Operations Research Proceedings 1994 pp 270-275 | Cite as

# Indices of Structural Changes in the Theory of the Price Index

## Summary

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.

## Keywords

Price Index Structure Index Price Structure Quantity Change Volume Aggregate## Preview

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