Real versus nominal value
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In economics
Economics
Economics is the social science that analyzes the production, distribution, and consumption of goods and services. The term economics comes from the Ancient Greek from + , hence "rules of the house"...

, nominal value refers to a value
Value (economics)
An economic value is the worth of a good or service as determined by the market.The economic value of a good or service has puzzled economists since the beginning of the discipline. First, economists tried to estimate the value of a good to an individual alone, and extend that definition to goods...

 expressed in money terms (that is, in units of a currency) in a given year or series of years. By contrast, real value adjusts nominal value to remove effects of price changes over time. For example, changes in the nominal value of some commodity bundle over time can happen because of a change in the quantities in the bundle or their associated prices, whereas changes in real values reflect only changes in quantities.

Real values over time are a measure purchasing power
Purchasing power
Purchasing power is the number of goods/services that can be purchased with a unit of currency. For example, if you had taken one dollar to a store in the 1950s, you would have been able to buy a greater number of items than you would today, indicating that you would have had a greater purchasing...

 net of any price changes over time. They are often used for restating nominal income to real income, thus adjusting that part of income changes that merely offset 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...

 (a general increase in prices). Similarly, for aggregate measures of output, such as gross domestic product
Gross domestic product
Gross domestic product refers to the market value of all final goods and services produced within a country in a given period. GDP per capita is often considered an indicator of a country's standard of living....

 (GDP), the nominal amount reflects production quantities and prices in that year, whereas real amounts in different years reflect only changes in quantities. A series of real values over time, such as for real GDP, measures relative quantities over time expressed in prices of one year, called the base year (or more generally the base period).

In a related fashion, the real value of a commodity bundle in a given year may be derived from its nominal value by replacing then-current prices of commodities in the bundle with prices that prevailed in the base year. Real values in different years then express values of the bundles as if prices had been constant for all the years, with any differences due to differences in underlying quantities.

The nominal value of a commodity bundle in a given year may be expressed in prices and quantities, namely, as a sum of prices times quantities for the different commodities in the bundle. In turn nominal values are related to real values by the following arithmetic
Arithmetic
Arithmetic or arithmetics is the oldest and most elementary branch of mathematics, used by almost everyone, for tasks ranging from simple day-to-day counting to advanced science and business calculations. It involves the study of quantity, especially as the result of combining numbers...

 definition:
nominal value / real value = P x Q / Q = P.

Here P serves as a price index
Price index
A price index is a normalized average of prices for a given class of goods or services in a given region, during a given interval of time...

, and Q serves as a quantity index of real value. In the equation, P is constructed to equal 1.00 in the base year. Alternatively, P can be constructed to equal 100 in the base year: x 100 = P.

note: the base year can be any year but government economists usually uses the same base year for 5 consecutive years. In Canada, a base year was 2002 then 2007 and Canadians will continue using 2007 as a base year up until 2013.

The nominal/real value distinction can apply not only to time-series data, as above, but to cross-section data varying by region, for example a cost-of-living index
Cost-of-living index
Cost of living is the cost of maintaining a certain standard of living. Changes in the cost of living over time are often operationalized in a cost of living index. Cost of living calculations are also used to compare the cost of maintaining a certain standard of living in different geographic areas...

.

Illustration, notation, and generalization

The simplest case of a bundle of commodities (goods) is one that has only one commodity. In that case, output or consumption may be measured either in terms of money value (nominal) or physical quantity (real). Let i designate that commodity and let:
Pi = the unit price of i, say, $5
Qi = the quantity of i, say, 10 units.

The nominal value of the bundle would then be price times quantity:
nominal value of i = Pi x Qi = $5 x 10 = $50.

Given only the nominal value and price, derivation of a real value is immediate:
real value of bundle i = Pi x Qi/Pi = Qi = 50/5 = 10.

The price "deflates" (divides) the nominal value to derive a real value, the quantity itself.

Similarly for a series of years, say five, given only nominal values of the good and prices in each year t, a real value can be derived for each of the five years:
real value of bundle i in year t = nominal value of Qit/Pit = Qit.


