Price index
It is a statistic designed to help to compare how these price relatives, taken as a whole, differ between time periods or geographical locations.
For particularly broad indices, the index can be said to measure the economy's general price level or cost of living.
The earliest reported research in this area came from Welshman 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's analysis indicated that price levels in England had risen six- to eight-fold over the preceding century.
[1] In 1707, Englishman William Fleetwood created perhaps the first true price index.
An Oxford student asked Fleetwood to help show how prices had changed.
Fleetwood proposed 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.
Of course, for any practical purpose, quantities purchased are rarely if ever identical across any two periods.
One might be tempted to modify the formula slightly to This new index, however, does not do anything to distinguish growth or reduction in quantities sold from price changes.
The two most basic formulae used to calculate price indices are the Paasche index (after the economist Hermann Paasche [ˈpaːʃɛ]) and the Laspeyres index (after the economist Etienne Laspeyres [lasˈpejres]).
The Laspeyres index tends to overstate inflation (in a cost of living framework), while the Paasche index tends to understate it, because the indices do not account for the fact that consumers typically react to price changes by changing the quantities that they buy.
Prices are drawn from the time period the index is supposed to summarize.
For a consumer price index, the weights on various kinds of expenditure are generally computed from surveys of households asking about their budgets, and such surveys are less frequent than price data collection is.
The Geary-Khamis method used in the World Bank's International Comparison Program is of this type.
: All these indices provide some overall measurement of relative prices between time periods or locations.
Price indices generally select a base year and make that index value equal to 100.
[10] In practice, price indices regularly compiled and released by national statistical agencies are of the Laspeyres type, due to the above-mentioned difficulties in obtaining current-period quantity or expenditure data.
[11] For these cases, the indices can be formulated in terms of relative prices and base year expenditures, rather than quantities.
We can substitute these values into our Laspeyres formula as follows: A similar transformation can be made for any index.
The above price indices were calculated relative to a fixed base period.
The index is then the result of these multiplications, and gives the price relative to period
Price index formulas can be evaluated based on their relation to economic concepts (like cost of living) or on their mathematical properties.
Several different tests of such properties have been proposed in index number theory literature.
Diewert summarized past research in a list of nine such tests for a price index
This could be overcome if the principal method for relating price and quality, namely hedonic regression, could be reversed.
For instance, computers rapidly improve and a specific model may quickly become obsolete.
Statistical agencies use several different methods to make such price comparisons.
[14] The problem discussed above can be represented as attempting to bridge the gap between the price for the old item at time t,
