A price index is any single number calculated from an array of prices and quantities over a period. In typical cases, not all prices and quantities of purchases can be recorded, so a representative sample is used instead. Inflation and other economic statistics are calculated using price indices. In economics and business, the price is the assigned numerical monetary value of a good, service or asset. ... Sampling is that part of statistical practice concerned with the selection of individual observations intended to yield some knowledge about a population of concern, especially for the purposes of statistical inference. ...

Notable price indices are

• Consumer price index
• Producer price index
• Personal consumption expenditures price index

The GDP deflator differs from the consumer and producer price indexes in that it does not assume a fixed market basket of goods and services. In economics, a consumer price index (CPI) or retail price index (RPI) is a statistical time-series measure of a weighted average of prices of a specified set of goods and services purchased by consumers. ... The Producer Price Index (PPI) measures average changes in prices received by domestic producers for their output. ... The PCE price index (PCEPI) (or PCE deflator, PCE price deflator, Implicit Price Deflator for Personal Consumption Expenditures (IPD for PCE) (by the Bureau of Economic Analysis) or the chain-type price index for personal consumption expenditures (CTPIPCE) (by the FOMC)) is a nation-wide indicator of the average increase... In economics, the GDP deflator (implicit price deflator for GDP) is a measure of the change in prices of all new, domestically produced, final goods and services in an economy. ... Market Basket is a grocery chain that serves southeast Texas and Louisiana. ...

Most price indexes are normalized to a value of 100 in the base year(s), to indicate the percentage level of the price index in each year relative to the base year. So a price-index value of 110 for a given year means that the price index is 10 percent higher in that year than the base year.

History of early price indices

No clear consensus has emerged on who created the first price index. The earliest reported research in this area came from Englishman Rice Vaughan who examined price level change in his 1675 book A Discourse of Coin and Coinage. Vaughan wanted to separate the inflationary impact of the influx of precious metals brought by Spain from the New World from the effect due to currency debasement. Vaughan compared labor statutes from his own time to similar statutes dating back to Edward III. These statutes set wages for certain tasks and provided a good record of the change in wage levels. Rice reasoned that the market for basic labor did not fluctuate much with time and that a basic laborers salary would probably buy the same amount of goods in different time periods, so that a laborer's salary acted as a basket of goods. Vaughan's analysis indicated that price levels in England had risen six to eight fold over the preceding century.^[1] Events January 5 - The Battle of Turckeim June 18 - Battle of Fehrbellin August 10 - King Charles II of England places the foundation stone of the Royal Greenwich Observatory in London - construction begins November 11 - Guru Gobind Singh becomes the Tenth Guru of the Sikhs. ... Carte dAmérique, Guillaume Delisle, c. ... Debasement is the practice of lowering the value of currency. ... The Statute of Labourers was a law enacted by the English parliament under King Edward III in 1351 in response to a labour shortage. ... Edward III King of England Edward III (13 November 1312–21 June 1377) was one of the most successful English Kings of medieval times. ...

While Vaughan can be considered a forerunner of price index research, his analysis did not actually involve calculating an index.^[2] In 1707 Vaughan's fellow Englishman William Fleetwood probably created the first true price index. Fleetwood studied price change in his at the behest of an Oxford student who stood to lose his fellowship. In the fifteenth century, Oxford stipulated that no student with an annual income over five pounds could have a fellowship. Fleetwood had collected a large amount of price data going back hundreds of years. Fleetwood proposed a an index consisting of averaged price relatives and used his methods to show that the value of five pounds had changed greatly over the course of 260 years. He argued on behalf of the Oxford students and published his findings anonymously in a volume entitled Chronicon Preciosum.^[3] Events January 1 - John V is crowned King of Portugal March 26 - The Acts of Union becomes law, making the separate Kingdoms of England and Scotland into one country, the Kingdom of Great Britain. ... William Fleetwood (January 1, 1656 - August 4, 1723) English preacher and Bishop of Ely remembered by economists and statisticians for constructing a price index in 1707. ...

Paasche versus Laspeyres price indices

Given a set C of goods and services, the total market value of transactions in C in some period t would be

where

represents the prevailing price of c

represents the quantity of c sold

If, across two periods t₁ and t₂, the same quantities of each good or service were sold, but under different prices, then

and

would be a measure of the price of the set in one period relative to that in the other, and would provide an index measuring relative prices overall, weighted by quantities sold. Various meters Measurement is the estimation of a physical quantity such as length, temperature, or time. ... In mathematics, an index is a superscript or subscript to a symbol. ...

