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2051.0 - Australian Census Analytic Program: Forecasting Births, 2006  
Latest ISSUE Released at 11:30 AM (CANBERRA TIME) 21/07/2011  First Issue
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By Professor Peter McDonald (1) and Dr. Rebecca Kippen (2)


A great deal of private and public expenditure is contingent upon the future number of births. In the short term, there are the costs and labour involved in the provision of pre-natal, maternity and post-natal services. Later, the number of births affects demand for early childhood education and care, then entries to primary school, secondary school and tertiary institutions. After 20 years or so, the number of births affects the number of new entrants to the labour force.

For age-related services at older ages, there is a great deal of time to plan for the future and the future is relatively well defined by the current age distribution of the population. For child-related services, however, there is little time to plan and to adjust to movements in the annual number of births. Most child-related services are also relatively 'lumpy' in that they come in large blocks like schools or universities. It is therefore vital that countries and regions are able to forecast the future number of births with accuracy.


In most advanced countries over the past 50 years, statistical agencies have performed poorly in estimating the future number of births (Wilson et al., 2010). Some national statistical organisations, such as the Australian Bureau of Statistics (ABS), do not even attempt to undertake forecasting and instead produce a series of projections which are illustrations of change if certain assumptions on fertility prevail. These projections are not predictions or forecasts. However, with that being said, there are several options potentially available to national statistical organisations to improve births projections. One possible approach is to undertake stochastic projections that provide estimates of the likely range of error of the projected numbers of births. Where this has been done for Australia (Wilson et al., 2010), the range of possible estimates is so wide that policy makers would still be required to make a stab in the dark in estimating future service needs for children. A second approach, the one suggested in this report, is to develop a more sophisticated approach to the measurement of fertility through an increase in the demographic parameters that are used in the projection of births.


The conventional method used for the projection of births employs just one parameter as a predictor of the likelihood that a woman will give birth, her age. Rates of birth at each age are 'projected' forward into the future and they are applied to the estimated future numbers of women at each age. Generally, the future level of age-specific birth rates is projected from past trends, or the opinions of experts are obtained. Much of this estimation revolves around the future course of a single summary measure, the Total Fertility Rate (TFR), which is the sum of the age-specific fertility rates in a given year.

Total Fertility Rate

The Total Fertility Rate (TFR) can be interpreted as the average number of births that a group of women would have across their life times if they experienced the age-specific fertility rates as measured at each age in one calendar year. This is what demographers call a 'synthetic' measure. It is not the real or actual experience of any group of women; it is a synthetically constructed experience based on the assumption that women have the fertility rates of the current calendar year throughout their life time (or, more precisely, between the ages of 15 and 50).

Figure 1 shows the movements in the Australian TFR from 1921 to 2009. It also shows how the TFR is the sum of the age-specific fertility rates in each year. The figure shows how fertility fell to low levels during the 1930s, but then rose again to reach a peak in 1961. For the years 1946 to 1971, the TFR was above 2.8 births per woman; this was the post-war baby-boom. Fertility rates then fell precipitously in the 1970s, falling to a low point of 1.9 by 1980. In more recent times, the TFR trended downwards at a relatively constant rate between 1992 and 2001 and it remained low until 2003.
Graph: Total fertility rate shown as the sum of five-year age-specific fertility rates.

Projections of fertility made at this time assumed the TFR would fall even further (ABS, 2003). A program of school closures began in most states and territories, and it was assumed that the then existing maternity services would be adequate. In contrast, a rise in fertility began in 2004 that was sustained through to 2009. By 2008, the TFR was at its highest point in 30 years. In the six years from 2004 to 2009, there have been 152,000 more births than there would have been if the number of births had remained constant at the 2003 level. This is equivalent to over 250 primary schools each with 600 students.

The TFR is a summary measure of the annual incidence of births. As such, it can be affected by numerous factors such as changes in economic conditions (employment, the cost of housing, the business cycle), changes in government support for families with children (taxes and transfers, child care, etc.) and changes in the composition of the population (by relationship status, education, religion, ethnicity, etc.). These factors are usually considered in very broad terms when projections of fertility are undertaken.

However, when fertility rates are low, the main factor that affects the annual incidence of births is changes in the timing of births, especially the ages at which successive cohorts of women have their first births, and this is rarely considered in making projections of fertility. As a simple illustration of this, in Figure 1, the correlation between the TFR in any calendar year and the fertility rate below age 25 years in the same calendar year is 0.92.

