RDP 2005-01: Long-Term Patterns in Australia's Terms of Trade Appendix B: Index Construction

The fixed base indices were constructed as follows:

where is the level of the price index at time t, n is the number of components contained in the index, is the price of component i at time t where is normalised to 1 and w_t is the weight of component i in the price index.

In the case where the export price series takes the form of a fixed base Paasche price index, its construction is as follows:

where P_t is the level of the Paasche price index at time t, P_r is the arbitrary level of the index at time r, P_i,t is the implicit price deflator for category i at time t and Q_i,t is the volume of component i exported at time t. This same method was used to construct the fixed base commodity price series.

In 1986, the ABS began constructing chain price measures of export volumes. This means that after 1986 the export price implicit price deflator is an annually re-weighted Paasche price index. Its construction is in Equation (B3):

where P_t is the level of the Paasche price index at time t, for t greater than r. The indices for each sample were spliced together to form century-long series.