How do the French control the size of the Sun? Hume vs Patinkin.

How do the French control the size of the Sun? How does the Fed control the size of the US economy? More importantly, how are those two questions related?

[I'm still thinking about this, but have decided to post it anyway.]

There is a metal rod in Paris that defines the length of the metre. (Actually, Wikipedia tells me that isn't true now, and was never exactly true, but never mind, because it makes a good metaphor). I think you could call that a "stipulative" definition of the metre. "See the length of that metal rod over there? That's a metre."

Suppose the French wanted to double the size of the Sun. They hacksaw the rod in two, throw one half away, et voila! The diameter of the Sun, measured in metres, is now doubled.

Someone who asked how a hacksaw in Paris could reach all the way to the Sun, and who enquired about the causal chain connecting the two, would be making something like a Category Mistake. The only causal chain worth enquiring about is the one between the rod in Paris and scientists' minds. Would scientists accept the new definition of the metre? The causal chain isn't physical; it's, um, metaphysical? It's perhaps a question of the Sociology of Knowledge.

You might say that the French control only the nominal size of the Sun, measured in metres, and not the real size of the Sun. And what the French have really done is halved the real size of the metre, not doubled the real size of the Sun. OK.

If you accept the analogy, you would say the Fed controls the definition of the US Dollar just as the French (in my story) control the definition of the metre. And you would say that the Fed controls only the nominal size of the US economy, not the real size of the US economy. The Fed, for example, controls nominal GDP but not real GDP. The Fed can double GDP measured in dollars by halving the real value of the dollar.

Some economists do believe something very close to that. But most of us believe that when the Fed changes the nominal size of the US economy it will also affect the real size of the US economy too, at least in the short run. And what is puzzling, for us, is not that the Fed can change the nominal size of the US economy; the puzzle is that doing so can affect the real size of the US economy too, at least in the short run. And we think it's got something to do with sticky prices and expectations. When the Fed changes the definition of the dollar, it takes time for that new definition to spread out across people's minds, and so changing the definition will have real effects in the interim. If lumber was sold in old metres, while architects worked in new metres, the French hacksaw might cause real effects in the housing market too.

If you will forgive the anachronism (the Fed wasn't around in David Hume's day), both Hume and Patinkin agree that the Fed controls the nominal size of the US economy in the long run, and can affect the real size of the US economy in the short run. But I think there's a big difference between the two.

I think that Hume would basically accept my metre analogy, and Patinkin wouldn't.

Hume's own analogy, between money and a system of counting, is similar to my metre analogy.

"It was a shrewd observation of ANACHARSIS the SCYTHIAN, who had never seen money in his own country, that gold and silver seemed to him of no use to the GREEKS, but to assist them in numeration and arithmetic. It is indeed evident, that money is nothing but the representation of labour and commodities, and serves only as a method of rating or estimating them. Where coin is in greater plenty; as a greater quantity of it is required to represent the same quantity of goods; it can have no effect, either good or bad, taking a nation within itself; any more than it would make an alteration on a merchant's books, if, instead of the ARABIAN method of notation, which requires few characters, he should make use of the ROMAN, which requires a great many. Nay, the greater quantity of money, like the ROMAN characters, is rather inconvenient, and requires greater trouble both to keep and transport it."

Hume discusses the causal chain between the quantity of money and the level of prices only in the context of discussing why a change in the quantity of money can have real effects in the short run.

"To account, then, for this phenomenon, we must consider, that though the high price of commodities be a necessary consequence of the encrease of gold and silver, yet it follows not immediately upon that encrease; but some time is required before the money circulates through the whole state, and makes its effect be felt on all ranks of people. At first, no alteration is perceived; by degrees the price rises, first of one commodity, then of another; till the whole at last reaches a just proportion with the new quantity of specie which is in the kingdom. In my opinion, it is only in this interval or intermediate situation, between the acquisition of money and rise of prices, that the encreasing quantity of gold and silver is favourable to industry. When any quantity of money is imported into a nation, it is not at first dispersed into many hands; but is confined to the coffers of a few persons, who immediately seek to employ it to advantage. Here are a set of manufacturers or merchants, we shall suppose, who have received returns of gold and silver for goods which they sent to CADIZ. They are thereby enabled to employ more workmen than formerly, who never dream of demanding higher wages, but are glad of employment from such good paymasters. If workmen become scarce, the manufacturer gives higher wages, but at first requires an encrease of labour; and this is willingly submitted to by the artisan, who can now eat and drink better, to compensate his additional toil and fatigue. He carries his money to market, where he, finds every thing at the same price as formerly, but returns with greater quantity and of better kinds, for the use of his family. The farmer and gardener, finding, that all their commodities are taken off, apply themselves with alacrity to the raising more; and at the same time can afford to take better and more cloths from their tradesmen, whose price is the same as formerly, and their industry only whetted by so much new gain. It is easy to trace the money in its progress through the whole commonwealth; where we shall find, that it must first quicken the diligence of every individual, before it encrease the price of labour."

To Hume, it is self-evident that the French control the nominal size of the Sun. What needs explaining is how the French can influence the real size of the Sun.

Don Patinkin's "Money Interest and Prices" is the opposite. The whole point is to explain how the French control the nominal size of the Sun. He deliberately rigs his example (by assuming flexible prices, that new money is distributed to individuals in proportion to their existing holdings of money, etc.) so that there will be no real effects. Starting in one equilibrium, a doubling of each individual's stock of money creates an excess supply of money, and by the logic of Walras' Law, that means an equal excess demand for non-money goods at the previous equilibrium price vector. And that excess supply of money/excess demand for non-money goods is what causes the price level to rise.

Patinkin thought that a reduced form equation like MV=PY or M=kPY wasn't good enought to explain why a doubling of the supply of money caused a doubling of the price level. And just to make sure people got the point, he repeated it in the form of a "stability experiment", by asking what would happen if all prices hypothetically  halved, while holding the nominal stock of money (and everything else) constant. He said it would create an excess supply of money/excess demand for non-money goods which would cause all prices to double back up again, to the original equilibrium.

Money Interest and Prices was a book of its time. At that time (the 1950s and 1960s), there was no expectations-augmented Phillips Curve. Prices rose because of an excess demand for goods. So Patinkin explained why an increase in the supply of money would create an excess demand for goods.

There are many specific criticisms one can make of Patinkin's theory. To my mind the most important comes from Clower's observations that: money is not really needed as a medium of exchange in Patinkin's Walrasian economy; if we ask what would happen at a disequilibrium price vector we must allow that agents will be quantity-constrained; and if we put these two observations together we realise that Walras' Law makes no sense in a monetary exchange economy. But there's a more general criticism I want to make here.

There is more than one way to define the metre. You can define it relative to a metal rod in Paris, relative to the circumference of the Earth, relative to the wavelength of krypton-86, or relative to the distance light travels in one second, etc. Similarly, there is more than one way to define a value for the dollar. You can define it relative to gold, or relative to silver, or relative to the CPI basket of goods (which is roughly what modern central banks do now). Or you can define it by fixing the quantity of dollars, which is what Patinkin assumed.

Once you have grasped the idea that the French can double the nominal size of the Sun by cutting the metre rod in half, and redefining the metre, it doesn't matter how the metre is defined, and who defines it. You can translate the same basic idea into the new dictionary. Similarly, once you have grasped David Hume's idea, it doesn't matter how the dollar is defined, and who defines it. You can translate the same basic idea into the new dictionary.

If the dollar is defined by fixing the quantity of dollars, then doubling the quantity of dollars halves the value of each dollar in terms of all goods, which means the prices of all goods double. If instead the dollar is defined by fixing the price of gold, then doubling the price of gold halves the value of each dollar, doubles the quantity of dollars, and doubles all prices. And so on. The Quantity Theory of Money does not need to take the quantity of money as the exogenous variable and the prices of all other goods as the endogenous variables. The same idea is equally valid if the price of gold, or some basket of goods, is the exogenous variable. The Quantity Theory of Money is a theory about units. It says the units don't matter, at least in the long run.

If Patinkin had written a third edition of Money Interest and Prices, in which the dollar price of gold was the exogenous variable, it would be a complete re-write. How would a doubling of the price of gold in terms of dollars cause all other prices to double and the stock of money to double too? That's quite a different question. And inflation targeting, or NGDP level-path targeting, would be complete re-writes again.

All of which makes me wonder: did Patinkin really fill a massive gap in monetary theory by explaining how a change in the quantity of money causes a change in the price level? Or, at the other extreme, is the magisterial Money Interest and Prices just one big Category Mistake?

Patinkin (or the reader) might object that I am confusing money as the medium of exchange with money as the medium of account. Changing the length of the metre is like changing the value of the unit of account, which is a question more like the Sociology of Knowledge, where we ask who decides what units will mean, and how those meanings get propagated into the population. But that still leaves open the question of the value of the good which serves as medium of exchange in terms of other goods, which was Patinkin's question. Patinkin was very careful to make that distinction; Hume didn't.

But I don't think I'm making that mistake here.

The Quantity Theory of Money would not work if we used cows as money. Patinkin could not put M/P in the utility function if M stood for "Cows", because a doubling of the number of cows plus a doubling of all prices in terms of cows would not leave us indifferent. We would be drinking more milk, for one thing.

