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# Mises's Regression Theorem and a Logical Proof

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Micah71381 posted on Mon, Apr 18 2011 7:29 PM

Premise: A thing must be valued for one or more non-exchange purposes by one or more people before it can be used for indirect exchange. (regression theorem)

Given: A specific thing is used for indirect exchange in a market of 3 or more people.

Conclusion: The specific thing must have been valued by one or more people for one or more non-exchange purposes at some point in history.

Is my premise incorrect or arguable?  Have I committed a logical fallacy in drawing my conclusion?

The premise is discussed here: http://mises.org/Community/forums/t/23938.aspx

The specific thing can be any object that is used for indirect exchange in a market of 3 or more people.  The market size of 3 comes from the above linked thread as well where it was established that one person must value a good and the market must be of size 3 or more in order for indirect exchange to occur.  It was touched on that technically 2 or more could result in indirect exchange but for the sake of this proof I went with the generally accepted market size of 3.

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Smiling Dave replied on Mon, Apr 18 2011 8:37 PM

My humble blog

It's easy to refute an argument if you first misrepresent it. William Keizer

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Think Blue replied on Mon, Apr 18 2011 10:49 PM

Micah71381:

Premise: A thing must be valued for one or more non-exchange purposes by one or more people before it can be used for indirect exchange. (regression theorem)

Not sure about this, but I suspect that indirect exchange may be a necessary, but not sufficient, condition for something to be a medium of exchange.

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Micah71381 replied on Mon, Apr 18 2011 10:57 PM

Think Blue:

Not sure about this, but I suspect that indirect exchange may be a necessary, but not sufficient, condition for something to be a medium of exchange.

While this is not directly related to my argument (I didn't mention medium of exchange anywhere) I would be curious what other requirements you can think of for something to be a medium of exchange.

In http://mises.org/rothbard/mes/chap3a.asp section 2 paragraph 2 it is referred to as "medium of indirect exchange" which is then shortened to "medium of exchange" after that and for most of the rest of that page.  I am not stuck on this definition (medium of exchange is a thing used in indirect exchange) so if you can provide an alternative definition I am open to using it if it seems to fit better.

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Think Blue replied on Mon, Apr 18 2011 11:38 PM

Micah71381:

Think Blue:

Not sure about this, but I suspect that indirect exchange may be a necessary, but not sufficient, condition for something to be a medium of exchange.

While this is not directly related to my argument (I didn't mention medium of exchange anywhere) I would be curious what other requirements you can think of for something to be a medium of exchange.

From your initial premise, you did mention "regression theorem" in parenthesis, so I assumed "medium of exchange" would be implicit within the statement.

Micah71381:

In http://mises.org/rothbard/mes/chap3a.asp section 2 paragraph 2 it is referred to as "medium of indirect exchange" which is then shortened to "medium of exchange" after that and for most of the rest of that page.  I am not stuck on this definition (medium of exchange is a thing used in indirect exchange) so if you can provide an alternative definition I am open to using it if it seems to fit better.

How I interpret the passage, "medium of indirect exchange" is distinct from "media of exchange", as there exists a transition from one point to the other.

By the way, have you seen the Mises Made Easier glossary?  This may help:

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filc replied on Tue, Apr 19 2011 12:19 AM

Micah:

Premise: A thing must be valued for one or more non-exchange purposes by one or more people before it can be used for indirect exchange. (regression theorem)

Given: A specific thing is used for indirect exchange in a market of 3 or more people.

Conclusion: The specific thing must have been valued by one or more people for one or more non-exchange purposes at some point in history.

Therefore we can conclude that USDollars were traded for on the market in direct exchange prior to their use as a money. They were used for direct  consumption prior to their function as money. IDK Maybe people used them as kindling in their fire places? Maybe they ate them? Used them as pillow stuffing? What Micah is telling me here is that the USDollar had industrial or consumptive use properties prior to it's functin a money.

Wait just a dern minute here!

Micah:
Is my premise incorrect or arguable?  Have I committed a logical fallacy in drawing my conclusion

Nope. Yes.

