balances. It's a purely administrative decision.

Suppose the central bank chooses to pay the same rate of interest on positive balances as it charges on negative balances. Nobody would choose to borrow at a higher rate of interest than that set by the central bank. Nobody would choose to lend at a lower rate of interest than that set by the central bank. So there will be no private borrowing or lending between individuals.

Suppose the positive and negative balances in those chequing accounts across all individuals sum to zero. The central bank itself has no assets except the negative balances, and no liabilities except the positive balances, and the two exactly cancel out. If one individual buys something for $20, his account goes down by $20 and the seller's account goes up by $20, so the net balances stay at zero. The central bank earns zero net revenue, because the interest it pays on positive balances exactly matches the interest it charges on negative balances. And suppose the central bank has zero administrative costs. The central bank therefore earns zero profits.

I have just described the monetary system of a New Keynesian macroeconomic model.

Monetary policy in that model is Gesellian, except the tax on central bank money is normally negative. It's a subsidy on positive balances, and a tax on negative balances. The central bank calls that negative tax rate "the rate of interest". If the central bank wants to speed up spending it reduces that rate of interest; if it wants to slow down spending it increases that rate of interest.

New Keynesians say their models are models of a "cashless" economy. We should ignore them. Forget what they say, and watch what they do with the equations. If there is no "cash", how can the central bank set the nominal rate of interest? If there is no "cash", how can the central bank influence people's spending decisions? What is it that people are spending when they buy goods? If it's a "cashless" economy, how come underemployed workers, who want to trade their labour for each others' consumption goods, don't just do a barter deal to get back to full employment?

It all makes perfect sense when you realise that there is money in the New Keynesian model, and people need to use that money to trade, and people spend that money when they buy things, and it is central bank money, and the central bank sets the rate of interest it pays on holdings of central bank money.

The only thing that doesn't make sense is the zero lower bound on nominal interest rates. The zero lower bound is an ad hoc constraint on the central bank's monetary policy that is stuck on afterwards.

And the real world does look very different. Very little borrowing and lending is done on the books of the Bank of Canada. Only commercial banks and the government have chequing accounts at the Bank of Canada that pay interest. Bank of Canada currency pays 0% nominal interest. Does it matter? It probably does, sometimes.

Comments

[Kevin Donoghue]

Nick, your desire to bring money into everything is reminiscent of Solow on Friedman. As I understand Gali's textbook model (the only NK model I know) it's cashless only in the sense that every agent holds precisely $0 in cash at the close of business each day.

If it's a "cashless" economy, how come underemployed workers, who want to trade their labour for each others' consumption goods, don't just do a barter deal to get back to full employment?

Workers aren't endowed with any goods; labour is all they can offer. True, the households own shares in firms, but they don't control the firms, so they can't just swap the firms' output and thumb their noses at the Calvo fairy. The NK model, whether you like it or loathe it (I do a bit of each), is as internally consistent as any you're likely to find.

[Nick Rowe]

Kevin: that Solow quote is so funny. Can you remember the exact words?

"As I understand Gali's textbook model (the only NK model I know) it's cashless only in the sense that every agent holds precisely $0 in cash at the close of business each day."

That will be true if all individuals are identical. Because then all individuals choose to spend the same amount and so earn the same amount from others' spending, so they all end the day with the same balance they started the day. So if they start at $0 they end at $0. But even here, in order to solve for the symmetric equilibrium we have to ask whether an individual would choose to deviate from that equilibrium, and spend a different amount from every other individual and so end the day with a positive or negative balance. Plus, if we introduce (random?) differences between individuals, then in equilibrium some will end the day with positive and some negative balances.

The firms would need to be be participants in the barter deal too. A barter deal would make both workers and firms (shareholders) better off.

[Kevin Donoghue]

Solow: “Everything reminds Milton of the money supply. Well, everything reminds me of sex, but I keep it out of the paper.”

I don't think Gali really needs all individuals to be identical. But if some are more thrifty than others that causes a problem: since the households are immortal, the spendthrifts will eventually be up to their necks in debt. But, on Gali's assumptions even the thrifty won't hold cash, they will hold bonds.

As to barter deals, they are really just a way of circumventing the Calvo mechanism. What you seem to be saying is that if we eliminate the only friction in the model, we get a frictionless model. Isn't that a bit trivial?

Off-topic, but a comment on David Glasner's blog reminded my of another of your obsessions. This is Marriner Eccles in 1938: "Is it so hard to understand that when an individual owes money he generally owes it to another individual, but when a nation owes money it owes it to itself? When an individual pays a debt, he pays it to someone else. When a nation pays a debt, it pays it to its own people." You might want to read the whole thing, if you haven't already:

https://fraser.stlouisfed.org/docs/historical/eccles/077_03_0002.pdf

[Nick Rowe]

Kevin: yep. Great quote. And yes, I do get stuck on certain topics (like everyone else, I suppose). I've been having an interesting related argument with Steve Williamson on his most recent blog post. I'm not saying much here I haven't said before. But sometimes I can say it more clearly a second time around.

"But if some are more thrifty than others that causes a problem: since the households are immortal, the spendthrifts will eventually be up to their necks in debt."

With infinite lives, and a permanent difference in time preference, that does create weird results in any model, IIRC. But my brain has shut down. But we could have temporary differences.

"But, on Gali's assumptions even the thrifty won't hold cash, they will hold bonds."

Who would issue bonds if they pay a higher interest rate than the central bank sets? Who would buy bonds, if they pay a lower interest rate than the central bank sets?

"As to barter deals, they are really just a way of circumventing the Calvo mechanism."