If we used gold bars as money I could define the physical quantity of money independently of its value in terms of the medium of account. Because I can measure the quantity of gold in kilograms, as well as in dollars. A 2 kilogram bar of gold will be worth twice a 1 kilogram bar of gold, because it's got twice as much gold. A $20 bill isn't worth twice a $10 bill because it's got twice as much paper. It's only worth twice as much because the central bank will exchange them two for one.

The history of money is like the story of the Cheshire Cat, which slowly disappears leaving only its smile. The usefulness of a unit of a good that is used purely as a medium of exchange (and not to produce milk as a byproduct) depends only on its exchange value. Except for the slight difficulties in counting the notes, and fitting them all in our pockets, there is no economic difference between multiplying the number of notes tenfold and adding a zero to each of the existing notes.

David Hume's idea works for a (pure) medium of exchange, even if it isn't the medium of account.

Comments

[Frances Woolley]

Nick, great to have you back on the blog! Afraid I'm too busy with marking to give this post justice, but one thing from the Hume quote struck me:
"where we shall find, that it must first quicken the diligence of every individual, before it encrease the price of labour."

Sounds like he figured there were real impacts from an increase in the money supply, i.e. there was a short-run increase in labour supply (quickening the diligence) before wages increased. Is that important, and is it still true now?

[Nick Rowe]

Frances: thanks. "Is that important, and is it still true now?"

Most macroeconomists think: yes, and yes.

[Peter N]

I'm afraid I don't see too much mystery here. People have benefits and obligations on different bases. Some like fixed mortgage payments are fixed nominal. Others like Social Security are inflation indexed. Some, like variable rate mortgages are priced on some sort of financial index.

A change in the nominal prices is good news to the payer and bad news to the receiver. Since everybody is in both positions directly or indirectly, the results can get very complicated.

Sellers who have benefited from reduced real costs can lower prices to increase market share. Those who haven't may not be able to compete. Delays occur because people try to take financial advantage of their situations when they can.

Anyone trying to prove anything about the real economy who "rigs his example (by assuming flexible prices, that new money is distributed to individuals in proportion to their existing holdings of money, etc.)" is a danger to himself and others and shouldn't be let out without a keeper.

We're in Ignobel Prize territory here. If he's alive, you could nominate him.

BTW, it's nice to have you back.

[Kevin Andrew]

Interesting post Nick. I was hoping you could shed light on something that I have always wondered about. The tightness of the relationship between M and P in the quantity theory identity requires V and T to be fixed. I was wondering if you had written any posts elaborating on the assumption that demand for money and the velocity of money is fixed. Surely we cannot take as given that this is the case.

As well, I believe there is something called the Cantillon effect which sounds a lot like Hume's theory on the short run effects of money increases on the real economy. Maybe Hume wrote first and Cantillon formalized this idea?

Lastly, if we accept that the real effects of an increase in money depend on who receives the money, is the next logical step that we can increase the welfare of society by targeting money supply increases. For instance, if there is a shortage of demand it makes sense to target transfers to borrowing constrained people who would like to increase consumption.

Just a smattering of thoughts after reading your post.

[rsj]

But implicit in this assumption is that you can "solve" for what happens with barter, and then overlay a quantity type argument to get prices.

And you need more than that. You need an argument that increasing the quantity of reserves will somehow cause all the prices to change as well, without any feedbacks at all.

The french, when they cut the length of the reference rod in half, do not change the distance to the sun, they only change the units. And there is a very important mechanism at play here -- they hold the reference unit by definition, and there is a hierarchy (an expensive, time consuming process employing many people) by which changes in the reference unit in Paris propagate down to changes in the scale of a butcher in Mexico City.

Without this mechanism, the french could do whatever they want, and the butcher in Mexico would not change his unit at all.

So you still need a mechanism. And you need to assume that the economy can be solved via barter and then have the prices overlayed by an independent set of equations.

Both of the above, IMO, require some justification, rather than just assertions. If the justification is not plausible, then this is a problem.

[rsj]

The more I think about it, this is a perfect example.

The central bank is the committee in paris. It cuts the kilogram in half. But none of the butchers care about what is inside the vault in paris, just as no one cares how many reserves are in the central bank. You need some mechanism -- in this case, state inspectors visiting each shop and forcing an adjustment of the scales.

It is really this mechanism which allows the Parisian committee to say that they set the meter. Without this mechanism, they do not set the units for the economy as a whole, they are like the boy standing on the log commanding the seas to change. Everyone ignores them and keeps on using their own units.

In order to really set the units for the economy as a whole, you need an enforcement mechanism.

[rsj]

Since we are talking about Parisiens trying to control units, this might be appropriate:
http://blog.quickanddirtytips.com/2011/10/13/french-academy-tries-to-ban-english-words-again/

[Nick Rowe]

Peter: Don Patinkin was very much aware that neutrality of money would only hold exactly under very stringent conditions. One of the things he was doing was figuring out what those conditions were. That's why he made those assumptions.

Kevin: The QTM doesn't strictly assume V and T are fixed, in the sense of constant over time. It does assume, or rather assert, that V and T won't be affected by an equiproportionate change in both M and P. That assertion wouldn't be exactly true, for example, if we used cows as money.

rsj: "But implicit in this assumption is that you can "solve" for what happens with barter, and then overlay a quantity type argument to get prices."

What does "this assumption" refer to?

In Patinkin's case, it is correct to say that he adds money to a Walrasian economy, and a Walrasian economy is not a barter economy, but it isn't strictly monetary either. But even in that case, it is not true that the equilibrium is the same as it would be M/P were zero.

Again, if we used cows as money then the physical quantity of money would matter. The real economy can't be the same with double the number of cows with each cow worth half as much. We get double the quantity of milk, which would have lots of other real effects. But with paper or electronic money, these effects are trivial, and we ignore them. Slightly fewer trees?

"...by which changes in the reference unit in Paris propagate down to changes in the scale of a butcher in Mexico City."

That's part of the Sociology of Knowledge, not physics. It's like asking how language propagates.

"In order to really set the units for the economy as a whole, you need an enforcement mechanism."

David Hume (somewhere) compares the Social Contract to two oarsmen in a boat. It is not obvious they need an overseer with a whip. It is in each individual's interest to keep time with the other. Racing eigts may need a cox, but he doesn't carry a whip. (Even Greek triremes, IIRC, which were manned by volunteers, didn't have a guy with a whip.)

Have a look at these examples of coordination games

[rsj]

Again, if we used cows as money then the physical quantity of money would matter. The real economy can't be the same with double the number of cows with each cow worth half as much. We get double the quantity of milk, which would have lots of other real effects. But with paper or electronic money, these effects are trivial, and we ignore them. Slightly fewer trees?

There are millions of markets. I walk into a bar and make a choice as to how much alcohol to buy. The bar owner makes a choice as to how much to charge. I make a choice as to my reservation wage, etc.

The question is, will all of those millions of markets move simultaneously so that all prices go up by 5%?

Is that even possible? I would like to see the argument that it is. In particular, an increase consumer prices causes bond prices to fall, and they fall in proportion to the duration of the bond. The prices of capital goods do not move in proportion to the prices of consumer goods.

But we know that the results of these million markets is what sets "the price level".

I think it is more than just running out of trees. Any change in price is going to have real effects, and must arise out of the choices of millions of people in the non-financial sector, none of whom care about the proportion of reserves backing their deposits.

[rsj]

Nick,

What I find to be really odd in this discussion, is that fiscal policy is assumed to be ineffective (or its effectiveness is constrained) by Ricardian equivalence, which is basically the non-financial sector undoing the effects of the policy.

But it is much easier for arbitrageurs in the financial sector to undo any quantity-type changes done by the central bank (I am not talking about nominal interest rate changes). When households want more deposits, banks can create them, and when the central bank creates excess reserves, banks can absorb them. When the central bank reduces the quantity of bonds, banks can supply more, etc.

So why does the possibility of financial sector entities undoing portfolio shifts of the central bank carry zero weight, yet the possibility of the non-financial sector undoing its portfolio shift via fiscal policy carries weight?

I can't help but think that the answer is due to economists (historically) ignoring the financial sector, rather than any plausible reason as to why monetary policy is more effective than fiscal policy. But I would be interested in hearing your thoughts on the matter.

[Ron Ronson]

In all prices (including the price of money) were set correctly then then RGDP would be optimized both in size and structure. If all prices were perfectly flexible then even if relative prices were set incorrectly things would soon adjust and we would get to optimal RGDP levels. If however relative prices (including the price of money) are not set correctly and prices are not only not perfectly flexible, but actually quite sticky then what is the fastest route back to optimal RGDP ?

If the main issue is that demand for money has risen and all other relative prices are more or less correct then just increasing the money supply in a way that does not disrupt other relative prices would seem like a quick fix.

If however something has happened that has knocked all prices out of kilter then the hope is that increasing the money supply will generate an inflation that will allow relative prices to readjust (those goods that are undervalued will have greater price inflation than those that are not). Is it realistic to believe that inflation will work in this way , or will inflation just cause prices to change for reason unrelated to their true relative values and cause the price system to move even further out of kilter than they already are ?

Based on the experience of the past 3.5 years I believe we are closer to the second scenario that the first and am concerned that generating higher inflation will further disrupt relative pricing,

[dlr]

Good post as usual.

