Inversion Tests for Price and Quantity Indices

Abstract

It is a primary occupation of axiomatic index theory to develop tests which help to assess an index formula's economic plausibility. Some of these tests find almost universal approval. Some other tests, however, are highly controversial.
Screened by the set of approved tests, some index formulas pass without any complaint. In the present study I show that in various situations these same index formulas may generate economically nonsensical results. This suggests that an additional screening device is required. I therefore introduce  the inversion test. Interestingly, the Marshall-Edgeworth and the Fisher formulas pass the inversion test, whereas the Laspeyres and Paasche formulas do not.