Money and the Government

Some Implications Resulting From the Relationship Between the Government and Money

Imagine a very simple Federal Government, consisting of merely two organizations, the Money Supply Control Agency (MSCA) and the Treasury Department. The Treasury Department prints money and the MSCA controls its supply. This is NOT what Austrians and Libertarians mean when they say they want a smaller government, but it serves for the purposes of demonstration.

Further imagine that these organizations are quite inactive, with years or even decades separating their actions, as described below.

The first action is a reduction in the supply of money to be carried out by the MSCA in 2010. In this action, the MSCA sends out agents to every home in America. At each home an agent asks the family for a $20 bill, which he then takes back to his office and proceeds to immediately destroy by burning. If there are 200M homes, the money supply is reduced by 200M x $20, or $4B.

The second action, carried out in 2060, is to increase the supply of money by distributing $20 bills to every home in America. The Treasury prints up new $20 bills, and MSCA agents deliver them. If there are still 200M homes, the money supply is increased by $4B.

There is nothing exceptional about the above, with the money supply decreasing by $4B in 2010 and increasing by $4B in 2060.

Now, change the particulars slightly. Instead of destroying the $20 bills in 2010 by fire, the MSCA agents instead take the bills away and store them in a Treasury Department warehouse. Then, in 2060, the distribution of $20 bills doesn't require any printing of new bills, just taking the stored bills out of the warehouse.

What can be learned by comparing the two situations?

The difference between the two situations is that between 2010 and 2060 the government has an additional $4B in $20 bills stored away in the Treasury Department warehouse for the case in which the $20 bills were not burned. But as far as the economy is concerned, there is NO difference between the two cases, and if the government security and secrecy are good enough, no one outside of the government can even know whether the $20 bills have been burned or stored.

The implication of this is that while the $4B in the Treasury warehouse would certainly appear in a hypothetical physical audit of the money supply, if the money supply is to be used as a theoretical input in applying the quantity theory of money to help determine the objective exchange value of money (its purchasing power), then money held by the government must be excluded from the effective total money supply. This is likely to be a controversial result, with a strange alignment of opposing schools of thought on the subject, but I find this conclusion unavoidable.

The structure of the example also lends itself to other implications, (suggestions welcome) which can be discussed later.



Follow-ups:
The SS Trust Fund
Rothbard vs. Fisher's Equation of Exchange, MV=PT

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Surely, though, your

Surely, though, your implication also holds if the MSCA agents pulled that money out of the economy by doing odd jobs around the neighborhood. And it also holds if they re-inject the money into the economy by buying hot-dogs. And it also holds over periods of less than your arbitrarily chosen twenty years.

Therefore, I do believe, you have proven that the money in my wallet shouldn't count in the money supply. I think your theory proves too much. Alternatively, it proves that the notion of "money supply" is too general to be meaningful.
--G

Grant's comment doesn't make

Grant's comment doesn't make sense to me. There is a continuum from holding money for a microsecond to holding it for a millenia. Of course the effects are different along that range!

The important thing w.r.t prices is the effect the removal of the money has on the total number of monetary transactions.

If you hold money for a period much less than the normal circulation, then you have not changed the number of transactions at all. If you hold money for a much longer period, you have changed the number of transactions almost as if that money didn't exist.

The money supply is not meaningless just because the amount of time you change it for matters!

I agree that the phrase "money held by the government must be excluded" is going too far. It matters how long the money is taken out of circulation for. But I don't think the govt tends to take money out of circulation for very long - they spend it all.

Grant, "Surely, though, your

Grant,

"Surely, though, your implication also holds if the MSCA agents pulled that money out of the economy by doing odd jobs around the neighborhood. And it also holds if they re-inject the money into the economy by buying hot-dogs. And it also holds over periods of less than your arbitrarily chosen twenty years...."

Not necessarily. You have to distinguish between the agents' personal money and the government's money.

Subject to correction, there are only two ways in which the concept of 'money supply' finds use in economic theory. First, a credit expansion in terms of business loans triggers the Austrian Business Cycle. Secondly, simply printing and distributing new money doesn't trigger the ABC, but it does tend to reduce the exchange value of money (its purchasing power) as it passes into and out of the hands of individuals who change their subjective buy/no buy decisions depending on how many discretionary dollars they hold as they are subject to the law of diminishing marginal utility.