Age at first birth

The cumulated first birth rates to given ages for Australian birth cohorts from 1950 to 1984 are shown in Figure 2. The rates are shown relative to those for the 1960 birth cohort. Cohorts born in the 1950s had higher cumulated first birth rates at each age than did the 1960 birth cohort. In other words, they had their first births at earlier ages than those born in 1960. However, cohorts born after 1960 have had their first births at later and later ages. The difference across cohorts is at its maximum at around ages 27 and 28. Across these cohorts, there has been a considerable shift from having the first birth before ages 27—28 to having it from ages 27—28 onwards.

Graph: Cumulated first birth rates to given ages for Australian birth cohorts from 1950 to 1984 relative to those for the 1960 cohort.

Figure 3 shows this trend in a different way. It shows the distribution of the number of children born to women reaching age 30 in a given year. The proportion having no children rises linearly from 20 per cent for those reaching age 30 in 1981, to 46 per cent for those reaching age 30 in 2001, the year that the TFR hit its lowest point. Implicitly, projections of fertility that were made around 2003 assumed that this upward trend in age at first birth for cohorts would continue. However, as is evident from Figure 3, the trend levelled off from around 2001 onwards. Figure 1 shows that, in the period from 1992 to 2001, the TFR had fallen because the fall in fertility rates for women aged less than 30 (due to later first births) was larger than the rise in fertility rates at ages above 30. From 2001 onwards, Figure 1 also shows that this situation reversed and the TFR rose. To summarise, the TFR has risen in recent years because women at older ages have been having the births that had been delayed in the past while women at younger ages have ceased delaying their births any further than earlier cohorts did.

Graph: The distribution of the number of children ever born to women reaching age 30 in the given year, 1981 to 2006.

Finally, Figure 4 shows a summary of how changes in the timing of births have affected the Australian TFR over a long period of time. Three lines are plotted:
      1. The Total Fertility Rate (as shown in Figure 1), labeled PTFR;
      2. A measure, Tempo Standardised Period Total Fertility Rate (TSPTFR1), which removes the effects of timing changes from the trend in the TFR; and,
      3. Completed Cohort Fertility Rate (CCFR), the actual average completed number of children born to cohorts of Australian women, plotted in the year equivalent to their year of birth plus their mean age at childbearing.

Figure 4: The Total Fertility Rate (PTFR), Tempo Standardised Period Total Fertility Rate (TSPTFR 1), and Completed Cohort Fertility Rate (CCFR)
Graph: The Total Fertility Rate (PTFR), Tempo Standardised Period Total Fertility Rate (TSPTFR 1), and Completed Cohort Fertility Rate (CCFR)

The trends for the second and third measures are very similar, suggesting that the standardised measure (TSPTFR1) provides a very reliable measure of the 'quantum' of fertility, or the underlying level of fertility. The impact of timing changes on the TFR is indicated by the difference between PTFR and TSPTFR1. Our results show that the post-war history of fertility in Australia can be divided into two periods: 1946—1972 and 1973—2007. In the first period (26 years), changes in the timing of fertility contributed to a higher TFR. Across the whole of this period, 61% of the higher fertility rates (relative to 1946) was due to earlier childbearing, while the remainder (39%), was due to increases in the quantum of childbearing.

In the second period (34 years), changes in the timing of fertility contributed to a lower TFR. In this period, 33% of the lower fertility rates (relative to 1973) was due to later childbearing and 67% to a lower quantum. We also concluded that the second period has now ended as the tempo effect on the 2007 PTFR has fallen to zero.


The above analysis has shown the extent to which the annual incidence of births is affected or distorted by changes in the timing of births. However, it is this annual distorted incidence rate that produces the annual number of births. It is useful to know the trend in the underlying quantum of births (how many births women are having across their lifetimes) but to project annual births we also need to project the timing of these births. Thus, the next step in the analysis is to define a way by which this can be done.

The first point to be made is that changes in the timing of births are driven almost entirely by changes in the timing of the first birth. To a very large extent, as we show below, a woman's later births follow in a fairly regular way given the age at her first birth. This means that, in addition to the women's age, we should project births on the basis of the number of births that a woman has had already (her parity). Furthermore, again as we show below, the time since the last birth has a considerable bearing on whether or not a woman has a birth in a given year. This is because we can normally expect fairly regular patterns for the intervals between successive births.


