**LxxxI** INnROOucTiON

# **_PrAjea Meoulty_**

Motlity is projected by extrapolating recent<sup>trends in male life expectancy, female life</sup> expectancy, and infant mortality and applying<sup>appropriate model life tables. The procedure is</sup> identical to that used last year, except that life<sup>expectancy is allowed to reach higher levels in the long</sup> rn. We explain this change and then discuss the elements<sup>of the procedure. Analysis of recent</sup> trends that provides some empirical basis<sup>for the procedure is reported by Bulatao and Bos (1989),</sup> who also provide further details.

Maximum male and female life expectancies<sup>are assumed to be 83.3 and 90 years,</sup> respectively, _7.5_ years higher in each case than<sup>the levels used last year. The previous maxima are</sup> berely above current levels for the lowest-mortality<sup>countries. Life expectancy in Japan, for instance,</sup> is now estimated at 75.6 years for males<sup>and 81.4 years for females. Some research (discussed in</sup> Bulatao and Bos 1989) suggests that much higher<sup>life expectancies are theoretically attainable, but the</sup> issue is still controversial. Since these projections<sup>cover almost 200 years, limiting life expectancy</sup> to current maximum levels did not seem appropriate.<sup>Using higher life expectancies was facilitated</sup> by the recent extension of the Coale-Demeny life<sup>tables (Coale and Cuo 1990), though the extended</sup> tables still needed further extension.

Future trends in life expectancy. Life expectancy<sup>at birth et by sex is projected from</sup> year 0 to year t using a logistic function over<sup>time of the form</sup> et = k0 + k / (I + exp [logit(, ) + rt]}, with logit(e.) = loL [(ko + k - _eo)_ / **(ej** - ko'l.

The minima (ko) for the logistic functions for<sup>both sexes are assumed to be 20 years, and the maxima</sup> (X0 + k) are assumed to be 90 years for females<sup>and 83.3 years for males. This allows the function</sup> to rise most rapidly from a level of SC years<sup>or so and increase more slowly at higher as well as</sup> lower levels. However, the key parameter is the<sup>rate of change (r). This is allowed to vary across</sup> countries, and for a given country to vary over<sup>time.</sup> The rate of change (r,) for the first quinquennium<sup>(1985-90) is estimated from the rate</sup> of change in the previous quinquennium (ro) aud<sup>from the female secondary enrolment ratio (so), using</sup> the equations r; - .00379 + .723 ro - .000254 S for female., and r, = .01 159 + .885 ro - .000318 so for males.

Percent urban is used in a few cases where<sup>secondary enrollment is not available; in fewer cases still</sup> the rate of change in the previous decade is<sup>used instead of the rate of change in the previous</sup> quinquennium, when the latter appears<sup>to have been affected by exceptional circumstances (see</sup> Bulatao and Bos 1989). Limits are imposed<sup>on the rate of change for the firs quinquennium (and for</sup> all other quinquennia), such that it cannot<sup>be greater than -.017 (which would give slow mortality</sup> decline) or less than -.053 (which would give<sup>rapid mortality decline).</sup> For the second quinquennium, the rate of change<sup>is estimated as a function of the rate</sup> of change for the first quinquennium: r2 - -0.007 + 0.7 r,.

The rate of change for the third quinquennium<sup>is estimated from the rate of change for the second</sup>