An Impossibility Theorem Concerning Multilateral International Comparison of Volumes

This paper considers the problem how to make real income comparisons between more than two countries or across more than two years. First, four basic requirements are formulated that we think a sensible way of comparing should satisfy. The Apples and Oranges theorem then shows that no method for making multilateral comparisons could ever have those four minimal properties. Going from bilateral to multilateral real income indices will therefore always come at a cost; at least one of these very modest requirements will have to be violated. Since the problem under consideration can be seen as a dual one, this impossibility theorem has serious consequences. After all, a method to compare price levels internationally implies a method to compare real income levels, and the same goes for its intertemporal equivalent; if we could find a consistent way of computing inflation, we would also have a consistent measure of real income growth. The theorem therefore implies that there is a limit to the meaning of both international price level and international income level comparisons as well as to the significance of reported inflation rates and growth rates. In all these cases, we should be aware which method is used and which requirement(s) that particular method fails to satisfy.