Quantity theory of money

Quantity theory of money

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In monetary economics, the quantity theory of money is the theory that money supply
Money supply
In economics, the money supply or money stock, is the total amount of money available in an economy at a specific time. There are several ways to define "money," but standard measures usually include currency in circulation and demand deposits .Money supply data are recorded and published, usually...

 has a direct, proportional relationship with the price level.

The theory was challenged by Keynesian economics
Keynesian economics
Keynesian economics is a school of macroeconomic thought based on the ideas of 20th-century English economist John Maynard Keynes.Keynesian economics argues that private sector decisions sometimes lead to inefficient macroeconomic outcomes and, therefore, advocates active policy responses by the...

, but updated and reinvigorated by the monetarist school of economics
Monetarism
Monetarism is a tendency in economic thought that emphasizes the role of governments in controlling the amount of money in circulation. It is the view within monetary economics that variation in the money supply has major influences on national output in the short run and the price level over...

. 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
Real bills doctrine
The real bills doctrine holds that issuing money in exchange for real bills is not inflationary. It is best known as "the decried doctrine of the old Bank Directors of 1810: that so long as a bank issues its notes only in the discount of good bills, at not more than sixty days’ date, it cannot go...

 and the more recent fiscal theory of the price level
Fiscal theory of the price level
The fiscal theory of the price level is the idea that government fiscal policy affects the price level: for the price level to be stable , government finances must be sustainable: they must run a balanced budget over the course of the business cycle, meaning they must not run a structural...

.

Origins and development of the quantity theory


The quantity theory descends from Copernicus, followers of the School of Salamanca
School of Salamanca
The School of Salamanca is the renaissance of thought in diverse intellectual areas by Spanish and Portuguese theologians, rooted in the intellectual and pedagogical work of Francisco de Vitoria...

, Jean Bodin
Jean Bodin
Jean Bodin was a French jurist and political philosopher, member of the Parlement of Paris and professor of law in Toulouse. He is best known for his theory of sovereignty; he was also an influential writer on demonology....

, 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
New World
The New World is one of the names used for the Western Hemisphere, specifically America and sometimes Oceania . The term originated in the late 15th century, when America had been recently discovered by European explorers, expanding the geographical horizon of the people of the European middle...

. The “equation of exchange” relating the supply of money to the value of money transactions was stated by John Stuart Mill
John Stuart Mill
John Stuart Mill was a British philosopher, economist and civil servant. An influential contributor to social theory, political theory, and political economy, his conception of liberty justified the freedom of the individual in opposition to unlimited state control. He was a proponent of...

 who expanded on the ideas of David Hume
David Hume
David Hume was a Scottish philosopher, historian, economist, and essayist, known especially for his philosophical empiricism and skepticism. He was one of the most important figures in the history of Western philosophy and the Scottish Enlightenment...

. The quantity theory was developed by Simon Newcomb
Simon Newcomb
Simon Newcomb was a Canadian-American astronomer and mathematician. Though he had little conventional schooling, he made important contributions to timekeeping as well as writing on economics and statistics and authoring a science fiction novel.-Early life:Simon Newcomb was born in the town of...

, Alfred de Foville, Irving Fisher
Irving Fisher
Irving Fisher was an American economist, inventor, and health campaigner, and one of the earliest American neoclassical economists, though his later work on debt deflation often regarded as belonging instead to the Post-Keynesian school.Fisher made important contributions to utility theory and...

, and Ludwig von Mises
Ludwig von Mises
Ludwig Heinrich Edler von Mises was an Austrian economist, philosopher, and classical liberal who had a significant influence on the modern Libertarian movement and the "Austrian School" of economic thought.-Biography:-Early life:...

 in the latter 19th and early 20th century, and was argued against by Karl Marx
Karl Marx
Karl Heinrich Marx was a German philosopher, economist, sociologist, historian, journalist, and revolutionary socialist. His ideas played a significant role in the development of social science and the socialist political movement...

. The theory was influentially restated by Milton Friedman
Milton Friedman
Milton Friedman was an American economist, statistician, academic, and author who taught at the University of Chicago for more than three decades...

 in response to Keynesianism.

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
Jean Bodin
Jean Bodin was a French jurist and political philosopher, member of the Parlement of Paris and professor of law in Toulouse. He is best known for his theory of sovereignty; he was also an influential writer on demonology....

