In
macroeconomics
Macroeconomics (from the Greek prefix ''makro-'' meaning "large" + ''economics'') is a branch of economics dealing with performance, structure, behavior, and decision-making of an economy as a whole.
For example, using interest rates, taxes, and ...
, a multiplier is a factor of proportionality that measures how much an
endogenous variable
In an economic model, an exogenous variable is one whose measure is determined outside the model and is imposed on the model, and an exogenous change is a change in an exogenous variable.Mankiw, N. Gregory. ''Macroeconomics'', third edition, 1997. ...
changes in response to a change in some
exogenous variable
In an economic model, an exogenous variable is one whose measure is determined outside the model and is imposed on the model, and an exogenous change is a change in an exogenous variable.Mankiw, N. Gregory. ''Macroeconomics'', third edition, 1997. ...
.
For example, suppose variable ''x''
changes by ''k'' units, which causes another variable ''y'' to change by ''M'' × ''k'' units. Then the multiplier is ''M''.
Common uses
Two multipliers are commonly discussed in introductory
macroeconomics
Macroeconomics (from the Greek prefix ''makro-'' meaning "large" + ''economics'') is a branch of economics dealing with performance, structure, behavior, and decision-making of an economy as a whole.
For example, using interest rates, taxes, and ...
.
Commercial banks create money, especially under the
fractional-reserve banking
Fractional-reserve banking is the system of banking operating in almost all countries worldwide, under which banks that take deposits from the public are required to hold a proportion of their deposit liabilities in liquid assets as a reserve, ...
system used throughout the world. In this system, money is created whenever a bank gives out a new loan. This is because the loan, when drawn on and spent, mostly finishes up as a deposit back in the banking system and is counted as part of money supply. After putting aside a part of these deposits as
mandated bank reserves
Bank reserves are a commercial bank's cash holdings physically held by the bank, and deposits held in the bank's account with the central bank. Under the fractional-reserve banking system used in most countries, central banks typically set minim ...
, the balance is available for the making of further loans by the bank. This process continues multiple times, and is called the multiplier effect.
The multiplier may vary across countries, and will also vary depending on what measures of money are being considered. For example, consider
M2 as a measure of the U.S. money supply, and
M0 as a measure of the U.S. monetary base. If a $1 increase in M0 by the
Federal Reserve
The Federal Reserve System (often shortened to the Federal Reserve, or simply the Fed) is the central banking system of the United States of America. It was created on December 23, 1913, with the enactment of the Federal Reserve Act, after a ...
causes M2 to increase by $10, then the money multiplier is 10.
Fiscal multipliers
Multipliers can be calculated to analyze the effects of
fiscal policy
In economics and political science, fiscal policy is the use of government revenue collection (taxes or tax cuts) and expenditure to influence a country's economy. The use of government revenue expenditures to influence macroeconomic variables ...
, or other exogenous changes in spending, on
aggregate output.
For example, if an increase in German government spending by €100, with no change in tax rates, causes German
GDP
Gross domestic product (GDP) is a monetary measure of the market value of all the final goods and services produced and sold (not resold) in a specific time period by countries. Due to its complex and subjective nature this measure is often ...
to increase by €150, then the ''spending multiplier'' is 1.5. Other types of fiscal multipliers can also be calculated, like multipliers that describe the effects of changing taxes (such as
lump-sum tax
A lump-sum tax is a special way of taxation, based on a fixed amount, rather than on the real circumstance of the taxed entity. es or
proportional tax
A proportional tax is a tax imposed so that the tax rate is fixed, with no change as the taxable base amount increases or decreases. The amount of the tax is in proportion to the amount subject to taxation. "Proportional" describes a distribution ...
es).
