The Comparative Proportionality Test
Of all the many types of index number examined by Irving Fisher none satisfies all the tests he designed (see p. 101); even the one he selected as being the best fails one of his tests. In view of this, it is surprising to find that the new index numbers, P S and Q S , satisfy all Fisher’s tests and the important aggregation test as well (see Table 4.1) Given the non-uniqueness of index-number measures of volume and price developments of commodity aggregates from base year to current year, this extraordinary performance of the new index numbers leads one to suspect that there must be one or more other tests on which P S and Q S fare worse. Some attempts have been made at formulating at least one such test. As a result of this we now have a test which requires that, if all current-year prices are multiplied by a constant factor k and all base-year prices as well as base-year and current-year quantities are left unchanged, then the price index should be multiplied by k and the quantity index should remain unchanged. In order to avoid confusion with Fisher’s proportionality test, we shall call this test the comparative proportionality test.
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