I wouldn't define coordination games as a-causal or metaphysical. It's just that if you are telling a causal story where expectations play an defining role, and you don't model the interaction of those expectations well, your story isn't going to be very useful. But the hydraulics of Patinkin's equilibirium can still be informative in a purely fiat MOE world, as long as they are thought of as mere pieces in the expectational dance. They reflect some of the ways that agents become informed of others' expectations and communicate their own expectations, and their own expectations of others' expectations, etc.

Admittedly, this means that any attempt to apply any kind of general equilibrium model without explicitly thiinking about expectations and the coordination game is doomed. But since we are not so good at modeling games as complex as this anyway, the conventional pieces end up still seeming important, because they might be good leads into how expectations might be formed. Will people believe the Queen when she talks? The Sociology of Knowledge doesn't have to abstract from interest rates or the hot potato effect. They could be just as important determinants of the focal point as the Queen's tone of voice or the people's knowledge of the Queen's incentives relative to their own incentives. It's just that we have to remember that expectations, not mechanics, act last. I think you should rename your post, "the only nominal anchor we have under fiat money is the nominal anchor itself."

[Edeast]

I don't know what you are saying. I still think someone needs to exchange money for something to set its price, or rsj enforcement. The Hume quotes reminded me of the bicycle post. First person to get the extra money gets the benefit. Other than that, not sure what you are saying moa vs moe.

[Nick Rowe]

rsj: "The question is, will all of those millions of markets move simultaneously so that all prices go up by 5%?"

In my opinion, it is very unlikely that they will (except in special circumstances like a currency reform). And that is probably one of the reasons (maybe the main reason) why money is non-neutral in the short run. The short run is lots of individuals hunting for the new equilibrium. The cox on a racing eight helps them coordinate on a new equilibrium, and tries to pick a good one.

"Is that even possible? I would like to see the argument that it is."

Yes it is, in principle. Suppose we go to bed one night, and while we sleep, Hume's fairy doubles every single variable that has the units "$". Dollar bills in or wallets and bank accounts, bank reserves, prices (consumer and capital goods), wages, etc. expectations of all future variables measured in $ units, etc., (Notice that interest rates have the units 1/year, not $, so Hume's fairy does not change interest rates.) If we were in equilibrium before (however you define "equilibrium") we are still in the same equilibrium in terms of all units not measured in $ units. And if we were in disequilibrium before (however you define "disequilibrium") we are still in the same real disequilibrium after. The only things that matter to us are "real" variables, like relative prices, and the real value of the contents of our wallets and bank accounts.

This is the most important insight of monetary theory.

Again, this only works with an "abstract" money, like paper. It doesn't work with cows. And how the economy actually transitions from the old equilibrium to the new one without Hume's fairy to help it, which is the whole question of short run effects of monetary policy, is a whole other question.

"What I find to be really odd in this discussion, is that fiscal policy is assumed to be ineffective (or its effectiveness is constrained) by Ricardian equivalence, which is basically the non-financial sector undoing the effects of the policy."

No it isn't assumed to be ineffective. Nowhere in this discussion is fiscal policy even mentioned, or relevant. It's a total red herring. Read this English skoolkid on fiscal policy. He explains it better than the rest of us.

[Edeast]

I rushed a comment, just to say something. Mainly don't understand patinkin. Think I agree with the other parts.

[Nick Rowe]

dlr: "I wouldn't define coordination games as a-causal or metaphysical."

I think I agree, and mostly agree with the rest of what you said.

We can maybe distinguish between:

1. Simple "linear" (in the Artsie sense) causation, like one billiard ball hitting the next. Concrete steppes stuff.

2. Simultaneous causation, like in supply and demand.

3. Simultaneous causation, where expectations of endogenous variables are part of the story. Like simple macro RE models.

4. Coordination games with multiple equilibria. Like "sunspot" models, where the sunspot picks the equilibrium, but the method by which the sunspot picks the equilibrium is not part of the model. Like the cox in a racing eight. These models are problematic, of course, because we want to explain how the sunspot can pick the equilibrium, and make it part of the model, but if we did that, it wouldn't strictly be a multiple equilibria. What we are really saying is that the method by which the sunspot works to pick an equilibria is fundamentally different in some way from the forces that choose the original set of equilibria.

The people of the concrete steppes assume that anyone who explains things in any way other than 1 must be saying "It's magic!"

[rsj]

If we were in equilibrium before (however you define "equilibrium") we are still in the same equilibrium in terms of all units not measured in $ units. And if we were in disequilibrium before (however you define "disequilibrium") we are still in the same real disequilibrium after.

I don't see how this is possible.

Suppose I write a contract that pays out $1 if the price of oil tomorrow is more than the price of oil 1 year ago. This contract also has a dollar value, so the only way that you can change all dollar values is to change all prices from the very beginning of the economic system, which means that the fairy never comes to visit.

And of course, I could write a contract that pays out $1 if the fairy visits and $0 if it does not visit. Say my entire net worth consists of these fairy contracts.

You will always be changing relative prices if you are "in" the model. Only the modeller who is outside the model has freedom to scale prices. No one within the model can scale prices without creating relative changes in prices.

[Joe]

Nick,

Let's say we're at full output and therefore perfect monetary equilibrium. The CB doubles M. In the short run real output goes up and P only slightly. However, in the long run real income goes back to its normal level and P full doubles to adjust for the new M. Nothing changes except for the doubling of P.

However, let us say we are in a recession and output gap. In response, the CB doubles M to get us out. Let's say the new M totally fills the output gap. Won't it be the case that P won't fully double because some of the M will be used to bring back real income?

In other words, shouldn't it be the case that P will only fully track M if the M is increased starting from full output. But if it is increased in the middle of an output gap, won't it the case that some of the M is used to bring back real income to full output, therefore never allowing P to fully track M.

I'm not sure if that made sense....

[rsj]

No it isn't assumed to be ineffective. Nowhere in this discussion is fiscal policy even mentioned, or relevant. It's a total red herring.

No, I don't care whether you think fiscal policy is effective or not. What I am asking is why is Modigliani-Miller is viewed as less important when applied to central bank operations rather than when applied to fiscal operations. In both cases, it says that the government is not able to accomplish its goals, whether those goals consist of adding nominal money to the economy or whether those goals consist of adding nominal wealth. And I don't care whether you believe in MM or not, but am interested in why MM seems to be applied against fiscal interventions (Ricardian equivalence is a form of MM) but is not applied against CB quantity interventions.

I am questioning the asymmetry only, not whether or not you believe that fiscal policy is effective.

Btw, all of the arguments against fiscal policy in the link you cited apply equally well to monetary policy. Again, I'm just interested in the relative value of one over the other, not whether you believe in one or the other in the absolute sense.

But feel free to ignore the comment, since I don't want to sidetrack the discussion. I only fundamentally disagree that the CB has any power to force nominal money balances on the non-financial sector.

[Nick Rowe]

Joe: That made perfect sense to me.

But there are two ways to think about it. When we say "P doubles", do we mean "P doubles relative to where it was before"? Or do we mean "P doubles relative to where it would have been otherwise"?

In your example, where the economy starts out in recession, we might argue that P would eventually ("in the long run") have fallen if M hadn't increased. So that doubling M does double P, relative to where P would eventually have fallen to.

Since there are lots of other things that might be changing at the same time, and it is unlikely anyway that P would have stayed constant over time if M hadn't doubled, economists usually (implicitly) mean "relative to where it would have been otherwise". And it is precisely to avoid this confusion that economists have an almost verbal tic of starting any discussion of the effects of anything on anything by saying "Assume we start in equilibrium, holding everything else constant, what is the effect of an increase in X on Y?". And this pisses of non-economists, who say "But what happens if the economy is not in equilibrium, and other things aren't constant, as they almost never are, realistically!"

[Peter N]

"Patinkin thought that a reduced form equation like MV=PY or M=kPY wasn't good enought to explain why a doubling of the supply of money caused a doubling of the price level. And just to make sure people got the point, he repeated it in the form of a "stability experiment", by asking what would happen if all prices hypothetically halved, while holding the nominal stock of money (and everything else) constant. He said it would create an excess supply of money/excess demand for non-money goods which would cause all prices to double back up again, to the original equilibrium."

This doesn't even work in its own terms without additional restrictions.

1) There's no reason to assume that V is constant, It probably won't be.

2) Exactly which prices will double? All of them exactly? Why won't the additional money accumulate in certain sectors. Prices will rise, but not evenly. It would depend on the demand for money at the start.

3) Aggregate demand isn't a real thing. It's a useful fiction. With multiple goods you can't have a price doubling without specifying how you determine it. Different inflation indices will produce different results.

4) Then there's equilibrium in which the example is supposed to start and end. Furthermore, the implication is that there is only 1 equilibrium, and it is stable, not just that one exists. He is therefor assuming all the conditions required by the Sonnenschein-Mantel-Debreu theorem.

5) Nothing is specified about contractual relationships. Are all contracts magically rewritten, or do some people make out better than others?

6) What exactly is money in the model? Can it be created or destroyed. Is there more than one kind? Related how? Is this realistic?

7) How can there be an increase in the demand for goods without an increase in their production?.Why should prices exactly double? There has been an increase in supply during the time of adjustment. What you would expect is a boom with inflation, followed by a bust when the artificially hyped demand ends. It looks almost Austrian.

I have no doubt you could define a model that would behave as expected, but it wouldn't have any application to any real economy. It's like saying "If my dog had wheels it would be a wagon." I don't how this model advances any argument other than over it's usefulness.

