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Can Population Projections be Used for Sensitivity Tests on Policy Models? - WP 03/07

3  Fertility, mortality, and migration assumptions exclude random shocks

Time series for fertility, morality, and migration can in principle be separated into trend and random shock components. Figure 2, for example, shows the time series for net annual permanent and long term (PLT) migration to New Zealand between 1970 and 2002.[2] The trend seems to be somewhere around zero, with large random shocks around this value.

Figure 2 – Estimates and 1999-base projection assumptions for net permanent and long term migration into New Zealand
Estimates and 1999-base projection assumptions for net permanent and long term migration into New Zealand
Source – All data obtained from documents on the Statistics New Zealand website Estimates for migration 1970-1979 obtained from Demographic Trends 2001, Table 5.01. Estimates for migration 1980-1998 obtained from Demographic Trends 2001, Table 5.01. Estimate for 1999, and description of migration assumptions obtained from National Population Projections, 1999(base)-2101, Table 3.01. Estimates for 1999-2002 obtained from Key demographic indicators, 1999-2002. The 1999 estimates from this and the previous source differ slightly.

The most natural interpretation of the assumptions used in the construction of population projections is that random shocks have been excluded (Lee 1998: 156; Bongaarts and Bulatao 2000: 191). Figure 2 again provides an example. The figure shows the first 11 years for two migration assumptions used by Statistics New Zealand to construct projections for the period 1999-2101.[3] The ‘0’ assumption is Statistics New Zealand’s lowest migration assumption, and the ‘20,000’ assumption its highest. Values over the first few years of each assumption reflect the fact that the migration in the launch year differed from assumed trend level. In subsequent years, however, the values are fixed at trend levels. There is none of the volatility apparent in the historical series. Using the typology introduced in the previous section, coverage of possible paths for fertility, mortality, and migration is ‘narrow.’

Virtually all statistical agencies omit random shocks from series for mortality, fertility, or migration. Omission of random shocks is essentially unavoidable when using the population variants approach. If only a handful of projection variants are calculated, and if shocks can take an indefinitely large number of forms, then having no shocks is the least arbitrary choice.

Omitting random shocks from population projections does not greatly reduce their coverage of plausible figures for long-run population size. It does, however, have clear and rather awkward consequences for short-run projections. As Figure 2 illustrates for migration, high and low assumption about fertility, mortality, and migration typically differ little in the early years of a projection. Moreover, because little time has passed, the effects of any differences have yet to accumulate. High and low variant projections for outcomes such as population size therefore cover a narrow range.

Random shocks to fertility, mortality, or migration early in a projection period often cause population size and other variables to fall outside this range. As Figure 2 shows, net migration to New Zealand experienced a large positive shock over the three years following the 1999-base projections. By 2002, migration levels were well above the trend level implied by the ‘20,000’ assumption. This is one reason why the New Zealand population (probably) reached 4 million by April 2003, although none of the projection variants calculated in 1999 had the New Zealand population attaining 4 million until early 2004. (Another reason for the early arrival at 4 million was that estimates of population size in the base year for the projection turned out to be too low.) This situation is certainly not unique. Around the world, actual outcomes frequently fall outside the range set by high and low projection variants soon after the projections are published (Lee 1998: 156).

Policy models that use short-term changes in population size as an input include funding formulas for health and education. Health and education budgets in New Zealand have, indeed, been revised in the wake of the recent, unexpectedly large, population increases. The revisions have been greater than would have appeared likely from demographic sensitivity testing at the time when the 1999-base projections were prepared. Demographic sensitivity tests at this time would have fallen under Case 6 of the typology set out in Table 1.


  • [2]Permanent or long term migrants, as distinguished from short-term visitors, are people entering New Zealand who state on their arrival cards that they intend to remain in the country for at least 12 months, or people leaving New Zealand who state on their departure cards that they intend to remain outside the country for at least 12 months.
  • [3]This paper uses the 1999-base projections rather than the more recent 2001-base projections in this and subsequent examples because, at the time of writing (May 2003), detailed series over a 100-year period for the 2001 base are not yet publicly available, and because the use of 1999-base projections permits comparison between projected and actual results.
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