It took all of about 2 seconds to find the flaw. The theorum is not referring to moneys by decree, and moneys of similar property(Objects of indirect exchange whos only use is for indirect exchange and offer no utility or consumptive properties outside of that)

@Smiling Dave - Aristotle still nodding his head?

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447 Posts
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Micah71381 replied on Tue, Apr 19 2011 3:21 AM

Think Blue:

By the way, have you seen the Mises Made Easier glossary?  This may help:

Thanks for that glossary link, very helpful.  :)  Here is the defenition of medium of exchange in that glossary:

Any good, such as money (q.v.), which people seek for use in exchange rather than for consumption or use in production. A highly marketable good for which one first exchanges his less marketable wares or services so as to be able to offer a more acceptable good to the sellers of goods and services one seeks to buy. Any good which, because of popular acceptance, serves to facilitate indirect exchange (q.v.).

Perhaps the additional requirement is that the thing must be more marketable than whatever it is being traded for?  That is, if I accept bottle caps in exchange for dollars because I know a particular person who only accepts bottle caps then I am participating in indirect exchange but the bottle caps are not a medium of exchange?

It seems that this will lead to a situation where something can be a medium of exchange in one transaction and then not a medium of exchange in the following transaction.  Say I trade a tractor (low marketability) for butter with the intent of trading that butter away later (not consuming it).  In this case, the butter is a medium of exchange.  In the following transaction I trade the butter for bottle caps with the intent of later trading away the bottle caps, which are more marketable than the butter.  In the second transaction butter is no longer a medium of exchange even though up until the instant prior to the transaction butter was a medium of exchange.

I can accept this variability in media of exchange but it seems to make the concept more complex than necessary.  There is no disadvantage that I can see to calling butter a medium of exchange during and after the second transaction because I had no intention of consuming it at any point, it was bought, held and sold for the purpose of facilitating exchange rather than for consumption.

If we assume that butter ceases to be a medium of exchange at the time of the second transaction, is there a term that can be applied to the butter that will still hold after the second transaction?  Some way to facilitate communication about items used in indirect exchange but not limited to the most marketable good in any particular indirect exchange?

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Micah71381 replied on Tue, Apr 19 2011 3:33 AM

filc:

Micah:

Premise: A thing must be valued for one or more non-exchange purposes by one or more people before it can be used for indirect exchange. (regression theorem)

Given: A specific thing is used for indirect exchange in a market of 3 or more people.

Conclusion: The specific thing must have been valued by one or more people for one or more non-exchange purposes at some point in history.

Therefore we can conclude that USDollars were traded for on the market in direct exchange prior to their use as a money. They were used for direct  consumption prior to their function as money. IDK Maybe people used them as kindling in their fire places? Maybe they ate them? Used them as pillow stuffing? What Micah is telling me here is that the USDollar had industrial or consumptive use properties prior to it's functin a money.

Wait just a dern minute here!

Micah:
Is my premise incorrect or arguable?  Have I committed a logical fallacy in drawing my conclusion

Nope. Yes.

It took all of about 2 seconds to find the flaw. The theorum is not referring to moneys by decree, and moneys of similar property(Objects of indirect exchange whos only use is for indirect exchange and offer no utility or consumptive properties outside of that)

@Smiling Dave - Aristotle still nodding his head?

To be clear, you are disagreeing with my premise, not the conclusion.  The "(regression theorem)" is simply a reference tag showing where I derived the premise but the premise was the sentence alone.  How would you suggest rewriting my premise to be in line with your understanding of the regression theorem such that my conclusion is no longer true?

Note: I tried rewriting my premise using your addition about money by decree and moneys of similar properties but ended up with something that was self referencing as seen here:

A thing must be valued for one or more non-exchange purposes by one or more people before it can be used for indirect exchange unless it is used in indirect exchange by threat of aggression (government) or unless it is first used for indirect exchange.

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Smiling Dave replied on Tue, Apr 19 2011 7:24 AM

The theorum is not referring to moneys by decree, and moneys of similar property(Objects of indirect exchange whos only use is for indirect exchange and offer no utility or consumptive properties outside of that)

@Smiling Dave - Aristotle still nodding his head?

