Compiling Tertiary price indexes
It is also possible to construct tertiary indexes, where price movements are retained but an entirely new weighting pattern is applied. In this case the resulting tertiary index has consistent price movements at the elementary aggregate level, but results in a different price movement at the top or root of the index. This device is a powerful analytical tool that allows further re-use of price samples.
Price Indexes and the Value Aggregate
A price index is only meaningful in relation to the basket to which it refers. The value aggregate is a measure that expresses the reference period quantities in terms of current period prices. For an input price index, a value aggregate is a measure of expenditure, and for an output price index it is a measure of revenue. A value aggregate, with prices from period t and quantities from period 0 is defined as:
\(V^{0,t} = {\displaystyle\sum_{i=1}^{N} P^t_iq^0i}\)
The value aggregate includes the specification of a group of included products (which items to include), the economic agents engaging in transactions involving those products (which transactions to include), as well as the valuation and time of recording principles motivating the behaviour of the economic agents undertaking the transactions (determination of prices). The included elementary items, their valuation (the \(p^t_i\)), the eligibility of the transactions and the item weights (the \(p^0_i\)) are all included in the definition of the value aggregate.