Figure 2 compares our estimates of parity-age-duration–adjusted total fertility with estimates for the same periods published by the United Nations in World Population Prospects (UN Population Division 2017). The two series agree closely, although the United Nations estimates tend to be slightly lower in populations with very high fertility and slightly higher in populations in which total fertility is between four and six children per woman. One would not expect the two series to be identical, not only because the United Nations estimates standardize only for age, not parity and interval duration, but also because they were made using sources other than fertility surveys. Nevertheless, the close agreement between the series represents external evidence of the validity of our model of parity-age-duration–specific fertility. The remainder of the analysis excludes the indices for Benin and El Salvador in 1965–1969, which yielded implausible estimates of the PADTFR, probably as a result of errors in women’s reports about a period several years before the earliest survey in each country.
Because it is infeasible to present and discuss detailed results for 83 countries, Fig. 3 presents illustrative results for two: India and Kenya.Footnote 5 India exemplifies a transition to low fertility that has been driven by parity-specific birth control. Fertility fell at all interval durations but by more at long durations than short ones. Although all the period PPRs dropped, the proportion of women progressing to a third and fourth birth fell the most. Thus, the plot of the period PPRs by parity are initially linear but become strongly concave over the 45-year period examined. The period median closed birth interval is about 34 months, varying only slightly by parity. Moreover, apart from having increased by two to three months last century among women progressing to their third and fourth births, it has changed little over time. The plots of the proportions of women by parity who want no more children are a mirror image of the PPRs: they are highly convex, rising dramatically for women who have had exactly two children, compared with those who just have one.Footnote 6
Fertility transition followed a different path in Kenya. Fertility declined far more at interval durations of less than five years than at longer durations, producing the flattening of the duration-specific fertility distribution that characterizes postponement. According to these fully standardized estimates, fertility decline slowed at the beginning of the twenty-first century but did not experience a reversal. As in India, the period median length of birth intervals varied little by parity. However, it has been increasing steadily since fertility began to fall. By 2010–2014, it was 41 months. Notably, the decline in the PPRs with increasing parity in Kenya remained close to linear even though the PPRs dropped substantially. It also became steeper: progression from the fourth to the eighth birth dropped by more than progression to the fourth birth. Thus, the more children that Kenyan women had, the more likely they were not to have another birth. Comparatively, in India by 2015, the proportion of women progressing varied very little with parity after the first three births.
To some extent, Kenyan women may have been prevented from progressing as intervals lengthened by the decline in their fecundity with age (i.e., the number of perpetual postponers may have risen). The drop in the higher-order progression ratios was so large, though, that it could be due only to the widespread use of birth control to stop childbearing. However, women cease childbearing at a wide range of family sizes. No evidence exists that their final outcomes converged on small desired family sizes. Mirroring this, the proportion of the women who want no more children rose steadily with parity rather than rising sharply after they had two children, as in India.
Panel a of Fig. 4 compares period probabilities of progression from the fourth to the eighth birth with those to the fourth birth in all 83 countries. The dashed lines enclose the set of countries in which the absolute difference between the measures is less than 0.1. Like Kenya, nearly all the other African countries experienced a decline in progression from the fourth to the eighth birth that was at least as large as the decline in progression to the fourth birth. The two exceptions are South Africa, where fertility was already fairly low, and The Gambia. Moreover, inspection of the detailed results for sub-Saharan Africa included in the online appendix (Fig. A1) reveals that for most countries, they resemble those for Kenya: they are characterized by linear declines in progression with parity that steepened over time. Note that all the countries in panel a (Fig. 4), apart from those in the lower-left corner, experienced large declines in period parity progression. In most of Africa, however, these have not taken the form of parity-specific family size limitation.
Most countries outside mainland sub-Saharan Africa exhibit the opposite pattern of change, with larger reductions in the period probability of progressing to the fourth birth than in that of progressing from the fourth to eighth birth. A few non-African countries, however, followed an “African” pattern of decline in parity progression, with relatively large reductions among higher-parity women and little evidence of parity-specific limitation. These countries include Afghanistan, Pakistan, Jordan, Yemen, Ecuador, and several countries in which the most recent surveys date back to the 1990s (i.e., Costa Rica, Mexico, Thailand, and Uzbekistan; see Fig. A1 in the online appendix). Table 2 lists whether each of the 83 countries has a larger, smaller, or similar drop in progression from the fourth to the eighth birth than progression to the fourth birth. It also presents additional series of summary measures of the pattern of fertility change in each country. We describe these indices with reference to Figs. 4 (panel b), 5, and 6.
