In
monetary economics, the
quantity theory of money is the theory that
money supply has a direct, positive
relationship with the price level.
The theory was challenged by
Keynesian economics, but updated and
reinvigorated by
the monetarist school of
economics. While mainstream economists agree that the quantity
theory holds true in the
long-run, there is
still disagreement about its applicability in the
short-run. Critics of the theory argue that money
velocity is not stable and, in the short-run, prices are
sticky, so the direct relationship between
money supply and price level does not hold.
Alternative theories include the
real bills doctrine and the more recent
fiscal theory of the
price level.
Origins and development of the quantity theory
The quantity theory descends from
Copernicus, followers of the
School of Salamanca,
Jean Bodin,, 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.
The “equation of exchange” relating the supply of money to the
value of money transactions was stated by
John Stuart Mill who expanded on the ideas
of
David Hume. The quantity theory was
developed by
Simon Newcomb,
Alfred de Foville,
Irving Fisher, and
Ludwig von Misesvon Mises, Ludwig Heinrich;
Theorie des
Geldes und der Umlaufsmittel [''The Theory of Money and
Credit''] in the latter 19th and early 20th century. It was
influentially restated by
Milton
Friedman in the post-
Keynesian
era.
Academic discussion remains over the degree to which different
figures developed the theory. For instance, Bieda argues that
Copernicus's observation
amounts to a statement of the theory, while other economic
historians date the discovery later, to figures such as
Jean Bodin,
David Hume,
and
John Stuart Mill.
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.
Equation of exchange
In its modern form, the quantity theory builds upon the following
definitional relationship.
- 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.
- p_i\, and q_i\, are the 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 a simplification, the
equation of exchange:
- M\cdot V_T = P_T\cdot T
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
- 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.
As an example, M might represent currency plus deposits in checking
and savings accounts held by the public, Q real output with P the
corresponding price level, and P\cdot Q the nominal (money) value
of output. In one empirical formulation, velocity was taken to be
“the ratio of net national product in current prices to the money
stock”.
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. Without further restrictions, it does
not require that change in the money supply would change the value
of any or all of P, Q, or P\cdot Q. For example, a 10% increase in
M could be accompanied by a 10% decrease in V, leaving P\cdot Q
unchanged.
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:
- \frac{d P}{P}= \frac{d M}{M}
and thus
- \frac{d P/P}{d t}=\frac{d M/M}{d 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.
Cambridge approach
Economists
Alfred Marshall,
A.C. Pigou, and John Maynard Keynes (before he developed
his own, eponymous school of thought) associated with Cambridge
University, took a slightly different approach to the quantity
theory, focusing on money demand instead of money supply.
They argued that a certain portion of the money supply will not be
used for transactions; instead, it will be held for the convenience
and security of having cash on hand. This portion of cash is
commonly represented as
k, a portion of nominal income (P
\cdot Y). The Cambridge economists also thought wealth would play a
role, but wealth is often omitted for simplicity. The Cambridge
equation is thus:
- M^{\textit{d}}=\textit{k} \cdot P\cdot Y
Assuming that the economy is at equilibrium (M^{\textit{d}} = M), Y
is exogenous, and
k is fixed in the short run, the
Cambridge equation is equivalent to the equation of exchange with
velocity equal to the inverse of
k:
- M\cdot\frac{1}{k} = P\cdot Y
The Cambridge version of the quantity theory led to both Keynes's
attack on the quantity theory and the Monetarist revival of the
theory.
Quantity theory and evidence
As restated by Milton Friedman, 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 :
- (1) PQ={f}(\overset{+}M)
- (2) P={g}(\overset{+}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).
Friedman 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.
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 in the precision, timing, and size of the relation. For
the
long-run, there has been stronger support for (1) and
(2) and no systematic association of Q and M.
Principles
The theory above is based on the following hypotheses:
- The source of inflation is
fundamentally derived from the growth rate of the money
supply.
- The supply of money is exogenous.
- The demand for money, as reflected in its velocity, is a stable
function of nominal income, interest rates, and so forth.
- 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).
Decline of money-supply targeting
An application of the quantity-theory approach aimed at removing
monetary policy as a source of
macroeconomic instability was to target a constant, low growth rate
of the money supply. Still, practical identification of the
relevant
money supply, including
measurement, was always somewhat controversial and difficult. As
financial intermediation grew
in complexity and sophistication in the 1980s and 1990s, it became
more so. As a result, some
central
banks, including the U.S.
Federal
Reserve, which had targeted the money supply, reverted to
targeting interest rates. But monetary aggregates remain a
leading economic indicator. with
"some evidence that the linkages between money and economic
activity arerobust even at relatively short-run frequencies."
Criticism
The theory attracted criticism from
John Maynard Keynes, particularly in his
work
General Theory.
References
- Friedman, Milton (1987 [2008]). “quantity
theory of money”, The New Palgrave: A
Dictionary of Economics, v. 4, pp. 3-20. Abstract. Arrow-page searchable preview at John Eatwell et al.(1989),
Money: The New Palgrave, pp. 1-40.
- Laidler, David E.W. (1991).
The Golden Age of the Quantity Theory: The Development of
Neoclassical Monetary Economics, 1870-1914. Princeton UP.
Description and review.
- Mises, Ludwig Heinrich Edler von; Human Action: A Treatise
on Economics (1949), Ch. XVII “Indirect Exchange”, §4. “The
Determination of the Purchasing Power of Money”.
- Minksy, H “John Maynard Keynes”, Mc Graw-Hill Professional,
2008 p.2
- Nicolaus Copernicus (1517), memorandum on monetary policy.
- Jean Bodin, Responses aux paradoxes du sieur de
Malestroict (1568).
- John Stuart Mill (1848), Principles of Political
Economy.
- David Hume (1748), “Of Interest,” "Of Interest" in Essays
Moral and Political.
- Simon Newcomb (1885), Principles of Political
Economy.
- Alfred de Foville (1907), La Monnaie.
- Irving Fisher (1911), The Purchasing Power of
Money,
- Milton Friedman (1956), “The Quantity Theory of Money: A
Restatement” in Studies in the Quantity Theory of Money,
edited by M. Friedman. Reprinted in M. Friedman The Optimum
Quantity of Money (2005), pp. 51- 67.
- Roy Green (1987), “real bills dcctrine”, in The New
Palgrave: A Dictionary of Economics, v. 4, pp. 101-02.
- Froyen, Richard T. Macroeconomics: Theories and
Policies. 3rd Edition. Macmillan Publishing Company: New York,
1990. p. 70-71.
- Milton Friedman (1987), “quantity theory of money”,
The New
Palgrave: A Dictionary of Economics, v. 4, p. 15.
- Summarized in Friedman (1987), “quantity theory of money”, pp.
15-17.
- Friedman (1987), “quantity theory of money”, p. 19.
- NA (2005), How Does the Fed Determine Interest Rates to Control
the Money Supply?”, Federal Reserve Bank of San Francisco.
February,[1]
- R.W. Hafer and David C. Wheelock (2001), “The Rise and Fall of a Policy Rule: Monetarism at
the St. Louis Fed, 1968-1986”, Federal Reserve Bank of St.
Louis, Review, January/February, p. 19.
See also
Alternative theories
External links