Cancelling on both sides of the Equation

It started innocently enough. A friend sent me a link and suggested it would be interesting to do a similar analysis on the velocity of circulation of money for Iceland. This link to be precise:

I’m not an Economist, I’m a Computer Scientist with a rather bizarre hobby - I had to go and look it up.

Something about the idea that the velocity of circulation of money, the number of times each physical note, or bank deposit electron changes hands could affect the price level bothered me, but I couldn’t put my finger on what. I went back to my rather quixotic task of trying to figure out how the banking system actually works. (Step 1, build a computer model, Step 2, discover almost no Economist you talk to about it has a clue how the banking system actually works…)

It stayed at the back of my mind though and continued to bother me. As a Computer Scientist, I specialise in networks and real time systems, so I’d come into Economics originally with a rather vague model of money as packets of information bouncing around and establishing a price level. Did the speed at which they did that really matter? It bothered me, I couldn’t say why, I went and looked it up again.

The original source for this particular version of the Quantity Theory of Money(it turns out there’s several, in and of itself not a good sign), turned out to be a book by an American Economist Irving Fisher written in 1911, called the Purchasing Power of Money:

The thing that immediately struck me about the book was the date. You see, as part of trying to figure out how the banking system works, I’d spent a month going through the 19th Journal of the Statistical Society of London, and a couple of other 19th century Economics Journals I’d found lurking online,  and I’d established to my own satisfaction that the earliest that British Economists even appeared to have an inkling about the inately expansionary behaviour of the banking system was 1900 or so, a discovery which was accompanied by a raging debate over whether bank deposits even qualified as money. Money, as far as 19th century Economists were concerned was physical notes and coins.

It’s fairly clear from his book that Fisher was in the bank deposits don’t exactly qualify as money camp.

The quantity theory of money itself, is a simple equation. M (quantity of money) * V (velocity of circulation of money) = P (average price level) * Q(total quantity of production). (If you’re an engineer or a scientist btw., the first thing that’s wrong about that equation is that the units don’t match, but I digress.)

The second problem becomes clear when you look at the example Fisher provides in Chapter 1 section 2, and expand it out a little. Fisher starts with $5 million in money, and total purchases in a year of 200,000,000 loaves of bread, 10,000,000 tons of coal and 30,000,000  yards of cloth, with the prices shown below.

With $5 million in physical cash, it isn’t possible to buy all the coal say at once, which would require $50 million, so a series of exchanges have to occur. $5 million buys 50 million loaves of bread say, the bread makers then buy 1 million tons of coal, the coal miners buy 5 million yards of cloth, and the cloth makers then get to buy some bread. All in all the money circulates around 20 times (which is of course the point), and on the other side of the equation, 20 separate transactions get made with it.

In other words, the velocity of circulation of money can’t affect the price level, because it cancels on both sides of the equation. Oops.

I always wanted to be a scientist. Don’t ask me why, I remember when I was a 9 year old writing an admission essay for the local grammar school, and describing why I wanted to be a scientist. Looking back I have no idea how a nine year old ends up wanting something like that, but I did, and the grammar school gave me a place, which ushered me onto the educational path that at least ends up giving you the training to be a scientist, even if I’ve spent most of my life doing something else. One of the most important things you learn is that extraordinary claims require extraordinary proofs. Questioning the quantity theory of money is right up there on that scale.

Still, I could also see why Fisher needed velocity. Fisher tried in his book to do something quite laudable, he tested his results against actual data. But Fisher didn’t count bank deposits as money, even though British Economists like Dunbar around the same time were pointing out that 90% of all fiancial transactions were being conducted not with notes and coins but cheques. With an unknown expansionary force acting on the total quantity of money, prices were varying in ways Fisher had no way of explaining - and the velocity of circulation of money became a very convenient fudge factor. It still is. The Bank of England uses it to adjust their M4 money supply measure.

Then somethng else dawned on me. When Economists talk about the economy growing, what they mean is that a measurement called the Gross Domestic Product (GDP) is growing. But GDP isn’t the total amount of things produced, it’s the total value of things produced. To get GDP you get the total value of everything that was sold in a year(price * quantity), modify by the inflation rate, and publish widely.

But if you take the quantity theory of money in any way seriously, then that can’t work, because if the total quantity of things produced increases - then the prices will drop. M = P * T’. Fruit is cheap in the autumn. Price is inversely related to quantity. GDP can only increase if either production decreases (causing price increases due to shortages), or the money supply increases. That of course, is why GDP ‘works’ - the money supply in most countries is more or less continuously increasing, and study the banking system for any length of time, and you will develop a rough feel for which countries have the fastest expanding money supplies. A quick check confirmed, they also had high GDP’s.

