Trouble with the equation of exchange.

[itfitzme]

The equation of exchange is one on the few physics equation in economics. It is typically presented as

MV=ΣPQ

Where M is the stock of money in the flow, V is the rate of turnover for that stock. P is the price of goods, and Q is the quantity of goods sold.

It says that, when all of the price times quantities of all goods are added together, the sum is equal to the stock of money in the flow times the number of times the money is used in the transactions.

V is, of course, not really velocity in the physics sense of distance per unit time. It is in units of $ used per $ in the stock, $/$. Never the less, it has the sense of flow and the term velocity suffices.

This equation of exchange is related to inflation. If the stock of money in the flow is increased while the velocity remains constant, then the price of goods increases, thus, inflation. This is what is being referred to when people say that "printing" money causes inflation.

An increase in GDP is not necessarily the result of inflation. Inflation refers to the process by which Q remains constant while P and GDP increase. This is the difference between real and nominal GDP. Nominal GDP may increase with no increase in output. As such, it is price inflation and real GDP has not changed.

On the other hand, if Q increases while P remains the same, GDP will increase if, in fact, either M or V increases. This is an increase in real GDP. And, of course, if Q increases but M and V remain constant, the P must decline which is deflation.

One thing to note is that if population increases without an increase in GDP due to Q, then standard of living has fallen as the quantity of goods consumed per person has declined.

As well, for the standard of living to increase, an increase in Q per person, without deflation occurring, then M must increase or the velocity of money must increase.

This equation, and the relationships, are valid for all economic systems, it is simply a description, as long as the definition of M being that of the money in the flow is adhered to.

For the economy that we are most interested in, our US economy of end user consumption, GDP = MV = ΣPQ.

And, the stock of money, M, in the equation of exchange is strictly the money in the flow. It is not the stock of money in reserve accounts at the bank. It isn't even the stock of money in checking and savings accounts.

For instance, a checking account may have $1000 in it at the beginning of the month, with two paychecks of $500 deposited during the month, $900 spent during the monthly, for a final balance of $1100. By measures of M1, this represents $1000 and $1100 for each successive measure while the actual money that flowed is $900.

There are measures of V published by the Federal Reserve of St. Louise. These are VM1, VM2 and VMzM. They differ in terms of the measure of money used, M1, M2, and MzM. Each captures an ever increasing set of money, from coins and currency in circulation, to checkable deposits, to savings and large time deposits. Another measure, the monetary base, included notes and coins in circulation along with and commercial banks' reserves with the central bank.

The problem with these measure of the money supply is that they do not represent the stock of money in the flow, only the stock of money that is available to flow. Being available doesn't necessitate that it will.

So, the basic equation of exchange, GDP = MV = ΣPQ, does not necessarily lead directly to the conclusion that inflation will occur when the monetary base is increased. The monetary base includes money in the reserve accounts at the Fed. For inflation to occur, the reserve accounts have to somehow get into the flow.

Arguments surrounding and modifications of this equation of exchange have to do with whether the velocity is constant and what the stock of money in the equation is. Is it the stock of money in the monetary base or M1? It is, in fact, neither. It is the money in the flow.

Other criticisms involve the interpretation of what is affected by a change in M. A change in M, as noted, can be reflected by a change in P or Q.

The current monetary policies of the Federal Reserve are basically three forms, increasing reserves of private banks, open market operations where securities are purchased and sold on the open market, and changes in the interest rate at the discount window.

There seems to be no other methods by which the money supply is affected. There does not appear to be any injection by "printing" a new quantity of money and using that to purchase t-bills, otherwise spend it or hand it out.

One affects the money supply by putting more money in the hands of the owners of securities, the others affects the availability of credit. None of them put money directly into the majority of the flow of money at a level of consumption that affects GDP.

One has to consider how the money supply in the flow has been increased, if and how the stock of money in the flow has increased due to an increase in M1 or the monetary base.

A finer issue is with regard to credit. There is no doubt that, in terms of ΣPQ, charging $200 on a credit card adds to the stock of money that flows. For the example above, if this $400 is also part of the months purchases, it adds to the $900 in cash, for a total of $1300 in the flow of ΣPQ. And, again, M1 at $1000 and $1100 doesn't represent the flow of money.

This addition of credit can occur if the demand for credit is up relative to the level of reserve accounts and the discount rate.