Whereas panel a of Fig. 4 examines changes over time in patterns of parity progression, panel b summarizes the degree of curvature in the plots of the most recent estimates of progression to the next birth against parity. The higher of the dashed lines represents the contour at which the difference between PPR4 and PPR8 equals that between PPR0 and PPR4; countries above this line have convex curves. The lower line identifies countries in which the difference between PPR0 and PPR4 is at least three times the difference between PPR4 and PPR8; countries below this line have highly concave curves. Most African countries have convex curves or fairly straight ones. The two outlying African countries are Lesotho and South Africa. In contrast, most countries in other regions have concave or highly concave curves, with parity progression falling away rapidly between the first and fourth births. The exceptions are Afghanistan; Pakistan; the Middle East and North Africa (MENA) region, except Egypt and Turkey; Mexico prior to 1990; and East Timor. As in India and Kenya, plots of the proportion of women by parity who want no more children generally mirror those in parity progression. Thus, in countries in which the curves for parity progression have become highly concave, those for women wanting no more children are strongly convex; in countries where the former have remained more linear, so have the latter (see Fig. A4, online appendix).
Figure 5 presents trends in the period median duration of closed birth intervals. As total fertility fell, birth intervals lengthened in most countries and regions of the world. Median pretransition birth intervals were of the order of 30 months, a result consistent with the pioneering work of Sheps et al. (1973). They lengthened substantially after total fertility dropped below five children per woman. By the end of the study period, the median interval exceeded four years throughout Southern Africa; in Bangladesh, the Maldives, Myanmar, and Indonesia in Asia; in Colombia, Paraguay, and Peru in South America; and in Moldova and Ukraine in Europe. Thus, these synthetic cohort estimates for intervals of all orders agree broadly with those that Casterline and Odden (2016) made for the interval to the second birth.
Except in Southern Africa, the rate of increase in the median length of birth intervals in sub-Saharan Africa was similar to that in other regions. However, outside sub-Saharan Africa and the Caribbean, the latter region being one in which intervals were very short initially, the lengthening of birth intervals was concentrated in the second half of the fertility transition. Thus, controlling for total fertility, virtually no overlap exists between median birth intervals in African countries and those elsewhere.Footnote 7 For example, outside sub-Saharan Africa, the only countries in which the median closed birth interval rose above three years before total fertility fell to fewer than 4.5 children per woman were Bangladesh and Tajikistan. In contrast, in every sub-Saharan African country in which total fertility dropped below 4.5 except Comoros, the median closed interval exceeded three years at that time.
A few countries saw no increase in the median length of closed birth intervals. The list includes several countries in the Sahel and Central Africa in which fertility changed little, but also Sierra Leone and Ethiopia, which are countries that saw a significant drop in total fertility. This group of countries also includes India (as shown in Fig. 3), Myanmar, Pakistan, and several countries in Central Asia.
Figure 6 examines the extent to which increases in the median length of birth intervals result from postponement and from birth spacing. Panel a looks at postponement. It compares changes in the period probability of having a birth 5–10 years after the previous birth, conditional on not having progressed before five years, with changes in the probability of progressing by five years since the previous birth. In countries above the upper dashed line, fertility fell by a relatively large amount at long durations, compared with medium and short durations. In countries below the lower dashed line, fertility rose over time at interval durations of 5–10 years, partly offsetting the drop in fertility that occurred at shorter durations.
The probability of progressing at birth intervals of 5–10 years is generally higher in sub-Saharan Africa than elsewhere. Moreover, many of the countries that saw progression at 5–10 years rise as progression before 5 years fell are in sub-Saharan Africa. In contrast, in most other countries, progression at 5–10 years fell along with progression before 5 years. The exceptions are Jordan, Morocco, Indonesia, Haiti, and some of the Latin American countries in which we could measure trends only prior to 1990. In many countries in which fertility at longer intervals fell, however, it did so relatively slowly, producing a flattening of the duration-specific fertility schedule. This flattening was more dramatic in sub-Saharan Africa than elsewhere.
