Laspeyres index - Laspeyres index

Japanese: ラスパイレス指数 - らすぱいれすしすう（英語表記）Laspeyres index

An index calculated based on a proposal by German economist Étienne Laspeyres (1834-1913). The formula was proposed in 1864, and after a number of debates, it was established in 1871. When calculating the index, the purchase ratio (weight) at the base time (the point in time used as the basis for comparison) is used.

An example of creating a price index for n types of goods (products) based on the Laspeyres formula can be explained as follows. Let the price of good i at the base time be p _{0 i} , the price at the comparison time (time t ) be p _ti , and the purchase amount of that good at the base time be q _{0 i} . The Laspeyres price index P _L ( t ) at time t is calculated using the following formula.

Additionally, if the purchase amount of good i at the base time is w _{0 i} = p _{0 i} q _{0 i} , then the Laspeyres price index P _L ( t ) at time t can also be expressed by the following equation, which shows that the price of each good is weighted averaged by the weights at the base time.

While the Laspeyres index is easy to calculate, it has the disadvantage that it does not reflect changes in the economic structure because the weights are fixed at the base period.

The Laspeyres index used to compare national and local government employee salaries is different from the one mentioned above. Specifically, the salary levels of local government employees in each municipality are indexed with the salary of national government employees set at 100, adjusting for differences in age structure, etc.

[Nobuo Iizuka February 18, 2019]

[Reference item] | Index | Price index

Source: Shogakukan Encyclopedia Nipponica About Encyclopedia Nipponica Information | Legend

Japanese:

ドイツの経済学者ラスパイレスÉtienne Laspeyres（1834―1913）の提案に基づいて算出される指数。その算式は1864年に提案され、数々の論争を経て1871年に確立された。指数を算出する際に、基準時（比較の基準となる時点）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ラスパイレス算式に基づいて作成する場合を例にして説明すると下記のとおりとなる。財iの基準時の価格をp_0i、比較時（t時点）の価格をp_tiとし、その財の基準時の購入量をq_0iとする。t時点のラスパイレスの価格指数P_L(t)は次の式で算出される。