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.
Worthwhile Canadian Initiative 
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.
Would you call then Ben Bernanke and John Taylor “finance theorists”?
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.
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.
This is just your interest rate differential framework restated in dynamic interest rate level terms isn’t it?
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.
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.
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.
“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.
“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?
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.)
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?
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!
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).
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).
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.
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.
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.
“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?
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.
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.
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…
“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.
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.
“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.
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
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.
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.
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.
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…
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.
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.
“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.
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.
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.
5% … basically I know what apples and bananas are. 😦
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.
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”.
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.
Jeff, could you apply elasticity of intertemporal substitution to Warren Buffett and Apple Inc.? Thanks!
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!
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.
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.
explanation vs “wrestling match”… well I’m fine with a cry of “Ah-ha!” … so long as someone is crying.
“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?
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.
“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.
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.
“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.