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

6  Fertility only changes early in the projection period

Figure 3 shows results from a simulation of the effects of fertility decline on the proportion of the population in the working ages. The fertility indicator used is the ‘total fertility rate’ (TFR), which is defined as the number of children the average woman would have over her lifetime if prevailing age-specific fertility rates were to be maintained indefinitely.[4] The TFR is constant at 2.15 for the first 20 years of the simulation, it declines to 1.65 over the next 20 years, and then again remains constant. Life expectancy (not shown) stays at 80 years throughout, and there is no migration.

Figure 3 – Simulation of the effects of a fertility decline
Simulation of the effects of a fertility decline

As can be seen in Figure 3, the effects of the fertility decline are complex. It initially drives the proportion in the working ages higher than it would otherwise have been, and then drives it lower. The reason for the rise and fall is essentially that a reduction in birth rates reduces the growth rate of younger age groups before it reduces the growth rate of older age groups (Preston, Heuveline, and Guillot 2000: 165-7). Fertility increases have the opposite effect: they drive the proportion in the working ages lower than they would otherwise have been, before driving them back upwards.

Changes in fertility rates have strong effects like these on any ‘intermediate’ age groups—age groups that have some proportion of the total population that is younger than them and some proportion that is older. Changes in mortality rates can generate similar effects for intermediate age groups when the changes are concentrated in the youngest age groups, but this no longer the case outside the least developed countries.

Figure 4 – Statistics New Zealand fertility assumptions and projected values for percentage of population aged 15-64, 1999(base)-2101 projections
(i) Fertility assumptions
Fertility assumptions
(ii) Percent of population aged 15-64
Percent of population aged 15-64
Source – National Population Projections, 1999(base)-2101, Tables 3.01, 4.01. and 4.08, downloaded in August 2002 from Statistics New Zealand website

Fertility assumptions are typically constructed so that all the changes occur early in the projection period, as fertility moves from its initial level to its trend level. An example is given in the upper panel of Figure 4, which shows the fertility assumptions from Statistics New Zealand’s 1999-base projections. Confining change to the beginning of the projection period is probably the least arbitrary approach. It does, however, cause problems for sensitivity testing.

As the simulation results suggest, the distinctive age structures created by changes in fertility rates, with unusually large or unusually small concentrations of population in the intermediate age groups, last for only a generation or two. Confining fertility changes to the early part of the projection also confines these peculiar age structures to the early part of the projection period, even though, in reality, they can occur at any time.

A related problem is that projection variants fail, in a rather striking way, to cover the plausible range for the percentage of the population in any intermediate age group. Confining fertility changes to early in the projection period can lead to situations where projection variants based on high and low fertility levels converge over time, instead of diverging. With certain choices for mortality and fertility, and a sufficiently long projection period, the variants may even cross. The lower panel of Figure 4 provides an example. The low fertility variant and high fertility variant initially diverge, as the fall in fertility rates drives the proportion in the working ages up and the rise in fertility rates drives the proportion in the working ages down. By the 2020s, however, these effects begin to dissipate, and the variants start to converge. In the case depicted in Figure 4, the variants eventually cross. The crossover itself does not create difficulties for sensitivity testing; what matters is the narrow range between variants during the years before and after the crossover.

These problems can undermine attempts to conduct sensitivity tests on policy models that depend on assumptions about the size of intermediate age groups. Many models do in fact depend on such assumptions. The size of the tax base, for instance, depends on the proportion of the population in the working ages, and the number of potential army recruits depends on the proportion in the prime combat ages.

These problems do not, however, appear to be widely recognised. Sensitivity tests are often carried out with fertility variants that are likely to have entered their convergent phase. One representative example is provided by a widely-cited OECD (1998: 123) report on population ageing. In a text box entitled ‘Different assumptions about demography make little difference’, a bar chart demonstrates that, 35 years into the projection, the proportion of the population aged 15-64 is much the same in the low and high fertility variants. This is another instance of Case 6. The restricted range for the fertility assumptions, leads to a restricted range for population variables, which removes the value of the sensitivity test.


  • [4]Equivalently, the total fertility rate is the sum of the single-year age-specific fertility rates.
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