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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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1 General introduction and elementary price Index theory 1

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1 Chapter 1 General introduction and elementary price Index theory The objective of this book is to integrate a comprehensibie presentation of the theory of index numbers and practical problems of price statistics in statistical offices.1 This textbook owes its existence to TES-Courses2 on "Price Index Theory and Price Sta- tistics". The theory of index numbers is dominated by mathematical considerations, and it focuses on the justification (foundation), and assessment of Index functions (formulas) against the background of formal aspects. The practice of price statistics on the other hand, has to cope with different problems, Ilke the regular compilation of prices as well as "weights", adjustments for quality changes and the like. For each group, Index theoreticians on one hand and official price statisticians on the other, it is not easy to understand the problems of the other. Moreover the two groups appear to diverge rather than to converge.3 Therefore we aim to build a bridge between mathematical theory and practice in statistical offices and ministries. The book at- tempts to help those who have to deal with the production and Interpretation of price statistics to understand Index numbers betten lt therefore tries to provide a balanced introduction with respect to both, Index theory and practice of official statistics. This also implies a kind of presentation which throughout the book is rather moderately mathematical. 1.1 Fundamental principles of price statistics and price indices In this section some most elementary and introductory aspects of index formulas will be discussed explicitly with...

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