Brad DeLong calls it my "self-imposed Sisyphean task". He's probably right. But it seems worth a try, as long as there's a small chance he's wrong. I have a Cunning Plan.
Like it or not (and there is much to like as well as dislike), New Keynesian macro has become the main accepted approach for teaching, research, and policy. It would be hard to persuade economists to ditch it. Rather than ditch it, I want to reinterpret the New Keynesian model as a model of a monetary exchange economy (and argue that it only makes sense as a model of a monetary exchange economy). Then I want to make small changes to the model so that the stock of money enters essentially (and argue that it only makes sense if the stock of money enters essentially). My Cunning Plan is a bait-and-switch.
Simplify massively, to clear the decks of anything that is not required for me to make my points. Large number of identical infinitely-lived self-employed agents who produce and consume haircuts (the only good). So wages and prices are the same thing, and output, consumption, and employment are the same thing. All agents set the same price (which may be sticky or flexible). The central banks sets a rate of interest (somehow, and this is a question that must and will be answered). To make it even simpler, we can assume the central bank indexes the nominal interest rate to the inflation rate, so it sets a real rate of interest. No shocks, nothing fundamental ever changes, and full employment equilibrium is 100 per period.
Suppose the central bank sets the rate of interest too high. Will this cause unemployment?
No. Any unemployed agent would simply cut his own hair.
Suppose we change the model so agents can't cut their own hair, to motivate trade. Can we get unemployment now?
No. Two unemployed agents would simply do a barter deal to cut each other's hair.
We need to change the model so that monetary exchange is essential — they can't trade without using money as a medium of exchange. So let's do that.
You can't cut the hair of anyone who cuts your hair. So we get a Wicksellian triangle. And agents can only meet pairwise, and have bad memories for names and faces and can only remember the central bank. Or whatever. So they have to use central bank money to buy haircuts. Every agent has a chequing account at the central bank. The central bank pays a rate of interest r on positive balances, and charges the same rate of interest r on negative balances. And the sum of the positive balances equals the sum of the negative balances, so the central bank has no other assets or liabilities and zero net worth and zero income.
Now we can get unemployment if the central bank sets the real interest rate too high. Each individual wants to accumulate a positive balance in his chequing account by spending less money than he earns, which is impossible in aggregate.
Reinterpreting the New Keynesian model as a model of a monetary exchange economy, where every agent has an interest-earning chequing account at the central bank, kills two birds with one stone (it explains how the central bank can set the rate of interest, and explains how this can cause deficient-demand unemployment). Yet it leaves the equations of the model unchanged. No sensible New Keynesian macroeconomist should object to this reinterpretation. It's a friendly amendment — and not even really an amendment.
That was the easy part — the bait part of my Cunning Plan to bait and switch. And I'm just recapitulating my old post on solving the riddle of the New Keynesian Cheshire Cat.
Now for the harder part — modifying the model to make the stock of money essential. That's the switch part.
There are two definitions of the stock of money that would be useful in a model like this:
- The Net money stock = the sum of positive balances minus negative balances.
- The Gross money stock = the (absolute) sum of positive balances plus negative balances.
In the model I have sketched above, Net money is zero by assumption. The central bank could make Net money positive by buying some asset, or negative by selling some asset (open market purchases or sales).
In the model I have sketched above, Gross money will be zero, because all agents are identical. Holding Net money constant, aggregate receipts of money must equal aggregate payments of money by accounting identity, but if agents are identical this also is true for each individual agent. Each agent's receipts and payments of money are perfectly synchronised, so his inventory of money will always be zero.
If we add individual-specific shocks to agents' receipts and/or expenditures of money, we can change the New Keynesian model so that agents' receipts and payments of money are not automatically perfectly synchronised, which means the Gross money stock is now strictly positive.
Assume that the central bank sets a spread between the interest rate it charges on negative balances and the interest rate it pays on positive balances. Assume it is costly for agents to synchronise their payments and receipts of money (for example by agents with a positive balance lending to agents with a negative balance). We now have a demand for gross money as a negative function of the spread set by the central bank.
We now have something that looks a bit more like a traditional macro model, because it does have a money demand function.
Hold that thought. Because I now want to take a detour, and talk about the New Keynesian IS equation.
There is a very big problem with the New Keynesian Macro model. It simply assumes, with zero justification for this additional (hidden) assumption, that agents in the model expect an automatic tendency towards full employment. As I explained in my old post, Old Keynesians would be screaming blue murder if they understood that New Keynesians were making this illicit assumption. Because it is precisely this question that Keynes wrote the General Theory to address.
To repeat the point I made in that old post, if the central bank always sets the real rate of interest equal to the natural rate of interest, that is a necessary but not a sufficient condition for output being at the natural ("full employment") level. There is a continuum of equilibria, with anything from 0% to 100% unemployment being an equilibrium. This result follows immediately from the Consumption-Euler equation. In the simple case of log preferences, where n is the rate of time preference proper, it is: C(t)/C(t+1) = (1+n)/(1+r(t)). The real interest rate only pins down the expected growth rate of consumption, not the level of consumption. And New Keynesians evade this problem by simply assuming that in the limit, as t approaches infinity, C(t) approaches the full employment level.
