In

_{1} = 101.
The inflation rate $i\_t$ between time $t-1$ and time $t$ is the change in the price index divided by the price index value at time $t-1$:
$i\_t\; =\; \backslash frac$
:$=\; \backslash frac\; -\; 1$
expressed as a percentage.

GDP price index.

In the U.S. National Income and Product Accounts, nominal GDP is called ''GDP in current dollars'' (that is, in prices current for each designated year), and real GDP is called ''GDP in ase-yeardollars'' (that is, in dollars that can

DataBasics: Deflating Nominal Values to Real Values

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economics
Economics () is a social science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services.
Economics focuses on the behaviour and interact ...

, nominal value is measured in terms of money, whereas real value is measured against goods or services. A real value is one which has been adjusted for inflation
In economics, inflation refers to a general progressive increase in prices of goods and services in an economy. When the general price level rises, each unit of currency buys fewer goods and services; consequently, inflation corresponds to a r ...

, enabling comparison of quantities as if the prices of goods had not changed on average. Changes in value in real terms therefore exclude the effect of inflation. In contrast with a real value, a nominal value has not been adjusted for inflation, and so changes in nominal value reflect at least in part the effect of inflation.
Commodity bundles, price indices and inflation

A commodity bundle is a sample ofgoods
In economics
Economics () is a social science
Social science is the branch
A branch ( or , ) or tree branch (sometimes referred to in botany
Botany, also called , plant biology or phytology, is the science of plant ...

, which is used to represent the sum total of goods across the economy to which the goods belong, for the purpose of comparison across different times (or locations).
At a single point of time, a commodity bundle consists of a list of goods, and each good in the list has a market price and a quantity. The market value of the good is the market price times the quantity at that point of time. The nominal value of the commodity bundle at a point of time is the total market value of the commodity bundle, depending on the market price, and the quantity, of each good in the commodity bundle which are current at the time.
A price index
A price index (''plural'': "price indices" or "price indexes") is a normalized average (typically a weighted average) of price
A price is the (usually not negative) quantity of payment or compensation given by one party to another in re ...

is the relative price of a commodity bundle. A price index can be measured over time, or at different locations or markets. If it is measured over time, it is a series of values $P\_t$ over time $t$.
A time series
In mathematics
Mathematics (from Greek: ) includes the study of such topics as numbers ( and ), formulas and related structures (), shapes and spaces in which they are contained (), and quantities and their changes ( and ). There is no gen ...

price index is calculated relative to a base or reference date. $P\_0$ is the value of the index at the base date. For example, if the base date is (the end of) 1992, $P\_0$ is the value of the index at (the end of) 1992. The price index is typically normalized to start at 100 at the base date, so $P\_0$ is set to 100.
The length of time between each value of $t$ and the next one, is normally constant regular time interval, such as a calendar year. $P\_t$ is the value of the price index at time $t$ after the base date. $P\_t$ equals 100 times the value of the commodity bundle at time $t$, divided by the value of the commodity bundle at the base date.
If the price of the commodity bundle has increased by one percent over the first period after the base date, then ''P''Real value

The nominal value of a commodity bundle tends to change over time. In contrast, by definition, the real value of the commodity bundle in aggregate remains the same over time. The real values of individual goods or commodities may rise or fall against each other, in relative terms, but a representative commodity bundle as a whole retains its real value as a constant from one period to the next. Real values can for example be expressed in constant 1992 dollars, with the price level fixed 100 at the base date. The price index is applied to adjust the nominal value $Q$ of a quantity, such as wages or total production, to obtain its real value. The real value is the value expressed in terms ofpurchasing power
Purchasing power is the amount of goods and services that can be purchased with a unit of currency
A currency, "in circulation", from la, currens, -entis, literally meaning "running" or "traversing" in the most specific sense is money
Im ...

in the base year.
The index price divided by its base-year value $P\_t\; /\; P\_0$ gives the growth factor of the price index.
Real values can be found by dividing the nominal value by the growth factor of a price index. Using the price index growth factor as a divisor for converting a nominal value into a real value, the real value at time ''t'' relative to the base date is:
:$\backslash frac$
Real growth rate

The real growth rate $r\_t$ is the change in a nominal quantity $Q\_t$ in real terms since the previous date $t-1$. It measures by how much the buying power of the quantity has changed over a single period. :$r\_t\; =\; \backslash frac\; /\; \backslash frac\; -\; 1$ ::$=\; \backslash frac\; -\; 1$ ::$=\; \backslash frac\; /\; \backslash frac\; -\; 1$ ::$=\; \backslash frac\; -\; 1$ where $g\_t$ is the nominal growth rate of $Q\_t$, and $i\_t$ is the inflation rate. :$1\; +\; r\_t\; =\; \backslash frac$ For values of $i\_t$ between −1 and 1 (i.e. ±100 percent), we have theTaylor series
In , the Taylor series of a is an of terms that are expressed in terms of the function's s at a single point. For most common functions, the function and the sum of its Taylor series are equal near this point. Taylor's series are named after ...

