Discussion Papers,
Statistics Norway, Research Department

Abstract: The paper presents a method for computing the curvature implicit in the use of superlative price indices. It extends the quadratic lemma and allows us to compute the elasticity of substitution of the underlying preferences in the direction of the observed price change for the Törnqvist and the quadratic mean of order r indices. It derives the expressions for the directional shadow elasticity of substitution and applies the results to the Norwegian CPI data base.

Keywords: elasticity of substitution; superlative index; consumer price index (CPI).

JEL-codes: C43; D12 February 2005

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