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Index Theory and Price Statistics

Peter von der Lippe

This textbook integrates mathematical index theory and its application in official price statistics. It tries to bridge theory and practice, due to the apparent divergence between mathematicians with ever more sophisticated and complex models and practitioners with problems that are more and more difficult to understand without broad knowledge and some experience. The text offers an introduction into axiomatic, microeconomic and stochastic reasoning as regards index numbers, with moderately difficult mathematics. It also summarizes many ongoing discussions concerning methodological merits and demerits of specific indices, such as consumer price-, producer price-, unit value- and chain indices, in official price statistics. The book is comprehensive and presents a readable overview of a great number of topics in modern price index theory and their application in inflation measurement, deflation of aggregates in National Accounts, sampling and quality adjustment in price collection and other important though controversial issues.

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7 Chain indices 429

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429 Chapter 7 Chain indices In this chapter an abbreviated account of some parts of my book an chain indices will be given. As I became more and more a non-chainer after having examined the ar- guments advanced by chainers,1 lt should be useful to consider first the reasons given for the superiority chain indices purportedly have over direct indices (sec. 7.1) along with a possible rebuttal of such arguments. lt then remains for us to give a sur- vey of the most important properties of chain indices (sec. 7.2), on which agreement or disagreement of this Index approach is grounded. lt is assumed that the presenta- tion in sec. 2.5 and the definitions, notations etc. introduced there are familiar to the reader. 7.1 Arguments in favor of the chain Index approach We first comment on some general observations concerning the rivalry of arguments followed by a survey of (alleged) advantages of chain indices compared to traditional (direct) Index formulas, discussing each argument one by one. a) Overview of arguments for chain indices and some general observations concerning the arguments of chainers lt is difficult to find a system for the arguments brought into play in favor of chaining. Nonetheless, an attempt is made in what follows. In principle there are five groups of arguments to support the idea of chaining (see fig. 7.1.1): A links These reasons given for the pretended superiority of chain indices fo- cus an links rather than an the chain and claim an advantage...

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