The Equation of Exchange

I would write the equation of exchange as MV = Py.

The second term, Py is equal to nominal GDP.    Assuming y is measured by real GDP, and that is calculated as Y/P, where Y is nominal GDP and P as measured by a price index, then y = Y/P  implies that Y = Py.

So, the equation of exchange implies that Y = MV.  

If M is the quantity of money and V is the number of times money is spent on final goods and services per period, then MV is spending on output per period.    More money, or a change in how fast (veloclity?) it is spent on current output, might cause changes in nominal GDP.

On the other hand, if V is defined so that V = Py/M, then V is whatever it takes to make MV = Py hold.   If M rises, then V falls.   If P rises, V rises, and so on.

I think that one way to understand what those economists who use the equation of exchange as a theory have in mind simply requires that M be given two different subscripts.   Ms for the quantity of money supplied and Md for quantity of money demanded.

The equation of exchange is Ms V = Py.

And V is defined such that V = Py/Md

By substitution,   Ms *Py/Md = Py.

This implies that Ms/Md = 1

Or Ms = Md.

The equation of exchange is an economy theory based upon the quantity of money supplied being equal to the quantity of money demanded.

Now, if you define the quantity of money demanded as the amount of money people are actually holding and the quantity of money supplied as the amount of money that actually exists, and then add that someone is always holding whatever money that exists, then Md = Ms always.

I think that is what it means to treat velocity as being defined as V = Py/M.

Of course, what is usually done instead is to understand the demand for money to be the amount of money that people would like to hold.   And further, that it is possible for people to actually be holding more or less money than they would like.

As an analogy, suppose quantity demanded is identified as the amount bought and quantity supplied as the amount sold.   Since the amount sold is always equal to the amount bought by definition, quantity supplied and demanded are always equal.    It is nonsensical, then, to claim that price depends on supply and demand, and in particular, the price adjusts so that quantity supplied and quantity demanded are equal.  Since the amount bought and sold are always equal, it is not intelligible.

But, of course, quantity supplied is how much sellers would like to sell and quantity demanded is how much buyers would like to buy.   Quantity supplied and demanded are not always equal.   It is possible that the amount sold is less than the amount sellers would like to sell.   Or that the amount bought is more than the amount buyers would like to buy.

Similarly, the amount of money people would like to hold may be more or less than the amount that they actually hold.

And that implies that velocity can differ from what people would like it to be.    Does that sound odd and awkward?   It does to me.   And that is why I usually prefer to think about monetary economics in terms of the quantity of money and the demand to hold it, rather in terms of the equation of exchange.   But still, I balk at claims that the equation of exchange is nothing but an identity.     Because if it is, so is the notion that prices and real income adjust to bring the quantity of money demanded into equilibrium with the quantity of money supplied.   And so is the notion that relative price adjusts to bring quantity supplied into equilibrium with quantity demanded.

Is NGDP found by multiplying "real output" by "the price level?"

Kevin Grier criticized Market Monetarism with the old:

Nominal GDP IS nothing more than the product of prices and output. To say that a fall in nominal GDP relative to trend "caused" the fall in the path of prices and output relative to trend is just gibberish.

In terms of the calculation of the statistics, it is more accurate to say that real GDP is nothing more than nominal GDP divided by a price index..  

Nominal GDP is calculated by adding up price times quantity for a variety of goods and services.   The prices and quantities are thing that are observed.   The product of each one is something that actually happened, the amount spent on each product by buyers and the amount earned as revenue by sellers.   And the sum is something that is true of the economy.

The price level is measured by calculating an index.   The index compares some weighted average of the prices to those in a base year.   While the prices today and those in the base year are actually measured, the weighting in the years and adjustments for the fact  that the goods are somewhat different makes the price index much more than something actually observed.   The price index is not something that happens in the economy.

And then when this created price index is divided into the nominal GDP, we have something that isn't really the volume of goods produced.   It is what the dollar value of the goods produced would have been if prices were what they were in the base year, leaving aside weighting issues and adjustments for quality.

If we model the macroeconomy with a single good, and imagine that the output of that good is given entirely by real factors, then real GDP is simple.   Say a billion bushels of corn are grown in an economy that solely grows corn.     Real GDP is a billion bushels of corn.

Of course, there are no relative prices in this economy.    The price level is simple.   It is just the money price of corn.   And so, nominal GDP is the simply the quantity of corn multiplied by the price of corn.  

