‘Rojak’ TFR

The Population White Paper recommends immigration as a means to make up for population shrinkage due to our low total fertility rate (TFR) of 1.2. In a letter to the Straits Times [1], Mr Ng Ya Ken makes a similar calling for us to find the ‘true’ reason for its formulation, which is our ‘dire’ demographic situation if foreigner intake is insufficient. It is Mr Ng’s hope that those who can see the ‘big picture’ help the rest see it.

The so-called ‘big’ picture rests on a single number – TFR of 1.2 in 2012. The TFR for any particular year is obtained by adding up the age-specific fertility rates for that year (and then dividing by 200) as shown in the table below.


The problem with this approach is that we end up with a ‘rojak’ TFR that combines the fertility of women from different generations at different stages of their fertility cycle. This ‘rojak’ TFR doesn’t reflect the fertility of any particular generation of women. To find out the fertility of any particular generation of women, we need to trace its fertility diagonally downwards across years. To do so more easily, we can align the age-specific fertility rates according to generation to create the table below which shows the ‘true’ TFR for each 5-year generation of women.


The importance of aligning age-specific fertility rates to obtain the ‘true’ TFR can be illustrated with an example. If we refer to the original, non-aligned TFR table, the ‘rojak’ TFR for 1985 is 1.59. But when we refer to the new, aligned TFR table, the generations of women that contributed to the ‘rojak’ TFR of 1.59 had ‘true’ TFRs ranging from 1.72 to 2.29, all higher than 1.59. Herein lies the problem with the ‘rojak’ TFR: it may not give a true picture of the fertility of our women. In a society where marriage and child bearing are being delayed, the bulk of the children of the younger generations of women may only come much later but this contributes to a lower ‘rojak’ TFR today. At the same time, the older generation of women who already had the bulk of their children earlier will also similarly contribute to a lower ‘rojak’ TFR today. The way to avoid all these distortions is to make use of the ‘true’ TFR instead.

The ‘true’ TFR approach is only available for those generations that have completed their fertility life cycles. These have to be extrapolated to obtain the ‘true’ TFRs of future generations. The following tables show the ‘true’ TFR data points of women who turned 15 between 1963 and 1987 (that means born between 1948 and 1972) and then extrapolated for another 73 years to the year 2060. Two models of extrapolation are used here: the log model and the power model (both provided by Excel). We can see that in the case of the log model, our true TFR hasn’t reached 1.2 yet even at year 2060. For the power model, our true TFR is about 1.4 at year 2060. Both models show that our true TFRs are far from as dire as our ‘rojak’ TFR suggests.

True TFR

It is worrying that our nation is being huddled along in accordance to a number that may not even reflect the true picture, let alone big picture. Previous governments have experimented with population control and ended up being off by a mile. Is the present government so much more prescient that they will not be off by more than a mile?


5 Responses to “‘Rojak’ TFR”

  1. Observer Says:

    This is period and cohort fertility in demographic theory. Period fertility of 1.2 is important in this context because it relates directly to the births of the year. If the low births and fertility continues, and we know period fertility has been about 1.2-1.3 for close to 10 yrs now, then Singapore will have a problem replacing its population. One can see this in the slowly inverting population pyramid.

    • trulysingapore Says:

      In the context of our issue, which is to determine how much of our population has been replaced by 2060, period fertility isn’t what we should be scrutinizing. It makes more sense instead to look at cohort fertility because that is really what we want to know, how much each cohort has replaced itself by the time 2060.

      Using the period fertility instead of cohort fertility to determine how much Singapore would have replaced itself by 2060 and then using it to galvanize the whole country into a particular direction is simply inappropriate and wrong.

      • Observer Says:

        Since we are talking about replacement, then period fertility, which directly relates to the births each year, will be the relevant indicator. If period fertility continues to be about 1.2-1.3 every year till 2060, then we will be seeing declining number of births, since successive birth cohorts shrink in size.

        Separately, in demographic theory, we know that cohort fertility lags period fertility. If we extrapolate each cohort Age-Specific fertilty rate further, we will see that in the absence of any external changes, the cohort fertility will also tend towards the period fertility in the mid term. Extending the Table 2 of your article, the estimates would be :
        1990 cohort 1.52 TFR (you just need to fill in 1 more cell, you can assume “6” and you won’t go far wrong)
        2000 = 1.33 (you just need to fill in 2 more cells, assume “44” and “6”)
        2005 = 1.26
        2010 = 1.2
        2015 = 1.2
        2020 = 1.2

      • trulysingapore Says:

        Disagree, based on the problem at hand, which is how much our population would have changed by 2060, it is cohort fertility that matters, not the period or rojak fertility. What we want to know is by 2060, how much each generation has replaced itself. That can only be answered by the cohort fertility, not the period / rojak fertility. The period / rojak fertility is merely a snapshot of the current picture. This current picture is not a true picture but a rojak picture that cannot even be extrapolated into the future. Fertility from cohort to cohort can be expected to change incrementally with reasonable expectation that can be extrapolated. Not for period / rojak fertility. At times when marriage is delayed, it paints a distorted picture where older generations that have largely completed their fertility cycles contributes to a lower rojak fertility today while the newer generations who are slow to start their fertility cycles will also contribute to a lower rojak fertility now. This rojak cohort is not based on any real generation or cohort and any such extrapolation would be meaningless.

        The period fertility doesn’t so much as lag the cohort fertility but mixes up the cohort fertility like rojak. In times of marriage delay, even without lowering of cohort fertility, the period fertility will end up decreasing first and then increasing later. So these two curves will end up not having the same shape. One remains constant, the other one decreases, then increases. So you can’t say one lags the other.

        The extensions are correct and depending on the model used can decay to either 1.4 or 1.2, not necessarily just 1.2. The extensions have been done correctly, otherwise the graphs cannot be produced. Not just extension of 1, 2 cells but many cells to produce the full graph.

  2. Observer Says:

    Replacement fertility is measured using period fertility. This is because it directly relates to the births of the year. If TFR is at 1.2, how many citizen males would you have serving NS is a particular intake? Contributions to any BIRTH cohort is made up of births of women from all ages, which is used to compute the period TFR. Read any demography text and one can understand the concept of replacement TFR.

    Regardless if the period TFR is extrapolated to 1.2 or 1.4 in 2060, though 1.2 is much more likely without external factors, it means an annual shortfall of about 1/3 of births we would have needed to replace a population at each successive single yr of age. Reminds me of Japan’s problem.

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