Introduction

A price index refers to a pair of consumption periods, and price-index formulae usually involve demand data from the reference periods alone. When there are many periods, a price index can be determined from any one period to any other, in each case using the data from just those two periods. But then consistency questions arise for the set of price indices so obtained. Especially, they must have the consistency that would follow from their being ratios of ‘price levels’. The well-known tests of Irving Fisher have their origin in such questions. When these tests are regarded as giving identities to be satisfied by a standard formula and are taken in combination, it is impossible to satisfy them. Such impossibility remains even with partial combinations. Eichhorn and Voeller (1976) have given a full account of the inconsistencies between Fisher's tests. Reference is made there for their results and for the history of the matter.

Fisher recognizes the consistency question also in his idea of the ‘rectification of pair comparisons’. In this the price indices are all calculated, as usual, separately and regardless of any consistency they should have together, and then they are all adjusted in some manner so that they can form a consistent set. For instance, by ‘crossing’ a formula with its ‘antithesis’ you got one that satisfied the ‘reversal’ test. Here he takes one of the tests separately as if any one could mean anything on its own, and contrives a formula to satisfy it.