# Index review methodology

As the economy evolves and industries emerge and change, the ABS regularly reviews the scope and composition of its Producer and International Trade Price Indexes. This process is known as an ‘index review’ and can result in changes being required to existing price indexes, and to implement these changes, three steps must be undertaken to effectively update the series without compromising the quality of the price index:

- A link period must be chosen
- Value data must be price updated to the link period
- The newly weighted index chained onto the existing price index.

This process can apply to changes to an exist index series, or when a new elementary aggregate (or any other component) is introduced into a price index structure.

### Identifying the Link Period

The link period is the designated time period where the index is calculated on both an old and new weighting basis. The link period is based on availability and timing of data, internal resource constraints, economic behaviour and should not coincide with changes to tax legislation or other significant regulatory amendments.

It is generally up to the index manager to identify an appropriate link period to implement a change to the index series, however, in practice the June quarter is the preferred period as it allows direct comparison of complete financial years without having to account for the link.

### Price updating value data

Weights are price updated to account for price changes between the weight reference period and the link period. Weighting data usually comes from an annual data source, and in some cases can span more than one year. The link period, however, is always chosen to be a single quarter, and is always a period subsequent to the weight reference period. Although only observed in aggregate, the value data can be considered as being composed of the product of prices and quantities from the weight reference period. For inclusion in the index, these data will be expressed in terms of quantities from the weight reference period and prices from the link period.

Price updating value data is achieved by multiplying the weighting data by the proportional price change between the weight period and the link period. This updating occurs at the elementary aggregate level, with the resulting upper level value aggregates determined by aggregating the price updated components along the index structure.

The proportional price change between the weight period and the link period is determined by the ratio of the price indexes for the two periods; here the price indexes are on the existing index structure. In the usual case where the weighting reference period is longer than a quarter, the price index for the weight period is determined as the average of the quarterly price indexes that the weighting period spans. The ratio is the link period index divided by the averaged weight period index.

The resulting link period value aggregate is then expressed in terms of prices from the link period and quantities from the weight reference period.

### Chain linking through a link period

Chain-linking is the process of joining together two indices that overlap in one period by rescaling one of them to make its value equal to that of the other in the same period therefore combining them into a single time series. This is achieved by multiplying the index value by the linking factor.

When new weights are introduced, the price reference period for the new index can be the last period of the old index, the old and the new indices being linked together at this point. The old and the new indices make a chained index.

Chain linking can best be illustrated by means of an example. In this example we will consider a price index at period \(k\), with the index constructed from weights introduced in the reference period \(0\). Using the terminology from Chapter 10, we would express the price index at period \(k\) as

\(I^k=\frac{VA^k_{OLD}}{VA^0_{OLD}}\times I^0\)

If we choose period \(k\) as the link period, any future period price indexes will make comparisons back to the link period, and be scaled by the link period index \(I^k\). Any such comparisons will use the same price index \(I^k\) but use a value aggregate calculated on the new weighting basis. If we consider \(t\), some period after \(k\), a price index measuring the average price change from period \(0\) to period \(t\) is given by

\(I^t=\frac{VA^t_{NEW}}{VA^k_{NEW}}\times I^k\)

Example of the chain linking process

The use of fixed weights (as in a Lowe formula) over a long period of time is not considered a sound practice.

For example, weights in a producer price index have to be changed to reflect changing production patterns. Production patterns change in response to longer term price movements, changes in preferences, and the introduction or displacement of products.

The Producer and International Trade Price Indexes use a Lowe index. There are two options for updating weights. Option one, known as the direct method, involves holding the weights constant over as long a period as seems reasonable, starting a new index each time, the weights are changed. This means that a longer-term series is not available. Option two is to update the weights more frequently and chain link the series together to form a long-term series. The latter is the method used for ABS price indexes.

The behaviour under chain linking of the Lowe index formula is explored in Table 3.8 below.

Table 3.8 A closer look at linking

Item | Period 0 | Period 1 | Period 2 | Period 3 | Period 4 | |
---|---|---|---|---|---|---|

Price ($) | ||||||

Electricity | 10 | 12 | 15 | 10 | 15 | |

Gas | 12 | 13 | 14 | 12 | 10 | |

Water | 15 | 17 | 18 | 15 | 12 | |

Quantity | ||||||

Electricity | 20 | 17 | 12 | 20 | 10 | |

Gas | 15 | 15 | 16 | 15 | 20 | |

Water | 10 | 12 | 8 | 10 | 15 | |

Index number | ||||||

Index Formula | ||||||

Lowe | ||||||

period 0 to 1 | 100.0 | 114.2 | ||||

period 1 to 2 | 100.0 | 112.9 | ||||

period 2 to 3 | 100.0 | 78.8 | ||||

period 3 to 4 | 100.0 | 107.5 | ||||

chain | 100.0 | 114.2 | 128.9 | 101.6 | 109.2 | |

direct | 100.0 | 114.2 | 130.2 | 100.0 | 107.5 |

In period 3, prices and quantities are returned to their index reference period values and in period 4 the index reference period prices and quantities are shuffled between items. The period 3 situation is sometimes described as time reversal and the period 4 situation as price bouncing.

The index number under direct estimation returns to 100.0 when prices and quantities of each item return to their index reference period levels; however, the chained index numbers do not.

This situation poses a quandary for prices statisticians when using a fixed weighted index. There are obvious attractions in frequent chaining; however, chaining in a fixed weighted index may lead to biased estimates. This can occur if there is seasonality or cycles in the price, and chaining coincides with the top or bottom of each cycle. For this reason, it is generally accepted that indexes should not be chained at intervals less than annual.