RDP 9810: The Distribution and Measurement of Inflation Appendix A: Derivation of the Weights

The data used in this paper cover the 9^th through 12^th CPI series. The CPI is based in the 11^th series at 1989/90 = 100. New weights were introduced, for each of the new series, on March 1982, December 1986 and June 1992. These dates will be denoted k₁, k₂ and k₃. Each series is spliced to the base period. The level of the CPI at time t is:

for

where Ρ_it is index level for the i^th component at time t, is the weight for the i^th component in the j^th series, and the splicing factors are:

Temporarily omitting the splicing factors

where

Manipulating Equation (A1) in the same manner as Equation (A3), the aggregate quarterly inflation rate can be derived as a weighted sum of the quarterly component inflation rates:

where

for