Economics
Economics () is the social science that studies the production, distribution, and consumption of goods and services.
Economics focuses on the behaviour and interactions of economic agents and how economies work. Microeconomics anal ...
, business,
accounting
Accounting, also known as accountancy, is the measurement, processing, and communication of financial and non financial information about economic entities such as businesses and corporations. Accounting, which has been called the "languag ...
, and related fields often distinguish between quantities that are stocks and those that are flows. These differ in their
units of measurement. A ''stock'' is measured at one specific time, and represents a quantity existing at that point in time (say, December 31, 2004), which may have
accumulated in the past. A ''flow'' variable is measured over an interval of time. Therefore, a flow would be measured ''per unit of time'' (say a year). Flow is roughly analogous to
rate or
speed
In everyday use and in kinematics, the speed (commonly referred to as ''v'') of an object is the magnitude of the change of its position over time or the magnitude of the change of its position per unit of time; it is thus a scalar quant ...
in this sense.
For example, U.S. nominal
gross domestic product
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 of ...
refers to a total number of dollars spent over a time period, such as a year. Therefore, it is a flow variable, and has units of dollars/year. In contrast, the U.S. nominal
capital stock is the total value, in dollars, of equipment, buildings, and other real productive assets in the U.S. economy, and has units of dollars. The diagram provides an intuitive illustration of how the ''stock'' of
capital
Capital may refer to:
Common uses
* Capital city, a municipality of primary status
** List of national capital cities
* Capital letter, an upper-case letter Economics and social sciences
* Capital (economics), the durable produced goods used fo ...
currently available is increased by the ''flow'' of new
investment and depleted by the ''flow'' of
depreciation
In accountancy, depreciation is a term that refers to two aspects of the same concept: first, the actual decrease of fair value of an asset, such as the decrease in value of factory equipment each year as it is used and wear, and second, the ...
.
Stocks and flows in accounting
Thus, a stock refers to the value of an asset at a balance date (or point in time), while a flow refers to the total value of transactions (sales or purchases, incomes or expenditures) during an accounting period. If the flow value of an economic activity is divided by the average stock value during an accounting period, we obtain a measure of the number of turnovers (or rotations) of a stock in that accounting period. Some accounting entries are normally always represented as a flow (e.g. profit or income), while others may be represented both as a stock or as a flow (e.g. capital).
A person or country might have stocks of
money
Money is any item or verifiable record that is generally accepted as payment for goods and services and repayment of debts, such as taxes, in a particular country or socio-economic context. The primary functions which distinguish money ar ...
, financial
assets,
liabilities,
wealth
Wealth is the abundance of valuable financial assets or physical possessions which can be converted into a form that can be used for transactions. This includes the core meaning as held in the originating Old English word , which is from an I ...
, real
means of production
The means of production is a term which describes land, labor and capital that can be used to produce products (such as goods or services); however, the term can also refer to anything that is used to produce products. It can also be used as a ...
, capital,
inventories, and
human capital (or
labor power). Flow magnitudes include
income,
spending,
saving, debt repayment,
fixed investment
Fixed investment in economics is the purchasing of newly produced fixed capital. It is measured as a flow variable – that is, as an amount per unit of time.
Thus, fixed investment is the accumulation of physical assets such as machinery, lan ...
,
inventory investment, and
labor utilization. These differ in their units of measurement.
Capital is a stock concept which yields a periodic income which is a flow concept.
Comparing stocks and flows
Stocks and flows have different units and are thus not ''
commensurable'' – they cannot be meaningfully ''compared, equated, added, or subtracted.'' However, one may meaningfully take ''ratios'' of stocks and flows, or multiply or divide them. This is a point of some confusion for some economics students, as some confuse taking ratios (valid) with comparing (invalid).
The ratio of a stock over a flow has units of (units)/(units/time) = time. For example, the
debt to GDP ratio has units of years (as GDP is measured in, for example, dollars per year whereas debt is measured in dollars), which yields the interpretation of the debt to GDP ratio as "number of years to pay off all debt, assuming all GDP devoted to debt repayment".
The ratio of a flow to a stock has units 1/time. For example, the
velocity of money is defined as
nominal GDP / nominal
money supply
In macroeconomics, the money supply (or money stock) refers to the total volume of currency held by the public at a particular point in time. There are several ways to define "money", but standard measures usually include currency in circu ...
; it has units of (dollars / year) / dollars = 1/year.
In
discrete time
In mathematical dynamics, discrete time and continuous time are two alternative frameworks within which variables that evolve over time are modeled.
