No Such Thing as a Free Lunch: Principles of Economics (Part 167)

We need to have a pro-growth policy put in place that offers people hope and offers the opportunity for businesses to expand and for them to have confidence in what the world is going to look like for the next two or three or four years with respect to economic policy.

Dick Cheney

Debates in Macroeconomics

(Part B)

by 

Charles Lamson

The Quantity Theory of Money

Recall from the end of last post that in practice, we use gross domestic product (GDP), instead of the total value of all transactions in the economy, to measure velocity, because GDP data are more available. The income velocity of money (V) is the ratio of nominal GDP to the stock of money (M):

V ☰ GDP/M

The triple equal sign indicates we are dealing with an identity which is something that is true all the time. If $6 trillion worth of final goods and services are produced in a year and if the money stock is $1 trillion, then the velocity of money is $6 trillion/$1 trillion, or 6.0.

We can expand this definition slightly by noting that nominal income (GDP) is equal to real output (income) (Y) * the overall price level (P):

GDP ☰ P * Y

Through substitution:

V ☰ P * Y / M

or

M * V ☰ P * Y

At this point, it is worth pausing to ask if our definition has provided us with any insights into the workings of the economy. The answer is no. Because we defined V as the ratio of GDP to the money supply, the statement M * V ☰ P * Y is an identity---it is true by definition. It contains no more useful information than the statement "a bachelor is an unmarried man." The definition does not, for example, say anything about what will happen to P x Y when M changes. The final value of P x Y depends on what happens to V. If V falls when M increases, the product M x V could stay the same, in which case the change in M would have had no effect on nominal income. To give monetarism some economic content, we turn to a simpler version of monetarism known as the quantity theory of money. 

The key is whether the velocity of money is really constant. Early economists believed the velocity of money was determined largely by institutional considerations, such as how often people are paid and how the banking system clears transactions between banks. Because these factors change gradually, early economists believed velocity was essentially constant.

If there is equilibrium in the money market, then the quantity of money supplied is equal to the quantity of money demanded. That could mean M in the quantity theory equation equals both the quantity of money supplied and the quantity of money demanded. If the quantity-theory equation is looked on as a demand-for-money equation, it says that the demand for money depends on nominal income (GDP, or P x Y), but not on the interest rate. If the interest rate changes and nominal income does not, the equation says that the quantity of money demanded will not change. This is contrary to the theory of the demand for money in parts 125 and 126 of this analysis, which had the demand for money depending on both income and the interest rate.

Testing the Quantity Theory of Money One way to test the validity of the quantity theory of money is to look at the demand for money using recent data on the U.S. economy. The key is: does money demand depend on the interest rate? Most empirical work says yes. When demand for money equations are estimated (or "fit to the data"), the interest rate usually turns out to be a factor. The demand for money does not appear to depend only on nominal income.

The debate over monetarist theories is more subtle than our discussion so far indicates. First, there are many definitions of the money supply. M1 is a narrow measure of the money supply that includes physical currency, demand deposits, traveler's checks, and other checkable deposits. M1 does not include financial assets, such as savings accounts and bonds. M2 includes both checking accounts and money market accounts.

Second, there may be a time lag between a change in the money supply and its effects on nominal GDP. Suppose we experience a 10 percent increase in the money supply today, but it takes 1 year for nominal GDP to increase by 10 percent. If we measured the ratio of today's money supply to today's GDP, it would seem that velocity had fallen by 10 percent. However if we measured today's money supply against GDP 1 year from now, when the increase in the supply of money had its full effect on income, then velocity would have been constant.

The debate over the usefulness of monetary theory is primarily empirical. It is a debate that can be resolved by looking at the facts about the real world and seeing whether they are in accord with the predictions of theory. Is there a measure of the money supply and a choice of the time lag between a change in the money supply and its effects on nominal GDP such that V is in effect constant? If so, then the monetarist theory is a useful approach to understanding how the macroeconomy works. If not, then some other theory is likely to be more appropriate.

*CASE & FAIR, 2004, PRINCIPLES OF ECONOMICS, 7TH ED., PP. 651-652*

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