Nominal GPD still tells us something about the economy.   It is how much money is spent on corn and how much money is earned by selling corn.   But still, it is entirely plausible to imagine that the price and quantity are first set and that nominal GDP is just price times quantity..

In the real world, nominal GDP and the price index must be calculated first, and only then can real GDP be calculated.

Of course, it is hard to understand why there would be any exchange in a one good economy.   What does the money price of corn really mean?   Why are there any exchanges?   Well, you can model overlapping generations.  That makes money a saving vehicle.   This means we ignore money's role as medium of exchange that is so important in the real world because there are many goods and resources.   And further, in the real world, while money can be a savings vehicle, there are many other ways of saving that are usually much better.

Finally, we can imagine a Walrasian Auctioneer determining the real output of all the products using an arbitrary numeraire.   And all output and resource use is determined.   Presumably, we could measure real GDP using any good as numeraire.      

Then, after that is done, the Walrasian Auctioneer could call out money prices to equate the quantity of money and the demand to hold money.   We can even imagine that money is fully neutral,, so that every money price is proportional to the numeraire price. 

So, real output is determined, and the price level is determined.  Nominal GDP is nothing more than the product of two independently determined things.

But the real world is a monetary exchange economy with many goods and resource.  These goods and resources are sold for money.  These goods and services are purchased with money.

And that is why nominal GDP--how much money is spent and earned--is not just a real thing that happens in the economy, it is also an important thing.

The actual prices and quantities of the various goods and services are also real things and important for many purposes.  In a monetary exchange economy, the amount of money spent on and earned from each good is a real thing and important.

The price index and its rate of change, is not the same thing as the market price of a  single good and its rate of change.   And real GDP is not the same thing as the market determined output of a single good and its rate of change.

NGDP Targeting in Developing Countries

Scott Sumner commented on the article by Pranjul Bhandri and Jeffrey Frankel arguing that Nominal GDP targeting is relatively desirable for developing countries.    Scott disagreed and argued that it would be better to target labor compensation.   He may be correct that labor compensation is the better target, but his argument was faulty.

Scott wrote:

However I've also argued that NGDP targeting is not optimal when countries depend heavily on the production of commodities with very volatile prices. Suppose 50% of Kuwait's NGDP were oil production. If global oil prices doubled, and Kuwaiti oil output remained unchanged in physical terms, then the central bank of Kuwait would have to reduce non-oil production to zero in order to keep NGDP stable. Obviously that would not be optimal.

If Kuwait's GDP (real and nominal) was composed 50% oil production and 50% of other things, and the world price of oil doubles and the number of barrels of oil produced stays the same, and real GDP is held constant, then real GDP from all other activities must drop to zero.  I grant that would not be optimal.

But nominal GDP targeting doesn't require that real GDP remain constant.  The factor Scott ignores is the exchange rate between the Kuwati Dinar and other currencies.   Assuming that the global price of oil is quoted in dollars, the immediate effect of doubling of global oil prices would be a doubling of the dollar price of the Kuwati Dinar.   While the dollar price of oil will have doubled, the price of oil in Kuwati Dinar would be the same, and assuming, for the moment, no other change in Kuwati economic activity, nominal GDP for Kuwait in Dinars is unchanged.

Of course, this large increase in the exchange rate of the Kuwaiti Dinar is going to have major effects on the Kuwaiti economy.   Prices of imported goods in the shops will fall substantially.   The unchanged nominal incomes will now purchase twice as many imported goods.    All Kuwatis benefit from the favorable supply shock.

In a not unrealistic scenario for Kuwait, suppose all the other goods produced by the economy are nontraded.    Kuwait exports oil and operates shops that sell imported goods and have barbers who give haircuts.   Suppose that the nontraded goods are normal.  The Kuwaitis can now buy more foreign consumer goods.   They need and desire bigger and more expensive shops.  They also get more frequent and fancier haircuts.

The increased demand for nontraded goods would tend to raises their prices in Kuwaiti Dinar, and so raise nominal GDP.   This would require a  further appreciation of the Kuwati Dinar.    This reduces the value of the unchanged quantity of oil in Dinars, and so reduces nominal GDP.     The Dinar must rise enough so the Dinar value of oil produced in Kuwait falls enough to exactly offset the increase in demand and so expenditure on nontraded Kuwati goods.

Now, the reduced price of oil in Dinars should result in a lower quantity of oil supplied and so free up labor and other resources to shift over to production in the nontraded goods sector.   Former oil workers shift over to work in shops selling imported consumer goods or else be barbers.  

