1995; prior to that it was 1982-1984.¹³ It is planned that, as of January 2002, the quantity-base period will be 1999-2000, and that it will be updated at 2-year intervals subsequently using information from the Consumer Expenditure Survey (CEX) ending 2 years prior to the update.

Finally, the are themselves not directly observed in the household expenditure survey. Rather, the survey provides quantity-base period expenditures for item n, and the quantities are calculated by dividing by where the quantity-base period prices are obtained from the monthly pricing survey.

The CPI can be expressed as a multiple of a Laspeyres index and the reciprocal of a modified Laspeyres index based on the quantity-base period and price-reference period, namely

As seen above, P_L^s,⁰ is a constant that relates the quantity-base period to the price-reference period. The critical element of the index is indeed P_L^t, which can be rewritten as

This index can be characterized as a “chained” index, where the previous period’s index P_L^t-1 is multiplied by a dollar-weighted average of price relatives, with the dollar expenditure weights being those of the quantity-base period quantities priced at the previous period’s prices and the price relative taken with respect to the price in the previous period. One should note that what is reported monthly by BLS is the period-to-period index, namely P_L^t/P_L^t-1.