, David Hume
David Hume
David Hume was a Scottish philosopher, historian, economist, and essayist, known especially for his philosophical empiricism and skepticism. He was one of the most important figures in the history of Western philosophy and the Scottish Enlightenment...

, and John Stuart Mill
John Stuart Mill
John Stuart Mill was a British philosopher, economist and civil servant. An influential contributor to social theory, political theory, and political economy, his conception of liberty justified the freedom of the individual in opposition to unlimited state control. He was a proponent of...

.

Historically, the main rival of the quantity theory was the real bills doctrine
Real bills doctrine
The real bills doctrine holds that issuing money in exchange for real bills is not inflationary. It is best known as "the decried doctrine of the old Bank Directors of 1810: that so long as a bank issues its notes only in the discount of good bills, at not more than sixty days’ date, it cannot go...

, 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.
where is the total amount of money
Money supply
In economics, the money supply or money stock, is the total amount of money available in an economy at a specific time. There are several ways to define "money," but standard measures usually include currency in circulation and demand deposits .Money supply data are recorded and published, usually...

 in circulation on average in an economy during the period, say a year. is the transactions velocity of money
Velocity of money
300px|thumb|Similar chart showing the velocity of a broader measure of money that covers M2 plus large institutional deposits, M3. The US no longer publishes official M3 measures, so the chart only runs through 2005....

, 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. and are the price and quantity of the i-th transaction. is a column vector of the , and the superscript T is the transpose
Transpose
In linear algebra, the transpose of a matrix A is another matrix AT created by any one of the following equivalent actions:...

 operator. is a column vector of the .

Mainstream economics accepts a simplification, the equation of exchange
Equation of exchange
In economics, the equation of exchange is the relation:M\cdot V = P\cdot Qwhere, for a given period,M\, is the total nominal amount of money in circulation on average in an economy.V\, is the velocity of money, that is the average frequency with which a unit of money is spent.P\, is the price...

:
where is the price level
Price level
A price level is a hypothetical measure of overall prices for some set of goods and services, in a given region during a given interval, normalized relative to some base set...

 associated with transactions for the economy during the period 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
National Income and Product Accounts
The National Income and Product Accounts are part of the national accounts of the United States. They are produced by the Bureau of Economic Analysis of the Department of Commerce...

, emphasis shifted to national-income or final-product transactions, rather than gross transactions. Economists may therefore work with the form
where is the velocity of money
Velocity of money
300px|thumb|Similar chart showing the velocity of a broader measure of money that covers M2 plus large institutional deposits, M3. The US no longer publishes official M3 measures, so the chart only runs through 2005....

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

As an example, might represent currency plus deposits in checking and savings accounts held by the public, real output (which equals real expenditure in macroeconomic equilibrium) with the corresponding price level, and 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, as the equation of exchange is an identity. A theory requires that assumptions be made about the causal relationships among the four variables in this one equation. There are debates about the extent to which each of these variables is dependent upon the others. Without further restrictions, the equation does not require that a change in the money supply would change the value of any or all of , , or . For example, a 10% increase in could be accompanied by a 10% decrease in , leaving unchanged. The quantity theory postulates that the primary causal effect is an effect of M on P.

A rudimentary version of the quantity theory


The equation of exchange can be used to form a rudimentary version of the quantity theory of the effect of monetary growth on inflation
Inflation
In economics, inflation is a rise in the general level of prices of goods and services in an economy over a period of time.When the general price level rises, each unit of currency buys fewer goods and services. Consequently, inflation also reflects an erosion in the purchasing power of money – a...

.
If and were constant, then:
and thus
where is time.
That is to say that, if and were constant, then the inflation rate (the rate of growth of the price level) would exactly equal the growth rate of the money supply. In short, the inflation rate is a function of the monetary growth rate.

Less restrictively, with time-varying V and Q, we have the identity


which says that the inflation rate equals the monetary growth rate plus the growth rate of the velocity of money minus the growth rate of real expenditure. If one makes the quantity theory assumptions that, at least in the long run, (i) the monetary growth rate is controlled by the central bank, (ii) the growth rate of velocity is purely determined by the evolution of payments mechanisms, and (iii) the growth rate of real expenditure is determined by the rate of technological progress plus the rate of labor force growth, then while the inflation rate need not equal the monetary growth rate, an x percentage point rise in the monetary growth rate will result in an x percentage point rise in the inflation rate.

Cambridge approach



Economists Alfred Marshall
Alfred Marshall
Alfred Marshall was an Englishman and one of the most influential economists of his time. His book, Principles of Economics , was the dominant economic textbook in England for many years...

