5  Operationalizing the model

5.1  The demographic-health sub-model

5.1.1  Mortality

The back-casting requires estimates of historical mortality rates, which were obtained from Statistics New Zealand and from unpublished vital registration data. The projections require assumptions about future mortality rates. Most health expenditure models use the assumptions constructed by the official statistical agency. However, most statistical agencies, including Statistics New Zealand, derive values for future mortality rates indirectly, via assumptions about life expectancy. Because mortality rates play a key role in our model, we have decided to use a method that is more direct.

We have assumed that mortality rates for both sexes, all age groups, and all years decline at a constant rate in future years. Our model is similar to that of Lee and Carter (1992), except that Lee and Carter allow mortality rates to decline faster in some age groups than in others. An obvious disadvantage of our assumption that mortality rates decline at the same pace in all age groups is that it reduces the model’s realism. It may not, however, reduce the model’s predictive power excessively, as analysis of historical trends shows that age groups that have experienced rapid declines in one period have not necessarily experienced rapid declines in subsequent periods (Booth, Maindonald and Smith 2002). The assumption also has several advantages: it is consistent with our treatment of disability; it is simple and transparent; and it allows alternative mortality scenarios to be easily summarized.

The problem remains, however, of choosing sensible values for the rate of decline. Our benchmark assumption is that the annual rate of decline for the period 2002-2051 equals the annual rate of decline for the period 1951-2002. There is room for disagreement on how to calculate the rate of decline, but, as described in Appendix 2, we have settled on a value of 1.5%. We also carry out sensitivity tests using a rate of decline of 1.0%.

5.1.2  Disability

As described in Section 2.1, estimates of disability prevalence in 2001 were calculated from data in the Post-Censal Disability Survey. Our baseline assumption for the back-casting is that disability prevalence within each age-sex group was constant over the period 1951-2002, though we conduct sensitivity tests using alternative assumptions.

For the projections, we assume that disability rates decline at a constant rate in all age-sex groups. We based our choice for a rate of decline on the systematic review described briefly in Section 2.3. Given the long time periods and the methodological rigour of the United States studies, we decided to place considerable weight on them. The US studies all found rapid disability decline. Accordingly, we decided that a plausible range for disability decline in New Zealand was between 0% and 1% a year. Our benchmark assumption is that disability rates decline at 0.5% per year, though we also carry out sensitivity tests based on an assumption that disability rates are constant.

There is some tension between the assumption that disability was constant until 2002 and the assumption that it declines after 2002. In the absence of long-term data, however, any choice of starting date for disability decline is unavoidably arbitrary. Sensitivity testing also shows that the choice of starting date has little effect on the major substantive result from the back-casting (which, to anticipate Section 6.2, is that changes in coverage and price dominate health expenditure trends.)

5.1.3  Population by age and sex

For the back-casting we use Statistics New Zealand data. For future years, population projections are constructed by the model itself, based on the assumed rate of mortality decline, and on Statistics New Zealand’s medium fertility and migration assumptions. The population projections use a standard cohort-component methodology (Preston, Heuveline and Guillot 2001)[4].

5.1.4  Health status within each age-sex group

With the assumptions and data described so far, it is possible to calculate the number of people in each age-sex group who are disabled, and the number who will die in the following year. Further data or assumptions are required, however, to calculate the numbers who are disabled and in their last year of life, disabled and not in their last year of life, and so on.

Our assumption is that the percentage of decedents in an age-sex group who are not disabled equals the proportion who die of “injury”, according to the cause-of-death statistics for 2001/02. Essentially, we assume that everyone who is in their last year of life is disabled, except for those who die of injury. An exception is that we assume that half of the people aged 65 and over who have non-injury deaths are disabled, on the grounds that many “injuries” among older people are actually attributable to underlying chronic conditions[5]. Under these assumptions, approximately 94% of decedents are disabled, and 6% of disabled people are decedents in 2001[6].