Topic: Monetary Policy
MV=PT A Classic Equation and Monetary Policy Using Irving Fisher's famous economic "Equation of Exchange" to analyze the differences between "Fiat" monetary policy and a "Fixed" currency .by Gene DeNardo
(libertarian)
Sunday, December 7, 2008
MV=PT
Irving Fisher was probably the most popular economist of the early twentieth century. That said, a popular economist is a bit like a monogamous rock star or a wild and crazy accountant or a Victoria Secret model without breast implants! Everything is relative!
In 1911 he came up with the "Equation of Exchange" concept. That equation was MV=PT, where M was representative of the amount of money, V equaled velocity, P was price and T represented transactions.
A landmark theory, many people consider the equation to this day to be the single most important mathematical description of economics. Others downplay its significance or find it mildly useful. It helps their case that Irving was quoted as proclaiming just before the crash of 1929, "Stock prices have reached what looks like a permanently high plateau". Needless to say his finances suffered in a significant way. He was also the first president of the "American Eugenics Society". These folks have strong beliefs on selective breeding, the human kind that is!
Since we are concerned with how this equation could be applied to monetary policy, whether "Fiat" or fixed, we can solve for M or Money by dividing both sides by V or velocity.
M= PT/V
Money equals price times transactions divided by velocity. Now, the most common problem people have with Irving's formula is with V. If we omit V entirely, we come up with an equation that is hard to argue with.
M=PT
The amount of money equals the number of transactions times the price. Barring theft, fraud or force, we should be able to accept this as a basic truth.
Fisher's definition of V was the total expenditures for a time period, usually a year, divided by the average amount of money in circulation for the same time period.
Another practical definition for V or Velocity is the number of times that it takes the Money Supply to circulate before the total output or PT, of the economy is purchased. Whoever was following the greenbacks around to prove that one should be given an extra star! A valiant effort to say the least!
There is an argument that V never varies as all money in the economy is being used at all times. Money, aside from that in your wallet or under the mattress is used and reused constantly, whether by individuals or firms. But, what is critical to V or velocity is what it is used for. Satisfying debt may in a sense qualify as a transaction, but it does not add to the velocity of the economy. Boom times are times of great credit expansion and increasing velocity while bust times encourage people to pay up or go under, so the argument the V is a constant doesn't tred much water when viewed over time.
A simple solution for this example is the use of V as the "factor" in this equation. Since, for the context of our discussion, we know M or money and we know the amount of transactions and the price, V can be determined. It can represent the "phantom" or missing element. We could even perceive it as the "human" element. All the numbers are in, the results are not the same, V is the directional or determining force. A bit of mystery won't hurt too badly!
In our "Fiat" world, M can be altered and is altered, at any time by the actions of our Government. The policies and actions of the Federal Reserve and the Treasury determine the level of M. The Treasury, by issuing Securities, can introduce "outside" money to our economy, if they receive a foreign buyer. As you can imagine, this is an intricate web, and extremely hard to trace in a world market. Kind of like, "what goes around comes around". We can be certain though, except for rare instances, over time the money supply is increasing.
P=MV/T
When the value for M is made greater, the hope is that the number of transactions will increase or the Velocity will fall or a combination of the two will occur. As you can see by the equation above where we solved for P or Price, there isn't a lot of room to wiggle. If these results don't come to pass nor reach the extent needed to balance the change in M, then P increases. Even if this policy is successful, the possibility of price inflation looms on the horizon. The economy has been stimulated by "false" capital, an influence outside the usual realm of supply and demand of labor, resource or actual capital. Unless there was previously a significant overproduction with a corresponding slowdown in the demand for labor, inflation will be the usual result. This is all without considering "monetary inflation" which is the loss of value of the currency because there is more of it in circulation.
Often, the reason given for the dismissal of a "fixed" currency is the limits or constrictions it places on an economy. We have seen what a variable M does to Irving's equation, does a fixed value M place restrictions on output?
