In this study, we used female population counts by age and birth cohort and birth counts by birth order and mother’s cohort from the Human Fertility Database (HFD) (Human Fertility Database 2018). To avoid problems arising from truncation and censoring bias, we used completed cohort fertility data only. Based on these criteria, data from eight countries were selected: Canada (1929–1962 birth cohort), the Czech Republic (1935–1965 birth cohort), Japan (1953–1965 birth cohort), the Netherlands (1935–1963 birth cohort), Norway (1952–1965 birth cohort), Portugal (1944–1966 birth cohort), Sweden (1955–1965 birth cohort), and the US (1918–1965 birth cohort).

While the parametric model for overall fertility is well developed (see, for example, Kostaki and Paraskevi 2007), there are few models that measure the first birth. In this study, we use the Coale-McNeil model (CM model) to estimate the age-specific first birth rate. The parameters of the CM model have conventional demographic meanings, and fit best with the aim of our study, which is to quantify the effects of remaining permanently childless and postponing fertility.

The CM model was developed to estimate the age at first marriage patterns of a birth cohort (Coale and Trussell 1978). The CM model has since been extended beyond its original purpose, and has often been applied to the first birth distribution by age (Bloom 1982a,b; Bloom and Trussell 1984; Henz and Huinink 1999; Rao 1987; Trussell and Bloom 1983). Previous studies successfully applied the CM model to various countries, including Canada, Columbia, Finland, Germany, Italy, and the US. The advantage of using the CM model is that its parameters have clear demographic meanings, which are as follows. The probability of first birth at age x and time t, denoted as fx,t, is expressed as: fx,t=Ct1σta1 exp[a2(x-μtσt+a3)- exp{-a4(x-μtσt+a3)}],  (1)

where Ct pertains to the proportion of the cohort eventually having a child by age 50 at time t, μt refers to the mean age at first birth at time t, σt is a measure of the standard deviation of age at first birth at time t, and the usual values for the constants are a1=1.281, a2=-1.145, a3=0.805, and a4=1.896. This equation is known as a standardised version of the CM model developed by Rodríguez and Trussell (1980).

Although several models have been used to estimate first birth patterns, these models are not fully applicable to our study. First, for one feature of the CM model (the convolution structure), an additional term has been proposed: namely, an exponentially distributed waiting time segment to account for the time from first marriage to first birth. However, Trussell and Bloom (1983) reported that the original CM model fitted better than the model with the waiting term. Thus, previous research applied the CM model to first birth patterns without using the additional waiting time segment (Bloom 1982a,b; Bloom and Trussell 1984, Henz and Huinink 1999, Rao 1987, Trussell and Bloom 1983). In addition, this approach is not theoretically appropriate given the current data. As nonmarital childbirth has become common in many high-income countries (Eurostat 2018; Department of Health and Human Services 2018), the first birth does not always occur after marriage. Thus, the additional term that considers the period from marriage to childbirth is not relevant to the data in our study. The second model is a log-logistic function (LL model). Henz and Huinink (1999) applied it to the first birth in the German data. However, it does not have a scale parameter, which indicates the proportion of the population who never had children. Hence, it is not applicable given our aim and decomposition method.

Although the CM model is widely used to study first birth trends, whether the CM model fits well with the observed pattern of the age at first birth has not been statistically examined. The goodness-of-fit using the Kolmogorov-Smirnov tests shows that the CM model estimates well the data for all the countries and years (see Appendix A). For these reasons, we have chosen to use the CM model to explore the changes over time in first birth behaviours and the expected years without children (EYWC).

However, the limitations of the CM model should be mentioned. There are statistical issues when the CM model is used to estimate the mean and the standard deviation of age at first birth (Bloom and Trussell 1984): (1) if the sample available for estimation is restricted to women who have become mothers on or before the survey date, a truncation bias problem will arise; and (2) if the data used for estimation refer to a sample of all women, there will be a censoring problem if any of the women who will ultimately have a first birth have not done so by the time of the survey (Bloom and Trussell 1984). We avoid those problems by using completed cohort fertility data from the HFD.

