Indices of Structural Changes in the Theory of the Price Index
The aim of this contribution is to present a new approach in the theory of the price index, leaving the frame of the traditional theory. One application of the price index theory is to decompose the change of a volume (i. e. expenditure or turnover) aggregate into a price and a quantity component. Unfortunately, there is no unique pair of (price and quantity) indices in the sense of Eichhorn and Voeller (1983) permitting the decomposition of the volume change, and it is rather a political decision which pair to use in a specific situation. However, there is a unique “solution” in the special case where quantities remain unchanged (or change by a common factor λ): It is generally accepted that in this case the price index number should coincide with the ratio of the two volume aggregates (q 0 · p 1/q 0 · p 0), the quantity index number yielding unity (or λ). Defining this ratio as the “pure” price (level) index, and a “pure” quantity (level) index accordingly, the difference between the volume change and the product of these indices in the general case can be attributed to a third factor. This factor should equal unity if relative prices or relative quantities do not change, i. e. if the price structure or the quantity structure remains unchanged. Thus it can be regarded a measure of structural changes.
In this paper such a measure is derived by a true statistical approach, where the level indices are uniquely determined as the indices named after Laspeyres. The structure index is a function of (1) the (generalized) coefficient of correlation between the individual price and quantity changes and the (generalized) coefficients of variation of (2) the price and of (3) the quantity changes. The latter are frequently used measures of inequality.
KeywordsCovariance Income Erwin Lasp
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