If we set M as a constant amount, any increase in T must coincide with a decrease in P or an increase in V to maintain the equation. On the working side of the equation, prices must fall or the velocity must increase or both, when more transactions occur in an economy with a fixed currency. As the economy grows, prices can actually experience downward pressure, money is constant but gains value because there are more goods and services or commodities represented by the same amount of currency! Fixed M doesn't limit the economy; the economy limits or multiplies the value of M without changing the amount.
This isn't to say that prices can't inflate and/or transactions can't fall or velocity won't slow with fixed currency. What it is saying is that what happens in the economy directly affects the value of money without any change in the amount. That is, how we use our labor to craft resources to meet the needs of our daily lives determines the value of the medium of exchange [money]. When the economy grows in a healthy way, we all share in the profit as our currency becomes stronger and is able to purchase more.
The "Fiat" system in the best light would be hard pressed to offer us this combination. The basic idea behind money creation is to bring the future to the present. By entering a greater amount of M into the system now, we are attempting to jump ahead to a point in the future of the economy where greater output has already been reached. This is basically an attempt to experience the benefits without doing the work required. Although beyond the scope of this discussion, it should be noted that because this method of monetary control is a "directed" method, the benefits or the resulting drawbacks can and are directed by whoever is controlling the release of monies to wherever in the economy they deem worthy of the good effects or whoever is deserving of the bad effects.
In relation to the M=PT/V equation perhaps the biggest difference between a "Fiat" monetary system and one based on a fixed value is which side of the equation we deem the most vital. The "Fiat" policy stresses the importance of the left side of the equation, using different, almost always increasing amounts of M to attempt to determine the outcome of the right side. With a fixed system, the results that the economy provides us on the right side of the equation determine the value of the left.
If we leave the scope of both Economics and Mathematics and look at things a bit more philosophically, we might come up with another outlook. What is more important to us, what we do everyday to make our lives what they are or money? Do we value our labor and the natural world and how we bring the two together to survive, enjoy and create what we call our economy or do we grant the dollar excessive power over our lives? The choice seems simple, what does it take for us to be allowed to make that choice?
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You can always tell the devoted FANS by the body paint they wear! I'll bet you've got a big "IF" painted on your bare chest in Christmas red and green as you do your cheers for Irving Fisher just to be seasonal!
Saying that Irving Fisher was probably the "most popular" economist of the early twentieth century is about as misplaced a notion as saying that Dopey was the most popular of the non-female characters in Disney movies. You'd have to exclude Keynes, Veblen, Schumpeter, Hayek, Alfred Marshall, even Von Mises. In terms of twentieth century economists, he only placed 47th in a poll of readers of an economics review ([link edited for length])
But, your article is even more fanciful than merely having the inability to properly pick an enlightened economist because you run away with speculation like a Rush Limbaugh clone! You simply fail to see the distinction between a “teaching” example and reality. Fischer’s formula is unable to predict or anticipate anything. It is used to explain the mechanics of a totally two-dimensional world where all factors are "given" or "known" and that just doesn't happen anywhere we know of.
For instance, you make reference to P as the “price” of goods as if that’s a “real” concept. Why don’t you tell us what the “price” of goods is. Is it the price of an automobile or a bus token? Is it the price of an apple or an aircraft carrier? There is no single number for “price” anywhere to be found. The same with “velocity”. This is strictly a DERIVED value not an independently determined value. It is found by dividing prices times transactions and dividing that by the money supply. Do you really think that even if someone knew exactly how many transactions took place in the United States’ economy in one year that they could distinguish between which of those dollars were being spent for the first time and which for the umpteenth?
You refer to the money supply as if we could possibly know how much is in circulation. Do you think it’s only currency? If so, how do you know how much of it is circulating in other countries? For that matter, how many of the very liquid, easily exchanged investment tools (stocks, derivatives, credit default swaps, reits, etc) are to be counted as "money"? How about credit cards? If I charge $1,000 on my credit card for Christmas gifts and only pay $300 toward my debt when I get my statement, haven’t I just increased the money supply by $700? And, until I pay the $300 against my bill, haven't I increased the money supply by $1,000? And, that’s a modest increase. Think of all the millions of others who may even default on their credit cards. They’ve increased the money supply by whatever amount they’ve charged, and they’re not even going to pay it back! No one even has a CLUE as to what the "money supply" is because what constitutes "money" is merely a definition, not a real value.