[Dan Hirschman]

As a sociologist of knowledge, I feel obliged to recommend this fantastic, and very well-written, history of the meter: The Measure of All Things by historian Ken Alder. The tale is a fascinating one, and involves more politics - and scandal - than you might expect.

[Nick Rowe]

Edeast: "I don't know what you are saying. I still think someone needs to exchange money for something to set its price,.."

(My memory and my math are bad. I hope some mathematician will gently correct me if I screw this up.)

An equation is said to be "Homogenous of degree one(?) in nominal ($) variables" if and only if the equation still holds true if you double (or treble, whatever) all nominal variables and leave the other variables unchanged. For example, Y=F(M/P,Z) is HD1 in $ variables if M and P are $ variables and Y and Z are not. Because Y=F(2M/2P,Z) is the same thing as the original.

Suppose you had a complete model of an economy in which every single equation was HD1 in $ variables. Even if that system of equations has only one solution for all the real variables, it must have an infinite number of solutions for all the nominal variables. The price level (the value of money) is indeterminate in that model.

To make the price level determinate, you need one of those equations to be non-homogenous. The normal way to make the price level determinate is to make the equation that describes the behaviour of the central bank non homogenous. You need a "nominal anchor". The central bank needs to have "money illusion" to pin down an equilibrium for the nominal variables. M=100 works. That means the central bank fixes the nominal money supply. Pg=100 also works. That means the central bank stands ready to buy or sell paper money for gold at some fixed price. But those are just two examples.

[Nick Rowe]

rsj: "Suppose I write a contract that pays out $1 if the price of oil tomorrow is more than the price of oil 1 year ago."

The standard example is a long-term nominal debt contract between two individuals. If there is a doubling of the money supply that was not anticipated when that debt was negotiated, then the rise in the price level will cause a change in the distribution of wealth from creditor to debtor. And this change in the distribution of wealth may (or may not, depending on the model's assumptions) also affect aggregate variables. And this change in the distribution of wealth may (or may not, depending on the model's assumptions) persist forever. And you get exactly the same sort of wealth distribution effects if the new money is not helicoptered to individuals in exact proportion to their existing holdings of money. There was a long discussion of this sort of stuff between Patinkin and Archibald/Lipsey (can't remember who was on which side) and it's all laid out in the second edition, IIRC.

The general view is that these distribution effects exist, but are not the primary reason for the short-run non-neutrality of money. The primary reason is some sort of sticky price/expectations/coordination failure story.

[Nick Rowe]

Dan: when I talk about "sociology of knowledge" a couple of times in the post above, does what I say seem right/make sense to you? Thanks.

[Sergei]

The Fed can definitely control the nominal size of the economy as soon as it fully owns it. But does this fact extrapolate into a partially owned economy? It is not the question of whether the Fed can inflate the private economy. It is a question of whether the Fed can retain and inflate the private economy at the same time.

[Edeast]

Thanks,but I was more referencing the discussion I had with k a couple months ago, on units and measure systems. I think I'm done with models for a while.

[J.V. Dubois]

This is good stuff, I now have feeling that non-walrasian revolution starts knocking on the door of Macro as it already does for Micro. And you are right about most economists having issues with any non-causality, I would vote for compulsory reading of Bowles "Microeconomics: Behavior, Institutions, and Evolution" to all of them.

Anyways this bothered me for some time - that even if many (macro)economists claim that recessions is basically one huge coordination failure, they have only very basic knowledge of what is a coordination game, how expectations of behaviour of other actors /and or institutions/rules of the game impact the results, that there may be multiple equilibria and so forth. It is as if they give it a brief thought, feel scared and so they return back to their familiar world of oldschool models reasured by seeing everybody else doing the same thing.

[JKH]

Can you elaborate on this, Nick:

“If instead the dollar is defined by fixing the price of gold, then doubling the price of gold halves the value of each dollar, doubles the quantity of dollars, and doubles all prices. And so on.... How would a doubling of the price of gold in terms of dollars cause all other prices to double and the stock of money to double too? That's quite a different question.”

You didn’t (attempt to) answer that question here, did you?

Why and how does it double the quantity of dollars?

This seems important, but disjointed or incomplete relative to your post.

[Nick Rowe]

Sergei: "The Fed can definitely control the nominal size of the economy as soon as it fully owns it."

?? You really lost me there. Do the French fully own the Sun? Or do you mean something else by "fully own"? You might mean that the Fed can only control the nominal size of the economy that uses US dollars?

JV: there have been a few false dawns of the non-walrasian revolution in macro. I can almost quote the Intro to the 1968 Phelps volume from memory: "We have made a landing on the Non-Walrasian continent. Never again will we go back to delta P = F(demand-supply)'

Ah! Google tells me the correct quote:

"A landing on the non-Walrasian continent has been made. Whatever further
exploration may reveal, it has been a mind-expanding trip: We need never go back to Pdot = alpha(D - S) and q = min(D; S)."

The Diamond-Dybvig model of bank runs has 2 equilibria and is fairly widely accepted in macro. But it's not a full macro model. Some macroeconomists do build macro models with multiple equilibria. Roger Farmer is one - his model has a continuum of equilibria. But yes, it's rare.

I too have been a bit surprised at the resistance to the idea, and the resistance is because you can't even pretend to tell the story in terms of billiard ball causality. The basic idea is simple enough. Supply and demand curves (or whatever the curves are) may cross only once, like in ECON1000. But they may also cross twice, or three times, or even lie on top of each other part of the way. And it's not exactly a new idea. JJ Rousseau's StagHunt has 2 Nash equilibria: a good equilibrium where they hunt stag; and a bad equilibrium where they hunt hare. Each player does what he expects the other to do. And a pure self-fulfilling change in expectations will jump the economy from one equilibrium to the other. And this sounds so much like booms and busts in macro. And Roosevelt's "The only thing we have to fear is fear itself".

But the reaction to such ideas is so often "But where's the mechanism? Nick's relying on magic! Ho ho ho."

[Frances Woolley]

"But where's the mechanism? Nick's relying on magic! Ho ho ho."

Magic is just a name we give to things we don't understand.

[Nick Rowe]

JKH: "You didn’t (attempt to) answer that question here, did you?"

I didn't. At least not explicitly. But one answer, Hume's answer, is implicit.

"This seems important, but disjointed or incomplete relative to your post."

You are right. This is important. This is basically how Roosevelt raised the price level and helped the US economy escape the Depression. And the Fed could do some version of it right now, even at the ZLB. (Though the price of gold might not be the exact best thing nowadays, something like the S&P index might be better.)

Let me sketch out two answers:

1. It's obvious, once you have understood Hume's Quantity Theory and Neutrality of Money. For every equilibrium there's a second equilibrium where M, and all P (including Pg) are doubled. So if we start in one equilibrium, and the Fed announces a doubling of Pg (it will buy and sell gold at a price double the original target price), the economy just jumps to the new equilibrium. OK, it may not jump instantly, because some prices are sticky, and some people may take time to figure out the new equilibrium, and the Fed's commitment to the new Pg may not be credible, etc. Chuck Norris and expectations. Helped along by the Fed telling people where the new target equilibrium will be and that it is determined to get there.

2. Concrete steppes. What Patinkin might have written. Oh God. Let's see. The Fed starts buying gold at the new higher price. So the money supply starts to expand, and Pg rises. The increase in Pg relative to P affects the demand and supply of other goods relative to gold. Silver is now cheap relative to gold, so people start demanding silver, pushing up the price of silver, which increases the demand for, ummm, copper...and so on, with a ripple effect through all goods along a billiard ball chain starting with the closest substitutes for gold, eventually running right along the whole economy. Meanwhile, back at the ranch, the increased supply of money from the Fed buying gold to push up its price is causing a second ripple effect as people start buying other assets like stocks and bonds and houses and farmland, and furniture, etc. Oh God, there are so many interactive effects from all the billiard balls moving around bumping into each other I can't possibly keep track of them all. And this totally ignores how expectations will be changing too as all this happens.

But, the thing is, in 1932 when Roosevelt did it, what we actually saw is something much closer to 1 than 2, AFAIK. People knew that Roosevelt was going to make the dollar worth less in terms of gold, and in terms of everything. Because he said so. So prices started rising.

Here's a third version:

3. We know that the relative price of gold (relative to the prices of all other goods) is determined by supply and demand. The marginal cost of producing new gold gives the supply curve, and the industrial and jewelry demand gives the demand curve. So if those pin down equilibrium Pg/P, then if the Fed doubles Pg, that means P must double too. We also know that the demand for money is proportional to P, so if P doubles the quantity of money demanded must double too. And under the gold standard, where the Fed has a perfectly elastic money supply curve at the target price of gold, if the quantity of money demanded doubles, the quantity of money supplied will double too. (All of this leaves out the effects of the recovery itself, which will be big, and will screw up the whole analysis, because, for example, lesser fear will reduce the demand for money. And maybe the demand for gold too?