I disagree. Even if those barter deals must take place at Calvo relative prices, there are still mutually improving deals to be done, if the real interest rate is wrong. I agree to consume more of your overpriced goods if you agree to consume more of my overpriced goods. (Plus they circumvent monopoly power too).

This is easiest to see if we start with all prices the same, hold prices fixed forever, then have the central bank stupidly raise the nominal (and real) interest rate. This will not cause a drop in consumption if they just keep bartering the same amount at the existing relative prices, which makes them all better off than if they all cut consumption.

[louis]

I know less than nothing about NK models... but as I understand it, the CB has control only over the daily rate of interest on currency. Lots of people sell bonds at higher interest rates than the overnight CB rate in the real world, because they want to hedge against future rate rises or ensure access to liquidity for term. Is there something about the NK models that would change this desire to issue bonds vs borrow at the CB?

[Nick Rowe]

louis: good point. If everyone is identical (as in the simplest NK models) then they won't want to hedge. But if they are different, they might.

[Jonathan]

I accept your story of the New Keynesian model. And it seems a decent approximation for monetary policy in general.

One view of money, that I agree with, is that there's nothing "special" about money: it's just an asset, which happens to be highly liquid. If a country's currency is in good standing, it's probably the most liquid asset in that country, but this isn't always true.

Conventional monetary policy means that the central bank makes a market in short-term government debt at a particular nominal interest rate. This has two effects: first it implies a distortion in transactions by affecting the interest rate spread between two assets (money and short-term government debt). And second, it moves the short-term real interest rate because of nominal rigidities.

Importantly, this latter effect has nothing to do with money, other than that it is implemented through the spread between money and bonds. What's being changed is the intertemporal price of real goods, at the cost of some monetary distortions.

New Keynesian models make a strategic simplification: they assume that these monetary distortions are second-order compared to the real interest rate effect. So we just don't worry about the fact that monetary policy is implemented by exchanging two different types of assets.

(Of course, when we do optimal policy we need to account for these distortions, but under some assumptions it turns out the inflation rate is a sufficient statistic to compute these distortions, so we again don't need to explicitly model money.)

Then the question is what this assumption costs us relative to the clear gain. One thing it costs us is the zero lower bound: since monetary policy is implemented by targeting a particular spread, and that spread (normally) can't be negative, there is a constraint on our policy that we lose by assuming the Fed can just set short-term real interest rates.

If we think the ZLB is first-order (which it is), then we want to model it. One option is to explicitly add back in money and bonds as two different assets, and model the conduct of policy through this margin. A second option is just to set a constraint on monetary policy that i>=0.

The latter certainly seems easier to me, but what does it cost us? It's not clear to me what you think we lose from doing this, other than that it is a modelling hack. But we economists are in the model hacking business, so this doesn't bother me.

[Kevin Donoghue]

Nick: Who would issue bonds if they pay a higher interest rate than the central bank sets?

In the NK model they're all AAA so they don't have to. I'm looking again at Gali, trying to get a sense of what is going on in the bond market. The central bank sets the one-period nominal interest rate. So what ensures that it doesn't end up being a net lender or borrower? It can only avoid that if the real interest rate, which is endogenous, is such that the representative household is deterred from either holding or issuing bonds. (There's no government in the basic model.) Now, I'm pretty sure that the algebra gives exactly that result, but Gali's exposition focuses on current and future price-setting in the goods market rather than the bond market. Once the equilibrium condition C(t) = Y(t) is met, then bonds outstanding B(t) = 0 also.

Now I come to look at it, it's funny that Gali tells us explicitly that C = Y is the goods market clearing condition, but never draws attention to the obvious implication, dB = 0 (& in fact B(t) = 0 for all t). Of course it's quite possible I'm missing something. Paging Adam P!

[JP Koning]

When Neo Keynesians say their models are cashless, do they mean without paper money? Buiter says in the link below that:

"The solution can be found in Woodford’s (2003) characterisation of a cashless economy. In such an economy, currency (of any kind) no longer exists but the government still issues a financial instrument that can be interpreted as the other (noncurrency) component of the monetary base: commercial bank balances held with the central bank or bank reserves for short."

http://willembuiter.com/numerairology.pdf

[Nick Rowe]

Jonathan: thanks.

"One view of money, that I agree with, is that there's nothing "special" about money: it's just an asset, which happens to be highly liquid."

I disagree with that a bit. Line up all the assets from most liquid to least liquid. It's only a difference in degree. But being at the very front of the line matters, because that is the one we would choose as a medium of exchange. And if everyone makes the same choice, that asset gets traded more than the sum of the trades of all the other assets, which makes it even more liquid. It's a winner takes all race. (Though perhaps not quite all.)

Kevin: "The central bank sets the one-period nominal interest rate. So what ensures that it doesn't end up being a net lender or borrower?"

Not 100% sure I've got my head 100% round this either. But if the central bank refuses to buy or sell bonds itself, (and refuses to buy or sell consumption goods itself) I don't see how it can end up a net borrower or lender. If an individual wants to sell a bond, or sell goods, he can only sell them to some other individual. So C must equal Y, and dB must equal 0, even if individuals are different. So the net position of the central bank must stay the same. Yes. I think I've got that right.

JP: good find. But that component can also net to zero.

[Min]

Solow: “Everything reminds Milton of the money supply. Well, everything reminds me of sex, but I keep it out of the paper.”

Is Solow a Nude Keynesian?

[Jonathan]

Nick: I thought you would take issue with my statement that there is nothing "special" about money (though it is somewhat secondary to the rest of my comment), so I will expand on it a bit, with the caveat that I don't think I have this all figured out. I'm quite open to being wrong -- in fact, if I'm even a little wrong (which I surely am!), I would very much like to find out about it, so I can be less wrong in the future.

