lXViii DATA AND METHODS

# Projection methodology

Population projections were run using the cohort-component method on microcomputers with the software package, PROJ3L (A similar program, PROJ3S, is described in Hill (1990), the only difference being that this program allows for 75-year projections rather than long-term projections shown here. The assumptions about future trends in vital rates will be discussed in this section.

## _Projecting Mortality_

The procedures used to project mortality were developed from analysis of trends in life expectancy and infant mortality in available national data. (See Bulatao et al., 1989). These projections utilize extended life tables (see Coale and Guo, 1989) with maximum male and female life expectancy assumed to be 83.3 and 90 years, respectively. These maxima were revised upward in 1991 because previously used maxima are now barely above the currently estimated levels for the lowest mortality countries. Life expectancy In Japan, for instance, is estimated at 75.6 for males and 81.4 for females - only slightly below the previously used maxima. Research into the consequences of controlling major risk factors has found that thereotically much higher life expectancies are attainable. Bourgeois-Pichat, in an attempt to estimate the effect on the life span of eliminating wexogenous" causes of death, obtained a maximum life expectancy of 76.3 for males and 78.2 for females. In 1978, he revised the limit, putting life expectancy for males slightly lower at 73.8 years and that for females higher, at 80.3 years (barely above the current estimates for Norway). Manton (1986) showed that an increase in life expectancy of 12.3 to 12.8 years in the expectation of life at age 30 years was possible with effective control of major risk factors. Even if no changes in mortality under 30 occurred this would result in an increase in male life span to above 81 years. On the basis of this evidence and given the long range nature of these projections a higher maximum life span was considered appropriate.

## _Fuhue trends in fife expectancy at bb*d_

Life expectancy is projected from year 0 to year t using a logistic function over time of

# the form

et = ko + k /{1 + exp [logit(e0 ) + rtl}, with logit(e.) = log, [(ko + k - e.) / (e0 - ko)j.

Logistic functions are used because these flt past trends best, country by country. The schedules of medium change in life expectancy and infant mortality reflect median trends across countries, and the schedules for minimum and maximum change reflect the 10th and 90th percentile when country trends are ranked from slowest to fastest. The equations to predict short-term trends in life expectancy and infant mortality were estimated using these data; other socioeconomic factors, like per capita income, did not improve prediction.

The logistic function is set to rise most rapidly from a level of 50 years or so and increasingly slowly at higher levels. The minimum (kI) for the logistic functions for both sexes is assumed to be 20 years, and the maxima (ko + k) are assumed to be 90 years for females and 833 years for males. The rate of change (r) for the logistic function is allowed to vary across countries, and for a given country to vary over time.

For the fist quinquennium (1985-90), the rate of change (r1) is estimated from the rate of change in the previous quinquennium (ro) and from the female secondary enrolment ratio (s.),