The Making of Tests for Index Numbers: Mathematical Methods of Descriptive Statistics

ISBN-13: 9783790810110 / Angielski / Twarda / 1997 / 220 str.

Arthur Vogt;Janos Barta

Opis

Arthur Vogt has devoted a great deal of his scientific efforts to both person and work of Irving Fisher. This book, written with Janos Barta, gives an excellent impression of Fisher's great contributions to the theory of the price index on the one hand. On the other hand, it continues Fisher's work on this subject along the lines which several authors drew with respect to price index theory since Fisher's death fifty years ago.
"This is a highly instructive book on both the history and theory of measurement in economics. It is rather a rich source of interesting properties of more or less well known indices and famous men, especially Irving Fisher, than a precise mathematical text on the axiomatic foundations of indices." (From the Foreword by Wolfgang Eichhorn)"

Recenzje

"In summary, the book provides a valuable survey of traditional procedures in the construction of price indices and demonstrates new techniques to build indices and to test for their properties. Researchers and scientists who are engaged in the field of statistical index number theory can improve their understanding of modern index theory when reading the book." Zentralblatt für Mathematik, 878, 1998

Spis treści

Contents: Foreword by Wolfgang Eichhorn.- Preface.- Acknowledgement.- Introduction.- About Irving Fisher.- 1. Price indices: Some price indices illustrated with a two-commodities example.- The discrepancy between the indices of Laspeyres and Paasche.- The index of Divisia and some special cases.- Some other price indices.- 2. Traditional treating of properties of price indices: The price index problem: price indices as continuations of price relatives.- Properties of price relatives.- Three kinds of properties: axioms, theorems and tests.- Fisher's properties.- Axiom systems for price indices.- Some other porperties.- Characterizations of some indices.- 3. Modern treating of properties of indices: their automatic generation: The making of reversal tests of indices.- The making of antitheses of properties of indices.- Automated reasoning and one of its assistants: OTTER.- OTTER applied to properties of price indices.- 4. A new axiom system for price indices: Are there exact 'societal' sciences?- The new axiom system for price indices.- An antitheses invariant axiom system.- Consistency and independance.- The axiom system äPü for indices depending on 4 or 3 variables.- 5. First generalisations: Other interpretations of the 'prices' and 'quantities': Statistical masses and functions defined on them.- Quotas.- Densities.- Indices.- Cases where the set function m is also a content.- The Drobisch-Simpson's paradox and indices.- 6. Second generalisation: Functions other than the scalar product: Additive causal analysis.- Multiplicative causal analysis.- An example from health insurance.- 7. Third generalisation: Other statistical measures and their properties: Generalities.- The measurement of concentration and inequality.- Further measures of descriptive statistics.- Five properties.- Bibliography.- Annexes.