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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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# 4 Price collection and Index systems in official statistics 263

## Extract

263 Chapter 4 Price collection and Index systems in official statistics Index theory has often been criticized for its focus an the choice of the appropriate Index formula whilst in the practice of price statistics many other problems have to be solved, the consequences of which are perhaps much more influential (with respect to the results, published by price statisticians). Therefore it appears appropriate to devote a whole chapter to these types of problems. The following sections will outline • some general methodological discussions in price statistics, and • practical problems related to the most important price indices (to be continued in chapter 6 for some indices). lt is just this kind of practical problems we unfortunately would not be aware of if we would almost exclusively look at the problem of price Index fomulas. 4.1 The set up of a system of price quotations and price indices in official statistics The following considerations are devoted to a number of problems that arise in the practical work of official statistics, which has to provide a system of price observa- tions and price indices. The price quotationsl and compilations of indices have to be timely, regular and systematic. They should consistently cover a wide field of market activities (sales/purchases) and serve a great variety of users and purposes. In some instances it will be more, in other less difficult to arrive at correct prices and weighting schemes for price indices, and quite often there is also a need for compromises, sometimes even for...

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