, A.C. Pigou, and John Maynard Keynes
John Maynard Keynes
John Maynard Keynes, Baron Keynes of Tilton, CB FBA , was a British economist whose ideas have profoundly affected the theory and practice of modern macroeconomics, as well as the economic policies of governments...

 (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 (). The Cambridge economists also thought wealth would play a role, but wealth is often omitted for simplicity. The Cambridge equation is thus:


Assuming that the economy is at equilibrium (), 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:


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 and the price level to the quantity of money :


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
Ceteris paribus
or is a Latin phrase, literally translated as "with other things the same," or "all other things being equal or held constant." It is an example of an ablative absolute and is commonly rendered in English as "all other things being equal." A prediction, or a statement about causal or logical...

).

Friedman described the empirical
Empirical
The word empirical denotes information gained by means of observation or experimentation. Empirical data are data produced by an experiment or observation....

 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
Empirical
The word empirical denotes information gained by means of observation or experimentation. Empirical data are data produced by an experiment or observation....

 studies have found relations consistent with the models
Model (economics)
In economics, a model is a theoretical construct that represents economic processes by a set of variables and a set of logical and/or quantitative relationships between them. The economic model is a simplified framework designed to illustrate complex processes, often but not always using...

 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 than the price level 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 and .

Principles


The theory above is based on the following hypotheses:
  1. The source of inflation
    Inflation
    In economics, inflation is a rise in the general level of prices of goods and services in an economy over a period of time.When the general price level rises, each unit of currency buys fewer goods and services. Consequently, inflation also reflects an erosion in the purchasing power of money – a...

     is fundamentally derived from the growth rate of the money supply.
  2. The supply of money is exogenous
    Exogenous
    Exogenous refers to an action or object coming from outside a system. It is the opposite of endogenous, something generated from within the system....

    .
  3. The demand for money, as reflected in its velocity, is a stable function of nominal income
    Income
    Income is the consumption and savings opportunity gained by an entity within a specified time frame, which is generally expressed in monetary terms. However, for households and individuals, "income is the sum of all the wages, salaries, profits, interests payments, rents and other forms of earnings...

    , interest rate
    Interest rate
    An interest rate is the rate at which interest is paid by a borrower for the use of money that they borrow from a lender. For example, a small company borrows capital from a bank to buy new assets for their business, and in return the lender receives interest at a predetermined interest rate for...

    s, 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
    Real interest rate
    The "real interest rate" is the rate of interest an investor expects to receive after allowing for inflation. It can be described more formally by the Fisher equation, which states that the real interest rate is approximately the nominal interest rate minus the inflation rate...

     is determined by non-monetary factors: (productivity
    Productivity
    Productivity is a measure of the efficiency of production. Productivity is a ratio of what is produced to what is required to produce it. Usually this ratio is in the form of an average, expressing the total output divided by the total input...

     of capital
    Capital (economics)
    In economics, capital, capital goods, or real capital refers to already-produced durable goods used in production of goods or services. The capital goods are not significantly consumed, though they may depreciate in the production process...

    , time preference
    Time preference
    In economics, time preference pertains to how large a premium a consumer places on enjoyment nearer in time over more remote enjoyment....

    ).

Decline of money-supply targeting


An application of the quantity-theory approach aimed at removing monetary policy
Monetary policy
Monetary policy is the process by which the monetary authority of a country controls the supply of money, often targeting a rate of interest for the purpose of promoting economic growth and stability. The official goals usually include relatively stable prices and low unemployment...

 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
Money supply
In economics, the money supply or money stock, is the total amount of money available in an economy at a specific time. There are several ways to define "money," but standard measures usually include currency in circulation and demand deposits .Money supply data are recorded and published, usually...

, including measurement, was always somewhat controversial and difficult. As financial intermediation
Financial intermediary
Financial intermediation consists of “channeling funds between surplus and deficit agents”. A financial intermediary is a financial institution that connects surplus and deficit agents...

 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 are robust even at relatively short-run frequencies."

Criticisms


John Maynard Keynes
John Maynard Keynes
John Maynard Keynes, Baron Keynes of Tilton, CB FBA , was a British economist whose ideas have profoundly affected the theory and practice of modern macroeconomics, as well as the economic policies of governments...

 criticized the quantity theory of money in The General Theory of Employment, Interest and Money. Keynes had originally been a proponent of the theory, but he presented an alternative in the General Theory. Keynes argued that price level was not strictly determined by money supply. Changes in the money supply could have effects on real variables like output.

