Quantity Theory of Money

The quantity theory of money is the proposition that the general price level is determined mainly by the amount of money in circulation, so that a sustained increase in the money supply faster than the growth of real output leads to inflation. It is usually written as the equation of exchange, $MV = PY$, linking money, its rate of turnover, prices and output. The idea is one of the oldest in economics and underpins monetarism.

Versions of the theory were set out by thinkers including Nicolaus Copernicus, Jean Bodin and David Hume, and given its modern form by Irving Fisher in 1911 and Milton Friedman from the 1950s. Most economists accept a long-run link between money growth and inflation, especially in hyperinflation, but dispute how useful the theory is for short-run policy because the velocity of money is unstable.

Picture an island economy that produces a fixed number of coconuts each year and uses shells as money. If the islanders suddenly find a beach covered in shells and double the number in circulation, while the coconut harvest stays the same, sellers soon ask for more shells per coconut. Prices roughly double, and nobody is richer in coconuts.

The quantity theory says the same happens in modern economies: if the amount of money grows much faster than the goods and services available to buy, the main result is higher prices rather than more stuff. The complication is that people do not always spend money at the same speed, so the link is loose in the short run.

The theory starts from an identity:

• $M$ is the money stock, for example broad money (M2).
• $V$ is the income velocity of money, the average number of times each unit is spent on final output in a year.
• $P$ is the price level, such as the GDP deflator.
• $Y$ is real output, real gross domestic product (GDP), so $P \times Y$ is nominal GDP.

In growth rates it becomes approximately $\%\Delta M + \%\Delta V \approx \%\Delta P + \%\Delta Y$. The identity becomes a theory when one assumes that velocity is stable and that output is set by real factors such as labour and technology. Then money growth beyond output growth shows up as inflation.

Worked example: if the money supply grows 10% a year, velocity is constant and real output grows 3%, the theory predicts inflation of about $10\% + 0\% - 3\% = 7\%$. If instead velocity falls 5% because people hoard money, inflation would be only about 2%.

The theory emerged from experience. The flood of silver from the Americas into Europe in the sixteenth century coincided with a long rise in prices called the Price Revolution, which Jean Bodin attributed in 1568 to the abundance of precious metals. David Hume's 1752 essay "Of Money" argued that the quantity of money affects prices in the long run but can stimulate activity during the transition. Irving Fisher formalised the equation of exchange in The Purchasing Power of Money (1911). The Cambridge economists Alfred Marshall and Arthur Pigou developed an alternative version based on how much money people wish to hold, $M = kPY$, where $k$ is the inverse of velocity.

Milton Friedman restated the theory in 1956 as a theory of money demand, and with Anna Schwartz argued in A Monetary History of the United States (1963) that the contraction of money caused the depth of the Great Depression. His conclusion that "inflation is always and everywhere a monetary phenomenon" influenced central banks in the 1970s and 1980s.

In the late 1970s and early 1980s several central banks, including the Federal Reserve under Paul Volcker, the Bank of England and the Bundesbank, adopted targets for money growth. The approach worked poorly in many countries because financial innovation and deregulation made velocity unpredictable, breaking the stable link the theory needed. By the 1990s most central banks had moved to inflation targeting and steering the nominal interest rate, often guided by the Taylor rule. The ECB kept a "monetary pillar" in its strategy, now folded into its monetary and financial analysis.

The theory faced a second test after 2008. Large-scale quantitative easing (QE) greatly expanded central-bank money, yet inflation stayed low for a decade, partly because the extra reserve money sat in bank reserves and broad money and velocity moved differently. Then in 2020–2021 US broad money grew by about 40% over two years and inflation rose sharply in 2021–2022, which some economists cited as vindication and others attributed mainly to supply shocks and fiscal stimulus.

• Unstable velocity. Velocity changes with interest rates, confidence and payment technology, so the money–price link is weak at low inflation.
• Causation. Post-Keynesian and endogenous-money economists argue that money is created by bank lending in response to demand, so money growth may follow prices rather than cause them; see credit expansion.
• Output is not fixed. With sticky prices, more money can raise output in the short run, so the theory's neutrality holds only over long horizons.
• Liquidity traps. In a liquidity trap, extra money may be held rather than spent, as Keynesian economics emphasises.

Even critics generally accept the theory's core message for extreme cases: episodes of very high inflation, such as Zimbabwe in 2007–2008 or Weimar Germany in 1923, were accompanied by rapid money creation to fund governments.

• Federal Reserve: Money Stock Measures (H.6)
• European Central Bank: Monetary policy strategy