# Deriving annually linked quarterly Laspeyres-type volume indexes

Latest release
Australian System of National Accounts: Concepts, Sources and Methods
Reference period
2020-21 financial year

6.22    There are several ways of linking annually weighted quarterly Laspeyres-type volume indexes. Annex A to this chapter describes the three methods outlined in 2008 SNA, including the one-quarter overlap method which is used in the ASNA.

6.23    After linking, the quarterly chain volume estimates are benchmarked to their annual counterparts. This benchmarking serves two purposes:

1. It overcomes the inconsistency arising from the different linking methods required to compile quarterly chain volume estimates versus annual chain volume estimates; and
2. It ensures the quarterly chain volume estimates are consistent with the data from the annual S-U tables. The Supply-Use tables are explained in more detail in Chapter 7.

6.24    The one-quarter overlap method involves calculating a link factor using overlap values for a single quarter. To link the four quarters of year $$y-1$$ at year $$y-2$$ average prices with the four quarters of year $$y$$ at year $$y-1$$ average prices, a one-quarter overlap can be created for either the fourth quarter of year $$y-1$$ or the first quarter of year $$y$$. The link factor derived from an overlap for the fourth quarter of year $$y-1$$:

$$\large{ = \frac{{\sum\limits_{i = 1}^n {P_i^{y - 1}q_i^{4,\left( {y - 1} \right)}} }}{{\sum\limits_{i = 1}^n {P_i^{y - 2}q_i^{4,\left( {y - 1} \right)}} }}}$$

6.25     Multiplying the quarterly values for year $$y-1$$ at year $$y-2$$ average prices with this link factor puts them on to a comparable valuation basis with the quarterly estimates for year $$y$$ at year $$y-1$$ prices.