[E. Barandiaran]

Nick,

Some of your questions were discussed long ago by Julio Olivera in this paper

http://aleph.academica.mx/jspui/bitstream/56789/7318/1/DOCT2064838_ARTICULO_3.PDF

There is an English version published in JPE but my understanding is that to it's not the same paper (I read them both many years ago)

http://www.hilbertcorporation.com.ar/olivera1970.pdf

[Phil Koop]

A function F(x) is homogenous of degree k if F(a.x) = a^k F(x) for all a, with k an integer. Likewise, F(X), X = x1, x2, ... xN is homogenous of degree k if F(a.X) = a^k F(X). A linear function is homogeneous of degree one by definition, so it is conventional to describe such a function as linear rather than HD1. By extension, a function F(X;Z), X = x1, x2, ... xN, Z = z1, z2, ... zM is linear in X or HD1 in X. An equation with such a function on one side can be termed linear or HD1 too.

However, although we all knew what you really meant, your notation F(M/P,Z) is technically wrong because M/P is itself a function linear in M and P (cows won't work); you ought to write instead F(M,P,Z).

[Nick Rowe]

E Barandiaran: Allowing for my not very good Spanish, those two papers look basically the same to me. Yep, this is part of what I was getting at here. You can take the same system of equations, and solve them with either M exogenous and P endogenous, or vice versa. (And note well how Olivera says that the system is both overdetermined and underdetermined if you try to solve it with the central bank pegging the rate of interest, which is exactly the problem the Fed faces today).

[Phil Koop]

I too have been a bit surprised at the resistance to the idea

But if there are multiple equilibria, then money cannot be neutral unless it is superneutral? I mean, the thought experiment where all cash, account balances and contract terms have "dollars" replaced with "double-dollars" still works, but if a heterogeneous distribution of new money has short-term real effects, then it can determine the long-run equilibrium? And if there is a stochastic component then the long-run equilibrium is indeterminate? Quantity theory seems to be unrecognizable after multiple equilibria are introduced. What am I missing?

[K]

Nick,

"Would scientists accept the new definition of the metre?"

I doubt it! *If* the CIPM redefined the metre by a factor of two, I'm certain that scientists would not accept it. The result would be that the scientific community would feel free to ignore them, indeed probably mock them. They'd definitely need a credible threat of some concrete steps!

Given that we have n equations with n+1 unknowns, I see no reason why people couldn't follow the CB's directions on the general price level. On the other hand, I don't see any reason, given lots of other possible coordinating dynamics, why they necessarily *would*.

We've agreed before that the only reason that anybody would listen to the CB is because it's *their* liabilities that define money. Otherwise they'd just be yet another loud mouthed think tank. In which case, the exact way those liabilities do define money, and the restrictions on the CB in terms of effecting changes to their balance sheet become crucial in determining whether their voice will be the most powerful coordinating mechanism in any particular circumstance.

Take the following equilibrium:

1) Natural rate curve flat at 2%
2) Expected inflation curve flat at -3%
3) Nominal rate curve flat at -1%

The ruler unexpectedly suddenly mandates the CB to allow people to exchange deposits for 0% interest paper money, and the CB is forced to move the policy rate from -1% to 0%. Unless inflation expectations rise, the short real rate will suddenly rise to 3%. The CB could try commanding the people to move their inflation expectations to -2%. You say it's obvious that the people will follow. I don't think so. I wouldn't follow, and I don't think I'd be the only economic agent to expect inflation to drop hard.

Given the existence of this particular bad disequilibrium, it strikes me that the mere knowledge by the people of the existence of such an equilibrium severely limits the ability of the CB to command expectations except at much higher equilibrium inflation rates where the probability of such scenarios is essentially zero.

[Ritwik]

Nick

This post may be over my head, so apologies if I'm saying something stupid. But it seems to me like the Humean/ QTM idea that works for a pure medium of exchange as you posit in the last couple of paragraphs is the long run neutrality of money, not its short run non-neutrality.

The short-run non-neutrality of Hume seems to rely not so much on any properties of a medium of exchange, but rather on imperfect information and a decrease in real wages. It is the wage theory of the business cycle, ala Sumner.

[Ritwik]

Nick

With regards to the QTM not holding with cows as money, why not? Why would I start drinking more milk simply because more cows are around - perhaps the price of all things doubles in units of cows & milk? Or perhaps we drink a little more milk, but this effect is as significant as, say, increasing the number of currency notes tenfold vs. adding a zero.

Similarly, one can argue that a 2kg bar of gold is worth twice as much as a 1kg bar of gold simply because a central bank is willing to exchange it for two such bars. Why can't you imagine a central bank that wouldn't do so - changing convertibility rules is precisely that. Why should the knowledge of the physical concept of mass matter for monetary theory.

As K says, I'd expect a new equilibrium in which there are two metres, the French meter and the 'true' metre. You cannot escape the concrete steppes, and you cannot escape the medium of account.

[Nick Rowe]

Phil: Thanks! It's slowly coming back to me now. I did used to understand this stuff, sort of, honest!

I think I meant to say that all behavioural functions are Homogenous of Degree zero in nominal variables. That's what "no money illusion" means. So if Y=F(M,P,Z), where only M and P are nominal, then Y=F(kM,kP,Z)=k^0.F(M,P,Z)=F(M,P,Z) for all constants k (like k=2 in my verbal examples).

[email protected]:

"Neutrality" normally means that all real variables are invariant wrt the level of nominal variables; and "Superneutrality" normally means that all real variables are invariant wrt the rates of change of nominal variables. The conditions for superneutrality are even more stringent than those for neutrality. Basically, all new money must be paid as interest on existing money. Otherwise the opportunity cost of holding real money balances will be higher when the money growth rate and inflation rates are higher, so less real money balances (M/P) will be demanded, which is one real change, and this will lead to other real changes too.

Changes in the distribution (between individuals) of money will have real effects (they are just redistributive taxes and transfers, so clearly affect the distribution of income, plus other things that are affected by that).

Changes in the probability distribution (e.g. variance) of the total money supply will also (probably) have real effects too. The real risk of holding nominal assets, for starters. Actually, the theory of the optimal countercyclical monetary policy can be understood as trying to find the best possible probability distribution for the money supply. We want that probability distribution to be correlated in exactly the right way with exactly the right set of exogenous shocks. E.g. Make the money supply perfectly negatively correlated with exogenous shocks to Velocity.

But yes. It is not at all clear what the QTM/Neutrality Of Money actually means in a world of multiple equilibria. This is what I think we should interpret it to mean:

Take a model of a monetary economy with (say) two equilibria, one "good" and one "bad". The QTM/NOM says that if you double the stock of money, you get two new equilibria. The new good equilibrium has all nominal variables doubled and all real variables the same as in the old good equilibrium. And the new bad equilibrium also has all nominal variables doubled and all real variables the same as in the old bad equilibrium.

But, maybe, just maybe, a historical change in the money supply could "flip" the economy out of the old bad equilibrium into the new good equilibrium. Now, in principle, anything whatsoever could also flip the economy from the bad to the good equilibrium. A proverbial "sunspot', for example. Sacrificing a goat might work too, if people believe it will work. Simply because it is a model with 2 equilibria, the model itself is by definition silent on which equilibrium will be chosen. But thinking about the short-run non-neutralities of money leads us to think that monetary policy might be better than sacrificing goats. And "monetary policy" doesn't have to be understood as some fixed time-path for any particular variable. It could also be a threat strategy, where the time path reacts to beliefs. This was how interest rate policy was supposed to work. It was well-understood that it was possible to hold the time-path of the nominal interest rate fixed, if prices were not perfectly flexible, but that doing so created an infinite range of possible rational expectations equilibria, nearly all of which ended up in disaster. But a clearly-understood policy of adjusting the rate of interest strongly enough and quickly enough in response to changes in expected inflation was supposed to eliminate all those nasty equilibria. Well, it didn't work, and the Fed hit the ZLB, where the threat to lower the nominal rate of interest if needed is of course not credible. It always was Chuck Norris, except Chuck was making the wrong threats, didn't move quickly enough, and eventually hit the ZLB wall. But people think that interest rates are the only game in town. They aren't.

[Ritwik]

Nick

I just read and highly recommend Perry Mehrling's take on Don Patinkin and MIP. It is rather different from your reading, though there are many commonalities, of course.

http://economics.barnard.edu/sites/default/files/inline/don_patinkin_origins.pdf

[Saturos]

I love David Hume so, so very much. Although I don't think Patinkin is wrong, I think that way too sometimes, but of course you're right that the "units only" perspective ("Money is the unit of exchange", anyone?) is superior. The Cheshire Cat analogy is superb, that's exactly how I feel about money. And my own "foolproof escape from the liquidity trap" has always been a redenomination of the currency. I think that was basically the kernel of Svensson's idea too. When you think of it that way, it is truly absurd to suggest that monetary policy could ever be constrained in that sense. I think Bill Woolsey has advocated essentially defining a dollar as a fixed fraction of NGDP, after setting the level path.

(But note that Hume had no account for a prolonged depression due to inadequate nominal spending - he couldn't explain extreme wage rigidity, didn't invoke money illusion. Scott would say that supply factors have gotten mixed in, triggered by the demand shock, but I suspect there's more to it.)

Scott just called this the best blog post of the year. He may be right - although I think Scott's recent draft of a semi-formal Market Monetarist macromodel was also historic. And everybody is raving about the new McCloskey guest post on BHL. But this one is truly epic - right up there with Nick's other posts about Walras' Law, the Concrete Steppes, upward sloping IS and what's wrong with macro.

Ritwik, I would consume more food if there were suddenly twice as much available, even if only through expensive, wasteful recipies. The important thing about money is that the unit of account status has been affixed to a good with no intrinsic value other than its common acceptance as a facilitator of exchange.