Keynesian and Hansen–Samuelson multipliers
Keynesian
Keynesian economics ( ; sometimes Keynesianism, named after British economist John Maynard Keynes) are the various macroeconomic theories and models of how aggregate demand (total spending in the economy) strongly influences economic output and ...
economists often calculate multipliers that measure the effect on
aggregate demand
In macroeconomics, aggregate demand (AD) or domestic final demand (DFD) is the total demand for final goods and services in an economy at a given time. It is often called effective demand, though at other times this term is distinguished. This is ...
only. (To be precise, the usual ''Keynesian multiplier'' formulas measure how much the
IS curve
In linguistics, a copula (plural: copulas or copulae; abbreviated ) is a word or phrase that links the subject of a sentence to a subject complement, such as the word ''is'' in the sentence "The sky is blue" or the phrase ''was not being'' i ...
shifts left or right in response to an exogenous change in spending.)
American Economist
Paul Samuelson
Paul Anthony Samuelson (May 15, 1915 – December 13, 2009) was an American economist who was the first American to win the Nobel Memorial Prize in Economic Sciences. When awarding the prize in 1970, the Swedish Royal Academies stated that he "h ...
credited
Alvin Hansen
Alvin Harvey Hansen (August 23, 1887 – June 6, 1975) was an American economist who taught at the University of Minnesota and was later a chair professor of economics at Harvard University. Often referred to as "the American John Maynard Keynes ...
for the inspiration behind his seminal 1939 contribution. The original Samuelson multiplier-accelerator model (or, as he belatedly baptised it, the "Hansen-Samuelson" model) relies on a multiplier mechanism that is based on a simple Keynesian consumption function with a Robertsonian lag:
:
:
so present consumption is a function of past income (with c as the
marginal propensity to consume
In economics, the marginal propensity to consume (MPC) is a metric that quantifies induced consumption, the concept that the increase in personal consumer spending (consumption) occurs with an increase in disposable income (income after taxes and t ...
). Here, t is the tax rate and m is the ratio of imports to GDP. Investment, in turn, is assumed to be composed of three parts:
:
The first part is autonomous investment, the second is investment induced by interest rates and the final part is investment induced by changes in consumption demand (the "
acceleration
In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by the ...
" principle). It is assumed that b > 0. As we are concentrating on the income-expenditure side, let us assume I(r) = 0 (or alternatively, constant interest), so that:
:
Now, assuming away government and foreign sector, aggregate demand at time t is:
:
assuming goods market equilibrium (so
), then in equilibrium:
:
But we know the values of
and
are merely
and
respectively, then substituting these in:
:
or, rearranging and rewriting as a second order linear
difference equation
In mathematics, a recurrence relation is an equation according to which the nth term of a sequence of numbers is equal to some combination of the previous terms. Often, only k previous terms of the sequence appear in the equation, for a parameter ...
:
:
The solution to this system then becomes elementary. The equilibrium level of Y (call it
, the particular solution) is easily solved by letting
, or:
:
so:
:
The complementary function,
is also easy to determine. Namely, we know that it will have the form
where
and
are arbitrary constants to be defined and where
and
are the two
eigenvalues
In linear algebra, an eigenvector () or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted b ...
(characteristic roots) of the following characteristic equation:
:
Thus, the entire solution is written as
Opponents of Keynesianism have sometimes argued that Keynesian multiplier calculations are misleading; for example, according to the theory of
Ricardian equivalence
The Ricardian equivalence proposition (also known as the Ricardo–de Viti–Barro equivalence theorem) is an economic hypothesis holding that consumers are forward-looking and so internalize the government's budget constraint when making their con ...
, it is impossible to calculate the effect of deficit-financed government spending on demand without specifying how people expect the deficit to be paid off in the future.
General method
The general method for calculating short-run multipliers is called
comparative statics
In economics, comparative statics is the comparison of two different economic outcomes, before and after a change in some underlying exogenous variable, exogenous parameter.
As a type of ''static analysis'' it compares two different economic equ ...
. That is, comparative statics calculates how much one or more
endogenous
Endogenous substances and processes are those that originate from within a living system such as an organism, tissue, or cell.
In contrast, exogenous substances and processes are those that originate from outside of an organism.
For example, es ...
variables change in the short run, given a change in one or more exogenous variables. The comparative statics method is an application of the
implicit function theorem.