:$(1\; +\; i\_t)^\; =\; 1\; -\; i\_t\; +\; i\_t^2\; -\; i\_t^3\; +\; ...$
so
:$1\; +\; r\_t\; =\; (1\; +\; g\_t)(1\; -\; i\_t\; +\; i\_t^2\; -\; i\_t^3\; +\; ...)$
:::$=\; 1\; +\; g\_t\; -\; i\_t\; -\; g\_t\; i\_t\; +\; i\_t^2\; +\; \backslash text$
Hence as a first-order (''i.e.'' linear) approximation,
:$r\_t\; =\; g\_t\; -\; i\_t$
Real wages and real gross domestic products

The bundle of goods used to measure theConsumer Price Index#REDIRECT consumer price index
A consumer price index measures changes in the price level of a weighted average market basket of Goods, consumer goods and Services marketing, services purchased by households.
A CPI is a statistical estimate con ...

(CPI) is applicable to consumers. So for wage earners as consumers, an appropriate way to measure real wages (the buying power of wages) is to divide the nominal wage (after-tax) by the growth factor in the CPI.
Gross domestic product
Gross domestic product (GDP) is a monetary
Image:National-Debt-Gillray.jpeg, In a 1786 James Gillray caricature, the plentiful money bags handed to King George III are contrasted with the beggar whose legs and arms were amputated, in the ...

(GDP) is a measure of aggregate output. Nominal GDP in a particular period reflects prices that were current at the time, whereas real GDP compensates for inflation. Price indices and the U.S. National Income and Product Accounts
The national income and product accounts (NIPA) are part of the national accounts of the United States. They are produced by the Bureau of Economic Analysis of the Department of Commerce. They are one of the main sources of data on general econo ...

are constructed from bundles of commodities and their respective prices. In the case of GDP, a suitable price index is thGDP price index.

In the U.S. National Income and Product Accounts, nominal GDP is called ''GDP in current dollars'' (that is, in prices current for each designated year), and real GDP is called ''GDP in ase-yeardollars'' (that is, in dollars that can

purchase
Purchasing is the process a business or organization uses to acquire Good (economics), goods or Service (economics), services to accomplish its goals. Although there are several organizations that attempt to set standards in the purchasing proces ...

the same quantity of commodities as in the base year).
Example

Real interest rates

As was shown in the section above on the real growth rate, :$1\; +\; r\_t\; =\; \backslash frac$ where :$r\_t$ is the rate of increase of a quantity in real terms, :$g\_t$ is the rate of increase of the same quantity in nominal terms, and :$i\_t$ is the rate of inflation, and as a first-order approximation, :$r\_t\; =\; g\_t\; -\; i\_t.$ In the case where the growing quantity is afinancial asset
A financial asset is a non-physical asset
In financial accounting
Financial accounting is the field of accounting
Accounting or Accountancy is the measurement, processing, and communication of financial and non financial information abou ...

, $g\_t$ is a nominal interest rateIn finance and economics, the nominal interest rate or nominal rate of interest is either of two distinct things:
# the rate of interest
In finance
Finance is the study of financial institutions, financial markets and how they operate within ...

and $r\_t$ is the corresponding real interest rate
The real interest rate is the rate of interest an investor, saver or lender receives (or expects to receive) after allowing for inflation. It can be described more formally by the Fisher equation
In financial mathematicsMathematical finance, also ...

; the first-order approximation $r\_t\; =\; g\_t\; -\; i\_t$ is known as the Fisher equation
In financial mathematicsMathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling of financial markets. Generally, mathematical finance will derive a ...