A friend of mine heroically volunteered to plough through a bunch of Central Bank sites and pull out the relevant money supply and GDP data. A bit of jiggerypokery with matplotlib, and we had a paper showing what happens to GDP if you normalise it to correct for the growth in the money supply. (In the majority of countries it’s slowly shrinking, probably because money is getting pulled into the financial sector.) GDP it seems isn’t measuring economic growth at all - it’s just measuring the growth in the money supply.

Well, that’s what scientists do. They write papers, and try to get other people to read them (this it turns out is the really hard part.) With one honourable exception, none of the economists who so far admit to having read the paper understood what it meant to normalise data. [If you know that the tape measure you’re measuring with has magically doubled in length, you can still use it to measure if you halve all the measurements you make.] My fellow engineers get it immediately, they’re just not sure that that’s really how GDP is being measured.

Once friends and colleagues have been exposed to it, the next step for any paper is to try and get it into a conference or journal. So far the paper’s been rejected by two conferences and 2 journals. Without any response at all as to why.

In my own field that wouldn’t happen. Question one of the central tennets of computer science, and have the timerity to submit it to a conference, and you can expect to get either a detailed description of your own stupidity, or an invitation to explain further. But as I’d already learned with the Banking System, this is Economics, they do things differently over there.

So that’s science. Looking at a problem, and trying to figure out if you’re completely wrong, or if everybody else is, and with mild humiliation as the most likely outcome. Papering the wall with rejection emails.  Some peer review would be nice. In the meantime I’m building a computer model, it seems as good a way to explore the problem as any. A really simple economy with just a few employees, a farm, and a market to set prices. Something I can play around with, and try and figure out the math. So far it’s not looking good for GDP. It’s not looking good for the rest of the equation as it happens, but it’s too early to be sure.

There’s something about it all though. Reading economics papers and realising that almost none of them normalise for the money supply growth. Looking at a computer model, a few figures updating, trying to work out if its behaviour is a bug, or a real feature of the monetary system. Caught on the edge of knowledge and belief as the results begin to match the hypothesis. Knowing, if nothing else, that that nine year old was totally right about wanting to be scientist.

Happily hacking each other apart

Hey Jacky, this is superinteresting! As a nine year old I wanted to be a superhero, but lately scientist seems much more interesting than punching around a bunch of clowns in spandex. So let’s do some science! And the way we do it, in the time honored tradition, is by hacking each other’s arguments apart. So let me have a go. In love and deep respect for what you are doing.

To do this, I first need to understand your argument. Let me start here: in my (admittedly not very deep) understanding of Fisher’s equation, V does not affect anything, because it is not a variable. It is a parameter, which most people assume to be relatively stable in the short run. It increases with structural change in the transacting behavior of economic agents: suppose you are looking at V1 and suddenly people invent and start to use credit cards, you will see that you don’t need to increase M1 to accomodate an increased volume in transaction, because a smaller quota of transactions is now happening in cash. But those changes are slow: you are talking decades.

Also, GDP is separated from MV by the degree of vertical integration in the economy. What I mean is this: suppose I am a farmer. I grow wheat with no inputs other than my field, rainwater and sunlight. This year seeds come from last year’s harvest; so does my subsistence, because I live off bread that I bake from my wheat. Each year I sell my harvest (less the wheat I need to keep me going another year) to a man who lives in a city, and that is the only transaction that happens in this economy. Now suppose someone invents a plough. A plough is made of steel, so I can’t produce it off my time alone, but it makes my work easier and more productive. So now I take the money from my client, give it to the ploughmaker for him to make me a plough. With the plough, I can now produce more wheat, that I sell to my client at the end of the year.

Two things are happening here: possibly more wheat is being produced; and certainly there is another transaction going on, upstream of my field, between me and the ploughmaker. Only the first increases GDP, because wheat is something we, the economy, desire per se. The plough, instead, we don’t particularly want if not for its contribution to wheat production, of which it is a part. The point of all this is that - if V is constant - you need to increase the money supply as economic activity gets more vertically disintegrated, as it does. GDP measures value added, and it is not not NOT the sum of all the transactions. Modern finance, also, radicalizes the process, because it uses up a lot of transactions but produces very little. So you need a massive increase in money supply (of course I am not talking about M1) to sustain financialization.

