Caplan on Velocity and Money Demand

Bryan Caplan gave an nice discussion of velocity on Econlog.

He explains that velocity is defined to be V = Y/M, where Y is nominal income and M is the quantity of money.

He then argues that it is better understood as the reciprocal of the amount of money people keep relative to their nominal incomes.

He states:

Velocity is therefore essentially a measure of income-adjusted money demanded.

The only thing I would add is that Alfred Marshall came up with this idea, and called it "k" and in monetary economics we call it the "Cambridge k."

Caplan makes the interesting point that if there were no real output and income, nominal income would be zero and so would velocity. He says that money would still be spent multiple times on whatever assets or remaining goods existed.

Caplan makes a great point that the demand for money (adjusted for income or not) is something about which individuals can make a choice. And it is possible to add up individual money demands to get an aggregate demand to hold money. It isn't obvious how this can be managed for velocity understood as number of times a dollar is spent.

Finally, Caplan brings up the tautology canard:

Economists occasionally dismiss MV=PY as a mere tautology. Whenever I've
taught macroeconomics, however, I've found that it's an immensely useful
tautology.

Caplan is saying that it is useful even if it is a tautology, but I think that it isn't a tautology, and that this can be understood using Caplan's approach.

The equation of exchange follows from the equilibrium condition that the quantity of money is equal to the demand to hold money: Ms = Md.

As Caplan notes,

Md = kY

Where k is the income-adjusted demand for money.

Add the equilibrium condition Ms = Md

And solve for: Ms = kY

k = 1/V (definition)

MsV = Y

Y = Py (definition, nominal income equals the price level multiplied by real income)

M = Ms (convention to drop the "s" on the quantity of money)

And the result is the equation of exchange, MV = Py

So what's up with this notion that it is a tautology? Well, Ms = Md can be understood in two ways.

It is a tautology because all existing money is held by someone. In this sense, to hold money is to "demand" it.

What is the equilibrium condition?

It is that actual money balances must be equal to desired money balances. That is, people hold the money and they want to hold it.

The equilibrium condition is Ms = Md because people will adjust their spending until desired balances equal actual balances.

As Caplan notes, this only holds in the aggregate if nominal income adjusts, and it is certainly plausible that changes in aggregate expenditure will impact both the levels of production and prices, and so y and P.

But don't forget, there is this "liquidity effect" by which attempts to spend away excess money can impact the difference between the nominal yields on other assets and money, causing "k" to adjust. (Think about how a given increase in demand for a good raises its relative price and reduces its quantity demanded.)

In fact, I find it doubtful whether k or V are terribly useful.

Still, these ideas are the fundamental ideas of monetary theory.

It would be nice if all introductory macroeconomics students were as well grounded in these relationships as they are in basic supply and demand.

Money and Credit Confused

No one could be a student of Leland Yeager without having the distinction between money and credit drummed into their thinking.

Money is the medium of exchange. The quantity of money is the amount of money that exists at a point in time.

The demand for money is the amount of money that people want to hold at a point in time. To hold money is to not spend it.

The supply of credit is the amount of funds people want to lend during a period of time.

The demand for credit is the amount of funds that people want to borrow during a period of time.

An increase in the demand for money is not the same thing as an increase in the demand for credit.

An increase in the demand for credit means that households and firms want to borrow more. While it is possible that they want to borrow money in order to hold it, the more likely scenario is that they borrow in order to increase spending on some good or service, including, perhaps some other financial asset.

An increase in the demand for money could result in an increase in the demand for credit. People might borrow money in order to hold it. However, the more likely scenario is that people demanding more money will reduce expenditure out of current income, purchasing fewer other assets, goods, or services. Of course, they could also sell other assets.

An increase in the supply of credit isn't the same thing as an increase in the quantity of money. While it is possible that new money is lent into existence, raising the quantity of money over a period of time while augmenting the supply of credit, it is also possible for the supply of credit to rise without an increase in the quantity of money. Purchases of new corporate bonds by households or firms, for example, adds to the supply of credit without adding to the quantity of money.

Because shifts in the share of the total supply of credit associated with money creation are possible, the quantity of money can rise over a period of time when the supply of credit is shrinking.

There are relationships between the supply and demand for money and the supply and demand for credit, both in disequilibrium and equilibrium. But money and credit are not the same thing.

One of the first rules of monetary economics is to never confuse money and credit.

What is "Tight" or "Loose" Money?

What is "tight money?" What is "loose money?"

Scott Sumner continues to argue that most economists don't have a clue, here and here. I think for the most part this is just more of his frustration with interest rate targeting. The Fed cut its target for the Federal Funds rate over the last year, so money must be loose, right?

Nick Rowe uses simple IS-LM analyis to show how an expansive monetary policy could raise real and nominal interest rates, a point that Scott regularly makes. He then argues that interest rate targeting is a social construction. The theme is that interest rates do not effectively indicate the stance of monetary policy.

I don't use the terms "tight money" or "loose money" very often, but I know what they mean to me.

It's simple. An excess supply, or surplus, of money exists when the quantity of money is greater than the demand to hold money. I suppose I might call that "loose money."

An excess demand, or shortage, of money exists when the quantity of money is less than the demand to hold money. I suppose I might call that "tight money. "

Changed interest rates, nominal or real, play no part in my definition of "loose" or "tight" money. Perhaps loose or tight money will impact nominal or real interests, but the changes in interest rates don't define whether money is loose or tight.