Panel b of Fig. 6 presents an analogous analysis for birth spacing. It compares the period probability of closing the birth interval within 30 months of the previous birth with the probability of closing it in the following 30 months. The dotted line represents the regression of the first measure on the second one. Thus, we assess the trend toward postponement by comparing the standardized number of long intervals with the number of short and moderate ones, but we assess trends in spacing by comparing the standardized number of short intervals with the number of moderate length.
Trends in spacing have been muted in most countries. Short birth intervals became more common over time in about one-half the countries and less common in the others. In contrast to the previous figures, the cloud of points representing the sub-Saharan African countries largely overlaps with those for Europe and Asia. The dashed line of Fig. 6 identifies 11 countries in which a substantial reduction occurred in the proportion of closed intervals that were closed in less than 30 months. None of the 11 countries are in sub-Saharan Africa. Instead, they are confined to the MENA region, Latin America, and the Caribbean. The only countries that experienced increases in both postponement and spacing were Jordan, Morocco, and Costa Rica (where the run of data ends in 1990).
Based on the results presented in Figs. 4–6 and Table 2, Table 3 presents a three-way classification of the pathways toward low fertility taken by 78 countries during the part of their transition documented by the surveys. Five African countries (Angola, Central African Republic, Chad, Mali, and Niger) in which the most recent estimate of total fertility exceeds six children were excluded from the table because fertility has not fallen enough to classify them. Figure 7 maps the countries according to this classification in order to draw out the geographical patterning of the results.
Table 3 and panel a of Fig. 7 distinguish countries that have undergone a classic fertility transition, characterized by an increase in the proportion of women limiting childbearing to a small or moderate desired family size, from those in which stopping shows no evidence of being driven by parity-specific family size limitation. Countries that fall between these extremes are placed in a third, mixed category. The countries are divided horizontally in Table 3 and panel b of Fig. 7 into those characterized by the development of widespread and substantial postponement of the next birth, those with a smaller increase in postponement, and those in which no significant evidence of postponement exists. The upper of the two horizontal panels of Table 3 and hatched shading in panel b of Fig. 7 distinguish the 12 countries in which birth spacing increased substantially from those in which little change occurred or short birth intervals became more common.
Only a few countries followed a classic path to low fertility, characterized by parity-specific limitation with little increase in the length of birth intervals. This group is restricted to India and Nepal, together with Azerbaijan during the latter part of its transition. The only sub-Saharan African country in which family-size limitation predominated is South Africa. Although limitation is common outside sub-Saharan Africa, it is usually accompanied by increased postponement of the next birth, and in parts of Latin America, by birth spacing as well. Thus, in most countries characterized by parity-specific limitation, the median length of birth intervals has increased substantially.
In most of sub-Saharan Africa, in the Middle East and North African region, in Afghanistan, Pakistan, East Timor, and in Mexico prior to 1980, no evidence exists of family-size limitation. Instead, women reduced their number of births without converging on families of a particular size. Most of the African nations in this group of countries characterized by parity-independent curtailment of childbearing also experienced an increase in postponement. Most of its other members did not.
The intermediate group of countries that show evidence of a limited shift toward parity-specific limitation is fairly small. The countries are drawn from all regions of the world. They include the four Central Asian countries that were once part of the USSR and five mainland sub-Saharan African countries. With the exception of three of the Central Asian countries, this mixed group also saw an increase in postponement.
Fertility remained higher in most sub-Saharan African countries than in other regions at the end of the study period. This raises the possibility that postponement is not a geographically differentiated pattern of family building but rather a feature of the early phases of fertility transition. To assess whether this is the case, we repeated the classification of transitions into different pathways, examining only the initial drop in total fertility to four children per woman and discarding the more recent estimates (results not shown). The data on most African countries and the few other countries where the most recent total fertility rate exceeded four children were unaffected by this.
In most countries in which parity-specific limitation has played a part in the fertility transition, this pattern was already evident before total fertility fell to four children. Only a few countries experienced a period dominated by parity-independent curtailment followed by one dominated by parity-specific limitation. In addition to South Africa and the five relatively low fertility sub-Saharan African countries with a mixed pattern of parity progression at the end of the study period, these countries are Bangladesh, Egypt, and Indonesia. Turning to postponement, much of the lengthening of birth intervals in countries outside sub-Saharan Africa occurred during the second half of their fertility transition. Nevertheless, most countries characterized by substantial postponement at the end of the study period saw an initial shift in this direction before total fertility fell to four children per woman.