Stock and flow


, business, accounting, 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, 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. Flow is roughly analogous to rate or speed in this sense.
For example, U.S. nominal gross domestic product 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 currently available is increased by the flow of new investment and depleted by the flow of depreciation.

Stocks and flows in accounting

Thus, a stock refers to the value of an asset at a balance date, while a flow refers to the total value of transactions 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 of a stock in that accounting period. Some accounting entries are normally always represented as a flow, while others may be represented both as a stock or as a flow.
A person or country might have stocks of money, financial assets, liabilities, wealth, real means of production, capital, inventories, and human capital. Flow magnitudes include income, spending, saving, debt repayment, fixed investment, 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 with comparing.
The ratio of a stock over a flow has units of / = time. For example, the debt to GDP ratio has units of years, 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; it has units of / dollars = 1/year.
In discrete time, the change in a stock variable from one point in time to another point in time one time unit later is equal to the corresponding flow variable per unit of time. For example, if a country's stock of physical capital 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, and to materials such as in stoichiometry, 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 by manipulating the flows. In living systems, such as the human body, energy homeostasis describes the linear relationship between flows and the stock. In Earth system science, many stock and flow problems arise, such as in the carbon cycle, the nitrogen cycle, the water cycle, and Earth's energy budget. Thus stocks and flows are the basic building blocks of system dynamics models. Jay Forrester originally referred to them as "levels" and "rates".
A stock 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 changes a stock over time. Usually we can clearly distinguish inflows and outflows. Flows typically are measured over a certain interval of time – e.g., the number of births over a day or month.
Synonyms
StockFlow
LevelRate
IntegralDerivative
State Variable

Examples

Accounting, finance, etc.

Other contexts

Calculus interpretation

If the quantity of some stock variable at time is, then the derivative is the flow of changes in the stock. Likewise, the stock at some time t is the integral of the flow from some time when the time was zero until time t.
For example, if the capital stock is increased gradually over time by a flow of gross investment and decreased gradually over time by a flow of depreciation, 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. In economics, the distinction was formalized and terms were set in, in which Irving Fisher formalized capital.
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.