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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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# 6 Price indices and unit value indices in official statistics 371

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371 Chapter 6 Price indices and unit value indices in official statistics Arguably the best known price indices of official statistics are the following three indi- ces: Consumer Price Index (CP1), Producer Price Index (PPI) of industrial and agri- cultural production, as well as construction for example, and the price indices in for- eign trade (XPI for export and MPI for import). In the case of foreign trade but also regarding salaries and wages, we always have an alternative between a true-price- Index and a unit-value-index methodology. lt appears adequate to devote a whole chapter to the CPI and general problems of inflation measurement, to the PP1 (sec. 6.3), and unit-value in contrast to price-indices (sec. 6.4). 6.1 The Consumer Price Index (CPI) and the Harmonized Index of Consumer Prices (HICP) in Europe The CP1 is a well known Instrument for measuring inflation and for deriving "deflators" for National Accounts.1 Not surprisingiy, attempts to make national CP1s comparable have started early. Moreover, the (expanding) European Union (EU, the former Euro- pean Community) and the implementation2 and possible enlargement of the Euro- pean Monetary Union (EMU) gave rise to • a harmonization of the member countries' CP1s, and • the desire to establish a Harmonized Index of Consumer Prices (HICP) aggre- gated over a group of countries such as the EU, the EMU Member Countries, or the EEA which serves also as an Integrated measure of the EMU Inflation rate (if there is such a phenomenon).3 Thus Integration of monetary policy makes...

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