Discrete time
Discrete time views values of variables as occurring at distinct, separate "po ...
, the change in a stock variable from one point in time to another point in time one time unit later (the
first difference
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 paramet ...
of the stock) is equal to the corresponding flow variable per unit of time. For example, if a country's stock of
physical capital
Physical capital represents in economics one of the three primary factors of production. Physical capital is the apparatus used to produce a good and services. Physical capital represents the tangible man-made goods that help and support the pro ...
on January 1, 2010 is 20 machines and on January 1, 2011 is 23 machines, then the flow of
net investment during 2010 was 3 machines per year. If it then has 27 machines on January 1, 2012, the flow of net investment during 2010 and 2011 averaged
machines per year.
In
continuous time, the
time derivative of a stock variable is a flow variable.
More general uses
Stocks and flows also have natural meanings in many contexts outside of economics, business and related fields. The concepts apply to many
conserved quantities such as
energy
In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of ...
, and to
material
Material is a substance or mixture of substances that constitutes an object. Materials can be pure or impure, living or non-living matter. Materials can be classified on the basis of their physical and chemical properties, or on their geolo ...
s such as in
stoichiometry
Stoichiometry refers to the relationship between the quantities of reactants and products before, during, and following chemical reactions.
Stoichiometry is founded on the law of conservation of mass where the total mass of the reactants equ ...
,
water reservoir management, and
greenhouse gases and other durable
pollutants that accumulate in the environment or
in organisms.
Climate change mitigation, for example, is a fairly straightforward stock and flow problem with the primary goal of reducing the stock (the concentration of durable greenhouse gases in the atmosphere) by manipulating the flows (reducing inflows such as
greenhouse gas emissions
Greenhouse gas emissions from human activities strengthen the greenhouse effect, contributing to climate change. Most is carbon dioxide from burning fossil fuels: coal, oil, and natural gas. The largest emitters include coal in China and ...
into the atmosphere, and increasing outflows such as
carbon dioxide removal
Carbon dioxide removal (CDR), also known as negative emissions, is a process in which carbon dioxide gas () is removed from the atmosphere and sequestered for long periods of time. Similarly, greenhouse gas removal (GGR) or negative greenh ...
). In living systems, such as the human body,
energy homeostasis In biology, energy homeostasis, or the homeostatic control of energy balance, is a biological process that involves the coordinated homeostatic regulation of food intake (energy inflow) and energy expenditure (energy outflow). The human brain, part ...
describes the linear relationship between flows (the food we eat and the energy we expend along with the wastes we excrete) and the stock (manifesting as our gain or loss of body weight over time). In
Earth system science
Earth system science (ESS) is the application of systems science to the Earth. In particular, it considers interactions and 'feedbacks', through material and energy fluxes, between the Earth's sub-systems' cycles, processes and "spheres"— atmo ...
, many stock and flow problems arise, such as in the
carbon cycle
The carbon cycle is the biogeochemical cycle by which carbon is exchanged among the biosphere, pedosphere, geosphere, hydrosphere, and atmosphere of the Earth. Carbon is the main component of biological compounds as well as a major compon ...
, the
nitrogen cycle, the
water cycle
The water cycle, also known as the hydrologic cycle or the hydrological cycle, is a biogeochemical cycle that describes the continuous movement of water on, above and below the surface of the Earth. The mass of water on Earth remains fairly co ...
, and
Earth's energy budget. Thus stocks and flows are the basic building blocks of
system dynamics models
A model is an informative representation of an object, person or system. The term originally denoted the plans of a building in late 16th-century English, and derived via French and Italian ultimately from Latin ''modulus'', a measure.
Models c ...
.
Jay Forrester originally referred to them as "levels" rather than stocks, together with "rates" or "rates of flow".
A stock (or "level variable") in this broader sense is some entity that is accumulated over time by inflows and/or depleted by outflows. Stocks can only be changed via flows. Mathematically a stock can be seen as an accumulation or integration of flows over time – with outflows subtracting from the stock. Stocks typically have a certain value at each moment of time – e.g. the number of population at a certain moment, or the quantity of water in a reservoir.
A flow (or "rate") changes a stock over time. Usually we can clearly distinguish inflows (adding to the stock) and outflows (subtracting from the stock). Flows typically are measured over a certain interval of time – e.g., the number of births over a day or month.
Synonyms
Examples
Accounting, finance, etc.
Other contexts
Calculus interpretation
If the quantity of some ''stock'' variable at time
is
, then the
derivative
In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value). Derivatives are a fundamental tool of calculus. ...
is the ''flow'' of changes in the stock. Likewise, the ''stock'' at some time
is the
integral
In mathematics, an integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding integrals is called integration. Along with ...
of the ''flow'' from some moment set as zero until time
.
