2.2  Support ratios

2.2.1  Definition of support ratios

What is the economic significance of the differences in age structure? The index of age structure most commonly cited in discussions of population ageing is the ‘dependency ratio’, defined as the number of people outside the working ages divided by the number of people in the working ages. Cutler et al. (1990) introduce a more economically meaningful index called the ‘support ratio’, which incorporates information about variation by age and sex in productivity and consumption. The support ratio is defined as follows:

(1)    

where is the number of people in age-sex group , is a measure of the productivity of age-sex group , and is a measure of the consumption needs of age-sex group . Because the support ratio has no units and is a pure number, the analyst is free to choose a scaling factor. When conducting the simulations we set the scaling factor so that the support ratio equals 100 in the base year. Note that the support ratio reduces to the reciprocal of the dependency ratio if is set to 1 for all those in the working ages and 0 elsewhere, and is set to 1 for all those outside working ages and 0 elsewhere.

The effective labour force, effective population, and support ratio are key inputs for the model described below. To obtain series for these variables, we calculated values for the ’s and ’s, the consumption and productivity weights.

2.2.2  Consumption weights

Two sets of consumption weights—a ‘base’ set and an ‘alternative’ set—were constructed. The two sets have the same values for public consumption, and different values for private consumption. Data on public consumption by age and sex were calculated from Creedy and Scobie (2002), Ministry of Health (2002), and National Accounts data. Profiles for private consumption were constructed from adult equivalence scales, which are weights, used in analysis of household data, that are meant to capture the relative consumption needs of different age groups. The ‘Revised Jensen Equivalence Scale’, which has been applied in empirical work in New Zealand (Jensen 2001) was used to construct the base weights. A scale used by Guest and McDonald (2001: 123) in an application of the Ramsey model to Australia was used to construct the alternative weights. The two equivalence scales are shown in Table 3. The public and private age-sex profiles were both normalized, and a weighted mean was taken; the weights were equal to the proportion of total consumption accounted for by public and private consumption, as shown in the National Accounts. Consumption weights for males and females combined are graphed in Figure 6. The scaling factor has been chosen so that the weights equal weekly per capita consumption in the model during the initial year. Using the base weights, for instance, the average 0-4 year old has a consumption level of $340 per week in the initial year. The underlying numbers are presented in Appendix Table 1.

Figure 6 - Consumption and productivity weights, males and females combined

Source:

Note: The weights have been scaled so that they show age-specific consumption and production in the model during the initial year.

2.2.3  Productivity weights

‘Base’ and ‘alternative’ sets of productivity weights were also calculated. In both sets, real wages were assumed to equal the marginal product of labour, and the productivity weight for an age-sex group was proportional to the average wage for the group multiplied by the fraction of the group who are employed. The weights were held constant over the entire projection period. The base weights were constructed from data on wages and employment for 2001 were obtained from the Statistics New Zealand’s June Quarter 2001 New Zealand Income Survey. The alternative weights were designed to reflect the fact that future cohorts are likely to be longer-lived and better-educated than their predecessors (Dowrick and McDonald 2001). For males aged 15-49, wages and employment rates were assumed to be the same as they were in the 2001 survey. Above age 49, however, the profile for wages and employment were shifted 2.5 years to the right: wages and employment rates for males aged 50-54 were assumed to equal the average of the survey figures for males aged 45-49 and 50-54; wages and employment rates for males aged 55-59 were assumed to equal the average of the survey figures for males aged 50-54 and 55-59; and so on. Wages and employment rates for females were assumed to be identical to those for males, except that females’ employment rates during the prime childrearing ages of 25-39 were assumed to be only 90% as high as those of men. The base and alternative weights are shown in Figure 6. A scaling factor has been applied so that the graph shows age-specific production in the initial year of the model. The underlying data are given in Appendix Table 2.