Paasche index

Japanese: パーシェ指数 - ぱーしぇしすう（英語表記）Paasche index

An index based on a formula proposed by German economist Hermann Paasche (1851-1925) in 1874. The purchase ratio (weight) at the time of comparison is used to calculate the index.

An example of creating a price index for n types of goods (products) based on the Paasche formula can be explained as follows. Let the price of good i at the base time (the point in time used for comparison) be p _{0 i} , the price at the comparison time (time t ) be p _ti , and the purchase amount of that good at the comparison time be q _ti . Paasche's price index P _P ( t ) at time t is calculated using the following formula.

Furthermore, if the purchase amount of good i at the time of comparison is w _ti = p _ti q _ti , then Paasche's price index P _P ( t ) at time t can also be expressed by the following equation, which shows that the price of each good is calculated as a weighted average based on the weight at the time of comparison.

The Paasche index has the disadvantage that the weights must be changed each time the index is calculated, but it reflects changes in the economic structure.

[Nobuo Iizuka February 18, 2019]

[Reference item] | Index | Price index

Source: Shogakukan Encyclopedia Nipponica About Encyclopedia Nipponica Information | Legend

Japanese:

ドイツの経済学者パーシェHermann Paasche（1851―1925）により1874年に提案された算式に基づいてつくられる指数のこと。指数を算出するときに比較時の購入割合（ウェイト）を用いる。

　n種の財（商品）についての価格指数をパーシェの算式に基づいて作成する場合を例にして説明すると以下のとおりとなる。財iの基準時（比較の基準となる時点）の価格をp_0i、比較時（t時点）の価格をp_tiとし、その財の比較時の購入量をq_tiとする。t時点のパーシェの価格指数P_P(t)は次の式で算出される。