Of course, Scott's assumption that the the quantity of oil remains the same suggests a lower Dinar price of oil frees up no resources from the oil industry.   That is plausible enough.   It is all extraction of existing oil   The cost of the mechanics repairing the pumps and pipelines is trivial.    It is nearly all rent extraction.   Initially the Dinar rose enough that the nominal value of the rents were unchanged, but the income effect raising the demand for nontraded goods requires a further appreciation of oil so that the nominal rents from oil fall enough to keep total spending unchanged. Perhaps the Emir hires a few less soldiers and instead they go work in the shops and cut hair.   The remaining soldiers get more haircuts and go to fancier shops.   The barbers and shopkeepers also go to fancier shops and get more haircuts.   And everyone enjoys many more imported consumer goods.

However, let's suppose that some Kuwaitis are employed growing dates.   Perhaps they export dates.  Perhaps they solely sell dates domestically in competition with imported dates.   When the world price of oil doubles and the exchange value of the Kuwati Dinar doubles as well, the date growers are in trouble.   The prices they receive from exporting dates fall in half.   The price they can get for their dates from domestic retailers also fall in half.   

This would lead a collapse in Kuwait's domestic date industry.    The appreciation of the Kuwati Dinar would therefore need to be less than in the situation where oil is the only traded good.   Dinar expenditures on oil would rise, and Dinar expenditures on dates would fall.   This would be desirable to the degree it would create signals and incentives to shift resources away from date production to oil production.   Again, the assumption in Scott's scenario that the quantity of oil remains constant implies that no additional labor and other resources are needed in the oil industry.    Still, the lower prices of imported consumer goods increases real income, which increases demand in the nontraded goods sector as before.   For Kuwait, it is easy to imagine that the adverse impact of the change in world oil prices on the date industry would have no significant impact on the entire economy.

Of course, other developing economies might be different.   

Anyway, the problem Scott sees is not really that a developing country has a major product with a volatile price.   On the contrary, what nominal GDP targeting does is make the exchange rate and the prices of imported consumer goods adjust rather than wages and other nominal incomes.   The problem Scott really sees is where the product is one with an inelastic supply.    If expenditure on that product increases, there is little possibility of expanding its production by increasing the employment of resources.   Nominal GDP targeting requires that expenditure be reduced elsewhere in the economy to offset the increase.  The signal and incentive to contract output and employment in the rest of the economy to free up resources to expand the product where expenditure increased is inappropriate because it is difficult or impossible in the sector with increased expenditure.  

So, if there is some developing economy where a large portion of its output is oil, copper, diamonds, or gold, and it has substantial output of other traded goods, perhaps local farmers compete with imported grain, then shifts in the world demand for the good with inelastic supply will impact the exchange rate, spending in export and import competing industries.   Spending on the product with inelastic supply will change in terms of the domestic currency, requiring offsetting changes in spending in the rest of the economy. 

What are Banks?

There is a NY Times article about Adnat Admadi's view on banking regulation.   Her focus is on increasing capital requirements.   Like most free bankers, I see increased capital as desirable.   The article mentions that most firms don't have capital requirements at all.   Most firms are mostly funded by equity because lenders insist on it.   According to the article, banks are different because depositors are protected by the government from loss.

And that points to why I see increased capital as desirable.   Before deposit insurance, banks did keep much more capital.   At least in the U.S., it was the introduction of  deposit insurance that resulted in substantial decreases in bank capital ratios.

However, even without deposit insurance, banks were mostly funded by deposits.   Why?

It is because banks are financial intermediaries.   They are not simply suppliers of loans.   The deposits that banks issue to fund loans provide services to depositors.   Traditionally, these were monetary services.

Consider a grocery store.   It buys food products from wholesalers and then sells food, mostly to the final consumers.    The grocery store must finance its operation--the store, equipment, inventory, and so on.   The typical grocery story is mostly financed by equity, I suppose.   But there is no notion that the owners of the grocery store must have equity equal to a substantial portion of total sales of groceries.

A bank also has a building and equipment.   But its total assets also include loans and investments.   These are similar to the grocery store's sales of food.   Further, the deposits the bank uses to fund these assets are more similar to the grocery store's purchases of food from suppliers rather than the instruments issued toequity and debt holders that finance the grocery store.

While bank-issued currency provided important benefits in the past, and could do so in the future, for many years these monetary services involved checkable deposits.     While checkable deposits have come to make up a remarkably small portion of bank liabilities, at least part of the reason has been the development of sweep accounts.   By sweeping funds out of checkable deposits and into something else right before the time they must be reported, banks not only avoid regulation, but money and banking statistics are distorted.