That's a problem with the New Keynesian model. A very big problem. How can we fix it?
This big problem with the New Keynesian model is the result of the New Keynesian Long Run IS curve being horizontal. It is horizontal at the natural rate of interest. So if the central bank sets the real rate of interest equal to that natural rate, the long run equilibrium level of output is indeterminate. As any second-year economics student knows, if you have a horizontal IS curve, you need an upward-sloping LM curve to determine the level of output.
Back to that thought you were holding, about how we can modify the New Keynesian macro model so there is a well-defined demand function for the gross stock of money. What else do we need to get something like a standard upward-sloping LM curve? You guessed it: we need a supply function for the gross stock of money. And if we want the LM curve to slope up, so that the level of output is determinate, that supply function cannot be perfectly elastic at any given rate of interest.
It is not sufficient for a central bank to set a rate of interest (or one rate of interest plus a spread) and let the stock of money be determined by demand at that rate of interest. Long run output (not to mention the price level) is indeterminate if it does that, even if it sets the correct rate of interest. It needs to control the nominal quantity of money too. The central bank needs to set some nominal anchor, not just to make the price level determinate, but to make the level of output determinate.
The only mechanism that can provide an automatic tendency towards full employment (if, and that's a big "if", the central bank does the right thing) is the hot potato mechanism. If we reinterpret and reform the New Keynesian model the way it needs to be reinterpreted and reformed, we end up with Keynso-monetarism.
I ought to talk about "haircuts" in the financial market sense, and how collateral constraints mean the central bank puts limits on individual agents' negative balances, and how this creates a link between the Gross and Net stocks of money, and how Open Market purchases increase both Net and Gross money. But this post is already too long, so I will stop there.
Update: In a comment on my previous Cheshire Cat post, Brad DeLong asks: "If it isn't an RBC model minimally-tweaked to deliver Old Keynesian conclusions, why is it what it is at all? What other telos could it possibly have?"
On Thursday I heard Michael Woodford give a talk at a Bank of Canada conference. He started his talk by saying he visited the Bank of Canada in the late 1990's, spent time talking with Chuck Freedman and Kevin Clinton about how the Bank of Canada conducted monetary policy, which had been very influential in his subsequent work. I understood him to be talking about his "Interest and Prices". Indeed, the only important difference is that it is commercial banks, and not regular people, who have chequing accounts at the Bank of Canada. Otherwise, the model fits pretty exactly. I think that is the telos. Blame Canada.
Worthwhile Canadian Initiative 
Nick:
By a assuming that the CB sets an interest rate on a haircut-barber economy, didn’t we just make the CB the “owner” of this model economy? I ask because only an owner can redirect economic resources.
“This big problem with the New Keynesian model is the result of the New Keynesian Long Run IS curve being horizontal.”
Is this generally understood as explicit (or implicit) in the NK model, or an implication you’ve derived yourself from the Euler equation?
More generally, is the NK model formally/generally/usually disconnected from the formal ISLM analytical framework?
And are you “fitting” or reverse engineering the NK model into the ISLM framework?
Nick,
“Large number of identical infinitely-lived self-employed agents who produce and consume haircuts (the only good).”
Okay.
“To repeat the point I made in that old post, if the central bank always sets the real rate of interest equal to the natural rate of interest, that is a necessary but not a sufficient condition for output being at the natural (full employment) level.”
Question: With a large number of infinitely-lived agents (time is not supply constrained) and an infinite supply of haircuts (goods are not supply constrained), why would the natural rate of interest be anything but 0%?
The model seems to assume that infinitely-lived agents have some degree of impatience. Do these agents not know that they will live forever?
Roger: No. Read further.
JKH: It’s implicit. I don’t think it’s generally understood. There is limited translation between the ISLM and NK frameworks. And people don’t normally talk about a “LR IS curve”.
Frank: the NK model assumes impatience. On a per capita basis, there is a supply constraint on haircuts. No more comments till wednesday, because I am becoming impatient with you.
Doesn’t the population of agents has to be an even number?
I don’t understand this Gross Money.
How can a negative balance be considered money?
What can be bought with a negative balance?
Henry: For pairwise barter, you need an even number. Like infinity 😉
My father nearly always had an overdraft in his chequing account. Here’s my old post on negative money
How can there be unemployment in this model if there can be no stock of haircuts? (There could be scalps, yes, but then the population of living agents would quickly diminish. 🙂 )
“Doesn’t the population of agents has to be an even number?”
Forget this one.
“..”Doesn’t the population of agents has to be an even number?”
Forget this one….”
I guess I was thinking that all agents have to enter into a transaction – the model doesn’t necessarily call for this.