This example generalizes for nominal values relative to real values across different years for which P, a price index
Price index
A price index is a normalized average of prices for a given class of goods or services in a given region, during a given interval of time...

comparing the general price level across years, is available. Consider a nominal value (say of an hourly wage rate) in each different year t. To derive a real-value series from a series of nominal values in different years, divide nominal value in each year by Pt, the price index in that year. By definition then:
real value in year t = nominal value in year t/Pt.
Numerical example:
If for years 1 and 2 (say 20 years apart) the nominal wage and P are respectively
$10 and $16
$1.00 and $1.333,

real wages are respectively:
10 (= $10/$1.00) and 12 (= $16/$1.333).

The real wage so constructed in each different year indexes the amount of commodities in that year that could be purchased relative to other years. Thus, in the example the price level increased by 33 percent, but the real wage rate still increased by 20 percent, permitting a 20 percent increase in the quantity of commodities the nominal wage could purchase.

The generalization to a commodity bundle from the single-good illustration above is to a bundle of quantities of different commodities and different years. This has practical use, because price index
Price index
A price index is a normalized average of prices for a given class of goods or services in a given region, during a given interval of time...

es and the 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...

 are constructed from such bundles of commodities and their respective prices.

A sum of nominal values for each of the different commodities in the bundle is also called a nominal value. A bundle of n different commodities with corresponding prices and quantities for each year t defines:
nominal value of that bundle in year t = P1t x Q1t + . . . + Pnt x Qnt.


From the above:
Pt = the value of a price index in year t.


The nominal value of the bundle over a series of years and corresponding Pt define:
real value of the bundle in year t = Qt = nominal value of the bundle in year t/Pt.

Alternatively, multiplying both sides by
Pt:
nominal value of the bundle in year t = Pt x Qt.

So, every nominal value can be dichotomized
Dichotomy
A dichotomy is any splitting of a whole into exactly two non-overlapping parts, meaning it is a procedure in which a whole is divided into two parts...

 into a price-level part and a real part. The real part Qt is an index of the quantities in the bundle.

An illustration of a nominal-value sum is nominal GDP. An illustration of a real-value sum (or quotient) is real GDP
Real GDP
Real Gross Domestic Product is a macroeconomic measure of the value of output economy adjusted for price changes . The adjustment transforms the money-value measure, called nominal GDP, into an index for quantity of total output...

.

Uses and examples

Nominal values—such as nominal wages or (nominal) gross domestic product
Gross domestic product
Gross domestic product refers to the market value of all final goods and services produced within a country in a given period. GDP per capita is often considered an indicator of a country's standard of living....

—refer to amounts that are paid or earned in money
Money
Money is any object or record that is generally accepted as payment for goods and services and repayment of debts in a given country or socio-economic context. The main functions of money are distinguished as: a medium of exchange; a unit of account; a store of value; and, occasionally in the past,...

 terms. In the illustration of the previous section, for a single good with a nominal value, the nominal value of the good was divided by its unit price to calculate its real value, namely the quantity of the good. The same general method applies for calculation of other real values, except that a price index
Price index
A price index is a normalized average of prices for a given class of goods or services in a given region, during a given interval of time...

 is used instead of the price of a single commodity. Real values (such as real wages or real gross domestic product) can be derived by dividing the relevant nominal value (money wages or nominal GDP) by the appropriate price index. For consumers, a relevant bundle of goods is that used to compute the Consumer Price Index
Consumer price index
A consumer price index measures changes in the price level of consumer goods and services purchased by households. The CPI, in the United States is defined by the Bureau of Labor Statistics as "a measure of the average change over time in the prices paid by urban consumers for a market basket of...

. So, for wage earners as consumers a relevant real wage is the nominal wage (after-tax) divided by the CPI. A relevant divisor of nominal GDP is the GDP price index.

Real values represent the purchasing power
Purchasing power
Purchasing power is the number of goods/services that can be purchased with a unit of currency. For example, if you had taken one dollar to a store in the 1950s, you would have been able to buy a greater number of items than you would today, indicating that you would have had a greater purchasing...

 of nominal values in a given period, including wages, interest, or total production. In particular, price indexes are typically calculated relative to some base year. If for example the base year is 1992, real values are expressed in constant 1992 dollars
Constant dollars
The term constant dollars refers to a metric for valuing the price of something over time, without that metric changing due to inflation or deflation. The term specifically refers to dollars whose present value is linked to a given year. The term constant dollars refers to a metric for valuing the...