We use life expectancy to measure fertility behaviours. In classical life table methods, life expectancy between two ages (e.g., 0 and X) represents the area below a survival function from age zero to the fixed age X. This is interpreted as the average number of years people live between these ages (Preston et al. 2001). In this research analysing first birth trends, life expectancy is interpreted as the expected years without children, with a first birth representing a “death”. The minimum age is the age of first menstruation and the maximum age is the age of menopause. Therefore, the EYWC from age 15 to age 50, denoted as 35e15, is calculated as 35e15(t)=∫ 1550lx,tdx. It corresponds to the two shaded areas in Figure 1 for the 1940 and the 1962 birth cohorts. The use of EYWC has two primary advantages. First, as this index is able to capture fertility trends in one simple value, it can be used to numerically compare fertility trends at different times and in different countries. Second, it can take into account both the population having children and the population without children. While the most common indices used to study first birth trends are the mean age at first birth and the proportion of childless women, the EYWC index can reflect those two indices simultaneously. These features are very useful in the current context, in which both indices have an increasing trend.

We applied the decomposition method developed by Mogi and Canudas-Romo (2018). A detailed explanation can be found in their study (Mogi and Canudas-Romo 2018). The changes in EYWC over time, denoted as 35ė15(t), are decomposed into three parameters: scale (the proportion of the cohort eventually having a child), location (the mean age at first birth), and variance (the standard deviation of age at first birth). The decomposition of 35ė15(t) can be formulated as 35ė15(t)=∂35e15(t)∂CtCt·+∂35e15(t)∂μtμt·+∂35e15(t)∂σtσt·,  (2)

where each term is the change in 35ė15(t) resulting from changes in the scale, location, and variance. A dot on top of a variable indicates the derivative with respect to time. The largest value among these three components shows that the changes in EYWC are mainly caused by that factor; i.e., scale factor (∂35e15(t)∂CtCt·): remaining permanently childless, location (∂35e15(t)∂μtμt·): postponing first birth, or variance (∂35e15(t)∂σtσt·): expansion effect. Appendix C explains the detailed method for estimating the three parameters of the CM model and applying the decomposition equation to discrete data.

The trends in EYWC for the selected countries are presented in Figure 2.

Figure 2 shows that most of the countries in the study had an increasing trend in EYWC starting with the 1940s birth cohorts. The EYWC in Canada declined until the 1940s birth cohorts, and then started steeply increasing. The 1940 birth cohort in Canada had 12 years of EYWC. This value had increased to 16.6 years for the 1960 cohort. As EYWC represents the expected number of years without children starting from age 15, each number signifies that the expected age at first birth in the specific cohort in a country is 15+ EYWC. Thus, we can interpret these findings as showing that the expected age at first birth increased from 27 (15+12) in the 1940 birth cohort to 31.6 (15+16.6) in the 1960 birth cohort. The US had an increasing trend similar to that of Canada until the 1950s birth cohorts. In the US, the EYWC increased sharply from the 1940 birth cohort (10.5 years) to the 1950 birth cohort (13.6 years). However, this increasing trend slowed after the 1950 birth cohort. The EYWC in the US increased by only 1.3 years from the 1950 to the 1960 birth cohort. In the Netherlands, the EYWC increased starting with the 1945 birth cohort, from 13 years for the 1945 birth cohort to 17 years for the 1960 birth cohort. Moreover, in several other countries, such as in Japan and Norway, the EYWC displayed an increasing trend for all the observable periods. In Japan, the EYWC rose from 14 years for the 1953 birth cohort to 18 years for the 1965 birth cohort. In Norway, the EYWC increased from 12 years for the 1952 cohort to 15 years for the 1965 cohort.

The EYWC trends in Portugal, Sweden, and the Czech Republic differ from those in the countries discussed above. In Portugal, the EYWC fluctuated by approximately 10 years between the 1940s and 1950s birth cohorts. However, by the 1960 birth cohort, the EYWC in Portugal had increased, and it is currently estimated at 11.6 years for the latest observed birth cohort. By contrast, in the Czech Republic, the EYWC trend has been neither increasing nor decreasing, as it has plateaued at 10 years for all observable birth cohorts from 1935 to 1965. Interestingly, in Sweden, the EYWC trend has also plateaued in recent cohorts. After increasing starting with the 1955 birth cohort (14.4 years), the EYWC trend had plateaued at 16 years by the 1960 birth cohort.