Given this, I don’t understand what you are measuring when deflating GDP by money supply. I would expect to see the transactive intensity of GDP to increase over time: as both industrial organization and finance become more sophisticated, you need more units of transactions to make one unit of GDP. This, however, is arguably a sign of efficiency: a company brands my laptop, but another one makes the screen, yet another one makes the DVD driver, one the wi-fi antenna and so on. This is just Smith’s division of labor, which implies… more transaction.

Does this make sense or did I manage to miss the point entirely? Do you want to post a link to the paper?

Ah, but let’s think about this a little…

Hi Alberto,

Thanks for such a thoughtful response - and indeed :slight_smile:

So there’s actually one very simple counter example to the V is stable argument - High Frequency Trading. In its part of the economy, its been increasing the velocity of circulation of money around the stock market by several orders of magnitude. So if V did affect the price level to any degree at all, share prices would be through the roof in the last few years, and in fact it would be possible to track the affect just by the introduction of HFT on the different exchanges.

The other way to argue against that is through a thought experiment. Imagine an economy with 1 tool, 1 coin and two participants who exchange the tool for the coin any time they want to use it. It’s quite clear that however quickly or slowly they do that, they can’t affect the price level. [And as you probably know, formally in math, you only need one sucessful counter-example to disprove any theorem.]

As far as the wheat example goes. Strictly speaking, wheat doesn’t get included in GDP because it’s not a final good (but that’s just me being pedantic …) But if it did, in your example then it would be the total value of wheat sold (price * quantity). If the introduction of a plough increased the amount of wheat produced, all other things being equal, the price of wheat would drop, and GDP would stay the same. Except that since there are now extra transactions involving ploughs, and the money being used for that isn’t establishing the price level for wheat, the price level would drop due to monetary deflation, and so would GDP.

What normalising GDP against the money supply does, is correct for the underlying growth in the unit of measurement (money). It seems to go somewhat overlooked by economists that as the money supply grows, so does the unit of measurement, and although a lot of things get corrected for CPI inflation, this isn’t a sufficient correction - partly because CPI only applies to a sub-set of goods, and also because of the production/money supply inverse relationship. But the “transactive intensity” of GDP is the flip side of velocity - the more transactions - the more exchanges of money within the economy - and they cancel.

As to whether or not you need to increase the money suppply in the way many economists seem to think is necessary…

There certainly have been periods (the middle ages in Europe), where there were problems because of  physical shortages of monetary tokens (due to metal shortages, and localalised liquidity issues.). But I would gently submit that that hasn’t been a problem since banking was introduced, since the bookkeeping entry can always be arbitrarily sub-divided. What I personally think increasing the money supply does do is badly distort the signal that the price level is trying to provide, and also by virtue of where that money is introduced, artificially advantage some economic participants in the economy, and cause an accelerating wealth gap over time. (Decade long periods of time - as you say, this is intrinsically a very slow system.)

However - this is something that I really want to explore in a computer simulation - since i have a very nasty feeling that there’s something going on between debt and the money supply (outside of its interdependence in the banking system), that may be significant. I think it’s very hard to say anything at the moment - we can’t really argue about how an economy with a constant money supply would behave, because we’ve never had one under modern conditions.

I’ll get a copy of the paper up so you can read it in the next couple of days,

– jacky

Causality + time scales issues?

It seems there are causality issues here. What we were taught as undergraduates is that V is a parameter. In the short run, it can be treated as a constant one. This is the basis for Friedman’s claim that all a central bank must do is increase the money in such a way that there is not “too much” of it affecting price levels. Less HFT, that would mean “if the production of goods and services increases by 5%, increase money supply by 5%”. The production of goods and services If this is true:

  1. I can't interpret your claim that V does not affect price levels. Of course it is technically true, but then it is true also of my hemoglobine count. Parameters don't affect anything.
  2. If you deflate GDP by the increase of money supply in a perfect Friedmanian world you get this ratio GDP/M is a constant. An interpretation of this could be that the Friedmanian Central Bank is doing its job well. What gives? What is causing what?
  3. Plus, I don't recall the TOTAL quantity of money was ever the unit of measure of GDP. GDP is measured in monetary units, which (if you believe the welfare economy theorems) are more or less bottled happiness ("utility"). If you don't like that, look at GDP in PPPs, or in Big Macs, and you will still get an increasing time series.
As for your thought experiment, I do not know how to handle it for two reasons.
  1. it either rejects the Friedman-Fisher world  altogether, making V perfectly flexible, or is using a very long time scale to make it so. Either way, it has little to say about the world described by standard economics.
  2. The price of the tool is fixed by construction, so of course it cannot vary.
Finishing this rant off, Sen and Stiglitz forgive me, I am no fan of GDP. But it does correlate pretty well with other time series measuring pysical things, like employment. There must be something there. 

