Quantity theory of money

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

1 The equation of exchange
- 1.1 A rudimentary theory
2 Origins and development of the quantity theory
3 Friedman's restatement
- 3.1 Principles
- 3.2 Decline of testability and applicability
4 Critics
5 See also
6 References
7 External links

[edit] The equation of exchange

In its modern form, the quantity theory builds upon some straightforward mathematics.

$M\cdot V_T =\sum_{i} (p_i\cdot q_i)=\mathbf{p}^\mathrm{T}\cdot\mathbf{q}$

where

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

$V_T\,$ is the transactions' velocity of money, that is the average frequency across all transactions with which a unit of money is spent. This reflects availability of financial institutions, economic variables, and choices made as to how fast people turn over their money. (Some economist prefer to represent this value with the Greek letter “ν”.)

$p_i\,$ and $q_i\,$ are the respective price and quantity of the i-th transaction.

$\mathbf{p}$ is a vector of the $p_i\,$ .

$\mathbf{q}$ is a vector of the $q_i\,$ .

Mainstream economics accepts the simplification:

$M\cdot V_T = P\cdot T$

where

P

is the price level for the economy during the period.

T

is an index of the real value of aggregate transactions.

Most of what could be inferred from this simplification could be found, with greater effort, in the unsimplified first equation.

The previous equation, known as the “transactions form”, presents the difficulty that the associated data are not available. Data for final expenditures are more readily available. Economists may therefore work with the form

$M \cdot V = P \cdot Q$

where

V

is the velocity of money in final expenditures.

Q

is an index of the real value of final expenditures.

For example, $M$ might represent currency plus checking and savings-account money held by the public and $Q$ might represent real output with P the corresponding price level. In one empirical formulation, velocity was defined as “the ratio of net national product in current prices to the money stock”.^[1]

Thus far, the theory is not particularly controversial. But there are questions of the extent to which each of these variables is dependent upon the others.

[edit] A rudimentary theory

The equation of exchange can be used to form a rudimentary theory of inflation.

$P=\frac{M\cdot V}{Q}$

If $V$ and $Q$ were constant, then:

$\Delta P= \Delta M\,$

and thus

$\frac{\Delta P}{\Delta t}=\frac{\Delta M}{\Delta t}$

where

t

is time.

That is to say that, if $V$ and $Q$ were constant, then the inflation rate would exactly equal the growth rate of the money supply.

[edit] Origins and development of the quantity theory

The quantity theory descends from Copernicus,^[2] Jean Bodin,^[3] 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” in the section above was stated by John Stuart Mill^[4] who expanded on the ideas of David Hume.^[5] The quantity theory was developed by Simon Newcomb^[6], Alfred de Foville^[7], Irving Fisher^[8], and Ludwig von Mises^[9] in the latter 19th and early 20th century. It was influentially restated by Milton Friedman in the post-Keynesian era.^[10]

Historically, the main rival of the quantity theory was the real bills doctrine, which says that the real value of money $M$ / $P$ is determined by the assets and liabilities of the money-issuing entity, rather than by the ratio of money to nominal value of output.

[edit] Friedman's restatement

In the 1950s, contending that velocity were technologically determined and relatively stable, Milton Friedman presented two models, intended to be econometrically testable:

$P\cdot Q=f(M) \,\!$

and

$P=g(M)\!$

Friedman and others contended that the first model held relatively well in the short-run (supporting the notion that velocity were stable in the short-run) and that $M$ forecast changes in $P\cdot Q$ (nominal production). The further contended that in the long-run, the second model held relatively well, and that $M$ forecast changes in $P$ , with long-run effects on $Q$ being negligible.

[edit] Principles

The theory above is based on the following hypotheses:

The source of inflation is fundamentally derived from the money supply.
The supply of money is exogenous.
The demand for money is a function of wealth, the rate of return, and the value of liquidity.
The mechanism for injecting money into the economy is not that important in the long run.
The real interest rate is determined by non-monetary factors: (productivity of capital, time preference).

[edit] 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. 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.

[edit] Critics

Critics point to several principles presented above.

Money supply is endogeneous, as money is created by banks and other financial institutions in relation to a general optimism on the future return of investments. Private supply of money fluctuates in the short and long term and the central bank can only try to level off these fluctuations but has no control on the amount of supply of money. Indeed all central banks have failed in their attempts to target a given monetary growth.

There can be huge variation in the stock of goods (especially production goods), goods produced in former period, and held and not consumed by economic agents. Whether economic agents try to add to their stock of goods or to unload it, it has an impact on the number of transactions for a given level of production (flow) and hence on inflation-deflation. Thus money demand also depends on expectations. If consumers expect both a rising consumption and rising prices they tend to add to their stocks, stocks rotate faster, there are more transactions, money demand is higher, and for a given money supply, deflation happens.

Expectations are hence crucially important as optimism may lead to both higher money supply and higher money demand and pessimism to both lower money supply and money demand.

Private money supply often overreacts to money demand through credit booms and credit bust, just as investment overreacts variation in the demand of final goods in the real sphere, hence the central bankers must try to keep things stable and regulation of the finance industry is to be advocated.

Finally, for a given money supply, inflation can happen in consumption good prices or in production good prices (assets), and this depends from the relative strength of labor and management of the labor market.

[edit] See also

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

[edit] References

^ Friedman, Milton and Schwartz, Anna J. (1965). The Great Contraction 1929–1933. Princeton: Princeton University Press. ISBN 0-691-00350-5.
^ Copernicus, Nicolas; memorandum on monetary policy written in 1517.
^ Bodin, Jean; Responses aux paradoxes du sieur de Malestroict (1568).
^ Mill, John Stuart; Principles of Political Economy (1848).
^ Hume, David; “Of Interest” in Essays Moral and Political.
^ Newcomb, Simon; Principles of Political Economy (1885).
^ de Foville, Alfred; La Monnaie (1907).
^ Fisher, Irving; Purchasing Power of Money (1911).
^ von Mises, Ludwig Heinrich; Theorie des Geldes und der Umlaufsmittel [The Theory of Money and Credit] (1912).
^ Friedman, Milton; “The Quantity Theory of Money: A Restatement” in Studies in the Quantity Theory of Money (1956), edited by M. Friedman.