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At What Price?: Conceptualizing and Measuring Cost-of-Living and Price Indexes
cross classifications (e.g., Midwest Size A).15 The basic areas and item strata combine to form (218 × 54) = 11,772 basic CPI strata. Note that each of these basic CPI strata may be comprised of more than one ELI and more than one PSU.
Let h index the basic areas (h = 1, . . . ,54) and z index the item strata (z = 1, . . . . , 218). Until January 1999, BLS calculated Rthz—an estimate of the relative price change in basic area h, item stratum z, from period t - 1 to period t—using the formula when the samples of items within the item strata are selected with each unit having a probability proportional to quantity, or the formula
when the samples of items within the item strata are selected with each unit having a probability proportional to expenditure. In both forms the weights whi reflect the probability that item i in item stratum z is selected to be priced in basic area h—in the first of these the weights whi are essentially in the second the weights whi are essentially where phi is the probability that item i in item stratum z is selected to be priced in basic area h. Since January 1999, they have replaced this computation for most indexes (the housing index being the most notable exception) with a weighted geometric mean, namely
When one can obtain prices in basic area h for the universe of items in item stratum z, for both time periods t - 1 and t, then Rthz is given by the weighted average
or, if the geometric mean computation is used, is given by
where whi is the ratio of the expenditure in basic area h on item i of item stratum z to the expenditure in basic area h on all items of item stratum z. Since a census of the prices for the universe of items in item stratum z is impractical, BLS
This count is based on the 1998 CPI item strata spreadsheet provided by Dennis Fixler (personal communication, 2000).