(Didn’t see your prior response.)
“Every agent has a chequing account at the central bank.”
JKH, what happens if two agents both have positive balances and one decides to do an exchange for a haircut?
Thanks!
TMF: Jeez! What the Hell do you think happens? The seller’s balance rises by $20, and the buyer’s balance falls by $20.
And why are you asking JKH? No more comments till Wednesday.
Ok so this is all mostly over my head but in the 2013 post ( wow back when I was just an internet armchair economist pupil ) I got the haircut barter answer right so, I am going to make an attempt at another comment.
The thing I am unsure about is what makes the gross stock of money a suitable nominal anchor?
I can see it in normal times when there is no aggregate demand problems and the investment/labor markets are clearing. People need to hold a certain amount of cash for day to day transactions. There is a demand for liquidity which is expected to be fairly stable relative to GDP. People needing a bit of money in their pockets gives real utility to money which somewhat anchors its value.
But what about when money is overly tight and there are large amounts of excess reserves and most money is not held for liquidity but as a form of long term saving?
It seems to me that under such circumstances, demand for money may become more volatile and that changes in demand may become dominated by moneys expected performance as a store of value compared to other competing stores of value.
This means that the interplay between central bank interest rates and returns on other competing investments may be more important. Other stores of value’s returns are potentially volatile since they are subject to the perturbations of the world but also expected inflation being a crucial component in determining interest rates brings unfortunate circularity to the problem (Could this explain the indeterminacy of equilibrium output?).
Does the liquidity effects still matter, as excess reserves accumulate idly along with the government debt they are usually tied to, as money goes beyond its role as the medium of account and provider of basic liquidity to become promises with value somewhat tied to government solvency but also almost tautologically tied to how much people expect other people will trade for them in the future?
What if everyone is clinging to the giant hot potato at the same time but some shock will cause one person to decides to let go which trigger everybody else to let go too?
It seems to me that some of the anchors can become psychological and circular. The LM curve could jump suddenly. Are you sure Japan is not going to flip into high inflation at some point?
If there are risks of violent discontinuities in the future, is a long term anchor based on liquidity preference still relevant?
Maybe the best you can do is focus on interest rates and expectations and hope that you can move those levers faster than expectations can change under shocks. I don’t like the circular psychological expectations factor being dominant. The only way around it I can think of is to keep money always easy enough that the idle supply doesn’t grow too much, that people always keep so little moneythat the liquidity anchor does work. In which case your model’s hot potato effect would work. However, I’m not sure it’s the world we live in right now.
Or maybe I’m completely out in the potato field as they say around here.
Nick says “The central banks sets a rate of interest (somehow, and this is a question that must and will be answered).”
It is reasonable to assume that having interest rates at their free market level maximises GDP. So why have the CB set rates? As to how to dispose of any state interference with interest rates, certainly government should not borrow to fund CURRENT spending: that’s generally agreed. As for funding CAPITAL spending via government borrowing the arguments there are much more feeble than is generally assumed. Milton Friedman and Warren Mosler advocated zero government borrowing.
But if government does issue bonds to fund capital spending, the state cannot then print money and buy back those bonds so as to cut interest rates because that contravenes the purpose of those bonds. Ergo the state cannot logically interfere with interest rates, and in my view certainly shouldn’t.
Frank Restley,
I agree with your point that the rate of interest should be zero. That’s the basic point in this paper by Warren Mosler and Mathew Forstater:
Click to access WP37-MoslerForstater.pdf
Their argument (if I’ve got it right, which is big “if”) is that the state should issue enough base money to bring full employment, but not so much that the state then has to borrow some of that money back so as to constrain demand (and hence artificially raise interest rates). An implication of that point is that in order to make it possible for CBs to adjust interest rates, those rates have to be kept artificially high most of the time (a point which Stephanie Kelton made in some recent tweets – at least as I understood her).
1. The Net money stock = the sum of positive balances minus negative balances.
check
The Gross money stock = the (absolute) sum of positive balances plus negative balances.
eh?
Negative balances are the corresponding liabilities of the non-(central) bank economy to their assets. It’s double counting.
This is probably irrelevant to your point, though.
Bemoit: set aside the question of whether Gross money stock is a suitable (good/best) nominal anchor. It probably isn’t. All we are asking at this stage is whether it is a nominal anchor. The demand for gross money is presumably a positive function of nominal income, so the hot potato mechanism will (eventually) pin down an equilibrium level of nominal income at which the demand and supply of gross money are equalised.
Ralph: if the government-owned CB is in the business of producing money (which is what the model assumes) then it cannot duck the questions of what rate of interest (including 0%) it should pay on the money balances it creates, and how much to create. Though you could say that it should set that rate of interest by indexing it to some market rate (e.g prime minus 1%, or whatever). Or, more radically, you could say the government should get out of the money business altogether, and leave it to the private sector, but that is beyond the scope of this post.