Okay, to money (hear, hear!). One problem I have with your argument is that it seems a sort of "no true Scotsman" fallacy. If we DEFINE money as all approximately zero-interest nominal assets commonly used in exchanges, then it's true that money is pretty special. If we didn't have those assets, economic transactions would be much more costly, implying huge distortions in economic activity. But why are we defining money in this manner? In what sense am I using "money" when I use my debit card to draw on my account with Bank of America? How is that asset the same as a 20-dollar bill? If we just define them to both be money, we are begging the question! We are claiming that "money is really important to exchange", and then we define money as "that without which exchange is extremely costly"!

I think it makes more sense to say that there are many different sorts of assets, of which the most liquid are extremely liquid and used in most transactions. You can classify those assets as "money" if you like. But this is a statement about the equilibrium, not about an essential characteristic of those assets! In fact, many of the assets we categorize as "money" are just "highly liquid assets some private agent produced". By arbitrage, they're going to pay the same interest rate as government-issued money. But there's no fixed set of assets that you can isolate, and call money, as an eternal verity. The supply of liquid assets is endogenous.

So you could say "money is special!" But then somebody produces a new highly liquid asset that people start using for transactions, and I point to it and say "look, a close substitute for money!" Then you say, "Ah, but THAT'S money too!" (Hence the no true Scottsman).

We can look at historical episodes in which the government's supply of useful money was reduced in a way that severely affected trade, and observe that the economy responded by producing other liquid assets. In my original comment I used the example of foreign currencies being used when a country's own currency has become suspect, but you could list many other examples, many of which use private money. Sometimes this requires a black market to get around government regulation, but this happens.

This doesn't mean that government liquidity doesn't matter. When I said that there's nothing special about money, I considered writing "in general". Of course, governments can use their high market share in force to try to suppress other forms of liquidity. Moreover, since the private sector has a limited capacity to produce liquid assets, public liquidity will matter to some extent always, and CHANGES in public liquidity will matter still more because of costs in transitioning to a new monetary regime.

Anyway, I hope this clarifies my comment. I could go on, but I really should get back to my dissertation.

(Okay, one more comment: I guess you care a lot about quantities in the money market, while the New Keynesian model is all about prices. Of course, there is a duality here, so that the question becomes which is most important to focus on practically? I'm not sure why "You can't just talk about prices, what about the quantities?!" is right. In general, one should imply the other, and if we just care about the quantity of output and employment, the price of transactions and intertemporal prices are sufficient. We don't NEED to know what quantities correspond to a particular set of prices, we just need to know how government policies can move around the prices. I guess that was the main point of my earlier comment, and I would be interested in hearing your thoughts on why it's important IN GENERAL to consider the quantities explicitly in our models. Unless I'm misunderstanding your claim, which is quite possible!)

[Jonathan]

Okay, one more comment:

Suppose you had two sorts of assets in the economy, one slightly more liquid than the other. Then the equilibrium would probably be that nearly all transactions would use the more liquid asset. This is a sort of corner solution: when people are trying to decide which asset to use in transactions, they always pick the more liquid one.

But now suppose something happens to make the more liquid asset highly illiquid. Would this be a huge disaster? No, we would just switch to using the slightly more liquid (now much less liquid) asset for transactions!

So what matters is the cost of substituting between assets, etc.

Okay, last comment for today, I promise!

[Nick Rowe]

Jonathan: "If we DEFINE money as all approximately zero-interest nominal assets commonly used in exchanges, then it's true that money is pretty special."

I wouldn't *define* money as an approximately zero interest asset. I would define it as whatever people commonly use as a medium of exchange, and that asset could in principle pay any rate of interest, real or nominal.

"In what sense am I using "money" when I use my debit card to draw on my account with Bank of America? How is that asset the same as a 20-dollar bill?"

Well if the commercial banks have a clearing house, then very little (if any) base money needs to be involved when we pay by debit card/cheque on our accounts at commercial banks. I would count them as media of exchange too. It's the clearing house that makes them money in their own right. (I did a post on this once, trying to get my own head around it.)

But commercial bank promises to redeem its money in central bank money at a fixed exchange rate, and not vice versa, so the central bank is alpha and the commercial banks are beta.

But I agree that it is not written in stone that people will in fact choose to use a government asset as money. (Cubans often used US dollars even when it was highly illegal.)

"I guess you care a lot about quantities in the money market..."

Slightly off-topic, but I HATE the words "money market". ALL markets are markets in which money is traded (except barter markets)! You mean the market in non-money IOUs.

In this post I wasn't arguing quantities vs prices. I was trying to keep my head strictly within the New Keynesian perspective, just emphasising monetary exchange.

But in other posts I have tried to tackle that one. Not always successfully enough to my liking. The peanut theory of recessions was maybe one of my better attempts.

[Nick Rowe]

Jonathan: "But now suppose something happens to make the more liquid asset highly illiquid. Would this be a huge disaster? No, we would just switch to using the slightly more liquid (now much less liquid) asset for transactions!"

Aha! That's what you meant! Agreed. (But there would be a lot of hassle in the transition, if it's not handled right, like everyone learning a new language, see Zimbabwe, but you would probably agree with that.)

[W. Peden]

Great post Nick.

Have you commented on the negative bonds trading in Europe right now? What does this mean for the ZLB, if government securities can trade at less than 0%

[Majromax]

> I would define it as whatever people commonly use as a medium of exchange, and that asset could in principle pay any rate of interest, real or nominal.

What about "whatever people use as the medium of account, plus whatever can be widely exchanged on demand for goods and services at a fixed ratio to that unit of account?"

