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EU KLEMS Working Paper Series

No. 43

Milana, Carlo (2009) Solving the Index-Number Problem in a Historical Perspective, (January, 2009)


The index-number problem is typically a problem of aggregation of changes in heterogeneous elements. Mathematically, it consists in reducing the relative change of the elements of a vector into changes in one single numerical value, a scalar. In his famous Econometrica survey of general economic theory dedicated to the problem of index numbers, Ragnar Frisch (1936, p. 1) described it in these terms: “The index-number problem arises whenever we want a quantitative expression for a complex that is made up of individual measurements for which non common physical unit exists. The desire to unite such measurements and the fact that this cannot be done by using physical or technical principles of comparison only, constitute the essence of the index-number problem and all the difficulties center here”. In economics, the solution of this problem is necessary in every decomposition of changes of total nominal values into meaningful aggregate price and quantity components.

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Last changed on: November 6 2008