In this very simple model, if the economy were functioning well, the equilibrium market rate of interest would be n (though, trivially, there would be no private loans, because everyone is identical). And there is no government spending or (normal) taxation in this model — the government is the central bank.
Nick, I realize the “government owned CB” cannot duck the question as to what rate of interest it pays to those holding money at the CB. My answer to that question, as I argue above, is that the rate should ideally be zero (though I wouldn’t rule out occasional deviations from zero). Re the question as to “how much it should create”, there again I gave an answer to that above, which was “the state should issue enough base money to bring full employment, but not so much that the state then has to borrow some of that money back so as to constrain demand…”.
Re your suggestion that the rate paid on balances at the CB should be indexed to some market rate, I don’t see the justification. If someone wants to hoard money under their mattress or at the CB, then bully for them, but I don’t see any reason why the state (i.e. taxpayers) should pay the hoarder any interest.
My suggestion:
The Net money stock = the sum of positive money balances minus negative money balances.
The Gross money stock = the (absolute) sum of positive money balances.
Or, just to beat this dead horse a bit longer:
My father nearly always had an overdraft in his chequing account.
The level of your father’s overdraft already showed up (was accounted for) in the positive money balance of his respective payee(s).
Hi Nick,
I thought common wisdom was that the two major problems of NK models were the Euler equation AND labor supply. The Euler equation pins down the steady-state interest rate via consumption growth (or vice-versa) but, as you point out, has nothing to say about levels. NK models are solved from labor market clearing. With log utility of consumption and disutility v(L) of labor, you get that Cv'(L)=w/P=aY. Re-arranging(by using goods market clearing C=Y and Cobb-Douglas production function=L^a) yields v'(L)L=(wL/PC)=a (the—constant—labor share). This pins down employment, and then you unravel the rest (Y,C,w/P…) The crucial bit is that L is independent of demand variables at the SS. I thought that was what Farmer has been hammering about (and rightly so) like St John the Baptist in the desert, with his proposal to replace labor supply with an ‘animal-spirits’ equation to close the model. I understand your focus on the Euler equation, but the labor-supply angle is I think the more crucial one. Wouldn’t the NK model where the Euler equation is replaced with a traditional Keynesian consumption equation (linear in income) still suffer from the curse of exclusively-supply-driven employment in the long-run, if you maintain market-clearing in the labor market?
Good attempt but
1) Still relies on loanable funds
2) Value of money is indeterminate
3) Good part is the garsellian monetary triangle
Your two traders, 1 banker model is very grasellian and that I think is the solution. Replace the central bank with a private bank, and the agent having a liquidity preference and you find the model is indeterminate as there is no means of determining the stock of money.
Imagine however that there is a growth rate x, and there is a central bank. In order to satisfy liquidity preferences and achieve a goal or price stability the public sector must have a net deficit with the private sector of x.
Add in a fiscal theory of the price level type equation for government debt and you have a determinate system that holds in the most minimally simplistic investment-savings model without a dud hicks IS curve.
I would interpret that equation as the level of net monetary addition necessary to maintain price stability not a budget constraint (a circuitist approach) as in a sovereign currency there is no compunction to government bankruptcy – i.e. it is a price constraint not a budget constraint.
Ralph: In the simplest version of the model sketched above, where CB balances are the only asset, setting r =/= n is incompatible with full employment.
Oliver: I can’t make up my mind what’s the simplest/clearest way to write it. But readers seem to get what I mean, I think.
Pierre: I find it much clearer to delete the labour market from the model, by assuming workers are self-employed, and the production function is Y=L, so that Ls and Ys are the same thing. If money wages are perfectly flexible (even though prices are sticky) you get exactly the same level of output whether workers are employed by firms or are self-employed. And the only difference that flexible vs sticky wages makes is that when there is deficient Yd, wages instantly fall to convert involuntary underemployment into exactly the same level of “voluntary” underemployment.
Suppose you replaced the NK Euler IS equation with a regular Old Keynesian downward-sloping IS curve (Yd depends on r and current Y only). Then there is a unique r* and Y* at which Yd(Y,r)=Y=Ys. If the central bank sets r=r*, that is both necessary and sufficient for Yd=Ys. But in the NK model, setting r=r* is only necessary, not sufficient.
But I’m not 100% sure I get what you are saying.
Andrew: thanks.
“Good part is the garsellian monetary triangle”
“Garsellian” is a new one on me. Who that? (But I have recently suspected I might have more in common with the “circuitistes” than one would have thought.)
I don’t see the “loanable funds” angle in this post. The natural rate of interest is a pure time-preference theory. The actual rate of interest is whatever the central bank sets.
If the demand for gross money depends on nominal income (which is plausible), and if the central bank fixes gross money, then that creates an equilibrium level of nominal income. The supply side adds a second equation so that long run price flexibility can (in principle) determine both long run Y and P.
Pierre: having re-read your comment, we might be on the same page.