[Nick Rowe]

K: "Given that we have n equations with n+1 unknowns,..."

In the simple model, there are n equations and n unknowns, and a single solution. But that's when one of the equations represents the central bank's behaviour, and that equation is not HD0 in nominal variables (i.e. the central bank fixes some nominal anchor).

If we change that model slightly, by making the CB's behavioural equation HD0 in nominal variables (for example the CB tries to target a particular rate of interest, or tries to target "full employment") then we still have n equations and n unknowns, but that "counting equations and unknowns" condition is necessary but not sufficient for a solution (maths guys can explain why better than me). In particular, some of the variables (the real ones) are overdetermined, and other variables (the nominal ones) are underdetermined or have no solution.

[Patrick]

"Would scientists accepts the new definition of the meter"

Don't think they'd care. The numbers that hold the universe together (literally, in some sense) are dimensionless. For example, the fine structure constant. Now, if you could explain *why* the fine structure constant is approx. 1/137 ...

[K]

Nick,

"But that's when one of the equations represents the central bank's behaviour"

Agreed. And if one of the variables under the central banks control was the quantity of the medium of exchange then the price level would be fully determined via that system of equations. But because of the construction of our system, agents are able to convert the exchange medium to interest bearing bank liabilities and back again, without *any* other effect on bank balance sheets. Because this operation is *entirely* at the discretion of the money holders and *entirely* frictionless, there is no circumstance under which the CB can effect the price level via the quantity of money. If the potato is too hot, people trivially convert it into interest bearing bank debt, not consumption or investment.

Anyways, I suspect a purely theoretical debate would be fruitless. What about my example? Would you agree that given the operating constraints of a central bank (lets say all they're allowed to do is repo or buy government bonds), it is not necessarily the case that they will be able to talk their way out of that nasty equilibrium no matter what communication strategy they might adopt?

If you agree with that, then I'll agree that if they had been successfully running an NGDP targeting strategy for a long time, then it is far more likely that given, e.g. a sudden drop in the natural rate, inflation expectations would immediately adjust upwards (rather than downwards) in anticipation of otherwise getting pummelled by market forces, even under conditions that are closer to the ZLB than can currently be tolerated. Not guaranteed to work, but *way* better than the current dynamic. Essentially we'd be in the Kocherlakotan utopia in which inflation moves in parallel with the short rate, always in a state of optimal equilibrium. But getting to that dynamic is not feasible in the short run, given our current state of affairs.

[JKH]

Nick,

You responded to my question regarding:

“If instead the dollar is defined by fixing the price of gold, then doubling the price of gold halves the value of each dollar, doubles the quantity of dollars, and doubles all prices.

It’s the doubling of the dollars I asked about.

You said:

1. “The Fed announces a doubling of Pg (it will buy and sell gold at a price double the original target price)”

That sounds like concrete Fed steppes to me.

And presumably from your initial assertion and theory, you’re saying the Fed will double the money supply (through concrete steppes).

2. “Concrete steppes. What Patinkin might have written.”

I see no significant difference between that and the first version.

“People knew that Roosevelt was going to make the dollar worth less in terms of gold, and in terms of everything. Because he said so. So prices started rising.”

I understand that. But your assertion and theory says the money supply will eventually double. So either there is an expectation of concrete steppes, or concrete steppes overrule expectations.

3. “We also know that the demand for money is proportional to P, so if P doubles the quantity of money demanded must double too. And under the gold standard, where the Fed has a perfectly elastic money supply curve at the target price of gold, if the quantity of money demanded doubles, the quantity of money supplied will double too.

Same thing. Concrete steppes through elastic supply.

So I’m fine with all that, but I don’t understand why you have a problem with concrete steppes. Increasing the money supply in response to a doubling of prices requires concrete steppes according all three of your descriptions.

[Max]

K, if inflation expectations can change spontaneously (and we all believe they can, right?), then the CB doesn't need a policy instrument to escape the zero bound. It just has to promise to inflate after the escape from the zero bound - such a promise, if believed, will cause the zero bound escape to happen immediately. This is what Krugman calls "promising to be irresponsible".

Of course it's better to avoid this situation!

[K]

First, even in a highly optimistic model, such as the standard NK model, that is not an optimal solution. Excess inflation has costs, which means that your best result ends up trading off short term deficient output for longer term excess inflation.

Second, the depth and length of recession in the best path is totally dependent on structural model parameters. The best path might pass through 10 years of total liquidationist debt-deflation and depression, only then followed by a period of subsequent excess output and inflation so extreme that the pain is roughly equivalent to the depression. On top of it, while the standard NK model only produces second order losses (short term output deficiency offset by later excess) which would under any circumstance be big under a depression scenario, actual deep recessions cause real, first order, long term damage. I.e. you never get back onto the pre-recession level path.  I don't see why this could not be a reasonable scenario under the example I proposed.

"Of course it's better to avoid this situation!"

Yes, I suspect the great depression sucked.

[K]

Max,

Also, don't forget, unlike in the standard NK model, liquidity constrained agents don't have the ability to transport consumption from the future into the present. They're too busy going bankrupt. Under those circumstances there is not very much you can do with promises of distant inflation.

[FrankDeliquo]

I think the analogy is useful, but probably not in the way that you mean it to be.

If the French suddenly changed the definition of a metre, there would be massive changes required to all literature, systems, legislation etc. that use the term. The costs of the change would be immense, and would take a very long time to take effect.

Worse, if they decided to continually revise the definition, the unit would no longer be useable and would be abandoned in favour of one that was not continually being changed.

The analogy is of course unrealistic, but for reasons other than the ones that you might acknowledge.

The fundamental mistake you are making is to do with the nature of definition. Words are not defined by authorities, or even dictionaries. They are defined by their usage. The definition of metre cannot be changed by fiat, because the word "metre" is firmly embedded within billions of artefacts used every second in our society. It is this entwinement within the fabric of society that defines the word.

Similarly the dollar is, in modern times, defined by the huge mass of financial instruments that refer to it. Everything about each one of these instruments, the amount, the interest rate, the duration, who owes, who is owed, contingencies, and much more - all goes to defining what a dollar is right now. This includes fed-funds, as they are instruments that refer to the dollar. But fed-funds are a small subset of existent instruments.

The Fed can't directly alter the quantity of money. All it can do is alter the quantity of fed-funds - i.e. dollar units it owes financial institutions. This can influence the quantity of money, but not directly, not very predictably, and perhaps even ineffectually due to the many, many money-like USD instruments now in the world.

The Fed can only influence the unit of measure, not define it.

To refer to your analogy again - when the word "metre" was first used, its usage was obviously limited. This was the time when a change in definition would have been much more feasible.

It is the same with the dollar. When the USD was a small currency, with few credit instruments referring to it, the Fed did have a more direct influence and could more easily change its value.

In both the case of the metre and the dollar, those days are long past.

[rsj]

In the simple model, there are n equations and n unknowns, and a single solution. But that's when one of the equations represents the central bank's behaviour, and that equation is not HD0 in nominal variables (i.e. the central bank fixes some nominal anchor).

If we change that model slightly, by making the CB's behavioural equation HD0 in nominal variables (for example the CB tries to target a particular rate of interest, or tries to target "full employment") then we still have n equations and n unknowns, but that "counting equations and unknowns" condition is necessary but not sufficient for a solution (maths guys can explain why better than me).

I would say the reverse -- that you get homogeneous equations only with a walrassian process. If you change that assumption slightly, you no longer get homogeneous relations. We live in a world without Walrassian processes and yet we have prices.

Without meta-time bargaining, say firms need to hire workers prior to selling the output that the workers create, you get nominal contracts, in which case the equations are not homogenous. The lack of definition of the price level is a knife edge case that is due solely the Walrassian assumption, and is not an inherent economic feature.

Moreover, you do not have a convergence result that says if transactions occur in real time then the economy converges to the Walrassian equlibrium as the speed of transactions goes up. There is no analogue to Shapley-Folkman-Ross's approximation of u-shaped cost curves with a convexified economy.

So why assume that long run economic behavior is independent of money? If you have an approximation theorem, you would be justified in making that assumption, but you don't. There could be many explanations of why economies tend to rebound after they contract, e.g.

* technological growth is really all that matters in the long run, provided that there are halfway decent institutions to exploit technological change. Long run, all that matters is knowledge, and we could be in a socialist or a capitalist system, or some completely different system (resources allocated by lottery or birth), and it wouldn't make a difference at all for long run growth.

* the U.S. experience is a fluke, not shared by the rest of the world. There are no guarantees that long run growth is pre-determined for anyone.

* Our democracy is such that policy changes -- e.g. government -- ensures that long run growth is at a certain level, as we vote the bums out and make necessary changes (a la redistribution by F.D.R) when markets get too crazy. Nations with less responsive governments let markets run amock and are not able to rebound sufficiently after contractions, or, like Argentina may never recover from a decline.

There are many arguments to make here, and my favorite would not be the knife edge argument about homogeneity. I would much rather believe in thinks that are true in the generic sense -- e.g. deform the functions slightly, and see what you get. The generic solution is much more likely to be applicable to our economy than the solution in which everything is scale invariant.

[Greg Ransom]

Hume was NOT puzzled. Hume understood and explained the Cantillon Effect -- only failing to understand how changing stocks of money and shadow monies also shift the time structure of production, expanding and contracting output across time.