Given the affect of credit and drawing from savings (or taking the money out from under the mattress), the equation of exchange is better written as;

GDP(2) = &#931;PQ(2) <= (Mf(1) + dC(2) + dS(2) ) V

Where the GDP at time 2 is less than the monetary flow stock at time 1 plus the additional credit and savings added at time 2.

This form illuminates the effect of credit on the GDP. If the amount of money in the flow is otherwise constant, demand is high, and saving have been depleted, then given low interest rates, M may be increased through consumer borrowing on revolving.

This addition of credit can then increase the money supply. And, an increase in the money supply allows for either inflation or an increase in the standard of living.

The problem is that this increase is a one shot deal. In order for the money in the flow to continue to increase, incurred credit must continue to increase. And, at some point, servicing of credit becomes a limiting factor.

When servicing of credit becomes a limiting factor, borrowing stops. And, as people are reactionary, when the stop borrowing, the tend towards paying credit off. As such, the stock of money in the flow drops by both the amount of missing credit increase plus the amount that is being used to pay off credit.

 

[DSGE]

V is, of course, not really velocity in the physics sense of distance per unit time. It is in units of $ used per $ in the stock, $/$. Never the less, it has the sense of flow and the term velocity suffices.

I'm super tired and need to go to bed right now, but I'll read the whole post tomorrow and respond. For now, I disagree with this much. The right hand side of the equation of exchange is NGDP which is not a $/$ unit, it is a $/time unit. I submit that velocity is in fact of dimension "per unit time" and the money stock of dimension "dollars" in order for NGDP to be M*V = $ * time^(-1) = $/time.

 

[itfitzme]

V is, of course, not really velocity in the physics sense of distance per unit time. It is in units of $ used per $ in the stock, $/$. Never the less, it has the sense of flow and the term velocity suffices.

I'm super tired and need to go to bed right now, but I'll read the whole post tomorrow and respond. For now, I disagree with this much. The right hand side of the equation of exchange is NGDP which is not a $/$ unit, it is a $/time unit. I submit that velocity is in fact of dimension "per unit time" and the money stock of dimension "dollars" in order for NGDP to be M*V = $ * time^(-1) = $/time.

Nice. Yes, this is true. By $/$, I mean V specifically

I've gotta be strict about the units and they have to make sense physically per quantity and cancel out properly, of course. It's the physics training. I know, in econ, we "assume" the /time as often just understood. And, in many cases, it doesn't matter. Like in supply and demand curves, the axis can be $ and units, $/year and units/year, or $/month and units/month. It really doesn't matter as the whole thing just scales.

So, let's see how I got there.

Okay, how about P is $/unit and Q is units/year. So PQ is $/year. Of course, NGDP $/year, which is great.

I went back to wiki and get "The velocity of money (also called velocity of circulation) is the average frequency with which a unit of money is spent in a specific period of time. Velocity has to do with the amount of economic activity associated with a given money supply. When the period is understood, the velocity may be presented as a pure number; otherwise it should be given as a pure number over time. "

Wiki also says, "That $100 level is possible because each dollar was spent an average of twice a year, which is to say that the velocity was 2 / yr."

I really want to do Q in just units which gives

NGDP = $/year = MV = PQ=($/unit)*(units)

which isn't going to fly unless NGDP is taken as $ or Q is in units/year.

If we can go with the wiki "When the period is understood", we can do this thus, NGDP in just $, where the period is understood.

Sticking with Q in units then,

NGDP = $ = MV = PQ=($/unit)*(units)

Then with M in $, V is unitless. Still, $/$ is also unitless, and interprets at ($ used)/($ existing).

Alternatively, I can go with

NGDP = $/year = MV = PQ=($/unit)*(units/year)

So MV is in $/year and, unless I'm missing something, M is in $. That puts V in /year which is just as easily ($ used)/(( existing*year). M is in $ existing.

I do like, though, now that you mention it, V in $/($*year). There is the velocity in terms of time. Of course, it could be in year, months, or simply time.

"/year" is more like velocity, as in feet/second, than that $/$ is.

So, I stand corrected.

Or do I?

Still, it's not feet per second. Perhaps if I take it as ($/$)/year, it is more appealing. Still, no matter how I do it, I am just not happy with it as strictly "velocity".

 

[expat_panama]

Many people use a morass of big words to hide that fact they don't know anything and they just want to sink others into a pit of muddled thought. Is there a chance you could state your point in 25 or less small words?

