Another weird monetary world

Imagine you lived in a world where the central bank issued two types of money: paper money; and electronic money. If you want to pay for something with the paper money, you have to physically transfer it. If you want to pay for something with the electronic money, you just need to tell the central bank to transfer it for you, perhaps by setting up an automatic system (just like how I pay for my car insurance now).

The two monies have a pegged exchange rate of one. The central bank swaps paper money for electronic money at par, on demand.

Anyone can use the paper money, but only a very select group of customers are allowed to use the central bank's electronic money.

The paper money always pays 0% interest nominal. The electronic money can pay whatever nominal interest rate the central bank chooses to pay.

The nominal interest rate on paper money is always 0%, but that does not mean the real interest rate on paper money is always 0%.

The strategic objective of the central bank is to try to ensure that the real interest rate on the paper money does not vary over time. It targets a fixed real interest rate on paper money.

The central bank adjusts the nominal interest rate on electronic money to try to hit that target real interest rate on paper money.

The central bank has a theory about the relationship between the nominal interest rate on electronic money and the real interest rate on paper money.

According to that theory: if the central bank wants to lower the real interest rate on paper money (because it thinks there's a danger the real interest rate on paper money will rise above target unless it does something) it needs to lower the nominal interest rate on electronic money. The central bank calls this the "short run" part of its theory.

But, according to that same theory: if the central bank's target for the real interest rate on paper money were lower, the nominal interest rate on electronic money would need to be higher. The central bank calls this the "long run" part of its theory.

Very few people understand the central bank's theory. Even some very good monetary economists don't get the short run part, and think that if the central bank wants to lower the real interest rate on paper money, all it needs to do is raise the nominal interest rate on electronic money.

Just in case you haven't figured it out yet: this is not an imaginary world. It's the real world. But it definitely is weird. Only a finance theorist could have dreamed up a world this weird.

 

Comments

[Kevin Donoghue]

I wouldn't worry about the fact that very few people understand the central bank's theory. Few understand difference equations. The two failures of understanding are related, I think.

[Odie]

Would you call then Ben Bernanke and John Taylor "finance theorists"?

[Jeff]

I'm with Kevin. I'm sure lots of people complained that quantum mechanics was weird and complicated and couldn't possibly be right (Einstein did!). So it goes.

[Alex]

Nick,

I don't like this post. It looks convoluted and non-informative to me. I have a suggestion: try to reformulate it in the terms of supply and demand.

Regards.

[JKH]

This is just your interest rate differential framework restated in dynamic interest rate level terms isn't it?

[The Market Fiscalist]

Suppose the monetary authorities believe that the only way to decrease real interest rates on paper money is to increase the nominal rate on electronic money.

As long as they are prepared to keep increasing the qty of electronic money they will eventually succeed in getting the real return on paper money to be lower at the new higher nominal rate on electronic money. So they don't really need the short term theory. If they told everyone what they were doing it would probably not even take very long to get to the new equilibrium.

[Majromax]

> The central bank has a theory about the relationship between the nominal interest rate on electronic money and the real interest rate on paper money.

Isn't this almost exactly the problem of a bimetallic standard?

If the real rate of paper money is currently greater than the real rate of electronic money, everyone is incentivized to transfer as much money-holding from electronic to paper form as possible. Since the only holders of electronic money are those "select group" authorized to use it, there's ostensibly no problem for them to transfer as much stock into paper money as possible, keeping only the electronic money needed in the short-term (related to redemption delays).

If the real rate of electronic money is currently greater than the real rate of paper money, everyone is incentivized to hold only electronic money, keeping only the amount of paper money needed to cover inconvenient-transfer. Since "most people" cannot by law hold electronic money, they'll seek to do so by proxy, by holding debt instruments issued by those who can hold electronic money. This makes use of electronic money more inconvenient for ordinary people.

This is analagous to bimetalism, where the central bank operates by offering differential rates for the exchange of gold and silver. Such policies can only act to influence the economy insofar as people are willing to hold both metals (or here both electronic and paper money). This is true regardless of the truth of the theories -- decreasing the nominal interest rate on electronic money from minus-one-billion-percent to minus-two-billion-percent will do nothing, because nobody will hold electronic money in the first place.

That dual holding tendency is increased by liquidity difference (it's easier to pay for $0.50 in cash than via wire transfer) and by making conversion difficult or restricted (as ordinary citizens cannot directly hold bank reserves). However, the latter means that middlemen can act to extract unjustified profit by providing a transfer-by-proxy service, which suggests that such policies introduce a deadweight loss.

[Nick Rowe]

Alex: "I don't like this post. It looks convoluted and non-informative to me. I have a suggestion: try to reformulate it in the terms of supply and demand."

It is supposed to look convoluted and non-informative. The whole point of the post was to show how weird things look when you only talk about interest rates and don't talk about supply and demand!

Jeff and Kevin: but if I said that "increasing the money supply makes money worth less", I think most people would get it, at least at a simple level.

JKH: Yep. Same thing.

MF: Yep. They could do the same thing by increasing the growth rate of paper + electronic money.

Majromax: yes, interesting parallels with bimetallism. Remember that you can hold negative balances of electronic money too.

[Kevin Donoghue]

Nick: sure they'd get it, after a fashion. (Though you might be a bit disturbed by their answers if you asked them whether they understood your money supply to be a stock or a flow.) In the same way, if a 19th century physicist said "light waves are transmitted through the ether just as sound waves are transmitted through the air, people would have got that too. But now they tell us they don't need the ether to make their theory work. Likewise, Woodford doesn't need the money supply to make his theory work.

[Too Much Fed]

"If you want to pay for something with the paper money, you have to physically transfer it. If you want to pay for something with the electronic money, you just need to tell the central bank to transfer it for you, perhaps by setting up an automatic system (just like how I pay for my car insurance now)."

Does this imaginary world have commercial banks? Let's say yes. Your automatic system for car insurance is more about demand deposits. You instruct demand deposits to be transferred. Assume you and car insurance company bank at the same bank. You just swap demand deposits for the policy.

Let's call central bank electronic "money" central bank reserves. The central bank reserves only get involved to clear the payment if the car insurance company banks at a different bank.

I'm pretty sure withdrawing currency and using demand deposits to pay for the car insurance will end up with the same accounting if the currency is redeposited into a commercial bank whether the car insurance company banks at the same bank or not.

[Too Much Fed]

"The two monies have a pegged exchange rate of one. The central bank swaps paper money for electronic money at par, on demand."

Let's assume there are commercial banks. Are currency and demand deposits pegged with a fixed 1 to 1 conversion rate on demand?

[JP Koning]

Great post Nick. (With all the weird monetary worlds you've created over the years, someone could write a really good science fiction novel some day.)

[Tom Brown]

Nick, you write:

"Even some very good monetary economists don't get the short run part"

Sorry, I'm feeling a little thick about this post in general. Can you name names here? Which economists are you referring to? Isn't the short run part just following Taylor's rule, for example? Inflation rate is too low (i.e. real interest rate on paper money is too high), so let's lower the overnight rate? Did you leave out the phrase "magnitude of" somewhere?

Regarding the "long run" part, this again involves trying to lower the real rate on paper money, right? In other words increasing the inflation rate again, so here we raise the overnight rate? I kind of see what you're saying, but that seems like the part that "some very good monetary economists" might not get.

Am I on the wrong track in assuming the real rate on paper money is the negative of the inflation rate here?

[Nick Rowe]

Kevin: They might be thinking in terms of the stock M, or the flow MV. Yep, they might be a bit fuzzy on the distinction.

"Likewise, Woodford doesn't need the money supply to make his theory work."

I would say that's debatable. Woodford's theory wouldn't work in a barter economy.

TMF: "Does this imaginary world have commercial banks?"

This isn't an imaginary world. It's the real world. Who do you think are those "... very select group of customers [who] are allowed to use the central bank's electronic money."?

JP: thanks! But I think this one, the real world, is the weirdest!

[Jacques René Giguère]

Nick: in this weird world, we call the Bank of Canada "Bank" even though it's not a bank and does nothing a bank does, thus causing much confusion. And the electronic money is used by teenagers with debit card (old financially established guys use credit card).

