Fisher's Instrumental Approach to Index Numbers

Since the beginning of the nineteenth century, a large number of price index number formulae have been developed, mostly named after their inventors, such as the Paasche and Layspeyres indexes. Parallel with the invention of new index formulae, criteria were developed for distinguishing between them. These parallel developments culminated in Irving Fisher’s two classics on index numbers, The Purchasing Power of Money (1911) and The Making of Index Numbers (1922). In these, Fisher evaluated index formulae in a systematic way with respect to a number of “tests.” Although these two volumes are considered the “Old and New Testament” of Axiomatic Index Theory, the axiomatic approach originated from challenges to Fisher’s system of tests on grounds of their inconsistency and the seeming arbitrariness of the choice of tests. That debate started with Ragnar Frisch in 1930, but the Axiomatic Index Theory only got its current name and shape - based on functional equation analysis - from Wolfgang Eichhorn in 1973. In Axiomatic Index Theory, the tests are considered as requirements on the functional form of the index number from which the index formula can be derived. If these requirements are inconsistent, no formula can be constructed. So although Fisher’s work is seen as the forerunner of the Axiomatic Index Theory, his system of tests was much criticized because of its apparent internal inconsistency. The aim of this essay is to show that evaluating Fisher’s work from an axiomatic perspective leads to a misconception of his empirically inclined approach to the assessment of index numbers. For a better understanding of his work on index numbers, his background in mathematics, his philosophical thinking, and his inventions of measuring instruments will all be examined