When a price index is constructed in an attempt to measure relative prices for a given set of consumers or for the economy as a whole, quantities purchased are rarely if ever identical across any two periods. And a measure

would confuse growth or reduction in quantities sold with price changes. Various indices have been constructed in an attempt to compensate for this difficulty.

There are two main methods to calculate price indices, the Paasche index (after the German economist Hermann Paasche) and the Laspeyres index (after the German economist Etienne Laspeyres). Hermann Paasche (1851-1925) was a German economist. ... (Ernst Louis) Etienne Laspeyres (Halle an der Saale, November 28, 1834 – August 4, 1913) was Professor ordinarius of Economics and Statistics or State Sciences and cameralistics in Basel, Riga, Dorpat, Karlsruhe and finally for 26 years in Giessen. ...

The Paasche index is computed as

while the Laspeyres index is computed as

where P is the change in price level, t₀ is the base period (usually the first year), and t_n the period for which the index is computed.

When applied to bundles of individual consumers, a Paasche index of 1 would state that an agent could have consumed the same bundle in the base period as she is consuming in the current period, given that income has not changed; a Laspeyres index of 1 would state that an agent in the current period can afford to buy the same bundle as he consumed in the previous period, given that income has not changed.

Hence, one may think of the Paasche index as the inflation rate when taking the numeraire as the bundle of goods using previous prices but current quantities. Similarly, the Laspeyres index can be though of as the inflation rate when the numeraire is given by the bundle of goods using current prices and current quantities. Numéraire is one of the functions of money: to measure the worth of different goods and services relative to one another. ...

The Fisher Index

The Laspeyres index systematically overstates inflation, while the Paasche index understates it, because the indices do not account for the fact that consumers typically react to price changes by changing the quantities that they buy. For example, if prices go up for good c, then ceteris paribus, quantities of that good should go down. Ceteris paribus is a Latin phrase, literally translated as with other things [being] the same, and usually rendered in English as all other things being equal. ...

A third index, the Fisher index (after the American economist Irving Fisher), tries to overcome this problem. It is calculated as the geometric mean of P_P and P_L: Irving Fisher (February 27, 1867 Saugerties, New York — April 29, 1947, New York) was an American economist, health campaigner, and eugenicist. ... The geometric mean of a collection of positive data is defined as the nth root of the product of all the members of the data set, where n is the number of members. ...

However, there is no guarantee that the overstatement and understatement will thus exactly one cancel the other due to things like the substitution effect and technological innovation. While these indices were introduced to provide overall measurement of relative prices, there is ultimately no way of measuring the imperfections of any of these indices against reality. Consumer theory relates preferences, indifference curves and budget constraints to consumer demand curves. ... Various meters Measurement is the estimation of a physical quantity such as length, temperature, or time. ...

See also

• Aggregation problem
• Inflation
• GDP deflator
• Etienne Laspeyres
• Hermann Paasche
• Irving Fisher

The aggregation problem in economics refers to the difficulty of treating empirical or theoretical aggregates as though they reacted analogously to the behavior of optimizing individual agents as described in general microeconomic theory (Fisher, 1987, p. ... In economics, the GDP deflator (implicit price deflator for GDP) is a measure of the change in prices of all new, domestically produced, final goods and services in an economy. ... (Ernst Louis) Etienne Laspeyres (Halle an der Saale, November 28, 1834 – August 4, 1913) was Professor ordinarius of Economics and Statistics or State Sciences and cameralistics in Basel, Riga, Dorpat, Karlsruhe and finally for 26 years in Giessen. ... Hermann Paasche (1851-1925) was a German economist. ... Irving Fisher (February 27, 1867 Saugerties, New York — April 29, 1947, New York) was an American economist, health campaigner, and eugenicist. ...

Notes

1. ^ Chase, 108.
2. ^ Chase, 108.
3. ^ Chase, 108-109

References

• Chance, W.A. "A Note on the Origins of Index Numbers." The Review of Economics and Statistics, Vol. 48, No. 1. (Feb., 1966), pp. 108-110. Subscription URL

External links

• A discussion of alternative price indices at BEA
• PPI data from BLS
• Detailed information from BLS about how the PPI is calculated and applied

• Text of Rice Vaughan's A Discourse of Coin and Coinage by chapter or single page of text