However, there is little doubt banks have long issued deposit liabilities whose primary special characteristic is that they are guaranteed by the government.   Certificates of deposit have a lot in common with commercial paper, but the bank liabilities are guaranteed by the government.

While additional capital for banks is desirable, the key problem with capital requirements is that the purpose of capital should be to serve as a buffer.   That means that the buffer should be used when banks suffer losses.   And so, when a bank has exceptional difficulties, its ample capital buffer should be allowed to decrease without interfering with the continued business of the bank in both issuing deposits and making new sound loans.  Obviously, a bank should then rebuild its capital as it recovers.

Giving discretion to the regulators is probably worse than a strict rule.   During good times, when banks have few loses, so what if loose definitions of capital allow requirements to be met on paper.   And then, when banks are losing money, that is when the regulators get tough and make sure that banks rebuild their capital.   Just when banks should be using the cushion they should have built up during good times, the regulator starts strict enforcement.

The problem with a required capital ratio is that restricting new loans and using the funds to pay down deposits (or accumulating "safe assets" with low capital requirements,) is not desirable.   Of course, if it is only a single small bank in a healthy banking system that must shrink its balance sheet to meet the requirements, the effect on the economy is small.   This is especially true because other banks would be in a position to expand deposits and loans.   If necessary, they could issue new equity to take advantage of the profits from the added business.  

But what happens if many banks are in difficulty at the same time?   Having all banks shrink their balance sheets at the same time is not a good thing.

Further, as mentioned in the article, there will be a constant tendency for financial innovation aimed at getting around the regulation.    If those quasi-banks suffer runs, the run will be to the well-capitalized "safe" banking sector.   Those banks should be rapidly expanding in such a scenario.   Requiring that such banks raise capital (or even postpone paying dividends) will interfere with such a needed expansion.

For example, during the financial crisis of 2008, investment banks were issuing quasi-deposits to fund quasi-mortgage loans.   They were shadow banks.   When there was a loss in confidence, and the quasi-depositors ceased rolling over their overnight funds, they received payment in their conventional checkable accounts and simply held the funds at conventional banks.   Did the supply of money decrease?  Yes, if overnight repurchase agreements issued by investment banks are counted.   Or was it the demand for money increased?   Yes, if only checkable deposits issued by conventional banks count as money.   Regardless, what needed to happen is for conventional banks to expand their deposits and their lending.   Capital requirements made that more difficult.   (Of course, the fact that the commercial banks were also under diversified by being over invested in real estate loans made the problem doubly difficult.)

In my view, rather than requiring banks to fund their asset portfolio with some fixed ratio of capital relative to deposits, a better approach is to make the monetary liabilities that provide the rationale for banking more like equity.  

First, there should be an option clause that allows banks to stop a run.   Banks need to be able to postpone payment, though the banks should pay penalty interest.   In other words, depositors should be compensated for any postponement with bonus interest.  Further, the suspended deposits should be negotiable.   In particular, other banks should be able to accept them for deposit either at par or at a discount.  

Second, if a bank is insolvent, then each depositor should suffer a write down of their deposit balance with  compensation by equity--with the reorganized bank being well-capitalized.   And this reorganization of banks should be rapid.   Days, not months.

Kevin Dowd once explained it well.   Closing failed banks for months or more makes as much sense as wheeling out hospital patients into the street because the hospital has financial problems.

If banks have government deposit insurance, then these changes can be required as a condition of continuing that insurance.   Of course, the real point is that with these sorts of reforms, banks might be able to operate without deposit insurance.    And if banks have no deposit insurance, then they can maintain their own liquidity and capital policies in order to attract depositors.

Further, as soon as we explore systematic issues, the nature of the monetary regime becomes paramount.   A desirable nominal anchor--such as nominal GDP level targeting would help.   Further, avoiding a monetary base that has no nominal risk and a zero nominal yield is also desirable.

A century ago, the nominal anchor was the fixed price of gold, and gold served as a base money with zero nominal risk and a zero nominal yield.   Those days are gone.   The banking system does not need to be  able to withstand a massive shift from everything else to gold, which would require a massive deflation of nominal output and nominal income.  

Yes, a 30 percent capital ratio might make sense with a gold standard.   Maybe it is wise when hand-to-hand paper currency is the fundamental monetary base and central bankers insist on using a nominal interest rate instrument to target inflation.    In my view, those are the policies that need some radical revision.