 

[itfitzme]

So I reread that wiki, "The velocity of money (also called velocity of circulation) is the average frequency", and there you have it. Frequency is cycles per second. And this makes sense, with a one dollar used ( cycling ) twice (or whatever) for every dollar existing in a time period.

Frequency is a valid physical measure. It's typical in electrical and electronic engineering. It is also in mechanics of rotation.

So that is great. Thanks. It really bugged me.

 

[samjones]

Many people use a morass of big words to hide that fact they don't know anything and they just want to sink others into a pit of muddled thought. Is there a chance you could state your point in 25 or less small words?

Heh heh heh - he said "morass".

 

[expat_panama]

...he said "morass".

OK, so anyone could have said "chaotimyre" but at this juncture the operative specate is to always eschew obfuscation.

I think.

 

[itfitzme]

Many people use a morass of big words to hide that fact they don't know anything and they just want to sink others into a pit of muddled thought. Is there a chance you could state your point in 25 or less small words?

Yeah, I knew you were around somewhere. Really, is that why you post? To prove something? I realize that you don't get it. That's okay, then it's not for you. I really don't know what to tell you.

There aren't any big words in there. Unless you want to count "modifications" as a big word, it's got 13 letters.

It's just the detail that I have to think it through. And it doesn't even got no calculus. It is what it takes to say it.

It's just a bunch of statements about what MV=PQ means or implies. Each statement, itself, should be a "Duh!". There is nothing hidden, nothing complicated.

It really is simply a description of what is. Each should follow, in a manner, from something that comes before. And as it is based on what is a physical condition, then each that follows must be true. You won't find it much clearer.

And it leads to some interesting observations of how the economy must function. For instance it demonstrates that increasing the stock of money in the flow can lead to growth or inflation, depending on something else. And that is the key question, what the something else is, or the conditions.

And while I mentioned per population, I didn't play around with that. If you do it on a per capita basis, it reveals some other things.

I originally considered that MV>=PQ, representing an upper bound for GDP. That is, GDP=PQ<=MV. Instead, I went with sticking to the condition that M is restricted to the flow. As an upper bound, the M in GDP=PQ<=MV can then be M1, M2, MzM, or the monetary base.

You can skip to the end if you like.

Or you can go with "shit happens".

 

[expat_panama]

...a chance you could state your point in 25 or less small words?

...that why you post? To prove something? ...

LOL --neither of us knows what the other is saying, talk about a disconnect!!

My mistake was thinking you had some point you were making, that some particular policy was good or bad maybe. That's what me and most folk I run into here are always doing. OK, you weren't and you're just posting stuff for the heck of it. Sounds good, we can always use more diversity in approaches here --enjoy and cheers!

 

[DSGE]

So I reread that wiki, "The velocity of money (also called velocity of circulation) is the average frequency", and there you have it. Frequency is cycles per second. And this makes sense, with a one dollar used ( cycling ) twice (or whatever) for every dollar existing in a time period.

Frequency is a valid physical measure. It's typical in electrical and electronic engineering. It is also in mechanics of rotation.

So that is great. Thanks. It really bugged me.

Cool beans. I guess if you want to treat Q as just units, so NGDP as just $, you can treat V as being dimensionless, just a constant that multiplies the money stock. Kind of like angles in physics.

W is in joules (N*m), F is in newtons, d is in metres, which leaves &#952; dimensionless.

 

[itfitzme]

...a chance you could state your point in 25 or less small words?

...that why you post? To prove something? ...

LOL --neither of us knows what the other is saying, talk about a disconnect!!

My mistake was thinking you had some point you were making, that some particular policy was good or bad maybe. That's what me and most folk I run into here are always doing. OK, you weren't and you're just posting stuff for the heck of it. Sounds good, we can always use more diversity in approaches here --enjoy and cheers!

Then again, without knowing how things work, opinions aren't worth much. I wouldn't have a mechanic that can't describe how an internal combustion engine works. And I suppose an opinion from someone that can't discuss the fundamental of the equation of exchange doesn't have much value.

 

[DSGE]

Yeah so I don't agree with the part about M being "the stock of money in flow". It's just any stock of money, any measure you choose. There's not one "money stock" which is in flow which satisfies the equation of exchange or one "velocity". As you mentioned, the St Louis Fed publishes velocities for M1, M2 and MZM. How do they calculate velocity?

