ABSTRACT
Like any other statistics, the accuracy of an index number should be given in terms of its variance .... So far nobody seems to have attempted to produce any theory for index numbers in such terms, and it seems doubtful whether any such theory could be of any practical use .... The concept of an accurate index should be given up. Statisticians should not be forced to behave as if it were possible to make the index very accurate, if only much money is spent on its construction. If government policy requires great confidence in the index, the statisticians should not permit themselves to be used as hostage. Hofsten (1956), pp. 8, 14
What Hofsten is objecting to, in an index of prices at retail, is the purposive selection both of the commodity items to be priced and of the retail outlets for the pricing. In fact there is quite general agreement that a price index should be related to a specific aggregate such as consumers' expenditures and hence that the selection of items should be purposively directed at the aggregate. A comprehensive probability sample of items would be meddlesome and place in jeopardy the concept of a price index as (e.g.) the cost of maintaining some consumption level. The selection of outlets is something quite different and there is a strong case for a probability sample of outlets (e.g.) stratified by area and type. In an earlier publication
H ofsten seems to agree with this diagnosis: The selection of items ... based on common sense and not on proper sampling methods . . . is no serious drawback. There is another sampling problem involved, the selection of retail outlets where the prices shall be collected .... To be satisfactory the price collection should be based upon an efficient sample of retail outlets. The construction of such a sample cannot be too difficult. Hofsten (1952), p. 42
True, as some countries (e.g. Sweden) have demonstrated. Nevertheless purposive selection of outlets, as well as of items, is still the rule rather than the exception. There is room for considerable improvement in the design of price index numbers.