“I thought that was what Farmer has been hammering about (and rightly so) like St John the Baptist in the desert”
What I’m saying here certainly does sound similar to what Roger has been saying. Perhaps the difference is that I say that it is monetary exchange that creates this indeterminacy (it would disappear and we would have continuous full-employment if barter were easy), while I interpret Roger as saying something different about the underlying cause of this indeterminacy — that it’s due to labour market search and OLG sunspots.
Nick: I think you have to take seriously the concerns Henry, Oliver, I (repeatedly) and many others express every time you say this (or similar):
1. The Net money stock = the sum of positive balances minus negative balances.
2. The Gross money stock = the (absolute) sum of positive balances plus negative balances.
This might make sense to you, because you live in your world of green and red money, where the latter is “garbage”. I know how it is to live in a world of one’s own, where things seem to make a lot of sense — at least to oneself. Keynes knew it, too, and he put it like this in the Preface to his GT: “It is astonishing what foolish things one can temporarily believe if one thinks too long alone, particularly in economics (along with the other moral sciences), where it is often impossible to bring one’s ideas to a conclusive test either formal or experimental.”
You need to establish a stronger connection with reality to get us on board. I would really appreciate if you could answer this:
How could there be symmetry between positive and negative balances, when it is so much easier to get rid of positive than negative balances? Say, you have a positive balance of $200,000. I have a negative balance of $200,000. How fast can you get your balance to zero, if you really try? I’ll tell how fast I’ll get my balance to zero: in 5-10 YEARS. You see, Nick, a negative balance (an overdraft) is not much different from any other debt. It takes sales (incl. salary) to close it. There’s a reason why we are all used to call positive balances, not negative balances, “money”. The arithmetics you do with the negative and positive balances do not seem valid.
Btw, Nick: I might understand your conclusion regarding positive and negative money better than I have realized. It’s just that to me it makes a lot more sense to conclude that the positive balances are not money either — not at all like we are used to think of it — than to conclude that the negative balances are money. This might not ring any bells? Don’t worry — I’m working on my blog posts on the subject 🙂
OK, enough horse beating. Moving on.
Suppose the central bank sets the rate of interest too high. Will this cause unemployment?
No. Any unemployed agent would simply cut his own hair.
Suppose we change the model so agents can’t cut their own hair, to motivate trade. Can we get unemployment now?
No. Two unemployed agents would simply do a barter deal to cut each other’s hair.
We need to change the model so that monetary exchange is essential — they can’t trade without using money as a medium of exchange. So let’s do that.
What’s your definition of employment? Seems like by your above measure, most of Africa is currently enjoying full employment.
Would it not be smart to ditch the representative agent and insist on a division of labour to the extent that each individual is dependent on the output of various others to survive? That, plus a time factor that limits the ability of agents to do complex exchanges instantaneously. A kind of production period. Or is that too complicated already? In any case, my interpretation of your ‘fix’ is that you’re adding a stock of exogenously set gross money to induce exchange. But, to the extent that it does work, it would seem to do so only in nominal, not in real (no. of haircuts) terms. But that might be completely wrong.
Ralph,
“I agree with your point that the rate of interest should be zero.”
You missed my point entirely. I was asking Nick what the natural rate of interest should be with infinitely lived agents – I would presume it to be 0%.
[SNIP NR]
If you know what the optimal number of haircuts is then you can vary the interest rate to hit this number and you are done.
if you don’t know what the optimal level of haircuts (because is varies for random reasons) then you don’t know what number to target and you will instead need a nominal anchor to keep the number of haircuts at the right level. Gross money stock is a potential candidate for this nominal anchor role (within this model) as if you hold that constant (by varying the actual money stock) then people will be able to match the amount of money in their checking accounts without sub-optimal variation in the number of haircuts.
Is that roughly the idea of the post ?
“then people will be able to match the amount of money in their checking accounts” = “then people will be able to CHANGE the amount of money in their checking accounts”.
Antti: I thought that Oliver was making a point about how to define Gross vs Net money stocks more clearly. An example is best: I have a positive balance of $100, and you have a negative balance of $100 (ignore everyone else). Gross money stock is $200 and Net money stock is $0.
I can get rid of my positive balance by buying something from you, and you can get rid of your negative balance by selling something to me. It is nevertheless true that in an economy with deficient Aggregate Demand, the quantity of haircuts traded is determined by quantity demanded, not by quantity supplied (Q=min{Qd,Qs} aka the Short Side Rule). So I choose quantity I buy and you do not choose quantity you sell (at the margin).
MF: “If you know what the optimal number of haircuts is then you can vary the interest rate to hit this number and you are done.”
No. Suppose optimal C(t)=100 for all t. Look at the consumption-Euler equation. Setting r(t)=n for all t is necessary but not sufficient. C(t)=50 for all t also satisfies the same equation.
Oliver: as I have argued before, recessions are really reductions in the volume of trade, as opposed to reductions in employment. And we need some motivation for trade. Usually we talk about comparative advantage: I have a CA in apples and you have a CA in bananas. Here I’ve only got one good, so I need to rig it.
