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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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List of Figures and Tables XVII 1 General introduction and elementary price Index theory 1 1.1 Fundamental principles of price statistics and price indices 1 1.2 Unweighted indices 17 1.3 Index formulas of Laspeyres and Paasche 27 2 Approaches in index theory 47 2.1 Outline of index theories or "approaches" 47 2.2 Irving Fisher's approach and reversal tests 52 2.3 The stochastic approach in price index theory 78 2.4 Elements of the economic theory of index numbers 90 2.5 Chain indices and Divisia's approach, general introduction 132 2.6 Additive models, Stuvel's and Banerjee's index formulas 149 3 Axioms and more index formulas 165 3.1 The axiomatic approach, some theorems 165 and fundamental axioms 3.2 Fundamental axioms and their interpretation 185 3.3 Systems of axioms 216 3.4 Log-change Index numbers 1: Cobb-Douglas- and 226 Törnqvist-index 3.5 Log-change Index numbers 11: Vartia's Index formulas 243 3.6 Ideal Index functions and Theil's Best Linear Index (BLI) 255 4 Price collection and Index systems in official statistics 263 4.1 The set up of a system of price quotations and price indices in official 263 statistics 4.2 Quality adjustment in price statistics 271 4.3 Sampling in price statistics 299 5 Deflation and aggregation 315 5.1 Introduction to deflation methods 315 5.2 Deflation in volume terms, aggregation and double deflation 328 5.3 Harmonization of deflation methodology in Europe 350 5.4 Fisher's ideal Index far from being ideal 362 x 6 Price indices and unit value indices in official statistics 371 6.1 The Consumer Price Index...

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