If a MSCA agent spends government money on a hot dog, this may reduce the exchange value of money depending on who ends up with it in their personal money supply as the agent will not increase his own subjective valuation of money because HIS personal money supply does not decrease.

"Therefore, I do believe, you have proven that the money in my wallet shouldn't count in the money supply...."

Whether the money in your wallet is an effective part of the money supply that can impact prices depends on whether you consider it as a reserve when you make a decision as to whether a purchase is worth more to you than the money needed to make it. The simplest way to tell is to honestly consider whether a change in the amount in your wallet by a factor of .5X or 2X has any affect on your buying decisions. If it has an effect, it is part of your personal money supply and incrementally impacts prices.

Regards, Don

Patri, "...The important

Patri,

"...The important thing w.r.t prices is the effect the removal of the money has on the total number of monetary transactions.

If you hold money for a period much less than the normal circulation, then you have not changed the number of transactions at all. If you hold money for a much longer period, you have changed the number of transactions almost as if that money didn't exist...."

I have to disagree with this in the sense that the NUMBER of transactions has no fundamental economic significance. No matter times I give you 4 quarters for a dollar or 1.23 dollars for a euro nothing of economic significance has happened. What counts is the degree of mutual subjective benefit that results from an exchange that involves at least one use-valued good. People get rich through transactions that have large subjective psychic profits and often involve large financial profits as well as the exchanges play out through the market.

The value of money comes from the desire of individuals to hold a scarce resource. It has little to do with circulation except to the extent that circulation requires certain holding periods of the medium of exchange, although technology is continuously reducing this requirement.

Regards, Don

Certainly; I offered the

Certainly; I offered the idea mostly as a reductio. I think (although alas I've no formal instruction in Econ since High School) that the crucial difference is that of information. We are willing to admit that Don's example represents a withdrawal from the money supply precisely because it locks away the money in the warehousing equivalent of Schroedinger's catbox.

As you (I think correctly) note, it is the informational properties of that twenty dollar bill that make the difference. If the bill can still effect the world -- if an observer can determine whether or not I have the bill from my participation in the economy -- then it is to some extent in the money supply. If your argument doesn't prove too much in this regard, it may prove too little.

The money held by your imagined minimalist government is certainly out of the money supply. But the money held by any real government is not: It influences decisions, shapes policy, speaks in tiny little monetary whispers into the ears of rate-setters. It is not out of the money supply. It is just out of sight. Money which can have an effect is, at least in part or by some discount, in the money supply. The magnitude of that discount is doubtless an effect of the sort of government and in particular the nature, fixedness, and transparency of its policies with regard to that money.

For instance, if I knew the government were holding all those dollars in a warehouse, I would be willing to lend that government money at a rather cheap price, in precisely the same way that if it were holding debt in that warehouse I would not. Unless your warehouse is perfectly airtight to all flow of information, the money in it is exerting some force, however attenuated, on the money supply.

So to the extent that you are arguing that unobservable money is outside of the money supply, this is trivially true, a matter more for a zen monk than for an economist. And to the extent that you are arguing that your hypothetical minimal government can move money outside of the money supply, this follows. But to extend this to any sort of general rule rather stretches your hypo beyond its reach. No government is, or really ever will be that perfectly opaque about a warehouse full of legal tender cash, however hypothetical.
--G

Don, Extending your example

Don,

Extending your example -

The Treasury prints up 10^100 dollars worth of $100 bills, and the MSCA delivers them to a top-secret warehouse where the bills stay for the next 200 years.

Did the money supply increase in any way during those 200 years?
If a tree falls in the forest, and there's no one there to hear it, does it make a sound?

It makes sense to exclude the government's holdings from the total money supply when the marginal cost of creating new money is zero.

But I wonder if anything really changes under a gold standard when the marginal cost of production is finite? Doesn't it still make sense to exclude the govt's holdings of gold from the money supply?

"I have to disagree with

"I have to disagree with this in the sense that the NUMBER of transactions has no fundamental economic significance. No matter times I give you 4 quarters for a dollar or 1.23 dollars for a euro nothing of economic significance has happened."

True, but the government's taking $4B and storing it in a vault for 50 years will affect the velocity term in the quantity equation, right? Whereas if it destroys the money (then reprints it), it affects the money supply term.

Both can lead to the same result, no?

