Price Indices Depending on Prices and Quantities
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From a historical point of view, the test approach was first introduced in J. Fisher’s  and R. Frisch’s  publications on index numbers depending on both prices and quantities. This chapter deals with the properties both authors thought to be necessary to any price index. The consistency of certain subsets of these requirements (tests) is also examined and the general solution of the inconsistency problem of Fisher’s tests is presented. In addition, we offer an answer to the question of how far the original system of tests must be weakened in order to achieve a consistent set of tests.
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