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The Marshall-Edgeworth index, credited to Marshall (1887) and Edgeworth (1925), [11] is a weighted relative of current period to base period sets of prices. This index uses the arithmetic average of the current and based period quantities for weighting. It is considered a pseudo-superlative formula and is symmetric. [12]
Since upper and lower bounds of the true cost of living index can be found, respectively, through the Laspeyres and Paasche indices, the geometric average of the two, known as the Fisher price index, is a close approximation of the true cost of living index if the upper and lower bounds are not too far apart. [6]
Hence, one may think of the Paasche index as one where the numeraire is the bundle of goods using current year prices and current year quantities. Similarly, the Laspeyres index can be thought of as a price index taking the bundle of goods using current prices and base period quantities as the numeraire.
Ernst Louis Étienne Laspeyres (German: [lasˈpaɪrəs]; 28 November 1834 – 4 August 1913) was a German economist. He was Professor ordinarius of economics and statistics or State Sciences and cameralistics (public finance and administration) in Basel , Riga , Dorpat (now Tartu), Karlsruhe , and finally for 26 years in Gießen .
This is a Laspeyres index, because it is base-weighted. It would be possible to use a Paasche index or a Fisher index, but this is not customary. References. Neuberger, H and Caplan, D (1998) The measurement of real public sector output in the National Accounts. Economic Trends no. 531, February 1998, 29–35.
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This is because of Laspeyres or Paasche price index formula used to define inflation or price index on weighted scale, i.e. net consumption on a weighted scale (w). The index methods above use both price and qty in the ratios to define indices. The relationship stems from the base method being Laspeyres or Paasche. Another approximation:
The formula effect accounts for the different formulas used to calculate the two indexes. The PCE price index is based on the Fisher-Ideal formula, while the CPI is based on a modified Laspeyres formula. The weight effect accounts for the relative importance of the underlying commodities reflected in the construction of the two indexes.