Nick: I believe Oliver was suggesting that Gross stock is $100, not $200. For you, negative balances are money. That doesn’t make sense to me. If I’ve understood you correctly, it makes sense to you because you have defined negative balances as “red money” (but still “money”)? What you seem to say is that “Here we have 100 pieces of red money and here 100 pieces of green money. In total we have 200 pieces of money.” Is this all you are saying? I remember you have also said that “red/negative money” is a liability of its holder but an asset of no-one, and the opposite is true for “green/positive money”. If we have a $100 liability (negative balance) and a $100 asset (positive balance), then what on earth is the $200 Gross figure? 200 what? “Assetbilities”? Dollars?
I’ll move forward… In your previous post there were ‘units’, but in this post it seems you talk casually about “money” without touching neither the subject of unit-of-account nor numeraire. Can we still assume that your agents start with zero balances? I have written a blog post (in the comments to your previous post we agreed that it might be a good idea) and I “spam” the link here, because I take this post of yours as a continuation of the story you started in the previous one. Here’s my blog: http://gifteconomics.blogspot.com/2016/11/a-new-monetary-system-from-scratch-part.html . My first post is about unit-of-account and numeraire. I appreciate any feedback!
@ Nick. I see (I think).
re: I have a positive balance of $100, and you have a negative balance of $100 (ignore everyone else). Gross money stock is $200 and Net money stock is $0.
Maybe it’s just me but that sounds positively (grossly?) bizarre. I’d say, gross money stock is $100 and net is $0. But I think I see what you’re getting at. The negative balance is also a motivation to trade, as you say. So say even if all positive balances were confiscated, agents with debt would still want to trade to minimise their negative balances.
Antti: money is assumed to be the unit of account in NK models (it is money prices that are assumed sticky). I didn’t bother saying that, partly because NK indeed most) macroeconomists know that, and partly because it raises other issues that are not the focus of this post.
Antti and Oliver: assume for simplicity that what I call “net money” is set at zero by the central bank. Then it is what I call “gross money” that measures the degree of non-synchronisation of payments and receipts. I am harking back to a long literature on the inventory-theoretic demand for money (e.g. Baumol-Tobin), or money as a “buffer stock” (e.g. Laidler). If inflows and outlows are perfectly synchronised, you don’t need to hold inventory (whether we are talking about money, or canned food, or whatever).
There is something I’m not getting.
If everyone becomes pessimistic about the number of haircuts they are going to sell then they will cut back on the haircuts they buy. If the CB sets a rate consistent with these low expectations then we would have an equilibrium where haircuts stay constant and low through time.
But why wouldn’t reducing rates cause people to consume more haircuts ? The way the model is setup at any point in time some people have positive balances and some negative. If the CB set a low enough rate (or high enough negative interest rate) – then those with money will buy more haircuts than planned, causing those who receive additional income to increase consumption now they see their sales are more than they they expected. The low interest rates will cause a kind of HPE. Even if people continue to be pessimistic in future period I ma not seeing why the same low interest trick wouldn’t work again.
There is something I’m not getting.
If everyone becomes pessimistic about the number of haircuts they are going to sell then they will cut back on the haircuts they buy. If the CB sets a rate consistent with these low expectations then we would have an equilibrium where haircuts stay constant and low through time.
But why wouldn’t reducing rates cause people to consume more haircuts ? The way the model is setup at any point in time some people have positive balances and some negative. If the CB set a low enough rate (or high enough negative interest rate) – then those with money will buy more haircuts than planned, causing those who receive additional income to increase consumption now they see their sales are more than they they expected. The low interest rates will cause a kind of HPE. Even if people continue to be pessimistic in future period I ma not seeing why the same low interest trick wouldn’t work again.
Nick,
What on Earth is “=/=” as in r =/= n? If you’re going to use maths, I suggest you use mathematical symbols that people with an AVERAGE grasp of maths understand, as opposed to people who are experts in mathematical economics modeling.
Ralph: =/= means “is not equal to”. The only way I know how to write it, on a regular keyboard. Does != work better?
If inflows and outlows are perfectly synchronised, you don’t need to hold inventory (whether we are talking about money, or canned food, or whatever).
Ah, I see. And by that definition, the creation of net money will have an effect in the sense of adding to the inventory. My reading of Tobin (the one paper I’ve read, that is) though, is that the transformation of one inventory item, say a security, into money, can not be interpreted as a net addition to total (financial) inventory.
I also still can’t see what it is about the number 200 that the number 100 doesn’t capture, except that it makes accountants’ brains explode :-).
But anyway, the credit view is rather different in that the +-100 is seen simply as a record of the lack of synchronisation (of flows of goods and services), rather than its potential remidy. And any ‘artificial’ addition to or subtraction from net money by a central bank will not directly change the underlying (lack of) synchronisation.
