6.2 Prices
We now have various relative prices for each expenditure component (consumption, investment etc), but what we are interested in is absolute prices. Thus we would like a measure of the price of “other goods” (pydo) to multiply the individual relative prices to get the absolute price level. To do this we first model the non-housing consumption deflator (pyd_c) using the CPI excluding the housing component (cpixh). In theory, both price indices are designed to measure the same component of the consumption sector. Figure 12 shows the ratio of pyd_c to cpixh, which suggests a linear time trend over the sample period. The linear time trend could be due to different methods in constructing the indices. The CPI is based on a fixed-weight formula and the consumption deflator is based on a chain-linking formula. Currently, the CPI now has an expression base of June 2006 quarter = 1000. Chain linking means constructing price measures by cumulating movements in short-term indices with different base periods.
- Figure 12: The ratio of the consumption deflator to the CPI ex housing
- Source: Statistics New Zealand, New Zealand Treasury
Thus we express the non-housing consumption deflator relative to the CPI (excluding housing) with a constant and trend term to capture the differences:
The CPI (cpix) is determined elsewhere in the model (see section 5). Given the CPI we can use the following relationship to estimate cpixh.
where cpihouse is a price index of the CPI housing component.
Once pyd_c is estimated using equation (7.11), we can then use the non-housing consumption deflator to calculate the “other goods” price level (using rpyd_c=pyd_c/pydo). Finally we can use pydo to back out the rest of the individual deflators (business investment etc) from the relative prices for each component.
