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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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8 'rderspatlal comparisons of prices and volumes 497


497 Chapter 8 Interspatial comparisons of prices and volumes The presentation of Index formulas set out in the preceding chapters was focused on intertemporal comparisons. In Index theory the measurement of differences in price levels or production levels (quantity indices) of different countries and making consis- tent (transitive) multi-lateral comparisons between a number of different countries has been neglected for quite a long time, but the issue experienced a revival in the 1970s and 80s, due to growing activities in international comparisons and to European inte- gration.1 Interestingly, the methods proposed to solve problems of multinational compari- sons on the level of individual commodities and national CPI-baskets (in order to en- sure "pure" comparability) as well as the aggregation over countries seem to have fallen into oblivion when the euro- and thus the HICP-project emerged and chain in- dices became fashionable. The chapter starts with a general introduction (sec. 8.1). In sec. 8.2 we try to give an overview of methods as well as desirable properties of Index functions used with- out going into details and will then give more information concerning selected meth- ods in the following sections. 8.1 Introduction into interspatial comparisons In some aspects intertemporal (comparing points or intervals in time) and interspatial (interregional or international) comparisons face equivalent problems such that meth- ods developed for one case can easily be translated into the other case. But there are also dissimilarities we are going to work out first in this section (part a). The next point will...

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