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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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# 5 Deflation and aggregation 315

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315 Chapter 5 Deflation and aggregation Price indices are compiled for two different purposes: firstly, to provide measures of the year to year movement of specific price levels (e.g. the rise or decline of con- sumer prices), and secondiy to "deflate" aggregates. Chapter 6 is devoted to the first problem, and chapter 5 to the second. lt is not surprising that in general an index formula is not able to serve both purposes equally well and we should therefore re- gard the two major uses of Index numbers (measurement of price levels and deflation of aggregates respectively) as two distinct topics in index theory, each of which has a "logic" of its own.1 There are also some mathematical properties of index functions, like "aggregative consistency" and (to be kept distinct) "structural consistency" that turn out to be of particular importance in the context of deflation and give rise to some additional "axioms".2 This chapter also deals with international recommenda- tions concerning the deflation of specific aggregates in National Accounts,3 and once more with the so called "ideal index" of Irving Fisher. 5.1 Introduction to deflation methods The focus of this section is to show what deflation aims at, and the methods that can be used to this end. There are several approaches to deflation and their sultability depends an the type of aggregate to be deflated. a) Objectives and types of deflation The Operation called "deflating" or "deflation" is usually defined as isolating the vol- ume component (that...

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