[jt]

Nick. I`m not sure what point you're trying to make.
Is it ...
(1) why don't we have e-cash? Or, ...
(2) why do we try to conduct monetary policy with "the physical cash problem"; who set up this stupid system? Or ...???
For (2), yes portable e-cash would be "fairer", but up until 2008, it wasn't a problem, so I think the answer is "because it worked for a long time". And of course, there's a simple emergency backup plan if needed (you just announce a mandatory currency for demand deposit swap and issue new bills). That's no weirder than, nuclear reactors without backup power generators, one size of big macs, ... ha ha ha.

BTW I really do enjoy your parables, like a fine classic Russian novel, but sometimes the less intelligent people like me need a hint or punchline (maybe like a crossword, you could give the punchline in your next post).

[Nick Rowe]

Jacques Rene: Yes! The Bank of Canada (like most central banks) isn't really a bank.

When we use a debit card, the money we are using is commercial bank money, not Bank of Canada money.

jt: just how really weird the current system looks, when you stand back and look at it as an outsider from Mars. And how it's all based on interest rates.

[Peter N]

It looks like those with access to the electronic system have opportunities for rent collection and maybe arbitrage.

Your model seems to pass that particular realism test.

[Ralph Musgrave]

Good to see Nick describing interest rate adjustments as “weird”. MMTers will drink to that, since they tend to oppose interest rate adjustments as a means of adjusting AD. Indeed Warren Mosler proposes a permanent zero rate.

Another major flaw in interest rate adjustments is that they are distortionary: that is, given a recession, there is no particular reason to assume that its economic activity based on borrowing and investment that needs boosting rather than other types of spending.

[Too Much Fed]

"The paper money always pays 0% interest nominal. The electronic money can pay whatever nominal interest rate the central bank chooses to pay."

In this model with commercial banks, does it matter what rate is paid on commercial bank money?

[Jeff]

Nick,

"if I said that "increasing the money supply makes money worth less", I think most people would get it"

Sure, they'd think they got it. Even though you didn't say anything about what operation you carried out. Did you just print it up and give it away? Did you buy t-bills with it? Does it matter? Are you going to tax it all back next year or sell back the t-bills? Ever? What is the path of nominal t-bill rates between now and then? What about the path of IOR? Do the people still get it? I'm betting they don't get it at all. The problem is that Hume's money doubling thought experiment is a kind of half-assed ill-defined thing. Reality is quite complex, and involves expectations of long lived continuous time stochastic incomes and convenience yields. Ie finance.

"Woodford's theory wouldn't work in a barter economy."

He doesn't need any *outside* money. Just credit denominated in a common unit of account.

[Nick Rowe]

Ralph: there is a big difference between the central bank setting interest rates at some constant level regardless of what is happening in the economy, and letting the market set interest rates, and those market rates responding to shocks.

Jeff: "He doesn't need any *outside* money. Just credit denominated in a common unit of account."

Suppose the natural rate of interest is 5%. Suppose the central bank screws up, and sets the actual rate of interest at 10%. This causes an excess demand for bonds. Does this excess demand for bonds cause unemployment? No. Unemployed apple producers and unemployed banana producers simply get together and swap apples and bananas.

Plus, how exactly does the central bank set the interest rate on bonds at 10%? Could *I* set the interest rate on bonds at 10%? What power does the central bank have that I don't have?

Plus, even if the central bank does set the natural interest rate. Assume stationary economy with no shocks (for simplicity). Output = the natural rate for all periods is then an equilibrium. But it is not the only equilibrium. If we halve output for all periods the Euler equations are still satisfied. Woodford's model implicitly assumes outside money. It needs a Pigou effect to get it to the natural rate of output, even if the central bank sets the natural rate of interest for all periods.

[Jacques René Giguère]

Nick: at the end of the day, banks settle their accounts with central bank money because it is more efficient to do it once a day. But deep down, each debit card move is about shifting central bank money between banks. At least seen from an IO guy...

[Jeff]

"Unemployed apple producers and unemployed banana producers simply get together and swap apples and bananas."

The issue is not current, but intertemporal barter. If you want to exchange your bananas today for my apples next fall you have to lend me money via the banking system. We can't do the loan directly at the natural rate because it's not actually just bilateral barter, and in practice I have no idea who is going to buy my apples. So you give me a loan at the policy rate so I can buy your bananas, and later, if you buy my apples, we unwind the loan.

"What power does the central bank have that I don't have?"

You don't clear inter-bank payments. If the system were to fail to clear perfectly there would be some offsetting positive and negative balances of reserve positions in different banks. The net is actually a small positive number in Canada ($25M?), but it could just as well be zero or even negative. If a bank is in surplus, it receives the IOR rate and if in deficit, it pays the discount rate, so banks will only lend above IOR and borrow below the discount rate which puts the target rate in the "corridor." Since it's better for the banks to meet at a level inside the corridor, than receive IOR and pay discount, the system usually clears. The quantity of reserves is irrelevant. The effect a positive net balance is to produce a seignorage of some hundreds of thousands of dollars per year paid by the commercial banks to the Bank of Canada (the difference between the policy rate and IOR).

"Plus, even if the central bank does set the natural interest rate."

Did you mean the real rate?

"It needs a Pigou effect to get it to the natural rate of output"

It's in there, if you want. The central bank completely controls the real balance and *can* control the policy rate by doing OMOs and keeping IOR at zero (or some other fixed amount). Most central banks don't work like that anymore. Instead they adjust IOR and leave the real balance alone. The question is: given the path of interest rates, does the path of the real balance matter? Woodford 2003 says no.

[Nick Rowe]

Jeff: "The issue is not current, but intertemporal barter."

In Woodford's model, agents have identical time preference. There is no intertemporal trade, so a disruption in intertemporal trade cannot cause problems. If the central bank sets r (the real rate) too high, every agent wants to buy bonds for current apples and bananas, and will be unable to. But so what. What matters is whether they can sell current apples for money so they can buy current bananas. And if they can barter, they just barter current apples for current bananas.

"You don't clear inter-bank payments."

True. IOUs signed by Nick Rowe are not used as a medium of exchange. IOUs signed by the Bank of Canada (whether they are paper or electronic IOUs) are used as a medium of exchange by both people and commercial banks. Commercial bank IOUs are promises to pay Bank of Canada IOUs, at a fixed exchange rate.

"It's in there, if you want."

The Pigou effect *needs* to be in there. Otherwise real output is indeterminate in Woodford's model, even if the central bank always sets a (real) interest rate equal to the natural rate. Start in equilibrium, then halve Y for all time-periods, and the Euler equations are still satisfied. Setting the right interest rate is a necessary condition for output being at the natural rate. It is not a sufficient condition. Woodford just assumes (people expect) "full employment", even though there is nothing in his model to get the economy there.

[Jeff]

"There is no intertemporal trade, so a disruption in intertemporal trade cannot cause problems."

This is not correct. Of course, the representative agent doesn't trade at all, either spot or intertemporally. But the representative agent is an aggregate construct, the result of disparate agents with unlimited access to credit (between them) as well as either

1) a very particular set of types of utility functions; or
2) complete markets

So just like there is lots of trade between different agents with different preference for different goods, there is also lending between agents with different time preferences. The point is they trade, lend, etc until their preferences for each good (spot *and* future) are identical at the margin. Being identical at the margin is what reduces them to a representative agent. But they have to trade and lend to get there, and changing the terms of trade between spot and future goods (the real rate) will cause a suboptimal allocation.

You may not like all these assumptions but I don't think you have an alternative ratex model that doesn't suffer from the same criticisms. Anyways, this is just standard finance/DSGE macro, so I'm guessing you already know it, but disagree with it, and I'm probably missing the point.

"Woodford just assumes (people expect) "full employment""

I don't think that's correct. Off the top of my head, given a Taylor rule, solutions are either convergent or divergent. I don't think you can get an asymptotically stable state away from the optimum. On the other hand, if you don't assume a Taylor rule, I think you can get all kinds of "equilibria." Is this what you meant by: "Setting the right interest rate is a necessary condition for output being at the natural rate"?