For example, if the
capital stock is increased gradually over time by a flow of
gross investment
Gross private domestic investment is the measure of physical investment used in computing GDP in the measurement of nations' economic activity. This is an important component of GDP because it provides an indicator of the future productive capacit ...
and decreased gradually over time by a flow of
depreciation
In accountancy, depreciation is a term that refers to two aspects of the same concept: first, the actual decrease of fair value of an asset, such as the decrease in value of factory equipment each year as it is used and wear, and second, the ...
, then the instantaneous rate of change in the capital stock is given by
:
where the notation
refers to the flow of
net investment, which is the difference between gross investment and depreciation.
Example of dynamic stock and flow diagram
Equations that change the two stocks via the flow are:
:
:
List of all the equations, in their order of execution in each time, from time = 1 to 36:
:
:
:
History
The distinction between a stock and a flow variable is elementary, and dates back centuries in accounting practice (distinction between an asset and income, for instance). In economics, the distinction was formalized and terms were set in , in which
Irving Fisher
Irving Fisher (February 27, 1867 – April 29, 1947) was an American economist, statistician, inventor, eugenicist and progressive social campaigner. He was one of the earliest American neoclassical economists, though his later work on debt de ...
formalized
capital
Capital may refer to:
Common uses
* Capital city, a municipality of primary status
** List of national capital cities
* Capital letter, an upper-case letter Economics and social sciences
* Capital (economics), the durable produced goods used fo ...
(as a stock).
Polish economist
Michał Kalecki emphasized the centrality of the distinction of stocks and flows, caustically calling economics "the science of confusing stocks with flows" in his critique of the
quantity theory of money (circa 1936, frequently quoted by
Joan Robinson
Joan Violet Robinson (''née'' Maurice; 31 October 1903 – 5 August 1983) was a British economist well known for her wide-ranging contributions to economic theory. She was a central figure in what became known as post-Keynesian economics.
...
).
Joan Robinson
Joan Violet Robinson (''née'' Maurice; 31 October 1903 – 5 August 1983) was a British economist well known for her wide-ranging contributions to economic theory. She was a central figure in what became known as post-Keynesian economics.
...
,
Shedding Darkness
, ''Cambridge Journal of Economics
The ''Cambridge Journal of Economics'' is a peer-reviewed academic journal of economics. The journal was founded in 1977 by the ''Cambridge Political Economy Society'' with the aim of publishing articles that followed the economic traditions est ...
'', 6 (1982), 295–6: "it is the science of confusing stocks with flows. It is this confusion that has kept the Quantity Theory of Money alive until today."
See also
*
Flow (disambiguation)
Flow may refer to:
Science and technology
* Fluid flow, the motion of a gas or liquid
* Flow (geomorphology), a type of mass wasting or slope movement in geomorphology
* Flow (mathematics), a group action of the real numbers on a set
* Flow (ps ...
*
Intensive and extensive properties
*
Stock (disambiguation)
*
Stock-Flow consistent model
*
Systems thinking
Systems thinking is a way of making sense of the complexity of the world by looking at it in terms of wholes and relationships rather than by splitting it down into its parts. It has been used as a way of exploring and developing effective actio ...
*
System dynamics
*
Wealth (economics)
References
* {{citation
, title = What is Capital?
, authorlink = Irving Fisher
, first = Irving
, last = Fisher
, journal = The Economic Journal
, volume = 6
, date=December 1896
, pages = 509–534
, jstor = 2957184
, issue = 24
, doi = 10.2307/2957184
, url = https://zenodo.org/record/1449667
* D.W. Bushaw and R.W. Clower, 1957. ''Introduction to Mathematical Economics'', Ch. 3–6. "Section" & arrow-searchable pageChapter ("Section") and arrow-searchable pag
links.*
Robert W. Clower, 1954a. "An Investigation into the Dynamics of Investment," ''American Economic Review''. 44(l), pp
64��81.
* _____, 1954b. "Price Determination in a Stock-Flow Economy" with D. W. Bushaw, ''Econometrica '' 22(3),
p. 328��343.
* _____, 1968. "Stock-flow analysis," ''
International Encyclopedia of the Social Sciences'', v. 12.
* Glenn W. Harrison, 1987
008 "Stocks and flows," ''
The New Palgrave: A Dictionary of Economics'', v. 4, pp. 506–09.
Inventory
Accounting systems
Systems theory
Economics and time