By S.N. Afriat
The fee index, a pervasive lengthy verified establishment for economics, is a bunch issued by means of the Statistical place of work that are supposed to inform a person the ratio of prices of holding a given lifestyle in classes the place costs fluctuate. For a sequence of 3 sessions, the fabricated from the ratios for successive pairs needs to coincide with the ratio for the endpoints. this is often the chain consistency required of fee indices. A traditional supposition is that the index depends on a formulation concerning rate and volume facts for the 2 reference sessions, consistently joined with the query of which one to decide on, and the perplexity that chain consistency isn't really received with any. therefore eventually they need to all be deserted. this case displays ‘The Index quantity Problem’. This booklet brings jointly a coherent dialogue of 50 years of astonishingly artistic paintings in this topic.
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Additional resources for Economics and the Price Index (Routledge Frontiers of Political Economy)
Caves et. al. (1982) have considered the case of a translog functional form where the parameters of the second order terms are constant, that is atij = a¯ ij . In this case, l = 1/2. However, in view of the above-mentioned results, Diewert functional forms for superlative index numbers are not necessarily the geometric average of the two ‘true’ indexes. Alternatively, it is possible to deﬁne a quadratic mean-of-order-r quantity index number 1 0 1 0 r/2 r i si (qi /qi ) QD ≡ with r = 0, which reduces to the Fisher “ideal” 1 0 1 r/2 i si (qi /qi ) quantity index with r = 2, to the implicit Walsh quantity index with r = 1, and to the Törnqvist quantity index number at the limit as r → 0.
After the procedure for ﬁnding individual solutions, the further interest is in the collection of all solutions. The solutions describe a polyhedral convex cone in the price level space of dimension m, and the normalized solutions describe a bounded polyhedral convex region in the simplex of reference, with faces or vertices to be determined, the m simplex vertices being in correspondence with the m data periods, and price levels. Then there are approximation methods to serve for the case of inconsistency.
Since Mst is the coefﬁcient of some chain with extremities s, t it appears that the interval coefﬁcient Mts Mst of M is the coefﬁcient of some cycle of L through t, and therefore if the cycle test holds for L then so does the interval test hold for the derived system M . Given any solution for system L, and equivalently system M , necessarily Kst ≤ Hst ≤ Ps /Pt ≤ Mst ≤ Lst , showing how price indices, which on the basis of data just for the reference period are conﬁned to the ordinary Laspeyres-Paasche interval, become conﬁned to the narrower derived Laspeyres-Paasche interval when based on the more extended data.
Economics and the Price Index (Routledge Frontiers of Political Economy) by S.N. Afriat