Tuesday, October 30, 2012

Money and the Medium of Account

Scott Sumner has defined money to be the medium of account and has argued that the equation of exchange applies to the medium of account.

I define money to be the media of exchange.  I don't have much use for the equation of exchange, but to the degree it does have value, its value relates to the medium of exchange, not the medium of account.

Sumner argues that whether money is the medium of account or the media of exchange can be best explored by considering hypothetical monetary regimes where the medium of account is different from the media of exchange.

I agree that such regimes are instructive.    I began to study this issue nearly thirty years ago after reading Robert Greenfield and Leland Yeager's 1983 paper, "A Laissez-Faire Approach to Monetary Stability "      They were influenced by Fama's 1980 paper, "Banking in the Theory of Finance."   That is why Greenfield and Yeager included Fama's name in their proposed BFH payments system:  the Black-Fama-Hall payments system.

The Greenfield and Yeager system defines the unit of account in terms of a nearly-comprehensive bundle of goods and services.   In their first paper, the media of exchange were a variety of checkable mutual fund accounts.   Jurg Niehans defined the medium of account as the good that defines the unit of account, so Greenfield and Yeager were proposing that the medium of account be a bundle of goods and services.   There is no notion that people use the bundles to purchase items or even that anyone actually gathers up  all of the items in the bundle and trades them all at once.

The Fama paper comes closer to what Sumner discusses.   Fama suggested a steel ingot as the medium of account.   He describes a variety of scenarios regarding the media of exchange, but one interesting one is an Accounting System of Exchange where payments are made with ordinary stocks and bonds.   No one buys anything with steel ingots.   Those producing them sell them for media of exchange and people needing to use steel purchase it with media of exchange.

The price level is the inverse of the relative price of the medium of account.   In Fama's scenario, that would be steel.   The relative price of steel depends on supply and demand, as usual.    If there is an increase in the demand for steel, perhaps because a new use for steel is discovered, its relative price rises.  This implies a decrease in the prices of all other goods and services.   If, on the other hand, there is some technological improvement in steel manufacturing, its supply increases, its relative price falls, which implies an increase in the prices of all other goods and services.

How does that work exactly?   There is an increase in the demand for steel, and a shortage of steel at its current, fixed by definition, price.   Why does everyone else in the economy respond to a shortage of steel by lowering the prices they quote for other goods and services?   Why should they care about conditions in the steel market?

Now, if there were a Walrasian auctioneer, he would note that there is a shortage of steel.   Because steel is the numeraire, he cannot raise the price of steel.   He instead calls out lower prices for all other goods and services.   And so, the reason why other prices fall is simple.  The Walrasian auctioneer lowers them.

But there is no Walrasian auctioneer in reality.   In the real world, why does everyone else lower their prices because there is a shortage of steel?    In truth, the most likely scenario is that those actually quoting steel prices would raise the ingot price of an ingot.   That would mean that the definition of the unit of account in terms of the medium of account would be ineffective, and the "steel ingot" would be an abstract unit of account not tied to anything.

With the Greenfield and Yeager system, this is a much more serious problem.   We can at least imagine that those buying and selling steel would insist that a steel ingot is a steel ingot and so the price is fixed by definition.   When a bundle of goods and services is used as the medium of account, the price of each item in the bundle is free to vary.   It is just that the prices of the items must sum up to the defined total.   If the relative price of the bundle as a whole rises, then the prices of other goods must drop.   But why would any of those actually setting the prices of bundle items make sure that they total up to the defined amount, much less  those producing other goods adjust their prices to make that total consistent with general equilibrium?

If there were a Walrasian Auctioneer, there would be no problem.   While making sure that the prices he calls out for the bundle items add up the the correct total is more complicated than keeping one price fixed, it isn't too difficult.  And if the relative price of the bundle rises, the Walrasian auctioneer just calls out lower prices for the other items.

In my view, Fama never solved the problem.   Like usual, he just assumed market clearing.   And it wasn't like he was proposing the steel ingot as a medium of account in reality.   But, like usual, his equilibrium always perspective blinded him to important aspects of the economy.

Greenfield and Yeager, on the other hand, did solve the problem by examining how the media of exchange must be tied to the medium of account.   A "dollar" claim in the payments system would be settled with some "settlement media" that had an actual market price equal to the sum of the actual market prices of the items in the bundle.   This would create powerful market forces--monetary forces--that would keep the sum of the prices of the items in the bundle at the defined amount and cause all other prices, including wages, to adjust as well.   If the relative price of an item in the bundle rose, then all other prices in the economy would fall enough so that the sum of the prices of bundle items would equal the defined amount.

The solution for Fama's scheme is more or less the same.   But what it amounts to is thatthe  Accounting System of Exchange must set up procedures to make sure that the steel market clears at a price of one ingot of steel per ingot of steel.

Sumner imagines a system where Zimbabwe is on a gold standard.   Gold serves as medium of account.   All prices and wages and contracts are in terms of gold.  However, the people use Zimbabwe currency as the medium of exchange.    The amount of currency needed to make a payment is determined by dividing the amount of the payment in gold units by the gold price of currency.   Sumner supposes that there would be a sign by each cash register showing the gold price of Zimbabwean currency.

Sumner supposes that the Asians demand more gold, and this leads to deflation in Zimbabwe.  The demand for the medium of account has risen, its equilibrium relative price rises, and this implies a lower equilibrium price level.    Sumner just assumes that the price level drops.   Just like there is a Walrasian auctioneer noting that at the old relative price of gold, the old price level, there is a shortage of gold.   And so, new prices must be called out to everyone supplying and demanding the other goods in Zimbabwe.  Sumner supposes that wages, quoted in gold, are sticky, so the lower price level raises real wages and so employment falls.    (Or maybe it is that the lower price level, multiplied by the given level of real output makes up a smaller number.  When that is divided by the given wages, that implies less hours worked.)