Grant, "...As you (I think

Grant,

"...As you (I think correctly) note, it is the informational properties of that twenty dollar bill that make the difference...."

No, the information void is simply an additional description of the fact that there is no difference between the cases of storing and burning. The information has no value.

What you're missing is the fact that the government can effectively make money virtually costlessly out of thin air. If the government wants to increase the money supply, the only difference between the two cases is that in one case it calls in its engravers and printers and in the other case it calls in its forklift operators.

For the government money is not a scarce good because it can create it anew with neither effective limit or significant cost. The only real limit on the creation of money is the fear that politicians will be held responsible for the damage to the economy by the voters.

The capability of the government to inflate the supply of money is in no way limited by the stacks of money it may or may not have in its warehouses. Therefore, I have no reason to care whether it actually does have such money or not.

Regards, Don

Bill, "...True, but the

Bill,

"...True, but the government's taking $4B and storing it in a vault for 50 years will affect the velocity term in the quantity equation, right? Whereas if it destroys the money (then reprints it), it affects the money supply term...."

It jusr so happens that within the last 24 hours Rothbard's "Man, Economy and State" has become available in electronic .pdf form at Mises.org.

Within this work, Rothbard effectively destroys any economic significance that the 'Equation of Exchange' and the 'velocity of money' may have been thought to have.

Someone will dig that out sooner or later.

Regards, Don

Jonathan, "...But I wonder

Jonathan,

"...But I wonder if anything really changes under a gold standard when the marginal cost of production is finite? Doesn't it still make sense to exclude the govt's holdings of gold from the money supply?..."

I think it still makes sense, for two independent reasons.

First, the government can produce new gold without effective cost by putting Federal prisoners to work digging gold out of Federal lands. Of course, this is just a metaphor, but if the government wants to add to its gold, it can do so, even if it once again has to resort to theft and war. It need not be able to add an unlimited amount of gold, but only enough to reach the point where political or other considerations would limit monetary supply inflation anyway.

Secondly, the exchange value of money is determined by its marginal utility to its holders. When individuals trade money for goods, one individual ends up with more money and the other ends up with less. Through the application of the law of diminishing marginal utility, the individual adding money will value it less for the next possible transaction and vice versa. Statistically, these changes will tend to cancel out without changing the effective market value of money.

This doesn't apply to government. When the government expends money, it doesn't result in a restraint or price sensitivity for the next purchase. If the government starts to run out of money, it simply manufactures, taxes or steals more. On the other hand, the money the government spends will, in part, end up in the hands of individuals whose valuations of money are thereby decreased as their personal money supply increases.

Regards, Don

Don, Thanks for the Rothbard

Don,

Thanks for the Rothbard link.

I'm not sure what you are arguing, I guess. All I was saying is that you can determine that the following three events will lead to identical results without departing from the standard quantity theory of money.

1) Government takes $20 from each person, burns it, then reprints it 50 years later.
2) Government takes $20 from each person and puts it in a vault, then redistributes it 50 years later.
3) Government passes a law, perfectly enforced and obeyed, which says "Everyone must carry at least $20 on their person at all times," and then repeals the law 50 years later.

The first changes the money supply, the second and third change the velocity in the quantity equation

Mv = Py

where M is the money supply, v is the (income) velocity, P is the price level, and y is real income.

In other words, in 2 and 3, holders of money will be holding more money as a percent of their real income (in 2, the government holds a great deal more, while citizens hold less (I think), and in 3, citizens hold more).

I don't see why you need to depart from standard quantity theory, by redefining the money supply, when standard quantity can explain it just as well. I'll go read Rothbard now :-) but if you can explain my mistake in a simple way, I'd appreciate it.

"Rothbard effectively destroys any economic significance that the 'Equation of Exchange' and the 'velocity of money' may have been thought to have."

Hang on a second; I thought the velocity was just a manifestation of people's desire to hold money (which is what Rothbard argues is important, no?).

If people want to hold, say, 5% of their real income as money, then the (income) velocity is different than if they want to hold 2% of their income as money. But their desire to hold money is primary, and is calculated by standard supply and demand, no? (where nominal interest rate is the price)

Bill, "...All I was saying

Bill,

"...All I was saying is that you can determine that the following three events will lead to identical results without departing from the standard quantity theory of money...."