Velocity of M1 Money Stock (M1V) - FRED - St. Louis Fed (M1V)

"Calculated as the ratio of quarterly nominal GDP to the quarterly average of M1 money stock"

"Velocity" in the equation of exchange is just NGDP / M, where M is whatever money stock you've chosen.

So how is this consistent with the $1.6 trillion in free reserves but no hyperinflation? Because of the "liquidity trap". Liquidity trap theory tells us that when the interest rate on bonds becomes zero, the demand for money becomes perfectly elastic. Any increase in the monetary base will be offset by an equal increase in the demand for money (decrease in velocity). So dM = -dV.

Of course there are a myriad of problems with the liquidity trap stuff, but it gets to the point.

 

[EdwardBaiamonte]

When servicing of credit becomes a limiting factor, borrowing stops. .

is this some sort of thought experiment in which you assume no central bank?

 

[itfitzme]

When servicing of credit becomes a limiting factor, borrowing stops. .

is this some sort of thought experiment in which you assume no central bank?

Nice idea. And, yes there is, though we still have to work it out. And who knows what it will reveal. All those details, that I gave myself an aneurysm over, are sufficient to pin the economy down to the real elements. The trick then is to identify the appropriate economic elements, make sure they are all identified, and represent them properly.

In fact, the MV=PQ isn't restricted to just GDP. It is GDP when PQ is defined specifically to represent the end user products.

It was kinda inferred that, for GDP=MV=QP, it is not a closed system. That it isn't closed is apparent in the M=(Mx+dS+dC) where dS and dC are change in credit and savings. That is money coming from outside the flow of the system defined.

If we expand the boundary around the entire US economy, it still isn't closed and there are variations that include import and exports along with capital and security flows with interest.

Another comment in another forum presented;

FIELD MARSHALL MODEL of State's Money Supply, Market Price, Foreign Exchange Reserve, Fiscal and Monetary

S= PQ = (X-M)+(L-R)(1+i)^N1= (G-T)+(F-B)(1+j)^N2

at S= Supply of money, P= Price of Commodity matrix, Q= Quantity of Commodity matrix, X= Export matrix, M= Import matrix, L= Loan from foreign sources matrix, R= Repayment of foreign loan matrix, i= Interest of foreign loan, N1= number of foreign loan period, G= Government expenditures, T= Taxes, F= Financial notes bought by authority, B= Bank central's certificate bought by the market, j= Interest of net local monetary instruments and N2= Number of monetary instrument period.

These two are missing the V, assumed to be one. Once draws a boundary around the US, thus the import/exports and foreign loans. The other draws a boundary around the government in terms of taxes/expenditures and the T-bills.

But, you know what, it is a free market system and if there wasn't a central bank, some one would create a private one. So we should be careful what we wish for. It is never a good idea to jump out of the frying pan and into the fire.

Actually, the central bank is involved in the form I presented, in a manner speaking.

What I am getting out of

GDP(2) = &#931;PQ(2) <= (Mf(1) + dC(2) + dS(2) ) V is that the addition of credit, dC comes from somewhere.

We can add in the addition of the Fed QE or open market policy with an additional term,

GDP(2) = &#931;PQ(2) <= (Mf(1) +dMfed+ dC(2) + dS(2) ) V

And, as I have written it as an upper bound, it is still functional.

dMfed and dC are affected by the centeral bank. And, if it is taken out, well, what you get is deflation or no increase in standard of living. Take out the open market operations and the reserve markups, then the only place for dC to come from is other peoples personal saving.

What bothers me is that Mf hasn't ever increased except by some mechanism of trickle down by the open market policy. And the direct route for the consumer to increase the money supply is by credit card.

It just really bothers me that the system is designed to require the constant addition of credit. It screws the general population, creating a debtor class.

I haven't found any historical data of what the exact numbers have been for open market operations. It is the only way that the money supply increases without being tied to the debt bungy cord. And it it isn't incrementing the money supply, in the flow, then the system requires that debt be incurred because inflation is targeted at 3%, we expect to see an increase in the standard of living and population grows.

Figuring out how dMfed+ dC(2) are tied to the central bank, in the obnoxious details, is the issue. We know it is tied. We know what the process is, in general. It just becomes a question of magnitudes to determine if dMfed is simply inadequate such that it forces the unbounded accumulation of credit.

i am very suspicious, though. If you look at the revolving and non-revolving credit data, you find that it climbed constantly since 1968. It suddenly stopped and fell, right when the recession began. And, as the recession bottomed out, it bottomed out.

