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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

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XVII List of figures and tables Figure 1.1.1: General scope and structure of the book 3 Figure 1.1.2: Uses of price statistics and price indices 9 Figure 1.2.1: Indices as ratlos of average prices (as absolute figures) 19 Figure 1.2.2: Behaviour of unweighted indices by type of mean 23 Figure 1.3.1: Price and quantity indices 31 Figure 1.3.2:Conceptual differences in price level measurement 44 Figure 2.1.1: Structure of formal index theories 49 Figure 2.1.2: Some "constructive" approaches in index theory 51 Figure 2.2.1: Family tree of index formulas (according to Köves) 54 Figure 2.2.2: Interpretations of second and third generation indices 60 Figure 2.2.3: Crossing P with an antithesis as finder of formulas 66 Figure 2.2.4: Time reversal test and factor reversal test of second Generation indices (additive block only) 67 Figure 2.3.1: The place of the stochastic approach in index theory 80 Figure 2.3.2: Some "Budget share weighted average models" (BSW) models 83 Figure 2.3.3: Main ideas of the new stochastic approach 89 Figure 2.4.1: Indifference curve and cost minimization of a household in the microeconomic consumption theory 93 Figure 2.4.2: Income escalation at a rate of Kt and a constant structure of prices 101 Figure 2.4.3: Consumer equilibriums No and Nt 103 Figure 2.4.4: "Compensation" according to PL = 2.125 104 Figure 2.4.5: Equal values of functions in x = xo and first order approximation (tangent) 109 Figure 2.4.6: Types of sub-indices 116 Figure 2.5.1: Terminological distinctions referring to chain indices 132 Figure 2.5.2: Traditional ciassification of weighted...

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