Velocity (of Money)

In economics, the quantity theory of money is a theory emphasizing the positive relationship of overall prices or the nominal value of expenditures to the quantity of money.

Origins and development of the quantity theory

The quantity theory descends from Copernicus,^[1] Jean Bodin,^[2] and various others who noted the increase in prices following the import of gold and silver, used in the coinage of money, from the New World, and the accompanying increase in prices. The “equation of exchange” relating the supply of money to the value of money transactions was stated by John Stuart Mill^[3] who expanded on the ideas of David Hume.^[4] The quantity theory was developed by Simon Newcomb,^[5] Alfred de Foville,^[6] and Irving Fisher^[7] in the latter 19th and early 20th century. It was influentially restated by Milton Friedman in the post-Keynesian era.^[8] Ludwig von Mises^[9] developed the value theory of money that does not rely only on changes in the quantity of money but also the demand for money. This significantly set Mises apart from monetarists.

Historically, the main rival of the quantity theory was the real bills doctrine, which says that the issue of money does not raise prices, as long as the new money is issued in exchange for assets of sufficient value.^[10]

Equation of exchange

In its modern form, the quantity theory builds upon the following definitional relationship.

where

is the total amount of money in circulation on average in an economy during the period, say a year.

is the transactions' velocity of money, that is the average frequency across all transactions with which a unit of money is spent. It is derived from the other values in the equation.

and are the price and quantity of the i-th transaction.

is a vector of the .

is a vector of the .

A common simplification is the following equation of exchange:

where

P_T is the price level associated with transactions for the economy during the period

T is an index of the real value of aggregate transactions.

The previous equation presents the difficulty that the associated data are not available for all transactions. With the development of national income and product accounts, emphasis shifted to national-income or final-product transactions, rather than gross transactions. Economists may therefore work with the form

where

V is the velocity of money in final expenditures.

Q is an index of the real value of final expenditures.

This equation, like the previous one, holds, because V is constructed to make the two sides equal.

As an example, M might represent currency plus checking and savings-account money held by the public, Q real output with P the corresponding price level, and PQ the nominal (money) value of output. In one empirical formulation, velocity was defined as “the ratio of net national product in current prices to the money stock.”^[11]

As a definitional relationship, the equation of exchange is not controversial. But without further restrictions, it does require that change in the money supply would change the value of any or all of P, Q, or PQ. For example, a 10% increase in M could be accompanied by a 10% decrease in V, leaving PQ unchanged.

Quantity theory and evidence

The quantity theory emphasizes the following relationship of the nominal value of expenditures PQ and the price level P to the quantity of money M:

The plus signs indicate that a change in the money supply is hypothesized to change nominal expenditures and the price level in <the same direction (for other variables held constant).

Milton Friedman has described the empirical regularity of substantial changes in the quantity of money and in the level of prices as perhaps the most-evidenced economic phenomenon on record.^[12] Empirical studies have found relations consistent with the models above and with causation running from money to prices. The short-run relation of a change in the money supply in the past has been relatively more associated with a change in real output Q than the price level P in (1) but with much variation. For the long-run, there has been still stronger support for (1) and (2) and no systematic association of Q and M.^[13]

Principles

The theory above is based on the following hypotheses:

1. The source of inflation is fundamentally derived from the growth rate of the money supply.
2. The supply of money is exogenous.
3. The demand for money, as reflected in its velocity is a stable function of nominal income, interest rates, and so forth.
4. The mechanism for injecting money into the economy is not that important in the long run.
5. The real interest rate is determined by non-monetary factors: (productivity of capital, time preference).

Decline of testability and applicability

The practical identification and measurement of a relevant money supply was always somewhat controversial and difficult. As financial intermediation grew in complexity and sophistication in the 1980s and 1990s, it became greatly more so. On top of this, with the rapid growth of financial markets, transactions on capital goods have become a major source of money demand. In the face of these events, the reliance on the national income and product accounts as a proxy of all transactions has become flawed. For these reasons, many economists who had come to accept Friedman's theory and work came to believe that, in the face of these greater difficulties, it had lost much of its practical efficacy.