It's a bit awkward, but I'm trying to get at the separation between dollars and discounted bills. The latter were used for exchange, but not at par. Debit cards and previously cheques made demand deposits more moneylike than previously.

On the other hand, US dollars wouldn't be money in Cuba because while exchanged, prices are (presumably?) marked in Cuban pesos, with dollars exchanging at a variable rate.

[Nick Edmonds]

As you describe but for central bank read banking system. The interest rate is then set by the Central Bank as alpha bank with a vanishingly small balance sheet. that's what I understood "cashless" to mean.

[Frank Restly]

Nick,

"Silvio Gesell proposed a tax on currency. The higher the tax rate, the faster people would spend that currency. A tax is a negative subsidy. The higher the subsidy rate, the slower people would spend that currency."

Maybe, maybe not. If a tax on currency reduces the amount of currency in circulation (currency destruction), then what you say is probably true down to the divisibility of the currency. For the reduced quantity of money, the velocity of money would need to increase to maintain the same nominal GDP.

If a tax on currency is simply transferred to a beneficiary then the tax negative subsidy is offset by the beneficiary positive subsidy. Government taxes 50% of my $20 bill (negative subsidy) then hands me a $10 bill (positive subsidy) - what's changed?

[Nick Rowe]

W Peden: Thanks!

JP Koning is the man on limbo dancing under the ZLB. He has a couple of posts on this. Storage costs for currency are non-trivial, apparently. This creates a bit of wiggle room.

Majro: NK models assume that prices are sticky in terms of the unit of account. I'm trying to think how NK monetary policy would work if the central bank sets a nominal interest rate on the medium of exchange, but my brain is failing me.

In Cuba at that time, the US dollar was only used on the black market (and in tourist stores, where prices were marked in USD). Prices were negotiated, but were likely negotiated in dollars. Official store prices were in pesos, of course. The black market exchange rate peaked at 120 pesos per dollar, while the official exchange rate was roughly par!

Nick E: yes, we could add a commercial banking system too, if the central bank only let commercial banks have chequing accounts at the central bank.

I think the point is that "cashless" might mean "currencyless", but it does not mean "moneyless". And I'm not sure there is any theoretical difference between currency and balances in chequing accounts. A system with green notes worth +$1 and an equal number of red notes worth -$1 would work just the same. Just harder to administer.

Frank: see my old post.

[Majromax]

> NK models assume that prices are sticky in terms of the unit of account. I'm trying to think how NK monetary policy would work if the central bank sets a nominal interest rate on the medium of exchange, but my brain is failing me.

Right, because the bank really wants to set an interest rate on the store of value, since that is where money interacts with time-preference.

I wonder, is it possible to construct a world where all three roles of money are satisfied by disjoint things? That might be enlightening, but the thought of it starts to twist my brain into knots.

[Nick Edmonds]

But I don't think the chequing accounts of the commercial banks need to have anything in them. They can settle between themselves.

[Frank Restly]

Majormax,

"I wonder, is it possible to construct a world where all three roles of money are satisfied by disjoint things? That might be enlightening, but the thought of it starts to twist my brain into knots."

I presume you to mean medium of exchange, store of value, and unit of account.

Okay, suppose I had a super duper nuclear device that does direct energy to carbon and carbon to energy conversion. The energy that it produces is very high frequency electro-magnetic and does not thermally excite matter here on earth (you can't convert it to electricity).

Energy is my medium of exchange. It is has a low transportation cost in terms of time (travelling at speed of light), but a high storage cost in terms of space.

Carbon is my store of value. It has a high transportation cost in terms of time, but a low storage cost in terms of space.

What should I use for my unit of account? Grams / lbs mass or Joules / watt hours? If we assume that my super duper nuclear device is 100% efficient (no lead produced as a byproduct, no energy lost into space as heat), then it doesn't really matter which units I use.

Who should establish what the unit of account is and how should that unit be maintained for consistency? I am not the only person with a super duper nuclear device and for transactions, someone needs to make sure that one gram of carbon / joule of energy out of my machine is equivalent to one gram out of carbon / joule of energy out of Joe's machine. Enter a legal scholar with his set of scintillating scales. These scintillating scales can measure both mass and energy, and through Einstein's equation, compare energy that I want to sell for carbon that Joe wants to sell.

Now, my super duper nuclear device is 100% efficient but it does not do the conversion instantaneously. It takes time for my machine to work it's magic. And so if Paul brings me 1 kg of carbon, I may give him 1 million kilojoules of energy over a time period of 1 year. But the 1 kg of carbon has 1.05 million kilojoules of energy inside of it and so I am earning a nominal interest rate of 5% on the carbon that I convert to energy.

If we define the real interest rate as the growth rate on the amount of carbon created (store of value created), then my machine generates a negative real interest rate - I have destroyed store of value (1 kg of carbon) to create means of exchange (1 million kilojoules of energy).

If we define the real interest rate as my return on investment measured in kg of carbon, then I have received a 5% real interest rate if I held onto 5% of carbon that Paul gave me and converted the rest to energy.

[genauer]

there is already a tax on currency, and it is called inflation

[Jacques René Giguère]

Nick: my students all use debit cards (old guys like me use credit cards). When they buy something at the dépanneur, the account between them and the dep is settled by their respective "banks" moving their balances at the BoC through the Canadian Payments Association. Both students and dep owner have an account at the Boc. That one account is called BMO and the other BN is merely a) a political device so we don't have a "communist monopoly bank" like Cuba and b) a convenient way to pay some crony $20M as "bank president" instead of $ 200K as assistant deputy minister in the Banking Ministry.
Musing of a humble IO guy.