Then, you have a whole muliplier effect. For ever dollar paid back to the CC, that is two dollars less in consumer spending, $1 in CC not otherwise charged, and $1 in payment. For every 100,000 people doing that, you have one person unemployed due to loss in demand (totally made up numbers.) But you get the idea.

If I were troubleshooting a car engine, that is the one measure I'd go digging into. It isn't a question of if it is possible that the whole system could rely on credit to offset increase in pop, standard of living, and CPI. It isn't a question of if it could be driven by the fed interest rates and reserve markups combined with a lack of added real money and willingness of people to charge. It's just a question of if the magnitude can be shown as sufficient.

On the other hand, what the heck else do we think is responsible for it? Personally, if my life depended on it, I'd have the Treasury start printing money and slowly start paying bills with it. Not pay the debt, put it in the flow, then as taxes revenues increase, pay down the debt. And I'd start targeting credit as well as CPI and GDP because it is the only measure that seems to tie directly to the individual consumer who is looking in their wallet and choosing how much to pay in cash and how much to put on their Target card.

After all, isn't how that whole reserve system works, the money multiplier ends with Bank of Target and affects their interest rates? That is the dC in GDP(2) = &#931;PQ(2) <= (Mf(1) + dC(2) + dS(2) ) V

 

[expat_panama]

...an opinion from someone that can't discuss the fundamental of the equation of exchange doesn't have much value...

Actually it does. It matters a lot to the guy that holds it, and also to us when others vote in some clown that shares their ignorance. Just the same, teaching others how things work is nice, but what got me off track here was I wasn't aware of anyone asking for the info.

 

[EdwardBaiamonte]

Personally, if my life depended on it, I'd have the Treasury start printing money and slowly start paying bills with it.

this seems artificial, too subtle, too localized and so not likely to stimulate real growth. It would be better to announce 4% inflation so there would instantly be less incentive for everyone everywhere to sit on their money. Then, those who had the best prospects for real growth anywhere in the economy would be the first to take the plunge that they previously had not taken.

 

[itfitzme]

...an opinion from someone that can't discuss the fundamental of the equation of exchange doesn't have much value...

Actually it does. It matters a lot to the guy that holds it, and also to us when others vote in some clown that shares their ignorance. Just the same, teaching others how things work is nice, but what got me off track here was I wasn't aware of anyone asking for the info.

It never ceases to amaze me here territorial behavior can find expression.

Recall, you began with "Many people use a morass of big words to hide that fact they don't know anything and they just want to sink others into a pit of muddled thought. Is there a chance you could state your point in 25 or less small words?

Rather than discuss the subject, you choose to critique the author and presentation. Ad hominem is the term that is applicable.

On your recent comment, quoted above, you will find no disagreement from me. The value of your opinions stands on their value to you alone, regardless of any consideration of real mechanisms. Discussion of any real mechanisms is secondary.

Rather, you are looking for opinions to argue against. Lacking the ability to find an opinion to argue, you determine that "use a morass of big words to hide that fact they don't know anything and they just want to sink others into a pit of muddled thought." Or, perhaps, I might state any opinion in a manner that makes it easier for you to read, "in 25 or less small words."

You determine who's opinion is of value, who "us" is, those that hold your opinion, and who those "others" are that may "vote in some clown that shares their ignorance."

I wasn't, of course, aware that you have staked out this forum as your territory, requiring that others be asked before presenting their ideas or to get your permission to present information. For surely, lest they do, you will employ verbose elocution to shut them down. I mean, really, who uses the word, "morass"?

Nor was I aware that you see yourself as "the teacher", gracing everyone with your god given opinions. And they must be god given, or some how have been afforded you out of a connection to the ephirial plane as, by your own statement, how things work has no bearing on the value of those opinions. They are valuable in their value to you.

You seem have created some illusion for yourself that you are somehow the defender of all opinions that are true and correct.

Could it be that you are the clown who's opinion matters to you and also to "us" that have voted you in, sharing in your own ignorance? And then you follow by stroke your own ego by using "morass", a not so common term, while simultaneously accusing that another of using "big words" in saying, "state your point in 25 or less small words?" Clearly, as I pointed out, I used no big words.

Notice how, when you do something, you have a good reason. But when someone else does it, it hurts your feelings.

You might consider looking towards the ideas of "in group/out group", "actor/observer affect", "projection", and "transference".