Nick,
“If the government-owned CB is in the business of producing money (which is what the model assumes) then it cannot duck the questions of what rate of interest (including 0%) it should pay on the money balances it creates, and how much to create.”
I agree with this. I also think it is a salient and important point in how central banks work – in reality and in the simpler case of a model central bank without the complication of a commercial banking system attached to it, as you often describe for explanatory purposes in your posts
The CB must choose a rate to pay on money. An interest rate of 0 % is just one of those choices.
A little elaboration:
In the case of a model with no commercial banks and a single central bank, the interest rate paid on reserve balances is an administered rate, and the CB can choose to pay any rate it likes, including 0 % or a positive rate or a negative rate.
In the case of a model (or the real world) with commercial banks, the CB also chooses the rate to pay on reserve balances:
In an environment of limited excess reserves (e.g. pre-2008 Fed), the CB can pay an interest rate of 0 %, but can also constrain the supply of excess reserves to the point it can set an administered LLR rate at any level, thereby determining the general level of short term market rates. The administered LLR rate sets an effective ceiling on short term market rates while control over the quantity of excess reserves sets an effective floor.
In an environment of abundant excess reserves (e.g. QE), the CB can pay any interest rate on excess reserves and thereby set the corresponding general level for short term market rates as both an effective floor and an effective ceiling, through an arbitrage transmission effect.
In either environment, the CB can choose the interest rate it pays on excess reserves in such a way to ensure short term market rates at a general level of its choosing – simply as a result of the leverage it holds over the banking system in terms of the quantity and pricing of excess reserves, and the associated arbitrage action of short term market rates.
All of this points to the fact that 0 % is an interest rate of choice – not some “natural rate” that defaults when there is no “intervention” to set a rate. The Mosler paper assumes 0 % is somehow a default “non-choice”, thereby making it “natural”. It assumes that a choice of 0 is somehow a non-choice, which is nonsense. There is nothing particularly natural about a choice of 0 %.
This can be clearly seen by the simple model with no commercial banks. 0 % is a choice just as 1 % or (1) % is a choice. It is illogical to suggest that 0 % is an exception in that continuum in terms of the idea of what is “natural” and what is a choice.
The case of commercial banks is an extension of this, with institutional arrangements for how a choice of 0 % or anything other rate works. There is nothing special about the fact that abundant excess reserves earning 0 % force other short term market rates to 0 %. And there is nothing special about the fact that such excess reserves come about through either OMO or budget deficits whose raw reserve effects happen not to be reversed by OMO (or currency issuance).
I also agree with your measure of gross money.
Obviously, you defined both positive and negative money to be types of money.
So the gross is simply the sum of the two in that definitional framework.
JKH: we agree! Moreover, even if 0% nominal were “natural”, that would not mean 0% real, unless inflation is 0% too, and there are thousands of different inflation rates, depending on your choice of basket of goods with which to define “inflation”. It is simply that with paper currency, or coin, anything other than 0% is administratively difficult.
On my definitions of money: I do want to say these are also useful definitions, and that “gross money” as I define it captures the degree of non-synchronisation of payments and receipts of media of exchange in the same way that standard definitions do in a world with only green money.
JKH,
You claim Warren Mosler is wrong to say there is something “natural” about 0%. Strikes me he’s right and for the following reasons.
Given an inadequate stock of money, the private sector will try to save the stuff, which equals Keynes’s paradox of thrift: i.e. unemployment ensues.
In contrast, and given TOO MUCH money, the effect will be excess demand and excess inflation. To control that, the state will need to induce money holders to lodge their money with the state by offering them interest. But those “loans to the state” are not for any productive purpose. Ergo the result is an artificial rise in interest rates. Ergo the rate which does not interfere with the free market rate of interest is 0%, and that’s the rate which presumably maximises GDP.
Ralph Musgrave,
This is the key paragraph in that paper, IMO:
“In a state money system with flexible exchange rates running a budget deficit—in other words, under the ‘normal’ conditions or operations of the specified institutional context— without government intervention either to pay interest on reserves to offer securities to drain excess reserves to actively support a non-zero, positive interest rate, the natural or normal rate of interest of such a system is zero.”
That’s entirely based on the notion that budget deficits create raw reserves and that setting a non-zero rate is an alleged “artificial” “intervention” through institutional arrangements and is not “natural”. But that just assumes the conclusion by defining what is natural and what isn’t. It is not an effective argument. As I said before, the case of negative interest rates should point to the fact that 0 lies in the continuum between positive and negative rates of interest.
The most important point is that the central bank rate is an administered interest rate. It is not a market rate. This is clear in the single central bank case without an attached commercial banking system. In the case of a banking system, it is still the case that central banks intervene using OMO to enforce what is an administered” interest rate – whether that rate is the rate paid on excess reserves or the rate paid on loans of excess reserves, the mode depending on the excess reserve environment itself (i.e. pre-2008 or QE, for example). 0 % is just one possibility for that administered rate. So in that *administered sense, there is nothing natural about 0 % as the choice. I think the Mosler paradigm for the “natural rate” runs a step too far in exploiting his admittedly expert understanding of how the reserve system works.
