Year over Year Annual Indices

Using the notation introduced above, the Laspeyres and Paasche annual (chain link) indices comparing the prices of year t with those of year t+1 can be defined as follows:

;

.

where the revenue share for month m in year t is defined as:

; m = 1,2,…,12; t = 0,1,…,T

The current year weights, s_n^t,m and σ_m^t and s_n^t+1,m and σ_m^t+1 can be approximated by the corresponding base year weights, s_n^0,m and σ_m⁰.

There is no need to restrict attention to calendar year comparisons: any 12 consecutive months of price and quantity data could be compared to the price and quantity data of the base year, provided that the January data in the non-calendar year is compared to the January data of the base year, the February data of the non-calendar year is compared to the February data of the base year, …, and the December data of the non-calendar year is compared to the December data of the base year. Alterman, Diewert, and Feenstra (1999; 70) called the resulting indices rolling year or moving year indices.