In this case, it is not just the results that count. During all of the 50 year period the government has $4B more in one case than in the other, and the fact that this difference means NOTHING to the economy is in need of explanation.

Without knowing just what you mean by 'the standard quantity theory of money', I still suspect that I don't subscribe to it. Money doesn't circulate or flow. It makes instantaneous quantum mechanical leaps from one person's cash balance into another's as a result of every economic exchange that involves money. All money is always owned by someone.

The only valid quantity theory of money restricts itself to saying that more money will tend to increase the money prices of goods through the actions of individuals in comparing their marginal utilities of the money that THEY hold with their subjective marginal utilities of the goods that are available to be purchased with money, and acting or not acting as appropriate. There are no equations or constant relations involved.

"...I thought the velocity was just a manifestation of people's desire to hold money (which is what Rothbard argues is important, no?)...."

No. The question is HOW MUCH money to hold and how to value it. This question is answered by comparing the subjective marginal utility of present goods with the marginal utility of money, which is derived from a wide choice of future goods, discounted by a time preference for present goods over future goods, and allowing for the flexibility of money in dealing with the fundamental uncertainty of the future in all of its manifestations.

Regards, Don

Don, I don't have time

Don,

I don't have time right now to think through a complete reply, but I wanted to address one point.

"It makes instantaneous quantum mechanical leaps from one person's cash balance into another's as a result of every economic exchange that involves money. All money is always owned by someone."

True, but this doesn't invalidate the concept of velocity, does it? I always think of "velocity" as "frequency" instead, since it refers to the number of "dollar quantum mechanical leaps." per dollar per year (say).

For example, say that everyone holds each dollar they get for, on average, a week (i.e. they hold 1/52 of their nominal income as money). Then, on average, every dollar changes hands 52 times per year. That is the (transaction) velocity: the number of times each dollar changes hands divided by the number of dollars.

Bill, "...For example, say

Bill,

"...For example, say that everyone holds each dollar they get for, on average, a week (i.e. they hold 1/52 of their nominal income as money). Then, on average, every dollar changes hands 52 times per year. That is the (transaction) velocity: the number of times each dollar changes hands divided by the number of dollars...."

There is no limit to the number of words that can be defined or made up and associated with some mathematical operation or another, but that does not mean that the words have any useful economic explanatory power. The inherent scarcity of money is only opposed by the holding of money by individuals. The number of transactions has no economic significance except as a source of entertainment.

Given fast enough computers and communications a single dollar could serve the need for money in all of the world's economic transactions. But it can't serve the demand for holding money against an uncertain future.

Regards, Don

"There is no limit to the

"There is no limit to the number of words that can be defined or made up and associated with some mathematical operation or another, but that does not mean that the words have any useful economic explanatory power."

First, I just wanted to explain what is meant by velocity; I didn't understand your arguments against it.

Second, it seems to have explanatory power; it explains your hypothetical without having to change what we mean by money supply.

Quantity equation: Mv=Py

In your first example (burning, then reprinting), M decreases, then increases.

In your second example (taking, storing, then redistributing), v decreases, then increases.

I'm not a big expert on this; I'm just saying how the quantity equation already explains your examples.

It also explains why all these other situations are exactly the same as your two:

3. Government requires $20 to be carried by everyone all the time, then repeals the law.
4. Regular thief takes $20 from everyone, stores it in his cellar, then gives it all back.
5. Everyone burns $20, then counterfeits $20.

In 3 and 4, v changes. In 5, M changes.

So I don't see how you need anything more than the quantity equation to explain your hypotheticals. Do you disagree?

Bill, I have abstracted

Bill,

I have abstracted Rothbard's destruction of the Equation of Exchange in a new post, the first post on March 13th. You should see from that why I am unable to provide you with an answer that seems reasonable.

Regards, Don

Thanks Don! I appreciate it.

Thanks Don! I appreciate it.

I am confused as to why this

I am confused as to why this would not be properly handled by the usual velocity of money idea.

Suppose there are 100$ in circulation with an average velocity of 1.

Now the government removes 50$. On the one hand we can say there are only 50$ in circulation at a velocity of 1. M*V = 50 *1 = 50.

On the other hand let us think of the 50$ as being in circulation but since it is being held, it has a velocity of 0. This means an average velocity of .5. M*V = 100*.5 = 50.

So aren't the two really equivalent, and you dont have to appeal to time periods.

