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3.1  How population is projected

Population projections are calculated using the cohort component method.[6] This requires estimates in a base year of the number of people, male and female, at each age from birth to 100+. This also contains the history of past fertility, mortality and net migration. The projection method also requires the single-year fertility rate for women of child-bearing age (12 to 49) for each of the projection years, projected central mortality rates (or the associated survival rates), for each year of age, for males and females, for each of the projected years. Inward and outward migration also affects the size and composition of the population. So another input is the number of people entering, less those leaving the country, for each year of age, for males and females, for each year of the projection. Finally, the calculation requires an assumption about the ratio of males to females at birth (set at 105.5 males for every 100 females).

The cohort component method projects the base population forward by calculating the effect of deaths and migration within each age-sex group according to specified mortality and migration assumptions. New birth cohorts are generated by applying specified fertility assumptions to the female population of child-bearing age.

Work on the 2009 Statement began by using the official Statistics New Zealand 2006-base national population projections (released October 2007). Since 2006, fertility has been higher than the medium fertility assumption and this has an effect on the demand for schooling and eventually on the size of the labour force. So the Treasury commissioned Statistics New Zealand to review its assumptions and produce a set of projections based on estimated population at 30 June 2008. These were made available in March 2009.

On 27 October 2009, Statistics New Zealand published its 2009-based projections. This was too late to incorporate into the 2009 Statement, but Annex 1 of this paper shows how the 2009-based population projections affect the fiscal projections.

3.1.1  Uncertainty in population projections

The 2009 Statement uses the Statistics New Zealand's Series 5 population projection (2008-base) as its central case. This uses the long-term medium fertility, medium mortality and medium net migration assumptions. Uncertainty is illustrated by constructing “alternative central” projections around the central one, using symmetric settings around the central assumptions. An objection to this approach is that there is no quantification of the likelihood that any of these projections, central or alternative, will happen.

One way of addressing this is to construct stochastic population projections centred on a deterministic medium projection. Some experiments along these lines were done for the 2006 Statement.[7] There it was shown that, conditional on the Series 5 (mid-range) projection, the old age dependency ratio of people aged 65 years and older to those between 15 and 64 from 2040 onwards would be more than double the value in 2006, 95 times out of 100.

Figure 3.3 uses the distributions from the 2006 Statement to illustrate the uncertainty around the old age dependency ratio for central 2008-base Series 5 projection. The figure also has the two alternative central projections (Series 1 and Series 9) and shows that they lie well within the 25% to 75% probability interval. (By many other measures, these alternatives are more divergent from Series 5 than the old age dependency ratio indicates.)

For the 2009 Statement, we decided not to pursue the stochastic approach, preferring to look more closely into the supply and demand variables driving spending growth and be more concrete about what various policy options might mean for the average New Zealander. We use the alternative central projections to give an unquantified bracketing around the central scenario.

Figure 3.3 - Old age dependency ratios will almost certainly double
Figure 3.3 - Old age dependency ratios will almost certainly double.
Source: Statistics New Zealand, the Treasury


  • [6]For more on the cohort component method, see, or Preston et al, Chapter 6.
  • [7]New Zealand's Long-term Fiscal Position, 2006, p45.
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