Critics

Critics draw attention to several potentially problematic aspects of the above.

1 Money supply is endogenous.

It is created by banks and other financial institutions on the basis of expectations about the solvability of debtors. Those expectations depend of the debt level and the expectations in the future growth of debtors revenues and debtors wealth. Money creation is thus subject to herding behavior. Banks often trap their regulators. Therefore no exogenous control of money creation can be efficient. Private supply of money fluctuates in the short and long term. Central banks can only try to smooth these fluctuations. When central banks tried to adopt growth objectives for the monetary aggregates in the 1980's, they had trouble achieving their targets; they soon chose to target consumption goods inflation rates instead.

2 Speculation, reserve and transactions on capital goods are important sources of money demand.

Money can be needed for other purpose than transactions. Agents prefer money to bonds and other financial instruments when interests rates are expected to rise. Agents ask for money according to their expectations about future economic activity. Agents need money to buy financial instruments (stocks, bonds) and capital goods (land, houses, machinery). By moving from an equation of exchange including all transactions to one including only transactions on final products, all transactions on capital goods are hidden from view. This of course goes hand in hand with defining inflation by reference to a consumer price index, excluding a capital good price index.

3 The mechanism for injecting money is very important:

Endogenous money supply through private lending often overreacts to money demand. During a boom, too much credit money is generated, this money is then destroyed during the bust. Endogenous money creation amplifies the fluctuations in the real sphere and leads to severe misallocation of funds.

Contrary to credit based money, fiat money emitted by central bankers is not destroyed during a bust.

Therefore in order to ensure some stability, central bankers must continue to supply directly a decent share of money supply and must enforce strong regulation of the finance industry. Piloting endogenous money creation through the use of interest rate can only be efficient during a long term boom of credit as it requires a constant growth in credit based money supply.

Notes

1. ^ Nicolaus Copernicus (1517), memorandum on monetary policy.
2. ^ Jean Bodin, Responses aux paradoxes du sieur de Malestroict (1568).
3. ^ John Stuart Mill (1848), Principles of Political Economy.
4. ^ David Hume (1748), “Of Interest,” "Of Interest" in Essays Moral and Political.
5. ^ Simon Newcomb (1885), Principles of Political Economy.
6. ^ Alfred de Foville (1907), La Monnaie.
7. ^ Irving Fisher (1911), The Purchasing Power of Money.
8. ^ Milton Friedman (1956), “The Quantity Theory of Money: A Restatement” in Studies in the Quantity Theory of Money, edited by M. Friedman.
9. ^ Ludwig von Mises [1981 [1912], 3rd English ed.), The Theory of Money and Credit
10. ^ Roy Green (1987), “real bills dcctrine”, in The New Palgrave: A Dictionary of Economics, v. 4, pp. 101-02.
11. ^ Milton Friedman, and Anna J. Schwartz, (1965). The Great Contraction 1929–1933. Princeton: Princeton University Press. ISBN 0-691-00350-5. 
12. ^ Milton Friedman (1987), “quantity theory of money”, The New Palgrave: A Dictionary of Economics, v. 4, p. 15.
13. ^ Summarized in Friedman (1987), “quantity theory of money”, The New Palgrave: A Dictionary of Economics, v. 4, pp. 15-17.

References

• Friedman, Milton (1987). “quantity theory of money”, The New Palgrave: A Dictionary of Economics, v. 4, pp. 3-20.
• Rothbard, Murray Newton (1963). America's Great Depression.

See also

• Benjamin Anderson (critic of mainstream variant)
• Classical dichotomy
• Equation of exchange
• Income velocity of money
• Liquidity preference
• Monetarism
• Monetary Disequilibrium Theory
• Monetary policy
• Money illusion
• Neutrality of money

External links

• The Quantity Theory of Money from John Stuart Mill through Irving Fisher from the New School
• “Quantity theory of money” at Formularium.org — calculate M, V, P and Q with your own values to understand the equation
• How to Cure Inflation (from a Quantity Theory of Money perspective) from Aplia Econ Blog

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