You need to realize that Irving Fisher was born just after the Civil War (1867) and introduced his Nobel Prize winning formula in 1911 ~ during this period of time money was much different than it is today. In fact, it was gold-backed and limited in its distribution, that makes it MUCH different from fiat currency and certainly obliterates Fisher's forumla.
Anyone who thinks that MV=PT represents an economic insight probably also thinks that Santa is slim enough to fit down all those chimneys of houses that have chimneys, and that he just slips through an open window for those that don't.
I hope you ask for an economics textbook for Christmas by someone other than a man who died before the Edsel was even designed. The world has changed a lot since then.
Hi Master C, Your comment made basically the same points that were made in the article. I am surprised you didn't notice that during your thorough read! As for the poll you mention, what year in the "early twentieth century" was that taken?
Posted By: Jake, the champion of the constitution
Date: 2008-12-08 02:21:53
gene, thanks again for another great article. this arrow was able to pierce my dense Austrian Hard Money Hard Wired Mind (AHMHWM, am big on acronyms this week for some reason) and i was able to follow along; i found your logic to be pretty insightful.
Its for sure a nickpick, but when you each use of the word "equation", I find "relationship" to be more apt as it doesnt confer an absolute.
I thought your most powerful sentence "When the economy grows in a healthy way, we all share in the profit as our currency becomes stronger and is able to purchase more. " is screaming to be bolded and underlined. You found words for what I have been trying to express inside my AHMHWM.
Of course, for the time being, we have to put up with the elite few profiting while the many are plundered. Bastiat all the way, baby!!
I'm glad to have you agree that my points were basically the same as those in your article ~ because my points were that the formula is completely irrelevant, and is used for teaching purposes only. It has NO VALIDITY because of the nebulous qualities of its variables. And, because it was developed more than 80 years ago, it is as useless and meaningless as those scientific notions that are pre-EINSTEIN!
You completely fail to see that a "teaching example" is not REAL. We say "Let's assume the temperature of the Earth is.... blah, blah, blah." knowing full well that there is NO temperature of the Earth. It varies from one extreme to another depending upon where you take the temperature. Or, we say "Let's assume that all labor is homogeneous, blah, blah, blah." knowing full well that people vary as much as snowflakes in their variety and abilities.
These are meant to be EXAMPLES not TOOLS. And, even the examples are irrelevant because they exclude, assume, and universalize so much. Yet, some yokels who don't know enough about economics OR mathematics, think they are like a private word from God, giving them truth, reliability, and insight.
Your article didn't have the honesty or the admitted inaccuracy of my comment. Don't try to piggyback YOUR conclusions on MY explanations. The weight of your inaccuracies is much too heavy for a mere mortal like me to carry. Only someone with your ZEUSIAN insights could carry the kind of MUCK you seem to dish out like MANNA.
To say that the relationship is valid despite the absence of evidence, proof, or validation ~ and in the midst of overwhelming criticisms ~ is like saying that the presents are under the tree so, therefore, Santa must have brought them.
You and Jake are like the two little boys who stand in the rain and keep saying that it's not raining as your mom continues to call for you to come inside. Ha! Ha! Ha! Someday you'll learn that raincoats are for something other than covering yourself up with in the park!
Thanks for the insight Master, in all my years of teaching music I wasn't aware that teachers were suppose to teach theory or equations that don't actually work. Maybe that is one of the reasons the economy is in the mess it is in?
As for discounting a scholars work because he died before you were born, using music again, i guess i will toss all my Beethoven and Ellington CDs and start listening to Britney rather than just leering at her!
And as far as relevance, we can still agree, you just have the cart before the horse. The "Fiat" system has complicated and confused the basic equation just like it has complicated and confused the economy. However, score of books have been written, mounds of theories and schools of thought have been based on this equation. Like anything, it is debated, that is the nature of science. And of course, anyone with an open mind recognizes many valid theories.
You understand the underlying principle of the article, placing control of the economy in the hands of a select few rather than those who actually perform the work, you just believe otherwise. I have no problem with that, I just haven't heard anything to convince me to agree with your view.
