The Fisher index can be obtained by taking the geometric mean of the Laspeyres and Paasche indexes
. The latter two indexes are probably the two best-known price index formulas, whose inception dates back to the nineteenth century.
The Fisher Ideal Index is the weighted average of Laspeyres and Paasche Indexes
, which perfectly decomposes energy intensity into two efficiency ([F.sup.eff.sub.t]) and activity ([F.sup.act.sub.t]) elements with no residuals.
The calculation of the overall trading index were based on the Fisher index, which made it possible to get rid of the shortcomings of the Laspeyres and Paasche indexes
and obtain a more accurate assessment of changes in prices for the period analyzed.
* HIES 1990-91 contains 6,376 households ** All figures have been adapted using Paasche Index
. ** Data has been weighted.
Suffice to say that the Laspeyres and the Paasche indexes
are considered transitive, however a Laspeyres (hedonic) price index will tend to overestimate the true difference in rental prices while the Paasche (hedonic) price index will underestimate this difference.
The Laspeyres index uses base period weights and the Paasche index
uses current period weights.
(13.) The Fisher index is the product of the square root of a Laspeyres and a Paasche index
. As with all indexes, it is adimentional.
(10.) The Fisher index is a geometric average of the Laspeyres and the Paasche index
. It has several desirable properties, including its characterisation as "superlative", meaning that it can be directly derived from the microeconomic fundamentals of profit maximisation.
The Laspeyeres index tends to overstate price changes, while the Paasche index
tends to understate them.
For example, at a time when prices are arising, laspeyres price index usually shows a higher trend than a Paasche index
. This aspect of index numbers is termed as upward bias in Laspeyres index and downward bias in Paasche index
The implicit deflator for the personal consumption of medical care [(P.sub.PCE medical care.]) contrasts with the MCPI in that the former is a Paasche index
and the latter a Laspeyres index.
We use the Paasche index
number formula to construct an aggregate of gross output less intermediate input.