the speed of the decline in TFR during the transition and the level at which fertility ultimately stabilizes. Table S shows countries which appear to have bottomed out below replacement fertility, i.e., where no further fertility decline was measured for a quinquennium. Regressing the minimum TFR level on the rate of decline from one point above the minimum level shows a weak, nonsignificant relationship (R<sup>2</sup> equal to .35). Each country seems to have an unpredictable minimum TFR level to which it declines at a pace that is unrelated to this level. Once the minimum level has been reached, TFRs fluctuate within a narrow range. For example, this country-specific minimum fertility level is about 1.5 in Switzerland, where it has ranged between 1.49 and 1.60 for the past 12 years, and 1.8 in the U.S., where it has ranged between 1.74 and 1.88 for two decades. In some countries, such as Poland and the Soviet Union, the minimum Irvel TFR has been above replacement, varyung between 2.2 and 2.4 for some time now.

# APPLICATION TO POPULATION PROJECTIONS

This section attempts to formulate heuristic rules for projecting future fertility based on the findings in the previous section. In particular, rules are needed to determine the course of fertility before the pre-transitional stage; the timing of the start of fertility transition; the speed of fertility decline during the transition, both for countries that are already experiencing transition and for countries that have not yet started; and the course of fertility during the post-transitional stage, both for countries which are already post-transitional and for other countries. Table 6 summarizes the recommended rules. Application of the .ules requires that estimates are available or can be made of current TFR, TFR five years earlier, current life expectancies, and the percent of women of reproductive age who are sterile.

Pre-transition. Pre-transitional fertility was found in the analysis to fluctuate erratically at high or moderately high levels. In the absence of any convincing approach to predicting such fluctuations, we will use the rule that pre-transitional fertility is constant. We make an exception for countries where primary sterility is high. Such sterility appears to be due mainly to preventable sexually transmitted diseases (Frank 1983; Larsen 1985; Farley and Belsey 1988). As sterility declined in a number of countries, there have been increases in TFR over the past decade: in Gabon, for instance, TFR increased from 4.5 in the mid-1970s to 5.5 in the mid-1980s. Frank (1983) found that, for each percentage point increase in primary sterility, TFR fell .11 points. Many countries have sterility levels in the 3 to 6 percent range (Europe averages 5.4. Latin America 3.1, and North America 6.0); we take 6 percent as a lower limit below which the effect of sterility on fertility can be ignored. We assume that sterility, where it is high, will decline linearly to 6 percent by 2005 and, following Frank, adjust TFR by adding the quantitr

## .11 [(percent sterile - 6) / 3]

## to predicted TFR in each of the three quinquennia between 1990 and 2005.

Start and pace of transition. The start of the transition in countries where no fertility transition has been observed was not predictable from socioeconomic indicators. We rely, therefore, on previous studies showing a life expectancy threshold for fertility transition. We impose as a necessary condition for fertility decline that life expectancy must be at least 50 years and propose the following rule: where the fertility transition has not started, it will do so in the next quinquennium (1990-95), unless life expectancy at birth is below 50 years. In that case, the start of the transition will be postponed until projected life expectancy reaches 50 years. (How life expectancy is projected is discussed in Bulatao and Bos 1989.) A few pre-transitional countries are not projected to reach a life expectancy of 50 for as long as 30 years, often because of current conditions like war and famine. In these few cases, we allow fertility transition to start by 2005.

The pace of fertility decline in countries where transition has started was found to be countryspecific. It was also found to be poorly explained by other demographic or socioeconomic variables. A quinquennial decline in fertility was found to be strongly correlated with the decline in the preceding 16