.
Looking back into the past, the ''ex post'' real interest rate is approximately the historical nominal interest rate minus inflation. Looking forward into the future, the expected real interest rate is approximately the nominal interest rate minus the expected inflation rate.
Cross-sectional comparison

Not onlytime-series
In mathematics
Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). It ...

data, as above, but also cross-section data
Cross-sectional data, or a cross section of a study population, in statistics and econometrics is a type of data set, data collected by observing many subjects (such as individuals, firms, countries, or regions) at the one point or period of time. T ...

which depends on prices which may vary geographically for example, can be adjusted in a similar way. For example, the total value of a good produced in a region of a country depends on both the amount and the price. To compare the output of different regions, the nominal output in a region can be adjusted by repricing the goods at common or average prices.
See also

*Aggregation problem
An ''aggregate'' in economics
Economics () is the social science that studies how people interact with value; in particular, the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consum ...

*Classical dichotomyIn macroeconomics
Macroeconomics (from the Greek prefix ''makro-'' meaning "large" + ''economics'') is a branch of economics
Economics () is the social science that studies how people interact with value; in particular, the Production (eco ...

*Constant Item Purchasing Power Accounting
Constant purchasing power accounting (CPPA) is an accounting model approved by the International Accounting Standards Board
The International Accounting Standards Board (IASB) is the independent, accounting standard
Publicly traded companies typ ...

*Cost-of-living index
A cost-of-living index is a theoretical price index
A price index (''plural'': "price indices" or "price indexes") is a normalized average (typically a weighted average) of price
A price is the (usually not negative) quantity of payme ...

*Deflation
In economics
Economics () is a social science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services.
Economics focuses on the behav ...

*Financial repression
Financial repression comprises "policies that result in savers earning returns below the rate of inflation" in order to allow banks to "provide cheap loans to companies and governments, reducing the burden of repayments". It can be particularly eff ...

*Fisher equation
In financial mathematicsMathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling of financial markets. Generally, mathematical finance will derive a ...

*Index (economics)
In Statistics
Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data
Data (; ) are individual facts, statistics, or items of information, often numeric. In a mo ...

*Inflation
In economics, inflation refers to a general progressive increase in prices of goods and services in an economy. When the general price level rises, each unit of currency buys fewer goods and services; consequently, inflation corresponds to a r ...

*Inflation accounting
Inflation accounting comprises a range of accounting models designed to correct problems arising from historical cost
In accounting, an economic item's historical cost is the original nominal monetary value of that item. Historical cost accounting i ...

* Inflation hedge
*Interest
In finance
Finance is the study of financial institutions, financial markets and how they operate within the financial system. It is concerned with the creation and management of money and investments. Savers and investors have money availa ...

*Money illusion
In economics
Economics () is the social science that studies how people interact with value; in particular, the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods an ...

*National accounts
National accounts or national account systems (NAS) are the implementation of complete and consistent accounting technique
Technique or techniques may refer to:
Music
* The Techniques, a Jamaican rocksteady vocal group of the 1960s
*Technique ...

*Neutrality of money
Neutral or neutrality may refer to:
Mathematics and natural science Biology
* Neutral organisms, in ecology, those that obey the unified neutral theory of biodiversity
Chemistry and physics
* Neutralization (chemistry), a chemical reaction i ...

*Numéraire
The numéraire (or numeraire) is a basic standard by which value is computed. In mathematical economics it is a tradable economic entity in terms of whose price the relative prices of all other tradables are expressed. In a monetary economy, acting ...

*Real interest rate
The real interest rate is the rate of interest an investor, saver or lender receives (or expects to receive) after allowing for inflation. It can be described more formally by the Fisher equation
In financial mathematicsMathematical finance, also ...

*Real prices and ideal pricesThe distinction between real prices and ideal prices is a distinction between ''actual prices paid'' for products, services, assets and labour (the net amount of money that actually changes hands), and ''computed'' prices which are not actually charg ...

* Template:Inflation – for price conversions in Wikipedia articles
Notes

References

* * (Adam Smith
Adam Smith ( 1723 – 17 July 1790) was a Scottish economist, philosopher as well as a moral philosopher
Ethics or moral philosophy is a branch of philosophy that "involves systematizing, defending, and recommending concepts of right and ...

's early distinction vindicated)
*
*
External links

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The Federal Reserve Bank of Dallas covers the Eleventh Federal Reserve District, which includes Texas, northern Louisiana and southern New Mexico, a district sometimes referred to as the Oil Patch.
The Federal Reserve Bank of Dallas is one of 12 Fe ...

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Bureau of Labor Statistics
The Bureau of Labor Statistics (BLS) is a unit of the United States Department of Labor
The United States Department of Labor (DOL) is a cabinet-level department of the U.S. federal government responsible for occupational safety and health, ...

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