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The change in a Fisher index from one period to the next is the geometric mean of the changes in Laspeyres' and Paasche's indices between those periods, and these are chained together to make comparisons over many periods: = This is also called Fisher's "ideal" price index.
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 .
Setting equal to +: + gives Paasche-type index and so on. The Fisher-type index is defined as a square root of product of Laspeyres- and Paasche-type indexes. The Edgeworth-Marshall index uses the arithmetic mean of mean characteristics of two periods t and t+1. A Walsh-type index uses the geometric average of two periods.
Hermann Paasche (German pronunciation:; February 24, 1851 – April 11, 1925) was a German statistician and economist. He is known for his Paasche Index, which provides a calculation of the Price Index. Paasche studied economics, agriculture, statistics and philosophy at University of Halle.
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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]
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