All I was doing was presenting some basics that we can find anywhere else on the web, in a manner that I find clearer than the matix algebra or calculus common among those that have spend more time with the material in hopes that someone else might want to discuss it. You, on the other hand, seem to have projected or transferred some sort of personal issue about "teaching", "others vote in some clown that shares their ignorance".

Really dude....

 

[itfitzme]

Personally, if my life depended on it, I'd have the Treasury start printing money and slowly start paying bills with it.

this seems artificial, too subtle, too localized and so not likely to stimulate real growth. It would be better to announce 4% inflation so there would instantly be less incentive for everyone everywhere to sit on their money. Then, those who had the best prospects for real growth anywhere in the economy would be the first to take the plunge that they previously had not taken.

That makes me laugh. I like it.

Some one suggested that we do this to devalue the debt.

Some one else suggested using the new-printed money to pay welfare.

And I agree, there is an issue of relative effect.

My reason for going through that whole eye bleeding examination of what MV=PQ necessitates is that the entire economy is dependent on credit in order to keep the money supply up with growth and inflation. If we expect to not have deflation, and thus people sitting on the money, then somehow new non-debt money has to be injected.

If you look at the data on consumer credit at the Federal Reserve of St Louse, consumer credit has continued to add money to the flow since like 1968. It was this recession where it suddenly reversed direction, only returning to not declining (maybe rising) when the recession ended.

I don't know that we need the government to stimulate growth. I am a firm believer in the free market economy that, if competitive and balanced, can grow of it's own accord. Growth is a function of unsatisfied demand, at least. And by growth, we can mean RGDP or RGDP per capita, one being real value of products such that it keep up with population the other real value that improves the standard of living.

I do like the idea of using inflation to get the money out from under the matresses on those that have amassed huge quantities of it. The engine of the economy functions on the flow of money, not it sitting static. I am concerned that the past few decades of inflation have been offset by adding debt.

 

[itfitzme]

Yeah so I don't agree with the part about M being "the stock of money in flow". It's just any stock of money, any measure you choose. There's not one "money stock" which is in flow which satisfies the equation of exchange or one "velocity". As you mentioned, the St Louis Fed publishes velocities for M1, M2 and MZM. How do they calculate velocity?

Velocity of M1 Money Stock (M1V) - FRED - St. Louis Fed (M1V)

"Calculated as the ratio of quarterly nominal GDP to the quarterly average of M1 money stock"

"Velocity" in the equation of exchange is just NGDP / M, where M is whatever money stock you've chosen.

So how is this consistent with the $1.6 trillion in free reserves but no hyperinflation? Because of the "liquidity trap". Liquidity trap theory tells us that when the interest rate on bonds becomes zero, the demand for money becomes perfectly elastic. Any increase in the monetary base will be offset by an equal increase in the demand for money (decrease in velocity). So dM = -dV.

Of course there are a myriad of problems with the liquidity trap stuff, but it gets to the point.

Yeah, there is an issue. It's my physics and engineering training that has me looking for the physical quantities that are in existence. When I look at the physics of it, which is objective and stands on it's own, in order for GDP=MV=PQ to be correct, it has to match the objective physics. Unless we build a model based on the physical objects or information, it doesn't do much for us.

If I can choose any stock of money I want, I can choose anything. And, if we define V based on an arbitrary M, it is going to balance out, of course, it's self referential. To be valid, the model requires that it be defined according to the physical requirements. If we wish to use say, M1, and have V represent the physical frequency of use for the money in the flow, then we can add some sort of multiplier to account for the "liquidity trap"

M*(multiplier)*V = PQ.

But now we have an unknown multiplier that we cannot determine without first determining what amount of money exchanged hands.

It bugged the crap out of me, after all, these guys must know what they are doing, right? Who am I? Maybe they have some purpose for some form of M that tells them something that i am not aware of. For that matter, depending on what you want to look at, you can define M V P and Q to represent the system that you are looking at. But that doesn't do me much good.

If we look at where MV=PQ came from originally, if goes back to Copernicus, an economy that was a bit simpler. I know, based on all studies of Copernicus' ideas and theories, that he looked at physical objects. I have no doubt that he was looking at the physical coins that were exchanging hands in the process of exchange. Heck, it is called the equation of exchange.

So how might I present this such that it stands on objective and verifiable reality, rather than the "authority" of a person or group?

