Friday, December 01, 2006

CFR and TFR in Sweden

by Edward Hugh

This post is related to both the one which comes before it and the one which follows. CFR refers to cohort fertility rate and TFR to total fertility rate.

Fertility can be measured in a number of ways, and two of the most important of these are the total fertility rate and the cohort fertility rate. The total fertility rate (TFR) is an estimate of periodic fertility and is defined as the sum of number of children born by women in a defined age range (16-49) extrapolated to the lifetime fertility of the total number of women in that age group. The cohort fertility rate (CFR) is the average number of children which women actually give birth to during their lifetime fertility cycle, and is only known when the women in the cohort end their fertile life. CFR is an accurate and important indicator since it measures whether the completed fertility for women achieves replacement level or not. The replacement level is the number of children per woman (approximately 2.1) needed in order to hold the population constant.

In periods of rapid birth postponement significant differences may exist between the Tfr (estimate) and the final Cfr. This is clearly indicated in the case of Sweden by the two graphs below.

As can be seen while recorded Tfrs were continuously well below replacement level, Cfrs for cohorts up to the 1955-59 cohort have been quite stable, and at more or less the 2.0 level quite close to replacement level.

This is not to say that the postponement phenomenon is entirely benign, as the 'missing births' do of course influence the shape of the population pyramid.


Mark Amerman said...


Thanks for these graphs. I see that CFR is the actual
fertility curve for a population and that TFR is a
combination of actual and projected. The reason that
the CFR data stops at 1956 is that every woman born in
1956 is now 50, or safely beyond the child-bearing,
but that the same can't be said of a woman born in 1964.

The problem with the CFR is that by the time this data
is in it's almost of historical interest.

I see by comparing the TFR and CFR graphs that there
are some quite major discrepancies between the two.

I can't help wondering if it isn't possible to construct
a better algorithm than the TFR.

I see that I was wrong in my earlier assertion that
Sweden had never gotten near replacement fertility
since the 1930s. In fact they were close in 1956,
although still about a tenth of a point below.

Unless I'm mistaken a society needs 2.1 (instead of
2.0) to make up for deaths in childhood? Or is
that already implicitly covered by this data? In
other words, is CFR calculated from birth? If it
is then the crucial number would be 2.0.

Because of the problems with TFR it's hard to really
know what Sweden's real fertility situation is right

I suppose the argument could be made that Sweden
crossed over replacement levels in the middle of
the baby boom but is probably significantly below
that now.

Edward said...

Hi Mark

"I can't help wondering if it isn't possible to construct a better algorithm than the TFR."

Well obviously it is. The real difficulty is to get agreement on what this should be. There are various suggestions on offer. The extent of the problem, though, can be seem in a field like economics, and the difficulties involved in getting agreement on a way of measuring inflation, with all the fuss that things like hedonics cause.

In addition many countries aren't even offering up reliable data on TFRs, let alone on anything more sophistocated. There is, for example, a substantial and ongoing discrepancy between the data offered by the Population Reference Bureau and that offered by the CIA, and both of these are based in the US!

The best proposals I have found come from people like Wolfgang Lutz and Tomas Sobotka. Now be warned this is real heavy-duty (head banging) material, but if you are really interested and will not be deterred I would recommend this paper:

‘Missing Births’: Decomposing the Declining Number of Births in Europe into Tempo, Quantum, and Age Structure Effects

by Tomáš Sobotka, Wolfgang Lutz and Dimiter Philipov. Here the idea of a tempo-adjusted index of period fertility (adjPATFR) is advanced:


Most European societies have experienced a marked decline in the number of births during the last decades. This study aims to contribute to our understanding of the past twists in the number of births and our ability to foresee future patterns. It discusses various possibilities of decomposing the changing number of births, starting from a basic decomposition that distinguishes tempo, quantum, and ‘mean generation size’ components, and illustrating further extensions of this decomposition. The empirical analysis focuses on the impact of the three main components on the declining number of births from the onset of fertility postponement in 13 European societies. It reveals considerable variability: in all of the analysed countries, fertility postponement has put downward pressure on the number of observed births. Tempo distortions constituted the major force, negatively affecting the number of births in Austria, Denmark, Sweden, and in three post-communist societies: the Czech Republic, Hungary, and Poland. The analysis of the recent role of tempo distortions in period fertility may be used to project future trends. This paper argues that an explicit inclusion of assumptions concerning tempo effects may lead to a considerable improvement of the projection scenarios of fertility and births. Using examples of three countries with different intensity and duration of fertility postponement (Austria, the Czech Republic, and Finland) this study shows how the eventual stabilisation of the mean age at childbearing may affect the number of births in the future.

Me again:

Another paper would be this one from Sobotka:

Tempo-Quantum and Period-Cohort Interplay in Fertility Changes in Europe. Evidence from the Czech Republic, Italy, the Netherlands and Sweden


Using detailed data on period and cohort fertility in four European countries, this paper discusses various indicators of period fertility, including indicators adjusted for changes in fertility timing. Empirical analysis focuses on the comparison of cohort fertility and corresponding indicators of period fertility; particular attention is paid to the periods of intensive postponement of childbearing. Some period indicators come consistently closer to the completed cohort fertility than the total fertility rates. This pattern of differential period-cohort approximation widely varies by birth order. Quite a high level of approximation is provided by the tempo-adjusted birth probabilities of parity 1 and a combined indicator of total fertility. Two examples illustrate the use of indicators discussed in the paper: the first provides an estimation of the tempo (timing) and quantum (level) components in fertility change in the Czech Republic and the second presents projections of cohort fertility in the Czech Republic and Italy.

Me again:

Finally and most importantly I would recommend Sobotka's PhD Thesis, not only for the work on indexes, but since it offers the most comprehensive description and analysis of the birth postponement phenomenon in Europe, which is really the heart of the whole fertility issue, and may well help you to understand what comes next among the Latinos in the US. The whole thesis is online here (conveniently in Chapters) and the title is:

Postponement of childbearing and low fertility in Europe

Edward said...

Mark, a couple of loose points:

"Because of the problems with TFR it's hard to really know what Sweden's real fertility situation is right

Exactly, so don't believe anyone who tells you they KNOW exactly what is happening.

"I suppose the argument could be made that Sweden crossed over replacement levels in the middle of
the baby boom but is probably significantly below that now."

The argument could be made, amnd it is a plausible one, but as I am at pains to point out we simply don't know. This is very frustrating, since as you indicate all of this is quite important, yet we can only close or open the barn door long after the horse has or hasn't actually bolted. Which is why prudence is merited, and not a heavy reliance on best case scenarios and spin.

Борис Денисов said...

CFR is an overestimate of fertility, since some women measured in TFR do not survive to the end of their reproductive life span. Guess, these women are less fertile