On these assumptions, we set out to create a database for Australia that provided estimates of both births and the population of women by three characteristics measured simultaneously: age, parity and duration since previous birth. We require these estimates in great detail: by single years of age of the woman, by single parity (0, 1, 2, 3 etc) and single year of time since the previous birth (zero years, one year, two years and so on). Our approach was to use the Australian Censuses to derive these estimates. The methodology is described in Appendix 2 (Using Census data to create a detailed database for fertility analysis). Having obtained these estimates, we were then able to calculate age-parity-duration specific fertility rates. These rates can also be summed to a total fertility rate which is known in the literature as the Parity-Age-Duration TFR (Rallu and Toulemon, 1994).

The comparison of PADTFR and TFR is shown in Figure 5 for the years, 1990 to 2005. It is important to remember that these two measures are two ways of measuring the same thing: the annual incidence of births. The difference is that one takes account only of the ages of women (TFR) while the other, in addition to age, considers both parity and duration since the previous birth. Figure 5 shows that PADTFR was considerably higher than TFR in 1990 but fell faster than TFR during the 1990s so that the two measures were equal by 2002. They have remained essentially equal through to 2005. The two measures will be equal if the addition of parity and duration since the last birth is providing no additional impact beyond the effects of age. On the basis of observations made later in the report, this would occur if the cohort age-specific first birth rates had stabilised, as has already been argued. We argue, therefore, that Australian fertility has entered a new period of relative stability across cohorts. However, there is no guarantee that this situation will continue. New patterns of the timing of the first birth may emerge in the future.

Figure 5: The Age-Based Total Fertility Rate (TFR) and the Parity-Age-Duration TFR (PADTFR), Australia - 1990 to 2005
Graph: The Age-Based Total Fertility Rate (TFR) and the Parity-Age-Duration TFR (PADTFR), Australia—1990 to 2005

The most important finding from our research database is that for second and higher order births, the age-parity-duration specific birth rates have remained almost constant for over 20 years. This relative stability is indicated for the years 2001 to 2005 in the 15 figures shown in Appendix 1 (Charts of Age-Parity-Duration specific birth rates, 2001—2005). This is important because it means that, if it is assumed that this level of constancy will continue (a strong assumption), projection of future birth rates becomes only a matter of projecting age-specific first birth rates for cohorts.

The methodology was tested on Census data from the years, 2001 to 2006. Using information contained in the database up to the year 2000, births were projected forward to 2006 and compared with the actual outcomes. In these projections, it was assumed that trends in the probability of first birth would follow the trend in these probabilities in the previous five years (1996—2000). Then, we assume that all other transitions remain constant at their most recent value as indicated in the charts in Appendix 1. Importantly, for the population at risk of these birth rates, we use from our database the population of women classified simultaneously by age, parity and duration since the previous birth. Taking account of this more detailed population structure is an important aspect of the methodology.

Figure 6 shows the actual age-specific fertility rates for the years, 2002 and 2006, compared with their projected values. The actual and the projected results are very close. Figure 7 shows the actual and the projected TFR for the years, 2000—2006 using the McDonald-Kippen method. Again, the two are quite close. Indeed, the projection was able to predict the turning point in the Total Fertility Rate that actually occurred. It should be recalled that official projections made around 2003 projected a continuation of the downward trend in the Total Fertility Rate (Commonwealth of Australia, 2002; ABS, 2003). It is evident, at least in this one test, that the method that we propose performs considerably better than the simpler approaches used by official agencies. The error in the number of births projected for Australia from 2004 onwards would have been substantially avoided.

Given that many of the services and infrastructure used by the community, such as maternity services, early childhood facilities, and schools, are directly affected by the annual number of births, it is important that the number of future births can be more accurately forecast, or more realistically projected. Traditional methods used for the projection of births only take into account a woman's age through the use of the assumed TFR as a predictor of measuring future fertility. This article has shown that the McDonald-Kippen method of forecasting births, which incorporates age, parity and duration since last birth, produced a result that was very close to actual birth rates for 2002 and 2006. It is proposed that the findings from the present study be considered by national statistical organisations to improve the projection of births, which could ultimately lead to improved population projections into the future.
Graph: Actual age-specific fertility rates in 2002 and 2006 compared with those projected using the McDonald-Kippen method.

Figure 7: Actual, Estimated and Projected Total Fertility Rates, Australia - 1980 to 2006
Graph: Actual, Estimated and Projected Total Fertility Rates, Australia—1980 to 2006


1 - Director, Australian Demographic and Social Research Institute, The Australian National University <back
2 - Future Fellow, Centre for Health and Society, University of Melbourne <back

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