[Max]

My understanding of "cashless" is that interest on money = interest on (1-day) bonds, for any quantity of money. Banks could issue money, but it wouldn't be profitable.

It doesn't mean the quantity of money is zero. It could be $0.01. It does mean there is no money multiplier.

[notsneaky]

I can't remember if he explicitly cites Gesell, but Woodford in his book lays out his baseline framework in almost exactly the same terms as you do above (then adds stuff)

[rsj]

Yes, NK just assumes everyone transacts by writing checks to each other (or credit cards, money market funds, etc), which is already much better than assuming all transactions occur with cash (Friedman world). In reality, let's say 99% of transactions are check writing and 1% cash transactions. But if banks started charging high negative rates for checking accounts, then this mix would change, so it's not necessarily Gesellian. I don't think it's necessarily important to worry about this 1% of transactions except for something like negative interest rates, in which case just ban the negative rates and keep the all-check model.

Also, it's simple to consolidate the banking system and CB into a single financial sector that the non-financial sector interacts with. Again, this doesn't matter too much, IMO, unless one is explicitly modeling agency problems or the like with the banking sector.

I think it's odd that the old-monetarists who still focus on monetary aggregates, reserve multipliers, and money multipliers as instruments of policy would fuss about realism in modeling the financial sector.

[rsj]

..But if I could interject, if we believe that rates are too high because of the ZLB, why are we futzing around with currency taxes instead of directly taxing capital income?

[Jonathan]

Nick: I realize that I didn't fully answer the question implicit in your original post, namely where is the money in the New Keynesian model?

I think of the NK model this way:

(1) Take the standard competitive Neoclassical model with Walrasian markets, etc. Add monopolistic competition in the goods market.
(2) There is one asset traded, which we can call bonds. Make these bonds nominal. This changes nothing fundamental, it just makes it so there's a price level you can talk about (the price level is indeterminate however).
(3) Add a Calvo friction so that some firms can't adjust the price of their goods (denominated in bonds).
(4) Let the government set the nominal interest rate on bonds by fiat.

Now in REALITY (not in the model), we know that there are actually many different sorts of assets, and monetary policy is implemented by exchanging two assets (bonds and money) to affect the spread between them.

But in the MODEL, all we need is (1) a nominal price rigidity, and (2) the central bank sets the nominal price of bonds. It doesn't matter how this is implemented -- the government could just pass a law saying that i = 1% or whatever (like a minimum wage law).

I think you agree with me up to here, but now you want to say that these bonds are "money", and that this is implemented through a central bank clearing house. I don't fully agree -- there's just one asset here, and it serves as a unit of account and store of value, but NOT as a medium of exchange. You can imagine that all exchanges in the economy are real exchanges, they just are denominated in units of the bond, which ONLY matters for the fixed price firms.

The whole point of this formulation is that, as a strategic simplification, we are abstracting from differences between money and bonds (and other sorts of assets). You can call the bonds "interest bearing money" if you like, and your story accurately maps onto the model, but I'm not sure what this buys you in understanding the model. I think my original comment is a better way to think about it: The model isn't about money. It's about the government being able to set the real interest rate, at the cost of some inflation, together with a theory of inflation dynamics and real costs of inflation. Money's role in facilitating transactions is entirely absent.

In short, it is a model about monetary POLICY, not a model about MONEY. And "monetary policy" is a confusing name -- it might be better to call it interest rate policy.

[Nick Rowe]

Jonathan and notsneaky: I would like to see you two argue this one out, based on your understanding of Woodford and/or Gali:

Let's run with Jonathan's description. The *only* asset is one-period "bonds". Bonds have a price of $1, and an interest rate set administratively by the central bank. All agents are identical, so no bonds are traded in equilibrium. Start at the natural rate. Then the central bank raises the interest rate on bonds. Hold all firms' prices fixed (for simplicity). There is now an excess demand for bonds. But if those bonds are not used as a medium of exchange, why should that cause a recessions? Agents will continue to barter the same quantity of goods as before. Compare bonds to land. If there is no trade in land, because everyone is identical, an excess demand for land, and a sticky price of land, won't disrupt the rest of the economy at all.

But if the bonds are used as a medium of exchange, if people buy and sell the consumption good for bonds, so they are traded in equilibrium, then we get a recession.

[Nick Rowe]

Nick E: "But I don't think the chequing accounts of the commercial banks need to have anything in them."

I'm not sure what you mean by that. Net balances sum to zero? No base money reserves?

genauer: "there is already a tax on currency, and it is called inflation"

Correct. But in an NK model, the only way the central bank can change the inflation tax is by changing the interest rate subsidy. (And it's the difference between the two that matters).

Jacques Rene: that is roughly how I would describe it too (minus the bit about cronies!). But do we really want to nationalise the whole banking system?

Debit cards are just paperless cheque books.

Max: see my comment immediately above.

rsj: there is no theoretical difference between paper currency and paperless chequing accounts. These are just different ways of recording payments.

"But if I could interject, if we believe that rates are too high because of the ZLB, why are we futzing around with currency taxes instead of directly taxing capital income?"

You are missing the point. It's a tax on the medium of exchange that matters. A tax on capital income would make things worse. It would make holding currency even more attractive.

[Jonathan]

Nick: Excellent. Okay, so what happens after contractionary monetary policy in the NK model?

All prices are fixed, and the central bank (by fiat) raises the nominal rate of interest. And let's suppose this is temporary (otherwise we get explosive dynamics).