Among the latest birth cohorts we can observe, the EYWC was approximately 17.5 years in Canada, Japan, and the Netherlands; and was approximately 15 years in Norway, Sweden, and the US. The EYWC values in these countries were followed by those in Portugal, at 11.5 years; and in the Czech Republic, at less than 10 years. Lower EYWC values indicate that, on average, the women in the population gave birth to their first child at an early age. The latest cohort observed in Canada, Japan, and the Netherlands spent half of their reproductive period with no children (the expected age at first birth is 15+17.5=32.5). In other words, these women have only have 17.5 years left in their reproductive period, on average, to have any subsequent children.

The main objective of this study is to investigate whether the changes in EYWC, as shown in Figure 2, are attributable to women remaining permanently childless or postponing childbirth, or to the expansion effect. We decompose EYWC from 1940 onwards; the results are presented in Figure 3.

In Canada, the US, the Netherlands, Sweden, and Norway, the location parameter (the timing of first birth) was the most influential factor in the changes in EYWC after 1950. Table 1 shows that 74% of the increase in the EYWC in Canada from 1955 to 1960 was due to the increase in the average age at first birth. Similar results can be reported for the US: 68% of the increase in the EYWC from 1958 to 1963 in the US can be attributed to the increase in the average age at first birth. Likewise, in Norway, the increase in the average age at first birth was responsible for 81% of the increase in the EYWC from 1957 to 1962. The results for the Netherlands and Sweden were very similar. These findings suggest that larger shares of the current birth cohorts in these countries have postponed childbirth rather than remaining permanently childless. The changes in the scale parameter and the proportion of women having children influenced the current increase in the EYWC of these countries to a lesser extent.

In addition, in the Netherlands (1955–1960) and Sweden (1960–1965), the value for the scale parameter in the most recent birth cohort was negative, which implies that the proportions of women having a first child increased in those periods. The negative value of the scale factor in Sweden is consistent with the current decrease in the proportion of childless women (Persson 2010; Miettinen et al. 2015). The higher educational category has a more distinct decreasing trend (Persson 2010). Therefore, this negative value could be mainly driven by women in a higher educational group.

However, the trends in Japan and Portugal differ from those in the other countries. The scale parameter, which indicates the proportion of women who eventually have a child, is the most influential factor in the changes in the EYWC in these countries after 1955 and 1959, respectively. For instance, Table 1 shows that 62% of the change in the EYWC in Portugal from 1959 to 1964 can be attributed to the scale parameter, which means that the shift was mainly attributable to women remaining permanently childless. Likewise, in Japan, the increase in EYWC was mainly due to the changes in the scale parameter, even though the location parameter had only approximately half as much impact on the latest change. This result indicates that in these countries, more women remained permanently childless than postponed their first birth to a later age. For Japan, the strong linkage between marriage and childbearing may be the key to understanding the large impact of the scale factor. As the nonmarital birth rate in Japan is still at a low level – i.e., 2.29% in 2015 (National Institute of Population and Social Security Research 2017) – most births in that country occur in marital unions. Hence, the large influence of the scale factor in Japan may indicate that the never-married population in Japan is increasing. Indeed, between 1980 and 2015, the never-married population at age 50 increased from 2.6% to 23.4% for males and from 4.5% to 14.1% for females (National Institute of Population and Social Security Research 2017). In Japan, the shares of never-married people are almost equal to the shares of childless people. This explains why the scale factor plays a larger role in Japan than in the other countries. Interpreting the findings for the Czech Republic is difficult because its EYWC trend fluctuated.

The changes in the variance parameter were not found to be influential in the changes in the EYWC in any of the countries in our sample except the US. The much larger variance effect observed in the US may be attributable to the strong differentials in first birth behaviours by indicators of socio-economic status, such as educational level, union status, and race/ethnicity. Rendall et al. (2010) found that in the US, there has been a persistent trend of early first births among low-educated women, and a shift towards later first births among women with higher educational levels. Moreover, Chandola et al. (2002) suggested that this heterogeneity is related to marital status, with an early bulge linked to extra-marital births, often among solo mothers. They also argued that ethnic differences play an important role in explaining the variance in the first birth trends in the US. Likewise, Kostaki and Paraskevi (2007) linked the observed heterogeneity in first birth patterns in the US to a range of fertility determinants, including the rise of migrant populations in conjunction with racial and ethnic differences.

Overall, the results strongly indicate that changes in EYWC are mainly due to two factors: remaining permanently childless and postponing childbirth. Except in the US, the variability in the timing of childbirth is generally not found to be a factor in the changes in EYWC.