23 April 2012

What Total Fertility Rate Means

Total fertility rate is a concept used by politicians, statisticians and others when talking about population growth, especially when it is either excessive or inadequate.

But what exactly is TFR?

TFR is defined as the average number of children a hypothetical cohort of women would have at the end of their reproductive period if they were subject during their whole lives to the fertility rates of a given period and if they were not subject to mortality.  It is expressed as children per woman [see note 1 for the formula].

Several terms are key to understanding what TFR means and what it does not mean.

a. TFR is based on a hypothetical cohort of women.  This hypothetical cohort comprises women ranging in age from 15 years to 49 years typically.  Why this cohort is hypothetical will become apparent in the following paragraphs.

b. The number of children that this hypothetical cohort of women would have at the end of their reproductive period is based on the fertility rates of hypothetical sub-cohorts in a given period (usually one calendar year).

Each hypothetical sub-cohort comprises all the women in the community grouped in a 5-year age bands e.g., 15-19 years old, 20-24 years old etc. and ending with 45-49 years old.  The fertility rates (expressed in live births per thousand women) of each hypothetical sub-cohort are added up to derive TFR for that year (after applying a factor of 5, see note 1).

Because TFR of a community is based on women whose ages range from 15 years to 49 years, TFR is neither the actual nor projected fertility rate of women in any particular age group.  That is, TFR for 2011 is neither the actual nor projected fertility rate of a woman who was, for example, 15-19 years old in 2011.

Also, the fertility rate of women in any particular age group last year (for example) is not likely to be the same as the fertility rate of women in that same age group ten years ago or ten years from now because marriage and procreation preference and patterns change over time.

TFR for 2011 (or any other year) is not:

- The average number of children that women aged 50 years (the age usually taken to be the end of their reproductive period) in 2011 have ever given birth to.

- The average number of children that women aged 15 years (the age usually taken to be the beginning of their reproductive period) in 2011 are forecast to have when they reach the end of their reproductive period.

- The average number of children that any individual woman aged between 15 years and 49 years in 2011 is forecast to have when she reaches the end of her reproductive period.

- The average number of children that all women aged between 15 years and 49 years in 2011 are forecast to have when they reach the end of their respective reproductive periods.

- The number of children that a hypothetical cohort of married or ever married women would have at the end of their reproductive period is based on the fertility rates of a given period.

c. The hypothetical cohort of women is not subject to mortality until they reach the end of the reproductive period. Mortality reduces the number of women who may potentially reproduce.

The definition of TFR requires the construction of a hypothetical group of women who rush through their child-bearing years compressed into one single year!

It may be better or easier to think of TFR as the composite fertility rate of women in the community in a given year, and dispense with the concept of it being the number of children that these women would have at the end of their reproductive period.


Implications

A. Consider the following scenarios.

Couples decide not to have any babies in any year because of any reason whatsoever (e.g., social unrest, war, deep economic depression), TFR is zero.  Should we despair?

Many couples decide to have babies this year because it is the year of the dragon according to the Chinese zodiac, and TFR rises from 1.20 to 1.60.  Should we rejoice?  What if TFR resulted from parents deferring having babies in 2010 and 2011 and bringing forward having babies from 2013 and 2014?

Despite its conceptual limitations, the usefulness of TFR lies in its trend.  The year-to-year fluctuations in TFR may reflect the changes in the timing of births rather than changes in the underlying fertility rate of the population.

B. TFR by itself doesn't tell us how quickly or slowly the population is changing.  This depends (among other things) on the mean age at child-bearing (which is defined as the mean age of mothers at the birth of their children if women are subject throughout their lives to the age-specific fertility rates observed in a given year).

The lower the mean age at child-bearing, the more rapidly the population changes with any given TFR.  This more rapid rate of change of the population works both ways, resulting in a faster increase in the population if TFR is above the replacement rate and a faster decrease in the population if TFR is below the replacement rate.  The converse is this: the higher the mean age at child-bearing, the more slowly the population increases if TFR is above the replacement rate and the more slowly the population shrinks if TFR is below the replacement rate.

C. TFR is a fertility rate derived from the births of babies in a given year to women from as young as 15 years to as old as 49 years.  But the life-time procreation pattern of a woman who is 15 years old now will be different from the procreation pattern of a woman who was 15 years old in 2002 (10 years ago), and both will be different from the procreation pattern of a woman who was 15 years old in 1992 (20 years ago).  Procreation preferences and patterns change over time.

No woman approximates the hypothetical woman in the TFR definition, regardless whether or not she gives birth to the number of babies derived from TFR (even if we disregard the impossibility of giving birth to a non-integer number of babies).

D. TFR doesn't take into account children born to citizens outside Singapore who subsequently return to Singapore or children born to foreigners who subsequently decide to become citizens or permanent residents.

Neither does TFR take into account children born to citizens and permanent residents in Singapore who subsequently leave the country.  By itself, a higher TFR has little meaning for a society if these children and their parents leave Singapore during their economically productive years.

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Notes

1. TFR = (B15-19/W15-19 + B20-24/W20-24 + B25-29/W25-29 + . . . + B45-49/W45-49) x 5
where, for example, B15-19 is the number of babies born to mothers aged between 15 years and 19 years and W15-19 is the number of women in the general population aged between 15 years and 19 years in the year for which TFR is computed.  Babies born to mothers younger than 15 years or older than 49 years are added to the nearest age group.  The total is multiplied by 5 because each sub-cohort spans five years.

3 comments:

  1. Thanks for the quickie.

    I always suspected that statistics and numbers could be presented to sound very profound... when in simple layman terms, it is not.

    Its a common technique in politics, debates etc.

    ReplyDelete
  2. Cannot convinced you...... Confused you!! That their logic

    ReplyDelete
  3. THANK YOU!Could you also comment on NRR (net reproductive rate)- what it is and isnt?

    ReplyDelete