You say:
“In contrast, and given TOO MUCH money, the effect will be excess demand and excess inflation. To control that, the state will need to induce money holders to lodge their money with the state by offering them interest.”
That’s actually not his argument, and you won’t find it in the paper. What you’re suggesting is that there is a quantity of money paying 0 % which will be the “right” quantity of money in the suggested MMT arrangement. That could well be a consequence of the argument for a rate of 0 % – but it’s not the argument itself. Mosler’s argument is entirely based on a deemed “artificiality” of current institutional arrangements for setting an interest other than 0 % and “artificially” using “reserve drains” in the form of both Treasury bond issuance and central bank OMOs instead of paying an interest rate of 0 % on reserves creates by budget deficits. As I said, that just assumes the conclusion, and is not an effective argument for declaring a “natural” interest rate of 0 %.
Nick: “money is assumed to be the unit of account in NK models (it is money prices that are assumed sticky)”
I get this. But is this abstract money, or can it serve as a numeraire, too? There is no money, or ‘units’, in your initial system because all account balances are zero (gross money stock is zero — here we agree!). So the price of bananas, or haircuts, is expressed in money that doesn’t exist other than as a “unit of account”. Keynes talked about “Money-of-Account” (‘unit’) and “Money proper” (your positive ‘unit’/money balances). (I might be off-topic, but I hope you can bear with me. I’m trying to form a “big picture” of what you’re trying to say with all these posts.)
“If inflows and outlows are perfectly synchronised, you don’t need to hold inventory (whether we are talking about money, or canned food, or whatever)”
I do understand what you mean by non-synchronisation affecting the Gross stock, and as Oliver suggested earlier, it might not really matter whether we say Gross stock is $100 or $200: If I say it’s $100, that means there is a positive $100 balance and negative $100 balance. But when it comes to the “need to hold inventory” we must remember that there is initially no inventory, no “buffer”, at all. Gross stock is zero. Once “payments” and “receipts” get out of sync, positive and negative balances appear (almost automatically/”by strike of a pen”). (I think Oliver says the same when he says “the +-100 is seen simply as a record of the lack of synchronisation”; am I right, Oliver?) To use a buffer metaphor: My car didn’t have a buffer and there was a crash, but the only effect of the crash on my car was that the car got a buffer… So you must mean that only SOME agents need to hold inventory because they are credit-constrained?
Nick,
I also agree they are useful definitions.
Unorthodox, but helpful in illustrating the point about synchronization. More abstract and illuminating in that sense. It took me a while to see why you were doing this.
I think some people are confusing the usual interpretation of gross money in the orthodox asset-liability configuration with what is a different but consistent interpretation of gross in your unorthodox presentation of positive and negative money.
Obviously, you defined both positive and negative money to be types of money.
So the gross is simply the sum of the two in that definitional framework.
I’m trying to make sense of the sum.
If you look at the interest rates of each type of money seperately, it makes sense to treat them as separate entities that then I suppose you can add up. But the sum is still a weird number.
If I give Bill 100 bananas and he then owes me the equivalent of 100 bananas, there are only 100 bananas in that economy, not 200. Up until the point where where Bill gives me back the equivalent of 100 bananas, which is when he no longer owes me, i.e. which is when the numbers (Bill’s and mine) disappear. At no point are there 200 counters on the ledgers AND 200 banana equivalents in the economy. The numbers merely keep track during the time it takes Bill to repay his debt (plus interest) to me. But yes, in the end, when gross money goes back to 0, there will have been 200 banana equivalents that changed hands.
I still find it more accurate to say that there are (+&-)100 than saying that there are 200 money things in the economy. I suppose I’m saying the signs are important.
Antti: I remember reading a good paper by Colin Rogers (University of Adelaide) trying to make sense of the unit of account in NK models where money does not (otherwise) exist. It’s a problem. I have ducked that problem here, because I wanted to focus on the medium of exchange problem. If my Cunning Plan solves the medium of exchange problem, so that money exists, then I think it is easier to see how that money could also serve as unit of account.
“So you must mean that only SOME agents need to hold inventory because they are credit-constrained?”
You lost me at that point. But I’m fairly sure that is not what I mean.
Oliver: Start with a model with only green money. Suppose that people buy apples on odd days and bananas on even days. $100 each time. And each agent’s money stock keeps alternating between $100 and $0, but on average money is $50 per person. Now suppose the central bank allows overdrafts, and at the same time does an open market sale to reduce net money by $50 per person. But suppose the even/odd apples/bananas and $100 each trade stays the same. So each agent keeps alternating between +$50 and -$50. Net money falls from $50 to $0 per person, but Gross money (as I have defined it) is still the same $50 per person that it was originally. That is why my definition is useful.