In practice though, I think it's unwise to take the asymptotic behaviour of any model too seriously. Real agents always have time preferences/credit constraints that render horizons significantly shorter, and higher private discount rates make asymptotic assumptions irrelevant, and make solutions more robust. If the market for 30 year assets doesn't imply a divergent equilibrium you shouldn't worry about that state in your model. Instead you should worry about exactly how credit constraints are operating, and breaking your representative agent.

"The Pigou effect *needs* to be in there."

I don't know what you mean by Pigou effect, but if you mean that the CB controls the real balance, then it *is* in there, but it doesn't make any difference *except* to the extent that it moves the real interest rate. Is that a "Pigou effect"?

BTW, you never answered the criticism that Hume's thought experiment is neither well specified or simple.

[Nick Rowe]

Jeff: take the simplest possible NK model. All agents are identical, except each agent can only produce one of the n goods, but wants to consume all n of those goods (Dixit Stiglitz). (So each agent is a worker/firm, and output and employment are the same thing.) Let Y* and r* be the standard monopolistic competitive equilibrium. The standard NK model says that if the CB sets r above r*, then Y will be below Y*. It's a recession. Now suppose agents can barter the good they produce for the other goods they want to consume.

one old post here on NKs assuming full employment.

another old post on the Pigou effect

[Jeff]

Nick,

Yes, you set up your model to rule out intertemporal trade. And then, as you point out, barter solves the spot trade problem. But real agents need intertemporal (e.g. intergenerational) exchange, which means they need lending. We all move through the stages of life from debtor to creditor and so the real rate has a huge impact on our consumption/investment decisions. Therefore the lending rate matters, exactly as in the NK model. If you want, you can model all those disparate agents explicitly. If they all have the requisite utilities and unlimited access to credit between them, you will get exactly the representative agent result but you will see how lending balances evolve as a result of all their rational borrowing/consumption decisions as the model evolves. No real balance required. Just rational consumption/savings decisions.

The corollary of your example is that so long as we have the right quantity of money, the real rate doesn't matter, which is patently absurd. The BOC can simultaneously achieve *any* real balance and real rate at the same time (via OMOs and setting IOR). If they set IOR at 20%, it doesn't matter whatsoever where they set the real balance. The economy will collapse. It's the real rate, and the CBs ability to set it that matters.

[Jeff]

Nick,

If you want, just start with all agents the same except 99% of them are deep in debt to the other 1%, no credit constraints, simple (e.g. log) utilities as usual. I.e. a representative agent economy where borrowing rates matter a lot.

[Nick Rowe]

Jeff: " We all move through the stages of life from debtor to creditor and so the real rate has a huge impact on our consumption/investment decisions. Therefore the lending rate matters, exactly as in the NK model."

But that is not what is going on in the standard NK model. The simple models have no investment, and everyone has the same rate of time preference, but they still have recessions. How?

Sure relative prices matter. If a law sets a minimum price of apples relative to bananas, that will cause real problems. Getting the money supply right is necessary, but is not sufficient. But central banks, unlike governments, can't pass laws setting minimum or maximum interest rates. They can only control their own balance sheets.

[Jacques René Giguère]

Nick:" True. IOUs signed by Nick Rowe are not used as a medium of exchange. IOUs signed by the Bank of Canada (whether they are paper or electronic IOUs) are used as a medium of exchange by both people and commercial banks. Commercial bank IOUs are promises to pay Bank of Canada IOUs, at a fixed exchange rate."
So thanks for confirming what I said about debit cards...

[Nick Rowe]

Jacques Rene: yep. if we both bank at BMO, a debit card just shifts BMO money from my account at BMO to your account at BMO. If you bank at TD, it also shifts BoC money from BMO to TD.

[W. Peden]

Nick Rowe,

If I may embarass you with some praise: it's been a pleasure to watch you develop these arguments about NK and contemporary central banking over the past few years. Quite apart from being informative, they've also helped me learn a lot about macroeconomics, and NK & monetary economics in particular.

I don't praise every single post, which would get repetitive and even counter-productive, but I do find them very useful. I can still remember the Old Keynesian/New Keynesian post on "You're assuming full-employment!" that is a logical ancestor of this post.

[Jeff]

"The simple models have no investment"

OK, forget the investment, which is irrelevant. Just consumption/savings, like in the simple NK model. Assume some agents have debt to other agents by initial endowment. Apart from that they are all identical, and have convenient (for the modeller) utilities. Then you *do* get the representative agent economy despite the agents differing in wealth and savings position.

"everyone has the same rate of time preference, but they still have recessions."

If all the agents have the same rate of time preference, I'm guessing the elasticity of intertemporal substitution for the representative agent goes to zero (there is no lending so the real rate doesn't matter - it's the price of a good that doesn't trade), and the right side of the consumption euler equation is just zero. I.e. you won't have any output gap no matter what the real rate. (I think that's right, but I haven't thought about it before, so maybe it's wrong).

However, in practice we see that real rates are very important for agents in the economy, so in general the elasticity of intertemporal substitution for the representative agent will not be zero.

"But central banks, unlike governments, can't pass laws setting minimum or maximum interest rates. They can only control their own balance sheets."

Not correct! They can "pass a law" *setting* IOR, which is an absolute floor on rates.

"Getting the money supply right is necessary, but is not sufficient."

I'd say it's neither.

[Jeff]

I'm losing track, so I made a summary of points that I consider unanswered in this debate:

1) The Humean thought experiment doesn't settle anything. It sweeps all the important issues under the carpet. Therefore there is no trivial case in favour of monetarism.

2) The central bank can control *both* the real rate and the real balance independently (within the constraints of the ZLB). If you set IOR at 20%, it doesn't matter what the real balance is. The economy will tank.

3) What is a "Pigou effect"? The NK model is consistent with the idea that it is the real balance that determines the spread between the short rate and IOR in a floor system. The CB can control the real balance in the NK model. Is this not a Pigou effect?

4) Underlying agents in the NK model may be very different (you said they all have the same time preferences), and yet there may be an aggregate representative agent. It is not correct to say that agents have the same rate of intertemporal substitution or that "there is no intertemporal trade." (Of course, there is no net trade in aggregate!)

5) The intertemporal rate of substitution of the representative agent may not be zero, even though the net aggregate borrowing is zero. In practice the intertemporal rate of substitution of the representative agent is not zero because there are very large savings balances between real agents in the economy.

6) The NK model with a Taylor rule does *not* have asymptotically stable states away from the optimal allocation. Nobody's just assuming full employment.

I'm trying to respond to your points as carefully as possible but please let me know if you find that I have neglected something important.

[Tom Brown]

Jeff, I find your exchange w/ Nick fascinating, even though I'm only grasping about 10% of it. Well, OK, 5%. I'm hoping that one of you will cry uncle and concede defeat, though I expect that's unlikely. How would you describe yourself? A fan of Woodford and NK models? You should drop by more often.

[Tom Brown]

5% ... basically I know what apples and bananas are. :(

[Jeff]

Tom,

Nobody ever cries uncle on the internet! Usually one person just stops commenting, and then goes back to ignoring any points made during the discussion. I will try not do that here, and I really doubt Nick will either, because he seems like one of the few people who is actually using this medium to try to advance ideas and improve the discussion, rather than score political points (and this debate has big political implications).

And yes, Woodford is great. Everyone should read his book, which is massive, not because of the equations, but because it is packed with extensive deep and insightful discussion of pretty much every monetary issue that anyone has ever argued about on the internet. Compared to the amount of time some people spend arguing about this stuff, it's too bad that they don't take a couple of weeks to work through the most important modern book on the topic.

[Jeff]

Oops! In my point #5 above "intertemporal rate of substitution" should have been "elasticity of intertemporal substitution", both times.

What a stupid term! Why can't we have a simpler word for an important concept. I propose "time flexibility".