What is it exactly that motivates people selling bread, gasoline, diamonds or anything else to lower their gold prices?   Is it because they become more anxious to sell these goods?   Surely the more plausible explanation is that people in Zimbabwe reduce their purchases of bread, gasoline, diamonds and other goods at the currently quoted prices.   Why?

Now, the growing Asian demand for gold could strip the Zimbabwean gold shops of their stock.  There is a shortage of gold at the fixed by definition price of gold.   Zimbabweans going to the shops to get gold for dental work or jewelry find the shelves empty.  

How does that cause Zimbabweans to reduce their purchases of bread, gasoline, diamonds, and the like?   Why would firms be more anxious to sell bread, gasoline, or diamonds?    Why would those setting the prices of those goods lower them?

Sumner seems to think that the experience of the thirties is relevant.   In the thirties, money was redeemable for gold and so there was  obvious process by which an increase in the demand for gold would create a shortage of the media of exchange.   People short of money sell assets and spend less.  This results in reduced demands for goods and services.   This creates an incentive for those setting prices to lower them.

But in Sumner's Zimbabwe example, the currency used as the medium of exchange is not redeemable in gold.    But what exactly determines the gold price of Zimbabwean currency in this imaginary world?   Sumner assumes it is determined on the foreign exchange market.   Perhaps he is thinking back to an international gold standard, so that the foreign exchange market of Zimbabwe determines a gold price of Zimbabwean currency.   But in the real world, the foreign exchange market determines an exchange rate for Zimbabwean currency against U.S. dollars, Euros, and Yen, not gold.

So, what happens?    The purchases of gold in Asia raises the U.S. dollar price of gold.   Given the exchange rate between U.S. dollars and Zimbabwean currency, this raises the price of gold in terms of Zimbabwean currency.    But the Zimbabweans turn this around and say it has determined the gold price of Zimbabwean currency and the price of currency has fallen.  

When this lower price of currency is announced around the country, the amount of currency that must be paid for each and every good is now higher.   Alternatively, the quantity of currency measured in gold units is lower.   Given the demand to hold currency, there is now a shortage of the medium of exchange.  People spend less.   Firms lower their prices--the gold ones that the  quote.   Given the gold price of currency, this is also reducing the amount of currency that must be paid for each item.

Anyway, the reduction of spending on output results in a recession.   Yes, it is the greater demand for gold that gets the process started, but it is only because of the effect on the medium of exchange that it actually causes spending to fall.  And it is that fall in spending that directly causes the recession.

Now, once a market process is established such that market forces--monetary forces--will cause the price level to adjust, speculation will tend to cause appropriate changes in supply and demand.   In a traditional gold standard, where all the media of exchange are redeemable in gold, if people think the demand for gold is going to rise, prices will fall.   There is no need for the demand for gold to rise, money be redeemed for gold, the quantity of money fall, and a shortage of money cause less spending, and the lower spending cause lower output and prices.   The expectation of lower output and prices in the future will cause people to cut spending now.   But the market process must be there if speculation is going to forestall it.  

Anyway, the medium of account is not money.   The bundles of goods and services in the BFH system are not money.   The steel ingots in Fama's story are not money.   The money is the media of exchange.   But that doesn't mean that shifts in the relative price of the medium of account don't cause changes in the price level.

Money is whatever it is that such that changes in its "quantity" lead to inflation or deflation?   When the medium of account is an ordinary good like steel, talking about changes in the quantity of steel is wrongheaded.   It is flow supply and demand that counts.   When the medium of account is a bundle of goods, talking about the quantity of bundles is nonsense.

Further, recession is not caused by a deflation of prices pressing against sticky wages.   Recession is caused by a decrease in money expenditures on output along with a failure of prices and wages to fall enough to make it unnecessary for real output and employment to fall as well.

Money is what is spent.  Money is the medium of exchange.  It is intimately involved in the problem of too little or too much spending.  

But when money is tied to a separate medium of account, then the quantity, price, or yield on money must adjust so that there is a level of spending consistent with clearing the market for the medium of account at the defined price.   This forces the price level to change if necessary, but at the same time, it means that shifts in the supply or demand for media of exchange must be offset if they would otherwise force changes in the price level.

What does this have to do with Market Monetarism?   Well, I don't really understand what is the medium of account with NGDPL targeting, but the nominal anchor is the level of spending on output.   And the quantities of media of exchange must adjust so that they match their demands when nominal GDP is on target.   It is not currency or any type of deposit that serves as medium of account and whose quantity determines spending on output.   It is the level of spending on output that determines the needed quantity of money.


  1. well it certainly is a little disconcerting seeing economists disagree on things like the proper definition of money and the usefulness of the equation of exchange.
    those seem to be cornerstones of the field.
    i don't think chemists disagree on the usefulness of the periodic table, or physicists disagree on the definition of gravity.
    isn't a prerequisite for the advancement of a science that its practitioners at least 'speak the same language'?

  2. "Well, I don't really understand what is the medium of account with NGDPL targeting, but the nominal anchor is the level of spending on output. ."

    Aren't the medium of account and the nominal anchor the same thing?

  3. I read your blog, its so nice and provide good knowledge for us. I really like it and thanks to write this wonderful post.

  4. I like the equation of exchange. It really helps in explaining hyperinflation and in simulating hyperinflation.