Well, the money as defined by price in PQ? It is the money that has exchanged hands for the good or service provided. For GDP, q are the end use goods and p is the price of the product as sold. Q isn't the goods in stock at the warehouse, we know this. V references the circulation of the money in the flow, the frequency of it's use. M is the money in the flow.

Or, we can look towards the wiki, the source of all that is known, at the definition "is the total nominal amount of money in circulation on average in an economy", and ask what "circulation" means. V is "is the transactions velocity of money, that is the average frequency across all transactions with which a unit of money is spent", the key word being "transactions".

If you were to build a physical model of GDP = PQ = MV, what would you use for M, independent of what any "authority" says?

 

[DSGE]

Yeah, there is an issue. It's my physics and engineering training that has me looking for the physical quantities that are in existence. When I look at the physics of it, which is objective and stands on it's own, in order for GDP=MV=PQ to be correct, it has to match the objective physics. Unless we build a model based on the physical objects or information, it doesn't do much for us.

If I can choose any stock of money I want, I can choose anything. And, if we define V based on an arbitrary M, it is going to balance out, of course, it's self referential. To be valid, the model requires that it be defined according to the physical requirements. If we wish to use say, M1, and have V represent the physical frequency of use for the money in the flow, then we can add some sort of multiplier to account for the "liquidity trap"

M*(multiplier)*V = PQ.

But now we have an unknown multiplier that we cannot determine without first determining what amount of money exchanged hands.

It bugged the crap out of me, after all, these guys must know what they are doing, right? Who am I? Maybe they have some purpose for some form of M that tells them something that i am not aware of. For that matter, depending on what you want to look at, you can define M V P and Q to represent the system that you are looking at. But that doesn't do me much good.

If we look at where MV=PQ came from originally, if goes back to Copernicus, an economy that was a bit simpler. I know, based on all studies of Copernicus' ideas and theories, that he looked at physical objects. I have no doubt that he was looking at the physical coins that were exchanging hands in the process of exchange. Heck, it is called the equation of exchange.

So how might I present this such that it stands on objective and verifiable reality, rather than the "authority" of a person or group?

Well, the money as defined by price in PQ? It is the money that has exchanged hands for the good or service provided. For GDP, q are the end use goods and p is the price of the product as sold. Q isn't the goods in stock at the warehouse, we know this. V references the circulation of the money in the flow, the frequency of it's use. M is the money in the flow.

Or, we can look towards the wiki, the source of all that is known, at the definition "is the total nominal amount of money in circulation on average in an economy", and ask what "circulation" means. V is "is the transactions velocity of money, that is the average frequency across all transactions with which a unit of money is spent", the key word being "transactions".

If you were to build a physical model of GDP = PQ = MV, what would you use for M, independent of what any "authority" says?

Yeah see I have a pure maths background, so I approaching things with "is this a helpful way to think about something; does it yield any interesting results?" rather than trying to map concepts to some physical representations.

So the equation of exchange is just an identity. We can't get anything useful out of an identity. First off let's write it in terms of growth rates rather than levels, so MV=PY => %M + %V = %P + %Y. We have to add some rules to make it interesting. The first and most obvious being that Y returns to its natural rate in the long run, it's long run growth rate being the trend growth in productivity + trend growth in population. Say about 3%. Next we ask what measure of money we should pick for M. Friedman liked to use M2 because M2 did something cool. I can't find it now, but I recall seeing Friedman showing that the long run demand for money when money is measured as M2 is stable. So the velocity of M2 is stable, hence %V = 0. So the only things left to vary are M and P, which gives you the conclusion that inflation (%P) is everywhere and always a monetary phenomenon.

This turns the "equation of exchange", a useless identity, into "the quantity theory of money". An immediate consequence of which is that inflation = %Y - %M = 3% - %M. So if you want to have zero inflation, you should target M2 growth of 3% (Friedman's K-percent rule). On top of that, if there's a stable relationship between "how much" monetary base gets "turned into" M2, you can achieve stable prices with a constant monetary base rule.

Of course the problem is that over the short run velocity isn't stable (in the same way the exchange rate isn't stable around PPP in the short run), and the economy can be hit by productivity shocks which change the natural rate of ouput. And of course the way MB affects M2 is volatile.

So over the short run the quantity theory of money is useless. The reason you'll see me citing MV=PY all over the place is because people frequently misapply QTM thinking that velocity is constant over the short run. So you get shit like "interest rates rates were low, that means easy money!".