Since all prices are fixed, raising the nominal interest rate is equivalent to raising the real interest rate. Now we're out of equilibrium: there's excess demand for bonds. Through Walras' law, this implies excess supply of goods. Since all firms have fixed prices, they are obligated (by the Law of Calvo) to hire exactly enough workers to meet the (lower) demand they face. Therefore firms hire fewer workers. Since the labor market is competitive, this implies that wages fall, and so households work less (voluntarily!), and production and income fall. The Walrasian auctioneer decides that wages fall exactly enough so that desired saving falls back to S=0, and the economy's resource constraint is satisfied.

Here's a more mathematical way to put it: in the Neoclassical model, we have as many equilibrium conditions as endogenous variables. If the central bank sets r at some level, say r=r', this is one more equilibrium condition, and the system is overdetermined. Then unless the central bank sets exactly the right r, no equilibrium exists unless we relax one other equilibrium condition.

The NK model amounts to relaxing the labor demand condition (i.e. W = MPL).

(As an aside, Keynes' original formulation is conceptually equivalent to the above, except that he relaxes the labor SUPPLY condition, which has the advantage of interpretation that unemployment is involuntary).

[Nick Rowe]

Jonathan: "Now we're out of equilibrium: there's excess demand for bonds. Through Walras' law, this implies excess supply of goods."

NO! This is why you young guys need to re-read the old stuff, that everyone (except a few old farts like me) has forgotten. Clower, Patinkin, Benassy, Malinvaud, Barro-Gordon, the people from the old "disequilibrium macro" approach that died out in the 1970's, would immediately recognise your error.

Google notional vs effective demand to see where I'm coming from. Walras' Law is only true for notional demands.

If an agent is quantity-constrained in one market, that will affect his demands (and supplies) in other markets.

You have an excess demand for bonds. But you can't in fact buy any bonds, because nobody is selling. You have a *notional* excess supply of goods, but not an effective excess supply of goods. You CANNOT in fact buy bonds, so instead you continue to buy the same quantity of goods as before.

If barter is allowed, people are unable to sell goods in exchange for bonds (which they want to) but are still able to sell their goods in exchange for someone else's goods.

My old post on walras' law vs monetary disequilibrium theory.

[Nick Rowe]

Or, as I said in that old post: Walras' Law is the worst fallacy still being taught as gospel truth.

[Jonathan]

Nick: Awesome! It sounds like we're succeeding in getting to the heart of our disagreement here.

(As an aside, this will be my last post for today, but that's okay because I need to think more about this.)

First, I should point out that my description of what happens in the NK model is entirely logically coherent, and fully consistent with my understanding of the operation of the model. In the NK model, there is no disequilibrium adjustment: everyone submits their Walrasian demand functions to the auctioneer, except that the firms now don't submit their labor demand schedule, and the auctioneer finds the price vector that clears all markets. (Strictly speaking, even the auctioneer is just a story of what happens -- the market-clearing price vector automagically appears).

I think it's VERY important when discussing economics to be very clear about whether a particular statement is about a model or about reality, and if about a model, then what model in particular. Your statement is not about the NK model, it is about another model that I could call "NK plus a description of how adjustment happens in the NK model in the absence of a Walrasian auctioneer".

Now it so happens that (unlike many young macroeconomists) I AGREE with you that thinking about how adjustment works in the "NK plus a description of adjustment" model is useful, because it build conceptual understanding (that's another distinction I like to make -- between the mathematical content and the conceptual content of a model).

One way to formalize this is that we could imagine building a model of the adjustment process, and then taking the limit as adjustment happens faster and faster. Then the question is whether we can build such a series of models that converges to the NK model.

As an aside, you are correct that I haven't read the old macro disequilibrium literature, and I'm much less confident of myself here (and we're certainly on ground you know MUCH better than I do).

Let me express your point like this: Suppose the CB raises the real interest rate by fiat. Then lots of people will want to buy bonds to hold, but they can't -- they go to the bond market carrying their wages, and find "sold out" on all the store windows. Their wages are perishable, so they take them to the final goods market and buy goods with them instead. Demand doesn't fall, and so wages don't fall, and so employment doesn't fall.

I don't know the solution, but here is a rough sketch of a guess:

Suppose that when firms produce, they need to pay the workers in bonds. Since they don't have wealth, they borrow bonds from the government at the going interest rate (this is like working capital, borrowing to finance the wage bill.)

Now suppose that the government raises (by law) the interest rate on bonds. Firms are required by the Edict of Calvo to produce as much as they expect will be demanded of them, so they don't respond to the higher interest rate. But households are now paid in bonds that carry a higher promised interest rate. So now households save by sitting on these bonds instead of taking them to the goods market to buy final goods. But then the final good producer sees lower demand and reduces its demand for intermediate goods from the intermediate goods firms.

Now the adjustment process goes into effect: firms reduce the number of workers they want to hire, wages fall, etc. until aggregate desired savings falls to zero.

Now I'm not fully confident in this story, because I'm worried about how (for instance) the promise that the government will redeem a positive stock of bonds at a higher interest rate affects peoples' expectations of future taxes (say) during the adjustment. To really check this, you would need to work out a full model of this adjustment process and then see if it converges to the NK model as you let the adjustment happen faster and faster.

I guess you could say that now the bonds are more "money" like, because they're being used to get around the simultaneity problem in production. I'm not sure about this interpretation, but I guess it's some concession to the Monetarist view.

Okay, enough for today. Time for Matlab and Latex.

p.s. if I were to read just one paper from the macro disequilibrium literature, which should I read?

[Jacques René Giguère]

Nick:"Jacques Rene: that is roughly how I would describe it too (minus the bit about cronies!). But do we really want to nationalise the whole banking system?"
Nationalize the loan-allocating system? Maybe not,though comparing the effect of the Chinese crony system with the New-York-London bonus industry isn't that clear...Too many people working overtime to make deals.There is something for 9-5 civil service work ethic.
Anyway,do not confuse payment system and credit system. Even though we have unfortunately conflated the two.