One thing that does make sense to me is this: you seem to advocate a more sophisticated model, in which V is different in different parts of the economy. A dual model might suffice: finance and everything else. The duality is interesting because V can be assumed to be constant in the non-finance sector, but variable in the finance sector. What happens in such a world? Frankly, I have no idea.

I will be happy to read the paper.

Possibly what you were taught is incorrect…

I very much fear that you may need to consider that much of what is currently being taught in Economics, especially with respect to monetary theory, is probably incorrect. I know for example that the description of how the banking system operates can at best be described as extremely misleading.

Again, I don’t like these ideas that it is necessary to increase the money supply to allow production to increase. The price level can go down as well as up, and production deflation which occurs when more stuff gets produced benefits everybody. Also when Economist talk about increasing the money supply they somehow neglect to discuss who ends up receiving that money, and what that does to the wealth gap.

1)Not entirely sure what you mean here. Parameters do affect the equations, that’s the point of having them. It’s perfectly valid to make assumptions such as in the short run it doesn’t change very fast for example. But that’s just a simplifying argument, and again - I rather suspect what is actually happening is that V is being used as a convenient fudge factor to allow problems in current understanding of the money supply’s behaviour to be papered over. So it’s not a parameter - it’s a magic number - which the economic magician uses to divert attention from the underlying reality of the cold hard numbers.

  1. Once velocity is taken out of the equation, and with the assumption that the money supply is held constant, and that GDP is being measured based on the price of all goods and services exchange for money, then yes that is correct, GDP would be constant.

  2. GDP is measured as the sum of the value of a certain basket of goods sold, that is the price of those goods, multiplied by the quantity sold. The quantity theory of money says that Price (P) = Total Money Supply(M)/Total Number of transactions(T). Ergo, the total quantity of money is a factor in the calculation of GDP.

The thought experiment is just a simple example to show that there is at least one value of M, for which V doesn’t affect the price level. It’s a general rule of mathematics that one counter example is all that you need to disprove a theorem.

Correlation does not equal causation. Also, the money supply bounces around because of the banking system, and when it contracts it’s generally because of some kind of credit crisis.

I’m sure V doesn’t affect the price level. What if anything it does effect is an interesting question - I’m not quite ready to discard it entirely - but that’s why i’m building a simulation.

Age should not stop us

Whoa, I’m afraid I will not be so good a conversationalist with you. I am not an economist either, let alone a computer scientist.

But what a 9 year old thinks — at ONLY nine years old —, if it’s his/her heart that speaks, I am convinced that it’s absolutely relevant.

I realize now that 9 years old was probably one of the most important years of my life, and I was already what “I Am” at that age. It unfortunately took me decades to become what “I Am”. It would have been so much easier and simpler to just listen to myself, instead of chasing after things which did not really suit me, and loving what “I Am”, simply, withouth asking endless, complicated and convoluted questions.

We should not be deterred by our (apparent) limits.

Scientists are very often so focused on a small parcel of truth that they forget, mostly, to maintain a broader vision of problems.

You’re right, it absolutely shouldn’t

Don’t worry -  there’s plenty of things we can talk about - especially if you’re into open government. (The way I originally stumbled into economics was by realising that some important results in distributed computing could essentially provide explanations of why centralised power doesn’t scale very well, and also why in some eras there’s not much alternative. Then I got side tracked into the monetary system.)

But yes, you’re right - we really shouldn’t worry about age.

I will say, scientists vary a lot. Some of them are micro-focused, and i personally think that’s a mistake - but some of them are so broadly focused it’s hard to get them to concentrate on what day it is.

As always, it takes all kinds. Fortunately.

Got a link to that Paper?

Hey Jacky,

How are you? I’ve been reading and rereading this post. And have gotten into endless conversations with people who think they understand how finance and banking works and realising more and more how little I and others seem to know about it :slight_smile:

I’d like to read your paper. I’d also like to mention what you’re doing as part of a TEDx talk I’m doing this Saturday. Would that be ok with you? And if so how would you like me to present you and your work?

I’ve made a tentative first step in the preliminary draft of my talk. You can check it out here: