3 Effects on growth in GDP per capita
3.1 The framework
The effects of demographic trends on growth in GDP per capita can be approached using the decomposition
(1) 
where 
is GDP, 
is population, 
is hours worked, and 
is working-age population. The decomposition implies that per capita GDP is a product of labour productivity, participation (incorporating both employment levels and hours worked), and the proportion of the population in the working ages. If a demographic trend is to affect GDP per capita, it must do so by affecting one or more of these terms.
For some purposes it is useful to look at the effect of demographic trends on growth rates rather than levels. Taking logs of Equation 1 and differentiating with respect to time yields the following equation, where 
denotes the growth rate of 
:
(2) 
The growth rate of GDP per capita is equal to the sum of the growth rates of labour productivity, participation, and the proportion in the working ages. This equation can be used to decompose historical growth rates, or to project future growth rates.
3.2 The proportion of the population in the working ages and GDP per capita
Under the decomposition set out in Equation 1, the relationship between the proportion of the population in the working ages 
and GDP per capita is purely mechanical. If, for instance, the proportion in the working ages goes from 50% to 60%—an increase of 20%—then GDP per capita increases by 20%. An increase in the labour force might be expected to have additional indirect effects, but these must be appear as changes in the 
and 
terms, and not the term. Proportions in the working ages are graphed in Panel (ii) of Figure 5; the values, plus the changes in these values, are summarised in Table 2.
| Proportion of population in the working ages | Percentage increase* in the proportion in the working ages | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Historical | Projected | Historical | Projected | ||||||
| 1950 | 1975 | 2000 | 2025 | 2050 | 1950-1975 | 1975-2000 | 2000-2025 | 2025-2050 | |
| Australia | 58.6% | 54.7% | 60.1% | 57.8% | 54.0% | -6.5% | 9.9% | -3.9% | -6.6% |
| Europe | 58.2% | 55.7% | 60.9% | 58.6% | 51.2% | -4.3% | 9.3% | -3.8% | -12.7% |
| Japan | 49.3% | 60.6% | 62.2% | 54.3% | 46.7% | 23.0% | 2.6% | -12.7% | -14.1% |
| New Zealand | 55.0% | 51.6% | 58.3% | 57.8% | 53.9% | -6.1% | 12.9% | -0.9% | -6.7% |
| RDCs | 45.2% | 42.3% | 55.2% | 60.5% | 54.9% | -6.3% | 30.5% | 9.5% | -9.2% |
| North America | 57.4% | 54.7% | 59.3% | 57.1% | 54.3% | -4.7% | 8.3% | -3.6% | -5.0% |
| OECD total | 55.6% | 54.1% | 59.5% | 58.1% | 52.8% | -2.8% | 10.0% | -2.4% | -9.2% |
*This is the percentage increase, not the percentage point increase. For example, the result for Australia 1950-1975 is calculated as 100%*(54.7%/58.6%-1) = -6.5%.
Source: Calculated from data from the UN Population Division’s World Population Prospects online database.
As discussed earlier, for all countries and regions shown aside from Japan, the proportion in the working ages fell during the post-war baby boom, grew again afterwards, and will fall once more over coming decades. This is apparent in Table 2. Japan’s unusual dynamics advantaged it in the past, relative to the other countries and regions shown, but have begun to seriously disadvantage it. The swings in the RDCs are in the same direction as the majority of the OECD, but are more dramatic.
In 1975, the proportion of the New Zealand population in the working ages was only 51.6%, which was 2.5 percentage points below the OECD average, and lower than any country or region shown, other than the RDCs. Since that time, however, the gap between New Zealand and the rest of the OECD has been closing; under current projections the gap will continue to close in the near future. These population movements imply an increase in the growth rate of New Zealand’s per capita income, relative to the rest of the OECD. This is one case where New Zealand’s demographic profile is delivering it a small advantage over Australia and North America, as well as Europe and Japan.