Ludwig von Mises
Ludwig von Mises
Ludwig Heinrich Edler von Mises was an Austrian economist, philosopher, and classical liberal who had a significant influence on the modern Libertarian movement and the "Austrian School" of economic thought.-Biography:-Early life:...

 agreed that there was a core of truth in the Quantity Theory, but criticized its focus on the supply of money without adequately explaining the demand for money. He said the theory "fails to explain the mechanism of variations in the value of money".

See also

  • Classical dichotomy
    Classical dichotomy
    In macroeconomics, the classical dichotomy refers to an idea attributed to classical and pre-Keynesian economics that real and nominal variables can be analyzed separately...

  • Demand for money
  • Equation of exchange
    Equation of exchange
    In economics, the equation of exchange is the relation:M\cdot V = P\cdot Qwhere, for a given period,M\, is the total nominal amount of money in circulation on average in an economy.V\, is the velocity of money, that is the average frequency with which a unit of money is spent.P\, is the price...

  • Income velocity of money
  • Liquidity preference
    Liquidity preference
    In macroeconomic theory, Liquidity preference refers to the demand for money, considered as liquidity. The concept was first developed by John Maynard Keynes in his book The General Theory of Employment, Interest and Money to explain determination of the interest rate by the supply and demand...

  • Monetae cudendae ratio
    Monetae cudendae ratio
    Monetae cudendae ratio is a paper on coinage by Nicolaus Copernicus...

  • Monetarism
    Monetarism
    Monetarism is a tendency in economic thought that emphasizes the role of governments in controlling the amount of money in circulation. It is the view within monetary economics that variation in the money supply has major influences on national output in the short run and the price level over...

  • Monetary inflation
    Monetary inflation
    Monetary inflation is a sustained increase in the money supply of a country. It usually results in price inflation, which is a rise in the general level of prices of goods and services . Originally the term "inflation" was used to refer only to monetary inflation, whereas in present usage it...

  • Monetary policy
    Monetary policy
    Monetary policy is the process by which the monetary authority of a country controls the supply of money, often targeting a rate of interest for the purpose of promoting economic growth and stability. The official goals usually include relatively stable prices and low unemployment...

  • Neutrality of money
    Neutrality of money
    Neutrality of money is the idea that a change in the stock of money affects only nominal variables in the economy such as prices, wages and exchange rates, with no effect on real variables, like employment, real GDP, and real consumption....


Alternative theories

  • Benjamin Anderson
    Benjamin Anderson
    Benjamin McAlester Anderson, Jr. was an American economist in the Austrian tradition of Carl Menger.-Early life and education:...

     (critic of mainstream variant)
  • Fiscal theory of the price level
    Fiscal theory of the price level
    The fiscal theory of the price level is the idea that government fiscal policy affects the price level: for the price level to be stable , government finances must be sustainable: they must run a balanced budget over the course of the business cycle, meaning they must not run a structural...

  • Real bills doctrine
    Real bills doctrine
    The real bills doctrine holds that issuing money in exchange for real bills is not inflationary. It is best known as "the decried doctrine of the old Bank Directors of 1810: that so long as a bank issues its notes only in the discount of good bills, at not more than sixty days’ date, it cannot go...


Further reading

  • Friedman, Milton (1987 [2008
    The New Palgrave Dictionary of Economics
    The New Palgrave Dictionary of Economics , 2nd Edition, is an eight-volume reference work, edited by Steven N. Durlauf and Lawrence E. Blume. It contains 5.8 million words and spans 7,680 pages with 1,872 articles. Included are 1057 new articles and, from earlier, 80 essays that are designated as...

    ]). “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.
    David Laidler
    David Ernest William Laidler has been one of the foremost scholars of monetarism. He published major economics journal articles on the topic in the late 1960s and early 1970s...

     (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”.

External links

  • The Quantity Theory of Money from John Stuart Mill
    John Stuart Mill
    John Stuart Mill was a British philosopher, economist and civil servant. An influential contributor to social theory, political theory, and political economy, his conception of liberty justified the freedom of the individual in opposition to unlimited state control. He was a proponent of...

     through Irving Fisher
    Irving Fisher
    Irving Fisher was an American economist, inventor, and health campaigner, and one of the earliest American neoclassical economists, though his later work on debt deflation often regarded as belonging instead to the Post-Keynesian school.Fisher made important contributions to utility theory and...

    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