新物価指数算式とその背景

Abstract

According to J. M. Keynes, "Index Numbers of Prices are a series of Numbers indicative of price-levels." This concept of index numbers of prices seems to be the one which is broadly accepted. In accordance with this definition, we may define Pij, the index number of prices of the j-th year relative to the i-th year, as P_=(π_j)/(π_i) where iti and itj mean the price levels of the i-th year and the j-th year respectively Then, it is obvious that these index numbers should satisfy the so-called "Circular Test", namely, P_P_P_=1. Moreover, it is shown that there can be a formula for the index numbers of prices which [satisfies the "circular test" and the "factor reversal test* as well as the "proportionality test", though Irving Fisher and Abraham Wald once insisted to the contrary. The author is of the opinion that we should avoid the "fallacy of beauty contest" in making index numbers of prices, and that we should adopt variable weights, which also contribute much to the continuity of index numbers. From such a point of view, the author has constructed for trial a new formula of price index numbers with variable weights, .which satisfy the "circular test", the "factor reversal test" and the "proportionality test

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