[Nick Rowe]

Jonathan: read Barro Grossman 1971 (pdf). It's a simple model where money is the only asset, but it gives the gist of it.

If you look at Figure one, the NK equilibrium is at point C.

Back soon. Office hours.

[Nick Rowe]

Jonathan: you are definitely getting it.

"Let me express your point like this:..."

Basically yes. But allowing barter would make that point even simpler.

"I guess you could say that now the bonds are more "money" like,..."

I would say that "bonds" are now being used as money (the medium of exchange). bonds ARE money, in that example.

Let me sketch my own microfoundation:

Firms are worker owned coops (or Larry Ball Yeoman farmers) so we can simplify by eliminating the labour market.

This is the order of play:

Firms announce prices.

The central bank announces the rate of interest r paid on chequing account balances.

Individuals mail binding orders to firms, accompanied by a cheque. (A Cheque-In-Advance economy)

Individuals go to their own firms to work, open their mail, deposit those cheques, then produce the ordered goods, and mail those goods to the individual's homes.

Workers go home, and consume the goods.

The period ends.

Uneaten goods rot, so can't be used as money.

An individual who ends the period with M in his chequing account begines the next period with M(1+r).

[Too Much Fed]

Does this central bank/bank have any assets?

[Too Much Fed]

rsj said: "Yes, NK just assumes everyone transacts by writing checks to each other (or credit cards, money market funds, etc), which is already much better than assuming all transactions occur with cash (Friedman world)."

NK assumes no currency? Does it assume no central bank reserves?

I don't think writing checks and using credit cards should be considered the same.

[Too Much Fed]

"The central bank itself has no assets except the negative balances"

Never mind my 3:44 comment. I read too fast.

[Jonathan]

Nick: I will read Barro-Grossman.

I also took a quick look at your old post on Walras' Law. On a personal note I was surprised to encounter a younger version of myself in the comments (under the name "Jon"). It's always awkward to read yourself from 4 years ago, and I think our exchange there makes for a nice counterpoint to our current conversation.

[Niveditas98 .]

Nick/Jonathan, I would like to clarify something very basic in your discussion on bonds in the absence of money.

First, what does "bond" mean in this situation? Since there's no money, I assume it must mean something like "give me 100 apples today in exchange for my promise to give you 105 apples next month". Now there could be orange bonds and pineapple bonds in addition to apple bonds, with possibly different rates of interest, but let's focus on the apple bonds.

Assuming this is what is meant by "bond", how would the central bank set the interest rate on these bonds -- is it by government edict, saying the only apple borrowing and lending allowed is 100 apples today for 110 apples tomorrow?

Second, Let's make this more concrete. Assume in the previous equilibrium, 100 apples were produced by lenders and exchanged for promises of 105 apples next month. With the higher interest rate for apples, notional demand for apple bonds rises to 120, say, which represents 132 apples next month. Meanwhile notional supply of apple bonds falls to say 90, representing 99 apples next month.

Here Walras's law applies to the notional demands, with the excess demand of 120-90=30 for apple bonds matched by an excess supply of 30 apples today.

Now let's follow Nick's argument -- 120 apples can't be lent, since there is only demand for 90 apples of borrowing now. Fine, so 90 of the previous lenders continue to lend, the extra 20 new lenders find they can't lend, so they do whatever they were doing before with their apples. What happens, however to the 10 old lenders who can no longer lend? What do they exchange their apples for? What happens to the 10 old borrowers who no longer exchange next month's apples for apples today?

Also, next month, previously 105 apples were produced and given to the lenders to pay off the debt. Now there are only 90 borrowers, who pay off their lenders with 99 apples. What happens to the remaining 6 apples of production?

[Too Much Fed]

Jonathan said: "In what sense am I using "money" when I use my debit card to draw on my account with Bank of America? How is that asset the same as a 20-dollar bill?"

I'd say using your debit card is like an electronic check. It is instructions to move demand deposits.

Use your debit card. Next time, withdraw the $20 with the receiver redepositing it in a commercial bank. If you do the accounting, I am pretty sure you will get the same balance sheet results.

Nick said: "But commercial bank promises to redeem its money in central bank money at a fixed exchange rate, and not vice versa, so the central bank is alpha and the commercial banks are beta."

Jonathan, I don't agree with the alpha and beta distinction.

I'm going to say "bank deposits" and currency are both MOA and MOE. The commercial banks do not allow their "bank deposits" to rise in value. The central bank and deposit insurance do not allow the "bank deposits" to fall in value. The "bank deposits" stay fixed in value to currency. It just happens to be fixed 1 to 1.

If there is a bank run on a solvent commercial bank, the central bank should always "bail out" the commercial bank by issuing more currency. The 1 to 1 exchange rate stays fixed.

[Too Much Fed]

"If I hold a $20 banknote, issued by the Bank of Canada, it is as if I have a chequing account at the Bank of Canada with $20 in it. If I buy something from you, and give you that $20 banknote, it is as if I wrote you a cheque for $20, instructing the Bank of Canada to transfer $20 from my account at the Bank of Canada to your account at the Bank of Canada. It is as if we keep our $20 banknotes in little boxes at the Bank of Canada instead of in our pockets, and when I buy something from you the Bank of Canada switches one $20 banknote from my box to your box. These are just different ways of keeping a record of payments.

Imagine a world where every individual has a chequing account at the central bank. There are no other banks, and no other forms of money. People use cheques drawn on their accounts at the central bank to buy everything."

