Annual Basket Indices

The Lowe index for month m is defined by the following formula:

where p⁰ º [p₁⁰,…,p_N⁰] is the price reference period price vector, p^m º [p₁^m,…,p_N^m] is the current month m price vector and q º [q₁,…,q_N] is the weight reference year quantity vector.

The Young (1812) index is defined as follows:

where s º [s₁,…,s_N] is the weight reference year vector of revenue shares.

The geometric Laspeyres index is defined as follows:

Thus the geometric Laspeyres index makes use of the same information as the Young index except that a geometric average of the price relatives is taken instead of arithmetic one.

It is of interest to compare the above three indices that use annual baskets to the fixed base Laspeyres rolling year indices. However, the rolling year index that ends in the current month is centered five and a half months backwards. Hence the above annual basket type indices may be compared with an arithmetic average of two rolling year indices that have their last month 5 and 6 months forward. This latter centered rolling year index is labeled P_CRY.