But Hume understood well that its about limited knowledge and the non-sustainable stretching of the net of prices. "Sticky prices and expectations" are just a sliver and shadow of these more fundamental empirical elements.

"And what is puzzling, for us, is not that the Fed can change the nominal size of the US economy; the puzzle is that doing so can affect the real size of the US economy too, at least in the short run. And we think it's got something to do with sticky prices and expectations."

[J.V. Dubois]

Nick, Phil: About multiple equilibria and QTM I am with Nick on this one. Plus the reason we are doing this is that money is an "institution" that is important for coordination of economic activity. And since institutions "evolve" - sometimes getting worse (and as evolutionary biologists know, the probability of things getting worse is proportional to the level of optimization or to the level of how "good" things are) and we need to prevent this detoriation.

There was one story in Bowles Microeconomic book that put me on board. It was story of two villages in India that faced this problem: the wealth of villages depends on the harvest, which greatly depends on farmers planting their seed on time. However farmers also face dangers, one of the most important is flocks of birds that can eat all their freshly planted seed. So the coordination problem is that while collectively, everyone benefits from early planting, individually, farmers have incentives to postpone planting seeds just after other farmers do it so that they minimize the risk of their harvest being eaten by birds. It is given that sooner or later every farmer plants seeds as payoff of actually having something to eat next year is obviously greater than the risk of losing their harvest. So generally there are two equilibria: either everybody plants early or everybody plants late. One village developed a social technology called "festival" and every farmer knew that this is the time to plant. If someone did not plant, he risked becoming social pariah with very serious consequences. Other village did not develop anything like that and farmers decided the right time to plant on their own. It is not hard to predict what village was richer long-term and which one was poorer.

And this is it. If it is mayor of the village who decides when the festival starts, people of concrete steppes could immediately throw their objections - does mayor have enough power to personally punish somebody who does not participate? What are exactly the levers, how is his decision carried out? Some may focus on specifics, maybe Mayor uses village bell to announce the festival. People of concrete steppes could then object "So what if the bell gets stolen or if it is damaged? Then surely festival policy will be rendered ineffective because crucial point in the causal process of transmission mechanism is missing". Is this absurd? So is the current debate about crisis. And the sad thing about this is that if Mayor gets convinced by these people that he is powerless and that everyone is doomed then we really can witness dissolution of the institutional fabric that holds the society together.

Anyways, intellectually I am confident that Market Monetarism already won. It is the only macro school of thought that incorporates the best of what is now known in Macro an Micro economics. They learned from Keynesians that demand is important. They learned from Friedman that money is what is important for demand and they learned from Lucas that managing the demand is not the game of chess but poker. But unlike him they know that the rules of the game are very important and that they have real impact.

[Steve Roth]

Nick, just dropping this here in your latest post (another great one, btw), would love to hear your thoughts on this:

"“While the Fed hates being held hostage by market expectations, we doubt it will be prepared to disappoint global investors this week,” Lou Crandall, chief economist at Wrightson ICAP, wrote in a note to clients on Monday."

http://www.nytimes.com/2012/06/19/business/economy/fed-policy-making-panel-to-meet-as-growth-faces-threats.html?_r=1

Since the Fed at least to some extent creates those expectations...

[Nick Rowe]

Greg: Just to be clear, I interpret Hume as saying "The short run non-neutrality is a puzzle, and here is my resolution of that puzzle..[the passage I quoted]"

I agree with you and Kevin Andrew above that Hume's story sounds like the Cantillon story. But I also agree with Ritwik above that it sounds like a sticky wage/price/expectations story too. I will leave that one to the historians of thought, as to what Hume really meant. Personally, I don't think Hume is really explicit enough for us to be able to say for sure.

Kevin: Richard Cantillon wrote before David Hume.

[Nick Rowe]

JV: I keep getting Bowles and Gintis muddled (I first came across them in a joint paper they did on the Labour Theory of Value). At least one of them (probably both) is a great thinker, and your story confirms this (it sounds very Elinor Ostromy too). This is the very best sort of work in Institutional Economics. And yes, it is exactly that sort of institutional economics that needs to be applied to our understanding of monetary institutions too. Money, and monetary policy, have to be understood as social institutions -- a shared set of mutually-reinforcing expectations and rules of behaviour -- and not just the pulling of levers.

Funnily enough, on a personal note, this was exactly my original agenda when I set out to write my PhD thesis. I failed, of course, because I was laughably over-ambitious for my abilities. You might say I'm still trying, though. And still failing!

[Phil Koop]

Nick: thanks for your patient explanation, it is much appreciated.

I see that David Glasner has put up a post espousing the common-sense view of money neutrality (and that you have replied to him.) So there are more varieties of market monetarist under heaven than were dreamt of in my philosophy.

Suitable apologies to you all.

[Phil Koop]

J.V.Dubois: I like your comment, but I would never have disagreed with it in the first place. So I suspect we do not really understand each other.

[Nick Rowe]

FrankDeliquo: "Worse, if they decided to continually revise the definition [of the metre NR], the unit would no longer be useable and would be abandoned in favour of one that was not continually being changed."

Yes, and I think that's true for money too. Except it is easier to define the metre in a good way than it is to define money in a good way, because a lot of relative lengths in physics stay constant over time, whereas relative prices of almost everything in economics are always changing. But what surprises me is how long people will stick to a particular money, both as medium of exchange and medium of account, even in the face of very bad monetary policy. You have to really screw up before the Greeks start switching to "barter" and the Zimbabweans abandon the Zim dollar altogether.

"The fundamental mistake you are making is to do with the nature of definition. Words are not defined by authorities, or even dictionaries. They are defined by their usage."

Wittgenstein. And in some sense that's true for money too. People choose what money to use, and what prices to exchange that money at. So what gives central banks their power? "Asymmetric redeemability" is my answer. If all other monies (such as those issued by commercial banks) are redeemable at fixed exchange rates into central bank money, and it is the responsibility of the issuer, and not the central bank, to ensure they are redeemable, (why this should be so is another question), then the central bank is the one that is free to decide what all the other monies will mean. If everyone else decides they must translate their words into my words at par, then ultimately it is my usage of words that defines what words will mean. I get to play the role of Humpty Dumpty, and everyone else follows my usage.

[Nick Rowe]

Ritwik: That's a lovely piece by Perry Mehrling on Don Patinkin (pdf). He (Patinkin) taught us at Western for 6 weeks, but he wasn't an easy person for a student to get to know.

[Nick Rowe]

rsj: "I would say the reverse -- that you get homogeneous equations only with a walrassian process. If you change that assumption slightly, you no longer get homogeneous relations. We live in a world without Walrassian processes and yet we have prices."

Actually, I sort of agree.

Understanding the short-run non-neutrality of money can be understood as trying to understand which of those equations is non-HD0 in some sense, and moving away from a Walrasian model is (probably) the best way to do this. Taking your example, where a price must be set, based on expectations of future demand and supply, before agents know what monetary actions the central bank will take. (That's the standard New Keynesian story). The equation is still HDO if we include those lagged expectations and previously set prices but since those variables are pre-determined, the equation is no longer HD0 in current period nominal variables.

[rsj]

The equation is still HDO if we include those lagged expectations and previously set prices but since those variables are pre-determined, the equation is no longer HD0 in current period nominal variables.

I don't see how you can say that, as we have no idea what the equations are. Has there ever been a solution to a monetary exchange economy that does not assume meta-time tatonnment? If so, I would be interested to find out. I.e. remember the "circle economy" in which I buy some goods from the person on my left, and repay some debt I owe the person on my right. The solutions are not homogeneous in any sense. If many people are sequentially making expenditure decisions, where one person's expenditure defines the other person's revenues, then why should such a distributed system be solved by polynominal equations at all, let alone homogeneous polynominal equations that are all of the same degree. Without complete markets in which we can make all decisions in meta-time simultaneously, we are stuck with contingent plans in which we don't even know what national income will be until everyone has made their expenditure choices.

[123]

Nick: ""Asymmetric redeemability" is my answer."

So under NGDP futures convertibility there is no asymmetric redeemability. Central banks would have no power, and their role would be confined to keeping the metal rod in the safe.

[Nick Rowe]

123: I am free to choose. But once I have made my choice, and decided to stick by it, I am no longer free to choose. Central banks exercise their power by choosing NGDP futures convertibility, or gold convertibility, or the k% rule with no convertibility, or whatever. Conditional on how they choose to exercise their power, they have no power. They spent it, in exercising it.

rsj: "I don't see how you can say that, as we have no idea what the equations are."

That's the beauty of Hume's insight (and Milton Friedman made essentially the same argument in saying there's a natural rate of unemployment). Regardless of what the equations are that determine the structure of the economy, those equations should be invariant to the monetary unit. Real scientists use roughly the same "trick" in their search for dimensionless constants, as far as I understand it. Starting from that fundamental insight of monetary neutrality, we then work backwards and ask ourselves "Hmmm, now, under what circumstances might a change in the units, that happens in historical time, matter?"

It's a bit like the Modigliani Miller Theorem. Nobody believes MMT, including MM themselves. But it's a very good starting point from which to ask ourselves: "Hmmm, now, why might the debt/equity ratio matter, despite MMT?" Discussions of debt/equity ratios that are not informed by MMT (you still see them occasionally) just come across as hopelessly garbled, and "not even wrong". A lot of "heterodox" macro reads exactly the same way to me.