Ummm... so the moral is the money supply (as a stock term) only makes when multiplied by the velocity.... I think

Quantum, As Rothbard states,

Quantum,

As Rothbard states, "V is an absurd concept."

When Rothbard analyzes the Equation of Exchange, it turns out to be saying that money spent equals money received. This doesn't explain anything.

If your computer repeatedly trades 4 quarters for a dollar with mine and then reverses the trade a nanosecond later, the velocity will be enormous, but the economic effect will be negligible.

As ar as the 50 year time period goes, this was to fit into a later discussion of social security and also the real effects of a change in the money supply are transient. Fifty years is far more than enough time for the transient effect to decay away.

Regards, Don

Yes MV = PY just means money

Yes MV = PY just means money spent is equal to money recieved, but thats why its true. In the end any logical statement can be reduced to a trivial product of axioms.

Your computer trading should not count towards the velocity because it is not counted in nominal GDP. The two should clearly be calculated at the same standard. Otherwise the equation wouldn't make any sense. Money velocity is just as defined as nominal GDP. (Of course there are clearly arguments about the way nom. GDP is calculated)

Money velocity is equal to the number of times in a given year the average dollar is spent in economic transactions (in the sense that they are counted to GDP).

I think you make a very good argument, but then draw the wrong conclusion. You can construct an infinite number of economically equivalent situations with arbitrary money supply. Simply declare the that there are billions of additional dollars but they are all trapped 200 miles under the mantle. The money supply is different but clearly the economy is the same. However MV (or PY) remains the same.

The point should then be that money supply is not an observable economic quantity. Because it can be changed arbitrarily without changing the economic situation money supply alone cannot be appear in the 'final equations'.

I'm kind of a physics guy so I compare it to gauge transformations. You can change the gauge fields in certain ways without changing the physical situation - so called gauge transformations. Therefore these gauge fields only appear as observable quantities in ways that are invariant to the gauge transformations.

Similarly with money supply. By adding this shadow money which exists but isnt spent we can arbitralily change money supply, an economic gauge transformation. Therefore money supply should only in an invariant manner M*V.

I think thats right.

Quantum Taco

You are right - money held

You are right - money held by the treasury is irrelevant to the real money supply. In fact, it is in real life excluded from calculation of the money supply. The following is a typical "textbook" definition of M1 (the narrowest measure of money supply).

M1 - One measure of the money supply that includes all coins, currency held by the public, traveler's checks, checking account balances, NOW accounts, automatic transfer service accounts, and balances in credit unions.

Note the "held by the public" bit. M2, M3, L, etc. all are "M1" + something else (none of which are money in the treasury).

Quantum, "...Yes MV = PY

Quantum,

"...Yes MV = PY just means money spent is equal to money recieved, but thats why its true. In the end any logical statement can be reduced to a trivial product of axioms...."

The problem is that the equation of exchange was supposed to help to explain how the quantity theory of money results in changes in the purchasing power of money as the supply of money is varied. A truism that is an identity made up of variables that have no meaning independent of the identity itself can't be said to explain anything.

"...I'm kind of a physics guy so I compare it to gauge transformations...."

This is part of the problem. True economics is a social science. It is based on the logic of attempting to achieve desired ends using scarce means. Economics is NOT mathematics, nor physics, nor psychology nor behaviorism.

Regards, Don

rvman, "...You are right -

rvman,

"...You are right - money held by the treasury is irrelevant to the real money supply. In fact, it is in real life excluded from calculation of the money supply. The following is a typical "textbook" definition of M1 (the narrowest measure of money supply)...."

This why I alluded to something about different schools of economics having strange alignments on the question of money supply.

The Austrian School tends to only talk about what I would call a technical money supply, basically counting forms of money that serve as final payment, if memory serves. This tends to be useful for roughly gauging the degree to which the government is inflating the supply of money.

The mainstream 'textbook' does exclude government held money from its money supply, but I don't know the reasoning behind this. It seems unlikely that it will be a valid reason, given all of the mainstream fallacies about money.

My interest is in an 'effective' money supply that determines the marginal exchange value of money.
This only would include a portion of the technical money supply and would also include other exchange-valued goods other than actual money that affect the value of money from the money side as opposed to the goods side.

In any case, the 'money supply' has to be considered as a tool of thought, which needs to be reconfigured when it is used for different purposes.

Regards, Don