Producer Price Index Manual: Theory and Practice ... - METAC

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Producer Price Index Manual Thus, to the accuracy of a second-order approximation, the direct Young index will exceed its time antithesis by a term equal to the direct Young index times the weighted variance of the deviations of the price relatives from their weighted mean. Thus, the bigger the dispersion in relative prices, the more the direct Young index will exceed its time antithesis. 402
16. Axiomatic and Stochastic Approaches to Index Number Theory A. Introduction 16.1 As Chapter 15 demonstrated, it is useful to be able to evaluate various index number formulas that have been proposed in terms of their properties. If a formula turns out to have rather undesirable properties, then doubt is cast on its suitability as a target index that could be used by a statistical agency. Looking at the mathematical properties of index number formulas leads to the test or axiomatic approach to index number theory. In this approach, desirable properties for an index number formula are proposed; then it is determined whether any formula is consistent with these properties or tests. An ideal outcome is that the proposed tests are desirable and completely determine the functional form for the formula. 16.2 The axiomatic approach to index number theory is not completely straightforward, since choices have to be made in two dimensions: • The index number framework must be determined; • Once the framework has been decided upon, the tests or properties that should be imposed on the index number need to be determined. The second point is straightforward: different price statisticians may have different ideas about what tests are important, and alternative sets of axioms can lead to alternative best index number functional forms. This point must be kept in mind while reading this chapter, since there is no universal agreement on what the best set of reasonable axioms is. Hence, the axiomatic approach can lead to more than one best index number formula. 16.3 The first point about choices listed above requires further discussion. In the previous chapter, for the most part, the focus was on bilateral index number theory; that is, it was assumed that prices and quantities for the same n commodities were given for two periods, and the object of the index number formula was to compare the overall level of prices in one period with that of the other period. In this framework, both sets of price and quantity vectors were regarded as variables that could be independently varied, so that, for example, variations in the prices of one period did not affect the prices of the other period or the quantities in either period. The emphasis was on comparing the overall cost of a fixed basket of quantities in the two periods or taking averages of such fixed-basket indices. This is an example of an index number framework. 16.4 But other index number frameworks are possible. For example, instead of decomposing a value ratio into a term that represents price change between the two periods times another term that represents quantity change, one could attempt to decompose a value aggregate for one period into a single number that represents the price level in the period times another number that represents the quantity level in the period. In the first variant of this approach, the price index number is supposed to be a function of the n product prices pertaining to that aggregate in the period under consideration, and the quantity index number is supposed to be a function of the n product quantities pertaining to the aggregate in the period. The resulting price index function was called an absolute index number by Frisch (1930, p. 397), a price level by Eichhorn (1978, p. 141), and a unilateral price index by Anderson, Jones, and Nesmith (1997, p. 75). In a second variant of this approach, the price and quantity functions are allowed to depend on both the price and quantity vectors pertaining to the period under consideration. 1 These two variants of unilateral index number theory will be considered in Section B. 2 1 Eichhorn (1978 p. 144) and Diewert (1993d, p. 9) considered this approach. 2 In these unilateral index number approaches, the price and quantity vectors are allowed to vary independently. In (continued) 403
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Contents Foreword..................
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Contents D. The Incorporating of Ne
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Contents E. Industry Price Indices
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Contents Table 19.23 Manufacturing
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Foreword This Producer Price Index
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Preface The ILO, IMF, OECD, UNECE,
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Preface source (rather than requiri
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Preface tremendous concern with sam
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Preface among countries. However, t
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Preface Chapter 6 Chapter 7 Chapter
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Reader’s Guide International manu
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Reader’s Guide the System of Nati
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Abbreviations ABS ABS AF ANZIC ATM
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Abbreviations OLS Ottawa Group P C
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PART I Methods, Uses, and Coverage
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Producer Price Index Manual The exp
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Producer Price Index Manual B.1 Pri
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Producer Price Index Manual D. The
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Producer Price Index Manual theoret
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PART II Compilation Issues
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5. Sampling Issues in Price Collect
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13. Publication, Dissemination, and
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14. The System of Price Statistics
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