INTRODUCTION XVii

* Generally, a geometric function is imposed on total fertilitydecline from one point above replacement level to replacement level, with this decline assumed to take 15 years.

* Where total fertility has shown unusually slow decline, it is assumed to take 20 rather than 15 years for total fertility to fall one point to replacement.

* Where, toward the end of a fertility transition, total fertility is still recording rapid declines even though it is close to or even below replacement level (2.25 to 1.75), it i assumed to fall further for one period, generally going below replacement, to stay constant in the next period, and then to return to replacement.

* Where the transition has been completed and total fertility is below replacement, it is assumed to stay at the current level for two quinquennia, and then to return gradually to replacement, along a linear path, by 2030.

In applying late-transition procedures, the level of total fertility that provides replacement is approximated by a quadratic formula based on female life expectancy (e(,) in the replacement year:

**TFRNRR.I** = 6.702 - .1107 e(,Q + .0006592 eMj.

The replacement year is first approximated in order to determine life expectancy and then calculated given this formula and whichever pattern of fertility change above is appropriate.

For all stages of fertility transition, the age pattern of fertility is determined in the same fashion, depending on the level of total fertility (Figure 5). Two basic schedules of age-specific fertility are defined: for total fertility levels greater than six and for total fertility levels of three and lower. In between, age patterns are obtained by interpolation between the two schedules. At a total fertility level of six, a greater proportion of births are at younger and older ages of the reproductive span, and the mean age of childbearing is 28.9 years. At a total fertility level of three, births are concentrated in a narrower band of ages, and the mean age of childbearing is 28.0.

Comparison with other fertility projections. These procedures contrast with the procedures previously used, which depended essentially on subjective judgments of the replacement year for each country. We explain some of the basis for the procedures and contrast the results.

These procedures were developed from analysis of total fertility trends in cross-national data (Bos and Bulatao 1989). In the pretransition stage, countries showed mostly stable fertility. The transition stage was more interesting. Across 42 countries which started a fertility transition between 1955 and 1983, the average annual decline in total fertility ranged from 0.06 to 0.25 points. Countries which had initial sharp declines in fertility tended to continue declining rapidly, while those that started with more gradual declines continued along the same path. Rapid and slow decline were found in all regions. The rate of decline was predicted best by the rate in preceding periods; socioeconomic factors added little to this prediction. Other than the mortality threshold, socioeconomic factors also failed to predict the start of fertility transition.

The previous procedures involved a regression equaiion for the replacement year, derived after initial subjective judgments of this year. Reverse geometric and geometric curves weve then fit between current fertility and replacement level. By contrast, the current procedures focus on the pace of change in total fertility, determining the replacemcnt year as the outcome rather than the first step in the process.