Price index

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. More generally, it provides an indication of changes in the cost of living and is used as 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.

Methodology

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.

Weighting methods

Various answers to the weighting question have been put forward, none of them entirely free of shortcomings. 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 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. A chain-linked price index is calculated by taking the base year for each year to be the preceding year, and thereby avoids substitution bias. The Laspeyres and Pasche indexes can be used as deflators to derive volume changes from changes denominated in money terms. That cannot validly be done using chain-linked indexes, although it does not necessarily result in serious errors .

Quality bias

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. 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.