The way I understood it, the regression theorem is talking about all monies, real and fiat. A corollary of the regression theorem is that money by decreee will never get off the ground.

Dollars are not a counterexample, because they started off as being gold and silver pieces, then paper was introduced as tradable on demand for gold. At those stages they were still "intrinsically useful" more or less. Later dollars were taken off the gold standard.

One can sum up by saying that people are stupid enough to accept the loss of value of already accepted money [=dollars], but not to start right in with useless money from the get go [=regression theorem].

So that Aristotle just had a shot of gin, grinning.

My humble blog

It's easy to refute an argument if you first misrepresent it. William Keizer

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Smiling Dave replied on Tue, Apr 19 2011 7:33 AM

Lest I be charged with entrapment, I'll quote Uncle Bob Murphy right now:

...People today expect money to have a certain purchasing power tomorrow, because of their memory of its purchasing power yesterday. We then push the problem back one step. People yesterday anticipated today's purchasing power, because they remembered that money could be exchanged for other goods and services two days ago. And so on.

So far, Mises's explanation still seems dubious; it appears to involve an infinite regress. But this is not the case, because of Menger's explanation of the origin of money. We can trace the purchasing power of money back through time, until we reach the point at which people first emerged from a state of barter. And at that point, the purchasing power of the money commodity can be explained in just the same way that the exchange value of any commodity is explained. People valued gold for its own sake before it became a money, and thus a satisfactory theory of the current market value of gold must trace back its development until the point when gold was not a medium of exchange.

Then comes a key footnote:

* Notice that fiat moneys have always emerged through their initial ties to commodity moneys. For example, we can trace back the purchasing power of U.S. dollar bills until the point when the notes were redeemable in gold or silver, and at that point we need merely explain the purchasing power of gold and silver.

Bottom line: Micah had it right the first time. His logic was impeccable. No need to modify your initial premise, Micah.

To gild the lily [excuse the pun], here is the brilliant Tim Terrel, discussing dollars:

One of the consequences of the regression theorem is that money must arise from a commodity already in general use. If there is no nonmonetary use for the good, it will not develop the widespread demand that must precede its use as a medium of exchange. As Mises’s student Murray Rothbard wrote, money "cannot be created out of thin air by any sudden ‘social compact’ or edict of government."[2] But once a good develops a monetary nature, it is there to stay. The nonmonetary uses are no longer necessary to maintain the good’s monetary value, because there is already a set of prices based on that good.

Oh, and Rothbard too:

On the other hand, while money had to originate as a directly useful commodity, for example, gold, there is no reason, in the light of the regression theorem, why such direct uses must continue afterward for the commodity to be used as money. Once established as a money, gold or gold substitutes can lose or be deprived of their direct use function and still continue as money; for the historical reference to a previous day's purchasing power will already have been established.*53

Gild on Macduff, with a link to the kindly Professor Shostak.

My humble blog

It's easy to refute an argument if you first misrepresent it. William Keizer

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Micah71381 replied on Tue, Apr 19 2011 7:54 AM

Smiling Dave:

Lest I be charged with entrapment, I'll quote Uncle Bob Murphy right now:

...People today expect money to have a certain purchasing power tomorrow, because of their memory of its purchasing power yesterday. We then push the problem back one step. People yesterday anticipated today's purchasing power, because they remembered that money could be exchanged for other goods and services two days ago. And so on.

So far, Mises's explanation still seems dubious; it appears to involve an infinite regress. But this is not the case, because of Menger's explanation of the origin of money. We can trace the purchasing power of money back through time, until we reach the point at which people first emerged from a state of barter. And at that point, the purchasing power of the money commodity can be explained in just the same way that the exchange value of any commodity is explained. People valued gold for its own sake before it became a money, and thus a satisfactory theory of the current market value of gold must trace back its development until the point when gold was not a medium of exchange.

