Introduction

Since the beginning of the 19th century a large number of price and quantity indices have been invented. Every statistician knows at least the most famous names: Laspeyres, Paasche, Fisher. But there are many more indices, mostly named after their inventors.

Parallel with the invention of new indices went the development of criteria for distinguishing between them. This was a rather natural process. Inventing a new formula is not enough. One should also provide evidence that the newborn index is “better” than all existing ones. In the beginning of the 20th century this line of research culminated in the still impressive book The Making of Index Numbers by Irving Fisher (1922). In this book Fisher evaluated in a systematic manner a very large number of indices with respect to a number of criteria. These criteria were called tests.

Most of these tests were of older date. For instance, the identity test (saying that, if the prices of period 1 are the same as those of period 0, then the price index number should be equal to 1) is due to Laspeyres (1871). The time reversal test (saying that the price index number for period 1 relative to period 0 should be the reciprocal of the price index number for period 0 relative to period 1) and the dimensional invariance or commensurability test (saying that the price index should not be dependent on the units of measurement) have been proposed by Pierson (1896).