I don't think I've ever read so many imperfect analogies since root beer got wings! (I thought you might enjoy another completely ridiculous metaphor to go with your bizarre references.)
If you don't think that teachers are supposed to use unproven equations or those that can't be used to actually predict anything, I guess your music background seems to have insulated you from the mechanics of calculus and set theory ~ even chemistry. If you don't know the difference between a teaching example and an actual measurement of something try describing a CLOUD for me with measurements or measure the LOVE or LOYALTY someone has for someone or something. That's what the whole "let's assume that" reference is about.
To compare Beethoven or the Duke's music with outdated math or science just shows how little you know about building upon concepts or clarifying them and recognizing greatness that stands by itself. If you put Irving Fisher in a category with Beethoven, you don't know much about Beethoven.
I knew that your ultimate goal was to bash FIAT CURRENCY. And, my only objection is to those who do it by PRETEND CALCULATIONS. You put up a mythical relationship, then show that it leads to failure like the same people who say that if you eat too many french fries or smoke too many cigarettes, you're going to die. There are lots of people who die from many things, but it is very hard to prove that it was just french fries or cigarettes that did it.
No one is expecting you to change ANY of your beliefs ~ especially when someone tells you something that you don't understand. But, that's the same attitude GW Bush had ~ and you see where that got him. He's the one who led us into chaos!
I don't want to get into any slanging match about the veracity or otherwise of this article, but as some one who has used mathematics all my working life in Chemical Engineering, I know that it is important that equations have to be dimensionally correct. My question is , what are the units of velocity (V) in the equation. If P is in $ and T is a number, then the right hand side has units of US$, so if M is in dollars, V must be dimensionless, such as a number of times each dollar bill is used in a year.
Clearly a useful version of the eqation would involve sums. eg sigma (Pi.Ti) for all the transactions. I guess the equation gives an idea of some sort of relationship but could never be used in a quantitative way.
Hi Tom, yes I agree with you, it is only to show relationships. it could be used quantitatively but other than estimates i really don't know how the two systems could be comparable. to me, that is the problem with "fiat", I know there are libraries full of math about it, but i really think it is not quantifiable. maybe you could do an article throwing some numbers in?
Gene: Many thanks for exposing your readers to the concept of money velocity. I somehow found myself at your site while in search of data current to China. I am sure your readers understand the formula is a teaching tool. I was exposed to it and many others in undergratuate studies over 40 years ago, and I believe it is still taught today. Hey, lay Say's Law on them!!!
Shucks, Gene, I was really looking forward to this since I first read arguments using V as the basis to discount inflation in the future in spite of quantitative easing policies around the globe. Then you said …
"at any moment in the economy, all money is being used at all times. Money, aside from that in your wallet or under the mattress is used and reused constantly and essentially always has the same velocity"
…at which time I lost the ability to concentrate on the rest of your reasoning as the former requires a more deep, careful analysis of other less obvious claims. From that point everything else you posit is suspect.
That statement is just patently wrong. I don't understand why you declared it "good argument". For my part, money in my checking account is as good as money under my mattress -- it sits there not demanding goods and services (call it "products" for short). For my bank's part, they can "move" the money into loans for either products or investments. Regardless of the choice, there's no certainty that those funds stimulate demand for products - it might circulate repeatedly from one bond trader, to an equity trader, to a forex trader, etc., etc., until finally one of those "investors" decides to keep the cash from a trade and buy a product (car, rolex, night on the town, whatever).
So Velocity in this context is always variable. As you point out, it's the "human factor", the psychological drive in the Austrian theory of value that varies from time to time as people value cash on hand over products and services. You’re right, you can’t count it physically. It has to be deduced from other observations, just like the smallest parts in the physical world of the atom.
Since I now have to write out a mathematical proof to every other claim you make, I simply don’t have time to comment on the rest of your analysis. Especially lacking is any kind of conclusion other than “MV=PT is absurd in this modern world”, which is an interesting premise, but too important to just accept at face value. Even the comments from others have little supporting evidence or thoughtful criticism. I suppose we should throw out F=MA because it was designed so long ago, too?
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