[D. Tohmatsu]

Jeff, you said;

"Sure, they'd think they got it. Even though you didn't say anything about what operation you carried out. Did you just print it up and give it away? Did you buy t-bills with it? Does it matter? Are you going to tax it all back next year or sell back the t-bills? Ever? What is the path of nominal t-bill rates between now and then?.... "

This is an important point that you make. Most people don't get this and assume that the effect of a helicopter drop would be identical to OMP, which it is not ...just as the effect of a bank lending money would not be identical to the effect of a bank giving money away.

Your point on the level of bank reserves is also important and usually overlooked by monetarists. OMP which merely result in an increase of bank reserves held by commercial banks at the Fed will have no more effect on the economy than if the Minneapolis Fed did OMP with the St. Louis Fed as their counter-party.

[Too Much Fed]

Jeff, could you apply elasticity of intertemporal substitution to Warren Buffett and Apple Inc.? Thanks!

[Tom Brown]

Jeff, you write "Nobody ever cries uncle on the internet!" ... you must have missed the debate between Mark A. Sadowski and Steve Randy Waldman then. It took place at Steve's site and when it was over Steve had updated at least one of his posts so that his text was entirely in strikethrough and he added a large red "Bullshit" watermark to all of his charts!

[Nick Rowe]

W Peden: thanks! Yes, it's taken me a long time to develop my thoughts on this.

Tom: this is not a wrestling match. I am trying (and so far failing) to explain something to Jeff. (Jeff probably feels the same way).

Jeff: "Assume some agents have debt to other agents by initial endowment. Apart from that they are all identical, and have convenient (for the modeller) utilities. Then you *do* get the representative agent economy despite the agents differing in wealth and savings position."

Simple NK models assume all agents are identical (but each firm specialises in producing just one good). And they say that the economy will have a recession if the central bank sets the interest rate too high. For this discussion, I am quite happy to work with that simple model (but I would like to simplify further by assuming each agent is a firm).

The question is: in that simple model, does the CB setting the interest rate too high cause a recession, if agents can barter apples for bananas? I say no. Because if it did cause a recession, the underemployed apple and banana producers will just barter their way back to full-employment, because those barter trades would be mutually beneficial. Do you say yes?

Take an even simpler model. Start with a standard NK model. Identical agents, monopolistic competition, Calvo pricing. Now assume there is a taboo against all forms of borrowing and lending. So there are no interest rates. And people use shells as a medium of exchange, so there is no central bank. Can we get a recession? Yes. If some of the shells are destroyed, and if prices are sticky, there will be an excess demand for shells, and agents will buy fewer goods in an attempt to increase their individual stocks of shells, so we get a recession.

Now suppose the taboo on borrowing and lending is suddenly lifted. Does it make any difference to the equilibrium? No.

Now suppose the agents figure out a way to trade apples for bananas without using shells. Does it make a difference to the equilibrium? Yes. Because the apple producer prefers consuming bananas to apples on the margin, and the banana producer prefers consuming apples to bananas on the margin, so they do barter trades.

[Nick Rowe]

Jeff: the central bank can set the interest rates at which it is prepared to borrow and is prepared to lend. I can set the interest rates at which I am prepared to borrow and am prepared to lend. What is the difference between the central bank and me? The central bank's IOUs are used as money. Mine aren't.

[Tom Brown]

explanation vs "wrestling match"... well I'm fine with a cry of "Ah-ha!" ... so long as someone is crying.

[Too Much Fed]

“Imagine you lived in a world where the central bank issued two types of money: paper money; and electronic money.”

And, “The central bank adjusts the nominal interest rate on electronic money to try to hit that target real interest rate on paper money.”

For Tom, Jeff, or anyone else, let’s assume pre-2008 conditions in the USA. Currency yields 0%, electronic money of the central bank (central bank reserves) yield 0%, and the fed funds rate is 4%. The fed wants to lower the fed funds rate to 2%. It buys gov’t bonds and sells central bank reserves. There are excess central bank reserves. The fed funds rate starts falling towards zero. The fed sells the bonds and buys the central bank reserves back in the same amount so the fed funds rate is 2%.

The amount of currency remains the same, and currency still yields 0%. The amount of central bank reserves remains the same, and central bank reserves still yield 0%. What theory is the fed using under these conditions?

[Too Much Fed]

Nick's post said: "True. IOUs signed by Nick Rowe are not used as a medium of exchange. IOUs signed by the Bank of Canada (whether they are paper or electronic IOUs) are used as a medium of exchange by both people and commercial banks. Commercial bank IOUs are promises to pay Bank of Canada IOUs, at a fixed exchange rate."

By commercial bank IOUs, I'm pretty sure you mean commercial bank demand deposits. Commercial bank bonds and commercial bank stock are not at a fixed exchange rate.

[Jeff]

"Simple NK models assume all agents are identical"

No, I don't agree. They assume no borrowing constraints and agent preferences (or complete markets) such that you can aggregate the agent behaviour to a representative agent. When you see an NK model with a single agent (or where, as you say, all agents are the same), there are actually an infinite number of possible combinations of agents with disparate preferences that could aggregate to that representative agent. So it's simply not correct to say that the agents are all the same. You can't tell. All you know is that the aggregate agent has certain characteristics, such as a rate of intertemporal substitution and most critically for this discussion, a non-zero *eleasticity of intertemporal substitution* (EIS). I've made this point above (see 4 and 5), and I don't see how we can pass over it. If the real agents in the economy have large debts between them, then the representative agent will have a non-zero EIS. And then real rates away from the natural rate will cause an output gap.

This whole conversation is about the EIS. If the EIS of the representative agent is non-zero, a non-optimal real rate will cause an output gap. Just look at the Euler equation. We won't make progress in this conversation without settling this point.

"in that simple model, does the CB setting the interest rate too high cause a recession, if agents can barter apples for bananas? I say no. Because if it did cause a recession, the underemployed apple and banana producers will just barter their way back to full-employment, because those barter trades would be mutually beneficial. Do you say yes?"

If the real agents are identical, then there will be no borrowing, so I'm thinking the representative agent will have zero EIS, so no recession.

"If some of the shells are destroyed, and if prices are sticky, there will be an excess demand for shells, and agents will buy fewer goods in an attempt to increase their individual stocks of shells, so we get a recession."

A world of identical agents who can't borrow from each other, is a really bad model of the real world. I'm sure it can have recessions, but I don't see how it's relevant to the real world. The question is how to model worlds of agents who can and want to borrow from each other. The NK framework is exactly such a model. The NK rep agent is an aggregation of those agents.

"The central bank's IOUs are used as money. Mine aren't."

They matter because they are the unit of account. The quantity doesn't matter. See my point #2 above.

[Kevin Donoghue]

Nick: "The question is: in that simple [NK] model, does the CB setting the interest rate too high cause a recession, if agents can barter apples for bananas? I say no. Because if it did cause a recession, the underemployed apple and banana producers will just barter their way back to full-employment, because those barter trades would be mutually beneficial."

Suppose the market prices in money are Pa and Pb. Are you saying there are opportunities for Pareto-improving barter trade at that fixed exchange-rate Pa/Pb? I don't think that's true, in Gali's version at least. After all, any agent can sell at Pa and buy at Pb, with no net change in money held. There's no restriction and hence no advantage in being able to barter.

Of course, if they can barter at a price other than Pa/Pb that's another matter. That bypasses the Calvo price-setting apparatus, which changes the model in a fundamental way.

[Nick Rowe]

"Suppose the market prices in money are Pa and Pb. Are you saying there are opportunities for Pareto-improving barter trade at that fixed exchange-rate Pa/Pb? I don't think that's true, in Gali's version at least."

Kevin: yes, I am saying that. I have made this same point several times in the past. Let me explain why.

Just to make it easier for me to explain, suppose inflation has been zero for a long time, and there have been no shocks, so we are at the natural rate, and Pa=Pb. Then the central bank suddenly, for no reason at all, raise the interest rate above the natural rate. Ct and Yt drops, from the consumption-Euler equation. We are in a recession. The marginal utility of consumption rises, and the marginal utility of leisure falls. To keep it simple, suppose Calvo's fairy has visited neither the apple producer nor the banana producer, so Pa and Pb stay the same.

Now let the apple producer produce one more apple, and the banana producer produce one more banana, and let them both do a barter swap of one apple for one banana. Both agents are better off. The marginal utility of a extra banana (apple) exceeds the marginal disutility of the extra labour need to produce an extra apple (banana).

If Calvo's fairy is very slow, so the price stays the same for all goods, barter gets the whole economy back to the natural rate of output and employment.

Actually, we can go further than this: Barter can get the whole economy back to the ***competitive*** equilibrium. (Remember that both output and employment will be suboptimal at the natural rate in an NK model, due to monopolistic competition.) Because, given symmetry of monopoly power, all prices are above marginal costs of production by the same percentage, so relative prices Pa/Pb are equal to competitive equilibrium relative prices. The assumption that *all* firms having monopoly power and set prices above marginal costs only makes sense in a monetary exchange economy. Two monopolists will always want to do Pareto-Improving barter deals at their monopoly relative price. "I will only buy more from you at your price if you buy more from me at my price".

And I have made that second point before as well.

[Kevin Donoghue]

"Now let the apple producer produce one more apple, and the banana producer produce one more banana, and let them both do a barter swap of one apple for one banana."

In Gali's model, there's nothing to stop them from doing that; as I say, any agent can sell at Pa and buy at Pb, with no net change in money held. (You're not alone in having made these points before.)

[Nick Rowe]

The fact that both Kevin and Jeff are clearly very bright, and have been well-trained (or have trained themselves well) in New Keynesian (Neo-Wicksellian) macroeconomics, is what I find very depressing. Because it is being left to a clapped-out old guy like me to explain this very basic point in monetary economics. For all Woodford's brilliance (and he is brilliant) he has created another Dark Age in macroeconomics, by focussing our attention on interest rates and away from monetary exchange. People used to understand this point, back in the olden days, of disequilibrium macro.

[Kevin Donoghue]

A comment of mine seems to have gone astray. Such is life.

Nick, I haven't forgotten the days of disequilibrium macro. But you're making a claim about the NK model which is not a disequilibrium model. There's no axiom involved which effectively prohibits barter. If A and B want to swap apples for bananas, where does Gali say they can't? The problem is, they don't want to, because the prices they are required to trade at are not optimal prices.

[Nick Rowe]

Kevin: I fished your comment out of the spam filter. It seems to be playing up again.

"There's no axiom involved which effectively prohibits barter. If A and B want to swap apples for bananas, where does Gali say they can't?"

AFAIK, he doesn't. It's an implicit assumption. he probably doesn't realise he's making it. Which is the problem. Like Jeff, he is saying "Look at the consumption-Euler equation! See! Consumption and output must fall if the central bank sets r above r*!"!"

"The problem is, they don't want to, because the prices they are required to trade at are not optimal prices."

If both apple and banana producer have the same elasticity of demand curve, and if the Calvo fairy has visited neither since the last shock, then the relative price Pa/Pb will be exactly the same as in perfectly competitive frictionless equilibrium.

If you allow free barter at the NK relative prices, then the only difference that Calvo pricing makes is that relative outputs will be distorted.

[Kevin Donoghue]

Yes, relative prices can be exactly what they would be with no output gap. But that's not enough, because all agents know that the disruption caused by the creaky pricing mechanism will affect their real incomes.

Here's a version of your argument which does work, I think, though it doesn't quite give you what you want:

Suppose agents are allowed to make contingent contracts of the following sort: for as many future periods as A and B find themselves constrained to trade at their existing prices, they commit to supply each other with goods of equal value. Once one of them is free to change price, the contract expires. That arrangement increases the lifetime income of both parties and consequently it supports their demand for each others' products. I think that works. But it's crucial that it applies (with Prob > 0) to one or more future periods.

BTW, thanks for the kind words but at 62 I'm pretty sure I'm older than you and I'm certainly more clapped-out! Even thinking about this stuff wears me down, never mind blogging about it. Many thanks for the effort you put in.

Now for my nightcap.

[Tom Brown]

Nick, have you ever brought any of these points up to Woodford directly? JP Koning wrote him an email once and he responded. For all I know, you guys converse on a regular basis... but I don't get that impression.

[Tom Brown]

"clapped-out" eh? Is that a Canadian thing?

[Nick Rowe]

Kevin: "Yes, relative prices can be exactly what they would be with no output gap. But that's not enough, because all agents know that the disruption caused by the creaky pricing mechanism will affect their real incomes."

Fair point. Calvo pricing will disrupt relative output prices, which will make real income lower than it would be with perfectly flexible prices, even if we allow barter at those relative prices.

But this to me is the important point: the Consumption-Euler equation will *not* determine consumption, if we allow barter. Agents will be "off" their consumption-Euler equations.

[Nick Rowe]

Tom: "clapped out" is Brit (and Aussie and NZ and Irish?) slang. Usually applied to old cars.

[D. Tohmatsu]

Nick, you're description of the "long run" part of theory is somewhat misleading. The accurate way to state it is, "If the Central Bank successfully achieves it's target to lower the real interest rate on paper money, then the nominal rate on electronic money will be higher.

Which, BTW is obvious and trivial even when described in an obtuse manner.

[Nick Rowe]

D.T.: OK. Your wording of the long run part is better than my original.

Is the Fisher effect that obvious and trivial? Try explaining it to some heterodox economists!

(And remember that money will generally not be precisely super-neutral, if the nominal interest rate on currency is stuck at 0%.)

[Jeff]

"Like Jeff, he is saying "Look at the consumption-Euler equation! See! Consumption and output must fall if the central bank sets r above r*!"!""

Seriously?!? That stupid comment is all you heard me say? I must have patiently repeated at least 3 times how disparate agent preferences which result in inter-agent borrowing could aggregate to a representative agent with non-zero EIS. I gave you words about rational choices of indebted economic agents, not equations! You never replied to it, and now I see you simply ignored the explanation, and accuse me of just pointing moronically at an equation, like some kind of autistic savant.

[JKH]

Nick,

Was the Kocherlakota brouhaha about the sort of thing you explain in this post?

[JKH]

...........

Alex: "I don't like this post. It looks convoluted and non-informative to me. I have a suggestion: try to reformulate it in the terms of supply and demand."

NR: It is supposed to look convoluted and non-informative. The whole point of the post was to show how weird things look when you only talk about interest rates and don't talk about supply and demand!

...........

I like this post very much.

It looks like an incisive and very direct explanation of central bank generated interest rate cycles to me.

It's the opposite of convolution - as far as the explanation of how it works is concerned.

I suppose I should be worried.

[Nick Rowe]

Jeff: I am perfectly willing to grant the NK assumption of a representative agent with a non-zero elasticity of intertemporal substitution, (for the purposes of this argument).

In general you can not aggregate heterogenous agents into a representative agent, but all models need to make simplifying assumptions, and that assumption of a representative agent with non-zero elasticity of intertemporal substitution is not what I am arguing against.

The reason I ignored your argument about aggregating heterogenous agents into a representative agent is that you were using an argument I did not agree with to persuade me to accept an assumption I was already perfectly willing to accept without that argument.

The standard NK model assumes agents with identical preferences with non-zero EIS. Let us accept that assumption. The standard NK model says that if the central banks sets r above r*, then C and Y will fall below C* and Y*, according to the consumption Euler equation. Let us see if that conclusion still follows if agents can costlessly barter at the sticky relative prices.

[Nick Rowe]

JKH: "Was the Kocherlakota brouhaha about the sort of thing you explain in this post?"

Yes. I think it's related.

[D. Tohmatsu]

Nick: "Is the Fisher effect that obvious and trivial? Try explaining it to some heterodox economists!"

What is a heterodox economist?

Nick: "(And remember that money will generally not be precisely super-neutral, if the nominal interest rate on currency is stuck at 0%.)"

By this are you referring to changes in V caused by changes in nominal r on non-currency money.

[D. Tohmatsu]

Nick: "The standard NK model assumes agents with identical preferences with non-zero EIS. Let us accept that assumption. The standard NK model says that if the central banks sets r above r*, then C and Y will fall below C* and Y*, according to the consumption Euler equation. Let us see if that conclusion still follows if agents can costlessly barter at the sticky relative prices."

Don't want to jump into the middle of an entertaining discussion, but wouldn't that require perfectly elastic supply and demand curves.

[Kevin Donoghue]

Nick,
Having slept on it I think you have a point, but it's not the point you think you have. I'm pretty sure this monetary-exchange-versus-barter discussion obscures the issue. In Gali's model, any barter transaction you might contemplate can be accomplished simply by transforming it into a Goods -> Money -> Goods transaction. So nothing which barter can do is actually ruled out; at least, it's not explicitly ruled out.

Where I think you have a point is this: the equilibrium concept is a bit dodgy. The firms are monopolistic competitors whenever they get the okay from Calvo. But what are they at other times? They are price-takers of a sort. But of what sort, exactly? After all, Keynes's firms are price-takers too, but not in the sense that Walras intended.

I might look for Calvo's original paper which introduced this trick and see just what his ground-rules were.

[Nick Rowe]

DT: "What is a heterodox economist?"

Good question! I don't really like that term myself, because all of us have different beliefs about different things. But, for this purpose, it means "those who self-identify as heterodox economists".

"By this are you referring to changes in V caused by changes in nominal r on non-currency money."

That wasn't what I had in mind. What I had in mind was: if money growth increases, and inflation increases, the real rate of interest on currency falls, so people will hold smaller real currency balances, which is one real effect, and that real effect will sometimes cause other real effects too, depending on the model.

"Don't want to jump into the middle of an entertaining discussion, but wouldn't that require perfectly elastic supply and demand curves."

I don't think so. As long as they aren't perfectly inelastic.

Kevin: take a very simple case. Suppose you and I buy from each other. Start in competitive equilibrium, then double both our prices (by law). I want to buy less from you, and you want to buy less from me. You want to sell more to me, and I want to sell more to you. The short side rule says we both actually buy and sell less from each other. (It's a mini-recession.) But I can offer you a deal, that can get us both out of our mini-recession. "I will buy $100 more bananas from you if and only if you buy $100 more apples from me in return." You would accept that deal. But that deal, where I give you $100 in exchange for bananas, and you give me that same $100 right back in exchange for apples, is identical to a barter deal, where we forget about the $100.

The equilibrium concept: Suppose we have an economy with n goods, each good produced by one firm. Cournot Nash equilibrium is well-defined. Each firm sets its own Qi taking others' Qj as given. But Bertrand equilibrium is not well-defined. We cannot have n firms setting n-1 relative prices. We need some n+1st good, so that each of the n firms can set Pi in terms of the n+1st good. We definitely need an extra good to serve as medium of account. My argument is that it matters a lot whether that n=1st good also serves as medium of exchange.

The key assumption in NK models with monopolistic competition is that firms choose Pi (when the Calvo fairy lets them) and customers choose Qi. (I'm OK with that assumption, but if we changed it we would get very different results.)

[Kevin Donoghue]

"But that deal, where I give you $100 in exchange for bananas, and you give me that same $100 right back in exchange for apples, is identical to a barter deal, where we forget about the $100."

That's my point exactly! If an ideal barter economy can solve the problem, then a monetary economy can too, since it doesn't cost anything to book two deals involving money for goods, instead of one deal involving goods for goods. Barter solves nothing unless it permits a deal which would otherwise be impossible.

I had a quick look at Calvo (1983). There seems to be a tacit assumption that all trades take place in a market and the kind of deals you envisage are ruled out. But that's not stated explicitly.

In other words, I think there's an unstated assumption in the NK model that I can pocket your $100 and leave you holding both kinds of fruit. So naturally you won't part with your $100 in the first place. We can't write a contract which ensures completion of a compound, equivalent-to-barter deal.

[Nick Rowe]

Kevin: Great! We are in agreement.

In practice, of course, it would be very unlikely that the purely *pairwise* trades would get an economy out of recession. If I bought bananas from you, and you bought carrots from Jeff, and Jeff bought apples from me, then all three of us would need to meet together to do a 3-way deal. And that meeting would be hard to arrange. And this is precisely why people use a medium of exchange instead.

"There seems to be a tacit assumption that all trades take place in a market and the kind of deals you envisage are ruled out. But that's not stated explicitly."

I would say there seems to be a tacit assumption that all trades are pairwise trades using a medium of exchange and only one other good. But yes, it is not explicit. I think it needs to be made explicit. Otherwise people think that money is not in the model, except as a medium of account.

[Too Much Fed]

Nick said: “According to that theory: if the central bank wants to lower the real interest rate on paper money (because it thinks there's a danger the real interest rate on paper money will rise above target unless it does something) it needs to lower the nominal interest rate on electronic money. The central bank calls this the "short run" part of its theory.”

And, “That wasn't what I had in mind. What I had in mind was: if money growth increases, and inflation increases, the real rate of interest on currency falls, so people will hold smaller real currency balances, which is one real effect, and that real effect will sometimes cause other real effects too, depending on the model.”

Are you assuming that “money” growth increases means the nominal interest rate falls on electronic “money” of the central bank (EMCB)?

I don’t believe the second part has to be true for firms like Apple. If prices go up and quantities stay the same or go down, Apple is not going to use currency or demand deposits to expand capacity. I think you are assuming an aggregate demand shock. What if it isn’t an aggregate demand shock?

The central bank announces QE at the zero lower bound. They buy a gov’t bond from Apple. Apple holds the demand deposits. Nothing happens. The fed gets an existing bond. Apple gets new demand deposits as an asset and a liability of Apple’s bank. The bank where Apple has its account gets its EMCB account at the fed marked up where EMCB is its asset and the fed’s liability.

[Too Much Fed]

"The two monies have a pegged exchange rate of one. The central bank swaps paper money for electronic money at par, on demand."

Now add demand deposits that are 1 to 1 fixed convertible to currency.

And, "That wasn't what I had in mind. What I had in mind was: if money growth increases, and inflation increases, the real rate of interest on currency falls, so people will hold smaller real currency balances, which is one real effect, and that real effect will sometimes cause other real effects too, depending on the model."

Will that part still work if demand deposit growth is substituted for "money" growth?

[Jeff]

Nick,

"The reason I ignored your argument about aggregating heterogenous agents..."

If you repeatedly ignore someone's extensive explanations, and just keep reasserting your premise (agents are all the same), they are going to think you aren't listening at all. How would I know if you are even reading what I'm writing? This is a lot of work.

"let the apple producer produce one more apple, and the banana producer produce one more banana, and let them both do a barter swap of one apple for one banana. Both agents are better off. The marginal utility of a extra banana (apple) exceeds the marginal disutility of the extra labour need to produce an extra apple (banana)."

I'll give you a loan (at the policy rate) to buy my apple, but I'm not buying your banana! Instead I'll cut my consumption, invest my savings above the natural rate, wait one period and then have a fruit salad party when I collect your loan.

Am I being irrational?

[Nick Rowe]

Jeff: "Am I being irrational?"

That depends. If someone else wants to buy all the apples you want to sell, and wants to borrow from you to finance those apples, you are not being irrational. But if you find that other people don't want to do that, so you can't sell as many apples as you want to sell, and they can't sell as many bananas as they want to sell, then you (and they) would be irrational to turn down a barter deal.

[Jeff]

Nick,

Lets assume your barter solution works. In that case it must work for any pair of goods, including identical goods, so if you can prevent a recession in a two-good world, you can also prevent one in a one-good world, which makes the analysis simpler.

Lets say we have lots (millions) of agents. The CB sets the real rate at 100% and I decide to reduce my consumption by 100% this period (assume linear utility), so I can consume 300% (100% of my output plus I double my savings at the 100% real rate) in the next period. Since there are lots of agents and a large lending market, there is no way the rest of you can coordinate to prevent me from depositing almost all my attempted savings (lets assume that lending is anonymously intermediated). By defecting, I will fail to save my attempted savings only in proportion to my fraction of the whole economy. I.e. I will succeed almost perfectly. So I'm arbitraging the rest of you in a big way, and very quickly everyone is going to join in and help me cause a depression. But if the rest of you all hold out, I'm just going to make big profits. Your equilibrium is not stable. In a world with many players, there is no way to coordinate against a defector.

[Nick Rowe]

Jeff: OK. I'm pretty sure I am following you in this example. To keep it simple, assume zero investment, G, and NX. So C=Y.

So you buy zero output from others. Suppose everyone else does exactly the same as you. So nobody buys any output. So your income is zero, and so is everyone else's. We have a very big recession. 100% unemployment rate. And since your income is zero, you cannot save and lend.

[If it were literally a one-good world, you would now produce output for your own consumption, because it is better than sitting idle. But let's assume there is a taboo against eating apples you have produced yourself, so you can't do that.]

So I offer you a deal: I will buy X apples from you, and you in return will buy X apples from me. You will accept this deal (unless X is very large).

You would prefer that I buy apples from you, without you buying apples from me, so you could save and lend your income. But nobody is offering to do that, in a recession, if you are unemployed. So your second-best action is to accept my deal.

In a one-good world, a pairwise trade gets both people back to full-employment.

The tricky case is where we have n goods. A produces apples, and wants bananas; B produces bananas and wants carrots; C produces carrots and wants dates; D produces dates and wants eggs; and so on in a very big circle; until X produces xylophones and wants apples. All 26 people in the Wicksellian circle have to meet together to do a 26-way barter deal. Which is a hard deal to negotiate and a hard deal to enforce (witness the UN.)

But it is precisely because 26-person deals are hard to do that people use a medium of exchange. That's why people use money. If we assume that people need to use money as a medium of exchange, in the NK model, it all starts to make sense. But you can't implicitly assume a medium of exchange, and then turn around and say that money is only a medium of account in NK models.

[Jeff]

Nick,

I think you meant a 24-good economy!

"But it is precisely because 26-person deals are hard to do that people use a medium of exchange."

Not hard. Impossible! The problem is apples are produced in the fall and last a few days, while bananas are produced year round; dates are produced in the fall, but last a long time; a xylophone is really a capital good, bought rarely buy consumed frequently. All of which means that trade is intrinsically intertemporal so exchange happens via intermediated credit balances, not simultaneous exchange. So money doesn't solve anything that credit can't solve, but credit, *also* solves the intertemporal exchange problem. Now modern credit uses central bank liabilities as the unit of account, but nowhere have I "assumed" the need for any outstanding quantity of a medium of exchange. Just centrally intermediated credit balances.

Now back to our one-good example:

I see your game now. You are circumventing the banking system by
extracting a self-sufficient coalition, like in the core equivalence theorem (We're going Galt!). The problem is that in a modern economy such a coalition is going to have to be big enough to sustain its own currency and banking system, and also legally extract itself from the sovereign jurisdiction (governments don't take kindly to circumvention of their currency). The cost of doing so are probably well described by the optimal currency area literature, but it's obviously more favoured if the central bank is running a really crappy monetary policy. But given that Greece hasn't left the Euro, it must take some seriously bad policy for a coalition to break off.

Which is to say, real rates matter and can have huge impacts on economies without the financial system being circumvented by self-sufficient coalitions (or barter, as you say).

[Kevin Donoghue]

Nick: "But you can't implicitly assume a medium of exchange, and then turn around and say that money is only a medium of account in NK models."

I think we're in agreement and then you write something like this. This Medium of Account/Medium of Exchange stuff confuses the issue I think.

In the NK model we have a law which says:

Rule 1.1) You may not exchange apples directly for bananas;

Rule 1.2) If you try to circumvent Rule 1.1 by setting up a compound deal which exchanges apples for money and money for bananas, your counterparty can leave you with twice the amount of fruit you want and no money.

The crux of the matter is that you can't work around the Calvo pricing system. It's not about the nature of money. It's got more to do with how you calculate your lifetime income. That is defined in terms of how much you can sell on the trading-floor, so to speak; the fact that you could increase your purchasing power by doing fancy bespoke deals is irrelevant because such deals aren't enforceable, whether they employ money or not.

But I very much agree with you on the need for New Keynesians to make this aspect of the model explicit. What you've changed my mind about is the relevance of the old "Disequilibrium Macro" literature. That stuff clarified what was going on in Old Keynesian models. NK models need similar clarification.

[Too Much Fed]

Nick said: "So you buy zero output from others. Suppose everyone else does exactly the same as you. So nobody buys any output. So your income is zero, and so is everyone else's. We have a very big recession. 100% unemployment rate. And since your income is zero, you cannot save and lend."

Jeff, did you mean that you save all your income (say $1,000) and lend all $1,000 to someone else so that other person can keep spending?

[Too Much Fed]

Jeff said: "Now modern credit uses central bank liabilities as the unit of account"

What about demand deposits?

[Tom Brown]

Let's summarize: Kevin changed his mind slightly, but Nick and Jeff haven't budged a bit. Correct?

[Jeff]

Too Much Fed,

"did you mean that you save all your income"

Yes

"What about demand deposits?"

Those are also *denominated* in units of central bank liabilities. But we don't need any quantity of central bank liabilities as a medium of exchange (that would be way too much Fed!).

Kevin,

I agree with pretty much everything you are saying. But not this:

"I very much agree with you on the need for New Keynesians to make this aspect of the model explicit."

There is no shortage of literature complaining about Calvo pricing. It's a well publicized fact that explicitly time-dependent (rather than state-dependent) price setting is weird, and it would be nice to have better micro foundations. Even the chapter in Woodford's book is littered with discussion about the meaning and the theoretical limitations and evidence for and against the Calvo model. It's not like the experts have never thought about this stuff and are obliviously waiting for someone to notice.

[Too Much Fed]

Jeff said: ""What about demand deposits?"

"Those are also *denominated* in units of central bank liabilities."

I'm not sure about denominated in central bank liabilities. There is 1 to 1 fixed convertibility.

And, "But we don't need any quantity of central bank liabilities as a medium of exchange (that would be way too much Fed!)."

Can you expand on that one? Are you saying there should be no currency?

What do you think is the MOA in the USA? You can't just say dollars. Be more specific.

[Tom Brown]

Nick, just curious: have you read Woodford's book?

Too Much Fed:

"Can you expand on that one? Are you saying there should be no currency? What do you think is the MOA in the USA? You can't just say dollars. Be more specific."

It sounds like he's saying the UOA for bank deposits is dollars. I think he's implicitly also saying that bank deposits are an MOE, but they are not the MOA: thus bank deposits work fine for an MOE: no need to print up reserve notes to do the job. That would be "too much Fed" (Haha). That's my read! I'm not sure he's getting the idea that you are theorizing that bank deposits themselves are MOA. And if he is getting that, then I think he's implicitly rejecting it. You might still be the only one in the world that thinks that. :D ... well actually you might be able to convince Cullen Roche ... if you could get him to agree that UOA, MOA, and MOE are super important concepts, which I'm not sure he's inclined to do. I've tried to drag him into that kind of discussion and he's never shown much interest, suggesting that people are overthinking the concept(s). I also tried dragging Mark A. Sadowski into it (I was hoping Sadowski would swoop down with a storm of empirical data to demonstrate that either Nick or Scott were on thin ice regarding their differences on this subject). But he too was reluctant to get dragged in, saying he could find nothing testable to distinguish Nick's and Scott's views. So good luck with your quest!

[Kevin Donoghue]

Jeff,
Thanks, I should read Woodford's book. I've been relying on Gali, who does most things well but not quite all. I don't doubt that these guys think hard about their theory. But from what I've seen they have not done a good job of communicating it, to students and indeed to other professors. Something is wrong when John Cochrane can write "the marginal propensity to consume is exactly and precisely zero in the new-Keynesian model", which is really quite blatantly false, without being subjected to hoots of derision.

[Nick Rowe]

Jeff: "So money doesn't solve anything that credit can't solve, but credit, *also* solves the intertemporal exchange problem."

Since there is always a delay between selling and buying, and we hold money in between, money also solves the intertemporal exchange problem.

But I think money vs credit can be a false dichotomy. Some credit is not used as a medium of exchange (my IOU's for example). But other credit can be used as a medium of exchange (Bank of Canada IOUs for example).

Imagine that the central bank issues paper currency, which people use as a medium of exchange. Every other good is bought and sold for paper currency. The central bank pays interest on that paper currency (ignore the practical difficulties), and can vary that rate of interest, and chooses to vary that rate of interest to try to keep inflation on target (maybe by following a Taylor Rule). Now suppose, to reduce the risk of muggers, instead of physically transferring the paper currency to the seller of goods, you send an email to the central bank telling it to transfer currency from your "safety deposit box" to the seller's "safety deposit box". Now make that paper currency an electronic currency which is transferred between electronic safety deposit boxes (which makes no theoretical difference). Now allow people to have negative balances in their electronic currency accounts.

It's still money. Do we now have the New Keynesian model?

[Jeff]

Kevin,

The only thing that's more ridiculous than criticizing a book one hasn't read is blaming the author for one's not bothering to to read it.

Nick,

"Do we now have the New Keynesian model?"

Yes, I don't think any of those economies are fundamentally different. Like I said, you get the same equilibrium whether the quantity of outside money is positive, negative, or zero. So long as prices are a bit sticky, and people can lend and borrow, and the central bank exercises its ability to determine the short rate, I think you have everything you need to get an NK economy.

And, BTW, when the central bank raises IOR you get a recession.

[Nick Rowe]

Jeff: "Yes, I don't think any of those economies are fundamentally different."

Now we are on the same page.

I would say that both the interest rate the central bank pays on that money, and the quantity of that money, will matter. If the central bank raises the interest rate holding quantity constant, or cuts the quantity holding the interest rate constant, you get a recession.

[Jeff]

Nick,

"Now we are on the same page."

It's an internet first!

"I would say that both the interest rate the central bank pays on that money, and the quantity of that money, will matter."

I think Eggertsson and Woodford 2003 basically answered that question from a theoretical perspective (contingent on the rate, the quantity doesn't matter under fairly general assumptions). But also from the perspective of bank capital requirements and every other bank economic decision that I can think of, I find it hard to see how swaps of t-bills for equal yielding reserves can impact decisions of any economic agents in any significant way.

"If the central bank raises the interest rate holding quantity constant, or cuts the quantity holding the interest rate constant, you get a recession."

Are you saying they can offset each other or do you believe we need to get them both right to avoid a recession?

[Jeff]

Kevin,

The tone of that comment was unnecessarily harsh. The harshness wasn't really intended for you. Sorry.

[Kevin Donoghue]

Jeff,
No problem. People who criticise books they haven't read surely are ridiculous. I my own case, I've made it clear to Nick that when we're discussing the basic NK model I take that to mean Chapter 3 of Jordi Gali's book.

[Nick Rowe]

Jeff: "Are you saying they can offset each other or do you believe we need to get them both right to avoid a recession?"

Normally, within limits, they can offset each other. If I cut the quantity and cut the rate at the same time by the right amount, we can avoid a recession. Expected future rates and quantities matter too.

Central bank credit, that is used as a medium of exchange, is not generally a perfect substitute for other forms of credit.

[Jeff]

Nick,

The quantity offset must be very small. The Fed has done trillions of QE in the past five years. If they could have lowered the real rate by 10% instead, the impact would have been huge. So we have two policy
instruments, one of which has very large and clear effects and one of which appears to depend, at best, on how much economic agents believe in it. Given that I'd say that 1) the focus, during normal times, on rates policy makes a lot of sense and 2) we need to think about implementing ways to eliminate the ZLB (like revoking physical currency).

What is the mechanism whereby you think the quantity acts (contingent on an invariant path of rates), and how do we ballpark the size of the effect? (The exchange equation clearly can't help us, given that the Fed has changed M by several orders of magnitude in the last few years without any obvious economic effect.)

"Central bank credit, that is used as a medium of exchange, is not generally a perfect substitute for other forms of credit."

No, but the demand to hold it rather than t-bills can be satiated. The price that demand is the difference between the risk-free interbank rate and IOR. If that price is zero and demand is infinitely elastic, then t-bills and reserves are perfect substitutes and it's hard to see how OMOs could work. What price in the economy is being affected? What agent's decisions change?

[Nick Rowe]

Jeff: Here's how I think of it:

To keep it simple, consider only stationary equilibria (and with no recession). Nothing changes over time.

Start out in an equilibrium with a very low (i.e. very negative) real interest rate paid on central bank monetary liabilities. The quantity will be very small. I.e. the size of the central bank's balance sheet (both assets and liabilities) will be very small as a percentage of annual NGDP.

As we raise the interest rate on the central bank's monetary liabilities, the equilibrium size of the central bank's balance sheet (as a percentage of annual NGDP) gets bigger and bigger.

Eventually, as we keep on raising that interest rate, the central bank needs to own all of the short term bonds, then all of the long term bonds, then all of the commercial bonds, then all of the shares, then all of the land and houses, .....and so on.

Finally, if we push Milton Friedman's Optimum Quantity of Money to its logical conclusion, we end up with communism, where the government-owned central bank owns all the assets in the economy.

And the further we move along that spectrum of equilibria, the bigger the absolute change in the size of the central bank would be, for a given change in the interest rate paid on money (or to compensate for a given sized shock to the economy).

[Jeff]

Nick,

OK, but there is no mechanism there. I was really wondering *why* it would work. I.e. "What price in the economy is being affected? What agent's decisions change?" Especially given the fact that demand for reserve-tbill swaps is clearly satiated (the price is zero and doesn't change any more as a function of supply).

Also, I understand that buying stocks might have all kinds of portfolio balance effects (Woodford appears willing to go full Wallace here, but I'm not). But those effects aren't "monetary," (they could just as well be done by the treasury), and as you say, they are dangerous.

[Nick Rowe]

Jeff: "But those effects aren't "monetary," (they could just as well be done by the treasury), and as you say, they are dangerous."

Yep. As we transition along my spectrum of equilibria, at what point does "monetary" policy become "fiscal" policy? Who knows. One merges into the other. If central banks had always bought and sold and held farmland, rather than Tbills, we might think of "monetary" policy differently. But they are all "monetary" in the sense that the quantity of money changes.

As to the quantity mechanism: let me go old-school.

Start in equilibrium, hold the interest rate paid on money constant, then suppose the quantity of money magically halves. Each individual tries to sell more goods and buy fewer goods to rebuild his money balances. They would each fail to sell more goods (since nobody else wants to buy more from them) but would each succeed in buying fewer goods. In aggregate, of course, they all fail to rebuild their money balances, but their individual attempts to rebuild their money balances by buying fewer goods results in a reduction in the volume of trade (a recession). Until, much later (given sticky prices) the price level eventually halves, and each individual stops trying to increase his money balances.

[Jeff]

"But they are all "monetary" in the sense that the quantity of money changes."

If t-bills and reserves are the same, the treasury could just as easily issue t-bills and buy assets with the same effect, and no change in the quantity of money. So it has nothing to do with money. It's an asset swap between risky and risk-free assets.

Since we *can* separate the two kinds of swaps (reserve-tbill and tbill-risky asset), we *should* for clarity purposes. Woodford calls the first monetary policy and the second "targeted asset purchases." Keeps the conversation clear.

"suppose the quantity of money magically halves"

There's no magic allowed! Like I said above (Jan 25, 6:07 am), Hume's thought experiment is not well defined. To know what's going to happen we need details about what, exactly, the central bank is doing (buying, heli dopping, whatever...). So let's assume the Fed halves the quantity in the US by selling $2Tn of t-bills...

"Each individual tries to sell more goods and buy fewer goods to rebuild his money balances."

Except that the demand for money is satiated at both values of the quantity, before and after your OMO. So the spread between t-bills and IOR is unchanged by the operation.

[Nick Rowe]

In my old-school story above, I halved the supply of money. Now suppose instead that I had kept the money supply constant, but had increased the interest rate paid on money, to double the demand for money. The rest of my story would be exactly the same.

Quantity of money or interest rate paid on money; supply of money or demand for money; an excess demand for the medium of exchange causes a recession. One story to rule them all.