What about changes in some measure of the quantity of money?

An excess supply of money could result from an increase in the quantity of money combined with an unchanged demand to hold money. But it could also result from an unchanged quantity of money and a reduced demand to hold money. Further, it is possible that an excess supply of money could occur when the demand for money is rising. It simply requires that the quantity of money rise by more than the demand to hold money. And finally, an excess supply of money could occur if the quantity of money falls less than the demand to hold money.

The same is true of an excess demand for money. A decrease in the quantity of money, given the demand to hold money, would result in an excess demand for money. However, an increase in the demand for money, with an unchanged quantity of money has the same consequence. If the quantity of money rises, but the amount of money people choose to hold rises by more, an excess demand for money results. Finally, if the quantity of money falls by more than the demand to hold money, there is an excess demand for money.

So, there is no necessary relationship between a change in the quantity of money and whether money is "loose" or "tight." That simple relationship only holds ceteris paribus, that is, if the amount of money people choose to hold is unchanged.

Yes, it is simple. So far.

The problem is that an excess supply or demand for money can result in changes in interest rates, real income, and the price level, all of which impact the demand to hold money.

And that makes things complicated.

"Loose money" is when the quantity of money is greater than what the demand for money would be if interest rates, real income, and the price level are all where they should be.

"Tight money" is when the quantity of money is less than what the demand for money would be if interest rates, real income, and the price level are all where they should be.

And where should interest rates, real income, and the price level be? In my view, there are fundamental supply-side factors that determine where interest rates and real income should be

And the price level? Where the price level "should be" is arbitrary. It depends on the monetary regime.

Perhaps the price level should be consistent with a fixed nominal price for gold. Perhaps the price level should be held constant. My view is that the price level "should" be at a level consistent with slow, steady growth in nominal expenditure.

Watch for further posts on the relationship between "tight" and "loose" money, interest rates, real income, and the price level.

Whose Unemployment Rate?

The New York Times as a great little application that shows the unemployment rates for different demographic groups. Hat Tip to Alex Tabarrok.

For white college-educated males over 45, the average unemployment rate over the last year is 4.1%. (That includes me.)

For white, college-educated males between 15-24, the unemployment rate is 8.4%. (The majority of my students.)

For high school educated males, between 25 and 45, the unemployment rate is 10.2%. It is 8.1% for similar women.

For black males between 15 and 25 without a high school degree, the unemploymen rate is 48.5%. Pretty awful.

Sales of Final Product

Here is the graph for total final sales of domestic product for the last fifty years. Not much different than final sales to domestic purchasers.

Great Diagrams, David!

David Beckworth posted the following diagram regarding U.S. nominal expenditure. This shows the growth rate of nominal expenditures as measured by final sales to domestic purchasers.

The basic pattern is clear. Nominal expenditures were growing at a growing rate during during the sixties and seventies, a period where inflation became a growing problem--The Great Inflation. Nominal expenditure growth came down and "stabilized" during the nineties, the so-called "Great Moderation." Recently, the growth of nominal expenditures turned very negative--the Great Recession.

Some time ago, I picked a nit with Beckworth, arguing in favor of an alternative measure of nominal expenditure, total final sales. The difference between the two is exports. Final sales to domestic purchasers ignores the spending of foreigners on domestic output. David agreed this is a better approach. Scott Sumner advocates using nominal GDP as the more appropriate measure. He argues that nominal output is what really counts.

The difference between final sales and the measures of nominal output is inventory investment. Goods that are produced but not sold are counted as being "purchased" by the firms that produced them. While Sumner and I went back and forth on whether it is better to count that sort of expenditure as something whose aggregate value should be stabilized, all three of the series look pretty much the same with a 50 year time horizon.

Beckworth also looked at nominal expenditures for the OCED.

It is interesting that the pattern is so consistent. He shows the growth rate of nominal GDP here. Leaving aside trade between the OCED and the rest of the world, when aggregated, final sales to domestic purchasers and total final sales should sum to the same amount. The nominal GDP figures include inventory investment.

Beckworth's diagrams have generated a good bit of attention on the blogosphere. Even Paul Krugman took notice! Unfortunately, he used the opportunity to make bad arguments regarding the liquidity trap.

Well, the first step is for economists to understand that stable growth of nominal expenditure is the goal. Convincing them that appropriate monetary institutions can accomplish it is the next step.

What Should the Fed do 2

The third quarter GDP report is out, with a 3.5% growth rate for real GDP.

Of course, I was more interested in the level of total final sales of domestic product. At $14,448 billion, it has now increased for two consecutive quarters. After the slight increase of .62% for the 2nd quarter, there was a 3.4% increase in the third quarter.

However, the 5% trend growth path for total final sales for the third quarter quarter was $15,587 billion, leaving a 9% shortfall.

Even with a 3% noninflationary growth path (starting last year,) total final sales should have been $15,489 billion. So, it was about 7% below what I consider the appropriate target.

If the Fed targeted total final sales one year in the future, then the target for fourth quarter 2010 remains $16,081 billion. That would be a 11% increase from the third quarter level, and a 13% annual growth rate. (Once returned to that growth path, it would continue to increase at a 3% annual rate, consistent with close to zero inflation.)