Weighting of Index Numbers in Multilateral International Comparisons

The article reviews the methods used in practice and/or proposed by various authors for compiling indices in multilateral international comparisons. The various procedures are examined in the light of the following requirements: characteristicity (i.e. the weights should be characteristic to the countries which are compared), unbiasedness, circularity, internal consistency and factor relations. There is no perfect solution since characteristicity and circularity are always and unbiasedness and internal consistency often in conflict with each other. The indices which are best for bilateral purposes are not transitive and the basic problem of multilateral comparisons is to obtain circularity, without losing too much of the characteristicity of the bilateral comparisons. Different compromises between the two requirements are possible and this is first of all what distinguishes the various methods used in practice. Two main types of solution are applied in the various international comparisons. The first is based on the inter‐spatial Fisher's ideal formula (e.g. the Eltetö–Köves–Szulc method, the van Yzeren method, the “central country” solution); the second type uses some kind of average prices (e.g. the Geary–Khamis method). In the author's view there is no best method in absolute terms. Every method has some weaknesses and which of these weaknesses is the easiest to accept depends to a large extent on the actual aims of the comparison and on various other circumstances.