Theory of the Price Index: Fisher’s Test Approach and by Wolfgang Eichhorn

By Wolfgang Eichhorn

We desire to thank Georg Hasenkamp for necessary reviews on an prior draft of the manuscript and Steven Diamond for his kindness in studying the manu­ script and delivering recommendation concerning the kind of the exposition. we're additionally thankful to overlook Ingeborg Kasper for her cautious typing of the manu­ script. Contents 1. creation four 2. rate Indices based in simple terms on costs 2. 1 Definition, Examples, Implications four 2. 2 Characterizations of Pri~e Indices 15 three. expense Indices counting on costs and amounts 22 three. 1 Definition, Examples 23 three. 2 Fisher's method of assessments 29 three. three Implications and Characterizations 35 three. four Independence and Inconsistency of Fisher's exams forty four three. five common answer of the Inconsistency challenge fifty four four. expense degrees, cost Indices, and Fisher's Equation fifty nine of trade four. 1 Definition, Examples, Implications 60 four. 2 Characterizations of expense degrees sixty four four. three Fisher's Equation of alternate Reconsidered seventy two Bibliography five. eighty three 6. Index 88 1. creation within the face of the commercial, political, and social difficulties resul­ ting from world-wide inflation, theories of the fee index have won new recognition. This newfound curiosity in rate indices stems from the truth that all such indices are designed to function yardsticks for measuring the fee habit of products and providers. that's, all rate indices relate to the idea that of the 'purchasing energy of money'. If costs raise, then the worth of the unit of cash declines, i. e.

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E ,9. 5) is not satisfied, a contradiction is established. 0). 0) to be wrong, S. Swamy [1965J proved a nonexistence theorem for a set of tests which contains the weakened version of the Commensurability Test T4 (see footnote 1, page 24) in addition to Wald's subset. Furthermore, Swamy assumed the differentiability of the price index. 24)below. ~ .... lR I I which does not satisfy the remaining test. n T2), T3, and T4, but not TS'. 9E. -0 o-0 - 0 g E ap { ~ a,b vectors with n positive components (even T2), T3, and TS' 1), but not T4.

JR 1+ which satisfies T1, T2', and T5 at the same time. 20). The same is true for the differentiability assumption in Swamy's theorem. Thus far, it has been the purpose of the analysis to state or to derive non-existence theorems which demonstrate the inconsistency of certain subsets of Fisher's system of tests F = {T1,T1 ',T2,T2', T3,T4,T5,T5'} . Until now, it was impossible to answer the question of whether there exist any further or even more general non-existence theorems relating to Fisher's test system F.

1)From T1 one even concludes for A 1: Q) J 0 J 0 (g ,12. ,g d2 ) 1 0 (51 ,E ,51 ,E ) 1• 1. - 32 - We point out that the weakened versions T1', T2', and TS' of the Proportionality Test T1, the Circular Test T2, and the Factor Reversal Test TS, respectively, really make sense. 2 meets the Weak Proportionality Test T1', but not T1. j')** JR~~ ) + JR++ satisfies the Base Test T2', but not T2. 7) satisfies the Product Test TS', but not TS. 9) Remark: 1) a) T1 ' not satisfied ~ T1 not satisfied, b) T2' not satisfied => T2 not satisfied, c) TS' not satisfied => TS not satisfied.

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