, referenced as 1992=100, since the published index is usually normalized to equal 100 in the base year. To use the price index as a divisor for converting a nominal value into a real value, as in the previous section, the published index is first divided by the base-year price-index value of 100. In the U.S. 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...

, nominal GDP is called GDP in current dollars (that is, in prices current for each designated year), and real GDP is called GDP in [base-year] dollars (that is, in dollars that can purchase the same quantity of commodities as in the base year). In effect the price index of 100 for the base year is a numéraire
Numéraire
Numéraire is a basic standard by which values are measured. Acting as the numéraire is one of the functions of money, to serve as a unit of account: to measure the worth of different goods and services relative to one another, i.e. in same units...

 for price-index values in other years.

The terminology of classical economics used by Adam Smith
Adam Smith
Adam Smith was a Scottish social philosopher and a pioneer of political economy. One of the key figures of the Scottish Enlightenment, Smith is the author of The Theory of Moral Sentiments and An Inquiry into the Nature and Causes of the Wealth of Nations...

 used a unit of labour as the purchasing power unit, so monetary quantities were deflated by wages to indicate the number of hours of labour required to produce or purchase a given quantity.

Interest rates

  • 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...

    s are measured as the difference between nominal interest rate
    Nominal interest rate
    In finance and economics nominal interest rate or nominal rate of interest refers to the rate of interest before adjustment for inflation ; or, for interest rates "as stated" without adjustment for the full effect of compounding...

    s and the rate 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...

    .
    • The expected real interest rate is the nominal interest rate minus the inflation rate expected over the term of the loan.
    • The realized (ex post) real interest rate has the actual inflation rate subtracted from the nominal interest rate.


The relationship above is approximate only. The actual relationship is:
(1+IRN)=(1+IRR)(1+I), where:
IRN is the nominal interest rate,
IRR is the real interest rate, and
I is the inflation rate

See also

  • Constant Item Purchasing Power Accounting
  • Aggregation problem
    Aggregation problem
    An aggregate in economics is a summary measure describing a market or economy. The aggregation problem refers to the difficulty of treating an empirical or theoretical aggregate as if it reacted like a less-aggregated measure, say, about behavior of an individual agent as described in general...

  • 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...

  • Cost-of-living index
    Cost-of-living index
    Cost of living is the cost of maintaining a certain standard of living. Changes in the cost of living over time are often operationalized in a cost of living index. Cost of living calculations are also used to compare the cost of maintaining a certain standard of living in different geographic areas...

  • Deflation
  • Index (economics)
    Index (economics)
    In economics and finance, an index is a statistical measure of changes in a representative group of individual data points. These data may be derived from any number of sources, including company performance, prices, productivity, and employment. Economic indices track economic health from...

  • 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...

  • Money illusion
    Money illusion
    In economics, money illusion refers to the tendency of people to think of currency in nominal, rather than real, terms. In other words, the numerical/face value of money is mistaken for its purchasing power...

  • National accounts
    National accounts
    National accounts or national account systems are the implementation of complete and consistent accounting techniques for measuring the economic activity of a nation. These include detailed underlying measures that rely on double-entry accounting...

  • 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....

  • Numéraire
    Numéraire
    Numéraire is a basic standard by which values are measured. Acting as the numéraire is one of the functions of money, to serve as a unit of account: to measure the worth of different goods and services relative to one another, i.e. in same units...

  • Peppercorn (legal)
    Peppercorn (legal)
    A peppercorn in legal parlance is a metaphor for a very small payment, a nominal consideration, used to satisfy the requirements for the creation of a legal contract. "A peppercorn does not cease to be good consideration if it is established that the promisee does not like pepper and will throw...

    , a nominal fee paid to fulfill a contractual requirement
  • 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...

  • Inflation accounting
    Inflation accounting
    Inflation accounting is a term describing a range of accounting systems designed to correct problems arising from historical cost accounting in the presence of inflation. Inflation accounting is used in countries experiencing high inflation or hyperinflation...

  • real prices and ideal prices
    Real prices and ideal prices
    Real prices and ideal prices refers to a distinction between actual prices paid for products, services, assets and labour , and computed prices which are not actually charged or paid in market trade, although they may facilitate trade...

  • Financial repression
    Financial repression
    Financial repression is a term used to describe several measures which governments employ to channel funds to themselves which in a deregulated market would go elsewhere. Financial repression can be particularly effective at liquidating debt....


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