Dynamic multipliers can also be calculated. That is, one can ask how a change in some exogenous variable in year ''t'' affects endogenous variables in year ''t'', in year ''t''+1, in year ''t''+2, and so forth. A graph showing the impact on some endogenous variable, over time (that is, the multipliers for times ''t'', ''t''+1, ''t''+2, etc.), is called an
impulse-response function. The general method for calculating impulse response functions is sometimes called
comparative dynamics
In economics, economic equilibrium is a situation in which economic forces such as supply and demand are balanced and in the absence of external influences the (:wikt:equilibrium, equilibrium) values of economic variables will not change. For ...
.
History
![Quesnay Tableau](https://upload.wikimedia.org/wikipedia/commons/4/42/Quesnay_Tableau.jpg)
The
Tableau économique
The Tableau économique () or ''Economic Table'' is an economic model first described by French economist François Quesnay in 1758, which laid the foundation of the Physiocratic school of economics.Henry William Spiegel (1983) ''The Growth of Ec ...
(Economic Table) of
François Quesnay
François Quesnay (; 4 June 1694 – 16 December 1774) was a French economist and physician of the Physiocratic school. He is known for publishing the "Tableau économique" (Economic Table) in 1758, which provided the foundations of the ideas of ...
(1758), which laid the foundation of the
Physiocrat
Physiocracy (; from the Greek for "government of nature") is an economic theory developed by a group of 18th-century Age of Enlightenment French economists who believed that the wealth of nations derived solely from the value of "land agricultur ...
school of economics is credited as the "first precise formulation" of interdependent systems in economics and the origin of multiplier theory. In the tableau économique, one sees variables in one period (time ''t'') feeding into variables in the next period (time ''t''+1), and a constant rate of flow yields geometric series, which computes a multiplier.
The modern theory of the multiplier was developed in the 1930s, by
Kahn
Kahn is a surname of German origin. ''Kahn'' means "small boat", in German. It is also a Germanized form of the Jewish surname Cohen, another variant of which is ''Cahn''. ,
Keynes
John Maynard Keynes, 1st Baron Keynes, ( ; 5 June 1883 – 21 April 1946), was an English economist whose ideas fundamentally changed the theory and practice of macroeconomics and the economic policies of governments. Originally trained in m ...
,
Giblin Giblin is a surname. Notable people with the surname include:
* Anne E. Giblin, marine biologist
* :fr:Béatrice Giblin (born 1947), French scholar
* Belinda Giblin (born 1950), Australian actress
* Edmund Giblin (1923–2000), English footballe ...
, and others, following earlier work in the 1890s by the Australian economist Alfred De Lissa, the Danish economist
Julius Wulff
Julius Wulff (1852-1924) was a Danish conservative politician and journalist. His formal studies were in Zoology and he worked as a teacher in Hjørring
Hjørring () is a town on the island of Vendsyssel-Thy at the top of the Jutland peninsula ...
, and the German-American economist
N. A. J. L. Johannsen.
The origins of the Keynesian revolution
by Robert William Dimand
p. 117
/ref>
See also
*Complex multiplier :''This article deals with the concept in economics. For the multiplication of complex numbers, see Complex number#Multiplication.''
The complex multiplier is the multiplier principle in Keynesian economics (formulated by John Maynard Keynes). T ...
*Local multiplier effect The local multiplier effect (sometimes called the local premium) is the additional economic benefit accrued to an area from money being spent in the local economy. The concept has been taken up by advocates for "spend local" campaigns in addition to ...
*Multiplier uncertainty In macroeconomics, multiplier uncertainty is lack of perfect knowledge of the multiplier effect of a particular policy action, such as a monetary or fiscal policy change, upon the intended target of the policy. For example, a fiscal policy maker m ...
*Social Multiplier Effect The social multiplier effect is a term used in economics, economic geography, sociology, public health and other academic disciplines to describe certain social externalities. It is based on the principle that high levels of one attribute amongst o ...
References
{{Economics
Keynesian economics