The paper rationalizes certain functional forms for index numbers with functional forms for the underlying aggregator function. An aggregator functional form is said to be 'flexible' if it can provide a second order approximation to an arbitrary twice diffentiable linearly homogeneous function. An index number functional form is said to be 'superlative' if it is exact (i.e., consistent with) for a 'flexible' aggregator functional form. The paper shows that a certain family of index number formulae is exact for the 'flexible' quadratic mean of order r aggregator function, (ΣiΣjaijxi r 2xj r 2)1 r, defined by Den and others. For r equals 2, the resulting quantity index is Irving Fisher's ideal index. The paper also utilizes the Malmquist quantity index in order to rationalize the Törnqvist-Theil quantity indexin the nonhomothetic case. Finally, the paper attempts to justify the Jorgenson-Griliches productivity measurement technique for the case of discrete (as opposed to continuous) data. © 1976.
CITATION STYLE
Diewert, W. E. (1976). Exact and superlative index numbers. Journal of Econometrics, 4(2), 115–145. https://doi.org/10.1016/0304-4076(76)90009-9
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