3  Input data and projections

This section describes the key input variables, sources and the derivation of their projected values. In the case of fertility, mortality and labour force participation rates, their growth rates and standard deviations were estimated from the following regression:[14]

(14)      log y_t = α + β_t + u_t

This implies that the constant growth rate is given by where. As , the standard deviations are derived from the estimated standard error of the regression, . The log-linear specification was found to provide a good fit to the historical data. The growth rates for male and female mortality rates and fertility rates are given in Appendix Table 1, and the respective standard deviations are documented in Appendix Table 2.[15]

3.1  Fertility rates

Fertility rates by single age year of mother from 1980 to 2001 were used to estimate the trend annual rates of change using a regression of the logarithmic rates against time, as described above.[16] The decision to truncate the data for the regressions and start at 1980 was based on the finding that there is a marked turning point in the fertility rates around 1980, especially for older mothers.[17] The trends prior to 1980 were quite distinct and reflected the substantial decline in fertility following the 1960s.[18] These rates were used to form the projections for the next ten years, after which fertility rates were assumed to remain constant.[19] A selection of the actual and projected values is presented in Appendix Figure 1.

3.2  Mortality rates

Mortality rates are available by single year age groups (from 0 to 99) for three-year averages centered on the years 1971, 1976, 1981, 1986, 1991, and 1996.[20] For 1999, values were only available for 5-yearly age brackets for 1999-2001. Single year values for that year were interpolated by using the same proportions as in 1996. The values for ages 96 to 100 in 1999 were taken to be equal to those for 1996 to 2001. The resulting data set of seven observations for each single year of age were used to estimate the trend annual rates of change using the regression of the logarithm of mortality rates against time, as discussed above. These rates were used to form the projections of the mean rates for each age. The standard deviations were taken from the standard errors of each regression. Hence, as with fertility, each rate is assumed to be lognormally distributed. The precise values are given in Appendix Table 2.

Changes in mortality rates were projected for the next twenty years, after which these rates were assumed to remain constant.[21] Given the relatively small numbers involved, it was assumed for simplicity that 100 years is the upper limit of the age distribution. The actual and projected values of mortality rates for selected ages are presented in Appendix Figure 2.

3.3  Migration

For the last 100 years net migration (permanent and long-term) has averaged 5,000 per year, although major swings have frequently occurred. This long-term average was adopted as the benchmark rate for net migration with a corresponding gross level of immigration of 50,000. We assume that future inward and outward migration flows have the same age and gender distribution as the average for the years 1997 –2001.[22] Data for this period were used to estimate the standard deviations of the arrival and departure rates for males and females by single year of age. The average for the age group 99+ were assigned to age 99, and migration flows for those aged 100 were arbitrarily assumed to be zero.

3.4  Labour productivity growth

Bagrie (1997) reported a long-term average for labour productivity growth of 1.5% per year based on the period 1955-56 to 1995-96. This is close to the value reported by Diewert and Lawrence (Diewert and Lawrence 1999), Table 4.2, p.66) of 1.66% for the period 1978 to 1998. The Long Term Fiscal Model at the Treasury assumes 1.5 percent.[23] Downing et al find similar rates for more recent time periods: 1.28% for 1993 to 1997 and 1.54% for 1999 to 2002.[24] The present study adopted a rate of 1.5% for the benchmark average annual growth in labour productivity, assumed to remain constant over the projection period. The standard deviation of 0.01707 was obtained using data from 1979-2002. The initial value of labour productivity in the base year 2001 was given by GDP ($114,374m) per worker (1.804m) ie $63,400.

3.5  Labour force participation rates

Labour force and social expenditure data are available only for certain age groups, rather than single years. Hence, having obtained the single year age distributions using the demographic component of the projection model, these needed to be grouped for each of the social expenditure projection years, for the purposes of calculating GDP and social expenditure.

Significant changes have occurred in participation rates over recent years. The rates have typically fallen amongst the younger age groups, associated with increased tertiary education rates. Male participation rates up to age 50 have fallen, while most female rates have been rising. Data on age-specific rates for the years 1987 to 2002 were used to estimate the trend rates of growth.[25] These in turn were used to generate projected rates for the next 10 years, after which no further change was assumed. There are some exceptions to this – specifically in the case of older males, where a rise in participation following 1990 can be attributed to an increase in the age of eligibility for universal superannuation; for this reason the trend was not extrapolated. Appendix Figure 3 shows the actual and projected rates for a selection of age groups, while the means and standard deviations for both the participation and unemployment rates are given in Appendix Table 3.

3.6  Social expenditures

Social expenditures are divided into 14 categories. These are: Age Related; Medical/Surgical; Mental Health; Pregnancy/Childbirth; Primary Diagnostics; Primary General; Public Health; Education; NZ Superannuation; Domestic Purposes Benefit; Sickness Benefit; Invalids’ Benefit; Other Benefits; Unemployment Benefits. Hence, categories 1 through 7 refer to health and categories 10 through 13 are denominated social security and welfare. Data from Treasury’s Long Term Fiscal model for Categories 1 to 7 of health expenditures were used to compute the shares of each category by age and gender. These shares were applied to estimates of total health expenditures by age group (Johnston and Teasdale 1999).

Data from the Household Economic Survey were used to find the distribution by age and gender of other categories. Where there was no division by gender (in the cases of education, invalids’ and other benefits) the rates for males and females were set equal. Payments under Category 10 were assumed to be received by females, and no payments under category 4 were assigned to males.[26] Data from the HES were for 1997-98 and indexed to 2001 prices using the Consumer Price Index. A complete set of the social expenditure data by category, age and gender is given in Appendix Tables 4 (for males) and 4 (for females).

The growth rate of total social expenditure in each category was applied to all age and gender groups. This is because in most cases relevant information was available only at an aggregate level. Growth rates and standard deviations were derived from per capita expenditure series for health, education and superannuation from 1960 to 2000, and 1980 to 2000 in the case of unemployment benefits which are calculated on a per recipient rather than per capita basis. These are reported in Table 1. In the case of NZ Superannuation, it was assumed that there was a 100% take-up by all those over the age of 65, and all received the rate applying to single persons. A series for Social Expenditure for 1960 to 2000 was used to derive the growth rate and standard deviation applied to the sub-category Social Security and Welfare.[27] The historical trends and annual changes of the major categories of social expenditure are shown in Appendix Figure 4.

Sources: All data are from unpublished Treasury sources from the Long Term Data Series, except for social security and welfare from (Dalziel and Lattimore 2001)