I am going to call a $20 Bank of Canada banknote currency. Under this scenario, depositing $20 of currency at the Bank of Canada gets you $20 of demand deposits that are in your checking account. The $20 in currency becomes vault cash. Now write a check. That is an instruction to move demand deposits in exchange for something (assuming no gift). The demand deposits are acting as MOA and MOE.

The point is a checking account is about moving demand deposits, while the $20 of vault cash just sits there not moving.

[Too Much Fed]

"Suppose the positive and negative balances in those chequing accounts across all individuals sum to zero. The central bank itself has no assets except the negative balances, and no liabilities except the positive balances, and the two exactly cancel out. If one individual buys something for $20, his account goes down by $20 and the seller's account goes up by $20, so the net balances stay at zero. The central bank earns zero net revenue, because the interest it pays on positive balances exactly matches the interest it charges on negative balances. And suppose the central bank has zero administrative costs. The central bank therefore earns zero profits."

1) It appears this central bank/bank has no equity.

2) What if no one has a negative balance/issues a bond to the central bank? In other words, what if no one borrows from the central bank?

[Jacques René Giguère]

TMF: central banks don't need equity. They are not bank. They were but no longer are.They evolved out of them when the biggest ones acted in the spirit of salus populi suprema lex esto. They issue money out of thin air. Turtles all the way down. Tha't the beauty of it.
Some CB, like Switzerland still don't understand. The Swiss are beginning to pay for that ununderstanding.

[Too Much Fed]

"TMF: central banks don't need equity."

In this example, it looks like the central bank could be making risky loans.

What happens if the loans default causing the assets to lose value?

[Jonathan]

Niv: "First, what does "bond" mean in this situation? Since there's no money, I assume it must mean something like "give me 100 apples today in exchange for my promise to give you 105 apples next month"."

What you describe is a real bond, i.e. a promise to pay 1+r apples tomorrow for 1 apple today, where r is now a real rate of return (in apples). In the standard New Keynesian model, there are only NOMINAL bonds. Then one bond today is a claim on 1+i bonds tomorrow. What this comes to in apples depends on what happens to the price of apples (in bonds) between today and tomorrow.

You can call these bonds "interest-bearing money" if you like. But they're not a medium of exchange in the standard model.

"Assuming this is what is meant by "bond", how would the central bank set the interest rate on these bonds -- is it by government edict, saying the only apple borrowing and lending allowed is 100 apples today for 110 apples tomorrow?"

In the model, the central bank simply sets the nominal interest rate (not the real rate). You can imagine this is done by law. In reality, this is normally done through open market operations, i.e. the Fed buys or sells government bonds so that their interest rate equals its target.

[Niveditas98 .]

Jon, in the model without money, the central bank can't actually influence the interest rate by trading the bonds, since there's no money, and the bank doesn't have apples or any other real goods. So it would appear this has to be set by law.

Would this have an impact on real interest rates? In the model with money, the assumption is that when the central bank changes the nominal rate, in the short run inflation expectations don't change, and the change in the nominal rate flows through into a change in the real rate, right? Is this still a plausible model in the absence of a medium of exchange?

[Too Much Fed]

"In the model, the central bank simply sets the nominal interest rate (not the real rate). You can imagine this is done by law. In reality, this is normally done through open market operations, i.e. the Fed buys or sells government bonds so that their interest rate equals its target."

I don't totally agree with that. The fed can set the fed funds nominal rate thru an "announcement affect". They just say what it will be, and it goes there. Let's say the fed wants to lower the fed funds rate from 5% to 2%. They announce it. The "market" does not cooperate. They buy a bond and sell central bank reserves. There are excess central bank reserves in the banking system. The fed funds rate falls towards interest on central bank reserves, including zero. When the fed funds rate gets to where the fed wants it (say above the interest on central bank reserves), it sells the exact same amount of bonds and buys the exact same amount of central bank reserves.

The result of both an "announcement affect" and the second scenario is that the amount of currency can stay the same and the amount of central bank reserves can stay the same (the monetary base is unchanged) while changing the fed funds rate and probably other interest rates too. The scenario does not have to be more money/monetary base raises the price(s) of bonds meaning lower interest rates (monetarist thinking).

The commercial banks learn from this and pay attention to the "announcement affect".

[Jonathan]

TMF: While I agree that the "announcement effect" is important, I think this always involves the Fed actually trading in quantities. The announcement alone is not enough.

Consider the secondary market for treasuries, that trade at a certain interest rate. Then the Fed announces a higher interest rate target, and stands ready to buy or sell treasuries at that new interest rate. Will it actually have to make any trades?

I would say yes. The old interest rate is what cleared the market for treasuries. Now at the higher interest rate (lower price), some people who were willing to sell treasuries at the old price are no longer willing to sell at the new rate, and more people will want to buy treasuries at the new higher rate. The only way the new announced target rate can clear the market is if this excess demand for treasuries at the higher rate is met by the Fed -- i.e. some people are going to buy treasuries from the Fed at the higher rate, and there will be a net flow of bonds from the Fed to buyers, and a flow of reserves from buyers to the Fed.

I agree that this happens faster and with less total change of quantities than if the Fed hadn't announced the new rate and had simply started selling treasuries at a lower price.

[Best Beta Trading]

I'm starting to view the long-term economy as a system of trying to achieve an optimal basket of technologies. A certain level of dynamic activities but some WMDs out of easy reach. This would apply to the interest rate selection of major central banks as well as regional and sector specific actors. If they are part of the solution you'd want to encourage more economic growth. If part of the problem: less. Perhaps some of the politic checks on power might have economic parallels that don't yet exist.