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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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# 2 Approaches in index theory 47

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47 Chapter 2 Approaches in Index theory in this chapter an attempt is made to present an overview of theories or "approaches" in index theory along with some Index formulas (some of them, however, failed in gaining importance in the practice of official price statistics).1 There is no end to the search for more general Index functions or in attempts to derive classes of index functions an the basis of some few fundamental principles or some new ways of look- ing at the Index problem. Thus the chapter can necessarily present only fragments of more or less theoretical nature. 2.1 Outline of Index theories or "approaches" Index theory has a wide variety of "approaches" to offer. For the most part Index the- ory, and hence also the rivalling approaches, have to do with the assessment of in- dex formulas, lt is perhaps a fruitless effort to count all the different index formulas that have been invented and proposed by anybody, as being the "best" or "ultimate" formula. There are hundreds of formulas and the set of formulas we might think of being useful in some respect is unbounded. Introducing this chapter, therefore, the best we can do is to try to give a systematic, fair, and balanced overview. Reviewing textbooks on index theory and price statistics, a salient feature of most of them is that often some "approaches" are exempted from presentation, or that at least the place devoted to some topics may appear to be too small as...

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