A price index is the price of a group of products expressed as a percentage of the price of a comparable group of products at an earlier date. The Consumer Price Index (CPI), which is the most widely-used price index, is the price of the "basket" of products that is purchased by the typical consumer, expressed as a percentage of the price charged for a comparable basket at a stated base date. The CPI is often used as an inflation target by central banks and other monetary authorities, as described in the article on macroeconomics. More generally, it provides an indication of changes in the cost of living and is used as a factor to "index" past payments in order to maintain their purchasing power. Some price indexes can also be used as a divisors, or "deflators", that can be applied to percentage increases of quantities measured in monetary units, such as dollars, in order to estimate their percentages had they been measured in physical units, such as gallons. Indexes are available for a variety of prices including those of factory inputs and outputs, commodities and housing.
The construction of price indexes poses issues of which those affecting consumer price indexes are typical. Different countries have adopted different ways of calculating consumer price indexes    but they have important features in common. The subject of a consumer price index is the mix of the purchased items that are bought by a typical consumer. The price index is calculated as the weighted average of the current prices of those items expressed as a percentage of the weighted average of their prices in a previous year, termed the reference year. In calculating those averages, the weight applied to each item is an estimate of the share of that item in the total of consumers’ expenditure. The weights adopted can be derived from national accounts or from surveys set up for the purpose. However, since the composition of consumer expenditure is constantly changing, a choice has to be made whether to use weights corresponding to the current mix, or to the mix at a stipulated previous year, termed the base year (which is usually, but not always, the same as the reference year), or to some intermediate mix. Similar issues arise in the construction of other price indexes: for producer price indexes, the choice concerns the weighting of items in the mix of outputs; and for housing price indexes, the weighting of items in the mix of house types.
Various answers to the weighting question have been put forward, none of them entirely free of shortcomings. The best-known are the Laspeyres Index and the Paasche Index The Laspeyres price index uses the weights obtained for the base year for all succeeding years. It can be assumed to overstate inflation because it does not allow for the possibility that some consumers switch their purchases away from items that have shown the greatest price increases (resulting in what is known as substitution bias). The extent of the resulting bias is customarily limited by the periodic adoption of a more recent base year. The Paasche price index, on the other hand, uses weights obtained for the current year, and can be assumed to understate inflation for the converse reason. The Fisher Ideal price index is the geometric mean of the Laspeyres and Paasche indexes. It produces a smaller bias than either, simply because it lies between them. The "chain-linked" price index, which is calculated by repeatedly taking the base year for each year to be the year preceding that year has been tending to displace other indexes and it is now widely used in the construction of national accounts. However, unlike the Laspeyres and Pasche indexes, chain-linked indexes cannot validly be used as deflators to derive volume changes from changes denominated in money terms, although using them for that purpose does not necessarily result in serious errors .
Conventional consumer price indexes take no account of the fact that technological advances enable consumers to enjoy a higher living standard without increasing their expenditure. As a result they tend to overestimate the increase in the cost of living. In an extreme example the American economist William Nordhaus has calculated that the price of illumination has fallen by more than 99 per cent since 1800, whereas the price indexes for lighting equipment have risen by 180 per cent  . In 1996 an NBER working paper estimated that failure to take account of quality improvements had overstated the cost of living in the United States by about 1 per cent a year  and a report to the United States Senate estimated the overstatement to be 1-1.5 per cent . Methods of reducing such quality bias have been described in detail in an OECD handbook . The principle method depends upon estimates of the amount that consumers are prepared to pay for quality improvements. (The prices of different models on sale at the same time are treated as functions of measurable characteristics such as power and speed, and option costing or regression methods are used to estimate by how much the price depends upon each of those characteristics . Some improvements are not amenable to objective adjustments, however .) Hedonic price indexes, taking account of such estimates, are now used for computer equipment in official statistics in the United States and elsewhere, and have resulted in upward revisions of estimates of the growth of real gross domestic product.
Outlet substitution bias
Outlet substitution bias occurs when shifts to lower-price outlets are not taken into account
The GDP deflator
The procedure used to convert the current price estimate of gross domestic product (GDP) into a constant price estimate involves the application as divisors of hundreds of separate indexes for its individual components including, for example, indexes of the prices of investment goods and of imports of and exports, as well as the consumer price index  . The GDP deflator  is a synthetic index produced by expressing the current price GDP as a percentage of the resulting estimate of its constant price version. It is thus a weighted average of price indexes, rather than a directly-measured price index. It is sometimes used as an indicator of inflation, and it can be regarded as being the most comprehensive of such indicators.
- ↑ The Consumer Price Index US Bureau of Labor Statistics Handbook of Methods Ch 17 2007
- ↑ Consumer Price Indices Methodology UK Office of National Statistics
- ↑ Harmonised Indices of Consumer Prices Official Publications of the European Community 2004
- ↑ Intertemporal Index Numbers of Prices and Volumes United Nation Statistics Division 2007
- ↑ Jack Triplett: Economic Theory and BEA's Alternative Quantity and Price Indices, Survey of Current Business US Bureau of Economic Analysis April 1992
- ↑ Peter Hill Recent Developments in Index Theory and Practice OECD Economic Studies No. 10, 1988
- ↑ William Nordhaus Do real output and real wage measures capture reality? - in The Economics of New Goods pp29-66 University of Chicago Press 1997
- ↑ Matthew Shapiro and David Wilcox Mismeasurement in the consumer price index National Bureau of Economic Research Working Paper No 5590 1996
- ↑ Toward A More Accurate Measure Of The Cost of Living Report to the Senate Finance Committee 1996
- ↑ Jack Triplett Handbook on Hedonic Indexes and Quality Adjustments in Price Indexes OECD STI Working Paper 2004/9 OECD 2004
- ↑ David Fenwick Measuring Consumer Inflation in the United Kingdom in World Economics Vol 4 No1 2003 
- ↑ Ralph Turvey What a Consumer Price Index Can’t Do in World Economics Vol 5 No 3 2004 
- ↑ Jerry Hausman and Ephraim Leibtag: CPI Bias from Supercenters: Does the BLS Know that Wal-Mart Exists?, MIT, 10 June, 2005
- ↑ Alan Young Alternative Measures of Change in Real Output and Prices. Survey of Current Business Bureau of Economic Analysis 1992
- ↑ GDP Deflators- a User’s Guide HM Treasury 2007
- ↑ Inflation OECD Factbook 2007