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 R^t_hz—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 w_hi 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 w_hi are essentially in the second the weights w_hi are essentially where p_hi 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 R^t_hz is given by the weighted average

or, if the geometric mean computation is used, is given by

where w_hi 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