Then comes a key footnote:

* Notice that fiat moneys have always emerged through their initial ties to commodity moneys. For example, we can trace back the purchasing power of U.S. dollar bills until the point when the notes were redeemable in gold or silver, and at that point we need merely explain the purchasing power of gold and silver.

Bottom line: Micah had it right the first time. His logic was impeccable. No need to modify your initial premise, Micah.

I think filc's contention lies in things that he is unable to trace back to things with non-exchange value.  BitCoin is an example of something that is used in indirect exchange yet he is unable to trace back to something of non-exchange value.

Because of the argument in the OP, either the premise is false (meaning a failure of the regression theorem or a misrepresentation of it on my part) or BitCoins did have intrinsic value to someone at some point in history.

Personally, I am inclined to believe that as long as you don't narrowly define "value" then BitCoin's had intrinsic value at their inception to some people.  The intrinsic value of BitCoins was that of potential economic change.  Those first users wanted economic change and saw BitCoins as an opportunity for such a change and therefore they valued BitCoins not because they could trade them away but because BitCoins had psychological value to them.

The alternative is to conclued that Mises's regression theorem is incorrect and BitCoins truely did start out as mediums of exchange rather than starting out as commodities.  Unless I am misrepresenting Mises's regression theorem in which case I am open to a more accurate premise that falsifies my conclusion.

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Smiling Dave replied on Tue, Apr 19 2011 8:50 AM

I think filc's contention lies in things that he is unable to trace back to things with non-exchange value.

No such animal.

BitCoin is an example of something that is used in indirect exchange yet he is unable to trace back to something of non-exchange value.

I see that there is another thread out there tossing around bitcoins and the regression theorem.

Here is an article spelling it out, called, appropriately, Bitcoin does NOT violate Mises' Regression Theorem

The key part is this:

...The very first businesses in the Bitcoin economy were exchangers (NewLibertyStandard, BitcoinMarket, BitcoinExchange,....).  This is not an accident, but flows from the analysis above.  In order for Bitcoins to serve as a medium of exchange without commodity value for uses besides indirect exchange, there must be a translated knowledge of money prices.  Market exchangers fill this gap and give Bitcoin users access to this knowledge.  Bitcoins may therefore currently serve as a money intermediary for paypal dollars\pecunix\euros...

The essential point is that once exchange can occur between a money (USD) and Bitcoins, providers of goods have a means by which to value Bitcoins as a potential medium of exchange.  The money regression is satisfied, because taken back far enough we reach traditional commodity money: BITCOINS -> USD -> MONETIZED GOLD & SILVER [start monetary economy] -> [end barter economy] COMMODITY GOLD & SILVER.

My humble blog

It's easy to refute an argument if you first misrepresent it. William Keizer

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Smiling Dave replied on Thu, May 3 2012 2:13 PM

Bumping an old thread here, because I now know there are some mistakes.

1. The OP wrote that 3 or more people using something as money makes Mises' Regression Theorem apply to it. Which is not the case. Mises is talking about "generally accepted" stuff. 3 friends or brothers can use meaningless toy poker chips as money by mutual agreement. Need we go further than Krugman's baby sitters, who used pieces of paper as money exchangeable for baby sitting.

2. That article I linked to in the previous post is flawed, and for the same reason. Bitcoin is still not generally accepted, so it is not a money at all yet. And of course, never will be.

My humble blog

It's easy to refute an argument if you first misrepresent it. William Keizer

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AJ replied on Thu, May 3 2012 9:48 PM

"People valued X for non-exchange purposes" and "X was generally accepted as a medium of exchange" are moving targets. Can we at least decide on a lower bound on the percentage of the population signified by the words "people" and "generally accepted"?

"People valued ..." = more than 10% of the population? 30%? 80%?

"Generally accepted" means accepted by more than 50%? 80%? 95%?

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gotlucky replied on Thu, May 3 2012 9:57 PM

@AJ

I think the purpose of using words instead of specific numbers is because it is impossible to know precisely when something has become generally accepted.  Cigarettes might be generally accepted in prison, but they certainly aren't in the general population.  Why does it matter for a precise number?

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