Oh, and in answer to your earlier question: MMT does not apply to OMO because money is useful as a medium of exchange, so money and bonds would not be perfect substitutes. It's not just the distribution of returns on your money/bonds portfolio that matters.

[Nick Rowe]

rsj: my old post on "Units". Wikipedia on "Dimensional Analysis"

[123]

Nick, so basically central banks preserve their power by not making a choice. By not making a choice, they increase the M0/NGDP ratio, they earn monopoly profits, they grow the value of their franchise. They are earning excess profits by destabilizing the macroeconomy - we need a new James Bond movie with the central bank as a villain.

[rsj]

Starting from that fundamental insight of monetary neutrality, we then work backwards and ask ourselves

OK, so this is an axiom rather than a conclusion. Previously the argument was "the equations are homogenoeus and so money doesn't matter". Now, it is "we know money can't matter so the equations must be homogeneous".

MMT does not apply to OMO because money is useful as a medium of exchange, so money and bonds would not be perfect substitutes. I

But again, the role of the central bank, as this institution was designed and currently functions -- is to erase that distinction. If you have a bond -- or anything that the CB deems as appropriate collateral, but government bonds certainly are -- they you can instantly convert that bond into money at pre-defined rates of exchange.

The whole raison d'etre of the central bank is to guarantee that a select group of oligopolies known as banks have the monopoly of creating money for the non-financial sector. Inflation fighting is far, far down on the list of priorities next to ensuring that the payments system is functioning.

That is why you are getting so much push back when you pull out the quantity type arguments.

That's not how things are designed to work and that's not why the banks got together and forced the creation of a government reserve bank in the first place.

Looking at the behavior of central banks today, they will never take the power to create money out of the hands of the private sector, and they will never do anything to endanger that private monopoly or to encroach on it. Even if, within the context of an a-historical and institutionally-unaware model they *could*. Central banks restrict themselves to setting interest rates and let the private sector banking system create as much deposits as it can given those rates. They are even very hesitant about things like basic bank regulation, let alone squeezing the banks out of the money supply business.

[Nick Rowe]

'Nature doesn't care whether we measure her in ponds or kilograms.'

Is that an axiom of physics, or a conclusion, or an empirical regularity? I can imagine a world where it's false, where Greek Gods rule the physical universe, and care about all sorts of things, like the units men use.

If it's an axiom at the level of the individual unit, it could be a conclusion at the level of the economy as a whole.

If we used cows as money, the axiom would be false. I "know" that from casual empiricism. Cows give milk, people like drinking milk, cows eat grass, grass is scarce. Cow money is non-neutral.

"If you have a bond -- or anything that the CB deems as appropriate collateral, but government bonds certainly are -- they you can instantly convert that bond into money at pre-defined rates of exchange."

Nope. I currently hold $200 in notes in my pocket, earning 0% nominal, while the overnight rate target is 1%. If I could *instantly* and *costlessly* convert back and forth between money and bonds I would do so, just before I paid at the supermarket checkout or got my salary.

People hold inventories: of medium of exchange, and of groceries, and of other things. Precisely because life is very inconvenient if you try to hold zero inventories.

[rsj]

Nope. I currently hold $200 in notes in my pocket, earning 0% nominal, while the overnight rate target is 1%. If I could *instantly* and *costlessly* convert back and forth between money and bonds I would do so, just before I paid at the supermarket checkout or got my salary.

You can't. You are not supposed to. The overnight rate doesn't apply to you at all, as you cannot borrow or lend overnight.

You are in the non-financial sector, and money to you is primarily bank deposits, on which you are earning close to zero if not exactly zero. It is because you cannot costlessly and instantly convert that the banks earn seignorage income on those deposits. Which means that they are more than able to create as many deposits for you as you want to hold. Money to you is just an IOU from the bank.

Hence the privileged position that I was referring to earlier. They have access to the payment system, to automatic CB overdraft facilities, and to lending facilities. They also access netting and after-the-fact settlement. For you, when you pay, you settle. Banks pay to the non-financial sector and settle among themselves ex-post.

Therefore you have a demand for deposits far in excess of the banking system's demand for reserves.

As far as the private sector as a whole is concerned, the only difference between bonds and deposits is interest rates and interest rate risk. But that arbitrage is a privilege of the oligopoly, and it is not your privilege. As far as you are concerned, you can have as much money as you want, given your total wealth. All you need to do is sell your interest bearing bonds to the banking system and accept their non-interest bearing IOUs in exchange.

They can always accomodate you, so there is never any excess demand for money on the part of the non-financial system.

The financial system can never have an excess demand for reserves as the CB makes sure that this market always clears.

[Greg Ransom]

Fair enough.

Nick wrote:

"I agree with you and Kevin Andrew above that Hume's story sounds like the Cantillon story. But I also agree with Ritwik above that it sounds like a sticky wage/price/expectations story too. I will leave that one to the historians of thought, as to what Hume really meant. Personally, I don't think Hume is really explicit enough for us to be able to say for sure."

[Patrick]

'Nature doesn't care whether we measure her in ponds or kilograms.'

Is that an axiom of physics, or a conclusion, or an empirical regularity?

It's a consequence of that fact that multiplying by 1 doesn't change anything.

e.g. 1 mile = 1609.344 meters, and 1 hr = 3600s. Therefore, 1609.344 meters/1 mile = 1, and 1 hr / 3600s = 1. Now, given e.g. 5 miles/hr we convert: 5 miles/hr * 1609.344 meters/mile * 1/3600s = 2.2352 m/s

[Nick Rowe]

Patrick: suppose, just suppose, that the Universe were ruled by an Olde English Imperialist god, who didn't like the metric system? And metrification made him angry, and he created thunderstorms in response? Or a slightly confused French God, who suffered from metre illusion, thought a metre was a metre, and who halved the size of the Sun when the French hacksawed the metre in half? There's nothing logically impossible about that theory of the Universe.

I think it took the ancient Greeks to figure out that the Universe wasn't like this. We take it for granted, but I don't think it was always thus.

[Nick Rowe]

rsj: "The financial system can never have an excess demand for reserves as the CB makes sure that this market always clears."

My old post the peanut theory of recessions

[vimothy]

rsj,

And I don't care whether you believe in MM or not, but am interested in why MM seems to be applied against fiscal interventions (Ricardian equivalence is a form of MM) but is not applied against CB quantity interventions.

See:

Neil Wallace (1979), "A Modigliani-Miller Theorem for Open Market Operations"

http://www.minneapolisfed.org/research/sr/sr44.pdf

[Nick Rowe]

vimothy: yep. The fiscal theory of the price level guys also assume MM.

[rsj]

Vimothy,

You rock. Thanks!

[vimothy]

No worries. If you have access to JSTOR, I found a version with readable mathematical notation here: http://www.jstor.org/stable/1802777

[Patrick]

Nick: I dunno.. I think I'm probably just missing the point, but what the heck ... all the intelligent people have already made their contributions, so the peanut gallery might as well have a go now.

I'm trying to think of ways even an Angry Metric System Hating God could pull off what you describe, and I suspect that analogies between physical systems and economic systems just don't hold-up that well.

To shrink the size of the sun by half by compressing it would cause a much increased rate of nuclear fusion and blow the star apart or perhaps collapse it into a black-hole. If the star did achieve some kind of new equilibrium, the Earth would certainly be outside the habitable zone. In any case,life on earth would end shortly after the start was shrunk.

The only other think I can think of would be for Angry God to have a velocity in all directions relative to the inertia frame of the sun. If Angry God's relative velocity in all directions at once (this is the part requiring Godlike powers) was just right, the Lorentz contraction would make the sun appear half as big. Of course, it wouldn't affect humans at all, but the Angry God could appease himself by making the start appear smaller.

But I suspect I'm being too literal. Or perhaps God is an RBC macro-economist(there's a scary thought).

[Patrick]

Ugh. Somehow "star" came out as "start" above. Sorry.

[Nick Rowe]

Patrick: Oh man, but you are just so embedded in all this neoclassical scientific "units don't matter" worldview. Nah, the Sun is just a shining metal disk in the sky. Thor should be able to trim it down, no problem. After all, he sank those ships the other day with that thunderstorm. And he does put the Sun to sleep every night anyway, so cutting it in half shouldn't be any harder.

[Nick Rowe]

In any case, the so-called "external world", just like the so-called 'economy", doesn't exist outside of our thinking about it. It's all a figment of our imaginations. So it stands to reason that if we think in smaller units, the Sun we think of will be smaller too!

[Edeast]

I'm sporadically near the Internet, but here was a quick proof of non walras.
Remember I thought barter had n choose 2 markets, but that was 2-way trades, you later did a post explaining everything gets switched for everything. It's like having ratios or fractions with many different numbers, for numerators or denominators. Like using the rational numbers to approx the real numbers. Anyway you were right, 2^n markets exist, if the auctioneer, can take any basket, and switch them around. Or in other words the power set of a set is the possible trades. If there is an infinite number of goods the power set is uncomputable as it is in 1 to 1 correspondence with the real numbers. Using cantor's diagonalization argument, show it is uncountably infinite.

But I guess this is well known, with the computable general equilibrium models. I tried looking up some constructivist economics, like vela velupillai's but not sure if it is worth it. Lots of mathematicians aren't that strict.