# Total fertility rate

This article describes an attempt to use behavior of multiple birth cohorts in a single period and extrapolate from that to consider the outcomes for a hypothetical individual, who, at each age, behaves like the birth cohort for that age.

## Contents

## Definition

The **total fertility rate** (**TFR**), also called the **period fertility rate** or **period fertility** of a population is defined in the following equivalent ways:

- It is the sum of the age-specific fertility rates for females at all ages. Note that only birth cohorts of females in their childbearing years are expceted to have age-specific fertility rates that are noticeably different from zero, so we can also define TFR as the sum of age-specific fertility rates for all ages that fall within the defined span for childbearing years. Note that
**we use age-specific fertility rates scaled to a denominator of 1 rather than to a denominator of 1000 for this definition.** - It is the expected value of the fertility that a female would have if, at every age, she had the age-specific fertility rate observed for the current year (rather than the year when she'd actually be that age).

We use the term **period fertility** to describe the TFR because it is a form of period analysis: we are aggregating over people of different ages, all in a given period of time. This is in contrast with cohort analysis, where we are looking at people who share a common temporal experience (such as birth, school attendance, or marriage) and study their behavior over their whole lifetime or a long part thereof.

### Total fertility rate for a particular birth order

Suppose is a positive integer. The total fertility rate at birth order is defined in the following equivalent ways:

- It is the sum of the age-specific fertility rates at birth order .
- It is the probability that a female would have a birth at birth order if, at every age, she had the age-specific fertility rate observed for the birth order .

Note that the total fertility rate at any particular birth order is bounded between 0 and 1: it is at least 0 and at most 1.

## Distinction between total fertility rate and general fertility rate

`Further information: general fertility rate, total fertility rate versus general fertility rate`

The reason TFR and GFR are different is because, whereas the TFR is the *total* of age-specific fertility rates and it weighs the birth cohort for each year with a weight of 1 per birth cohort, the GFR is the *average* of age-specific fertility rates weighted by the population sizes for the ages.

TFR and GFR would be easily related in the following two cases:

- All the age-specific fertility rates are the same. In this case, the GFR would equal all the equal age-specific fertility rate values, and the TFR would be the product of that value and the number of childbearing years.
- The population size is the same for each age. In this case, the GFR would equal the average of the age-specific fertility rate values, and the TFR would be the sum of the age-specific fertility rate values. In this case again, the TFR would equal the product of the GFR and the number of childbearing years.

Of course, neither case occurs in practice: there is considerable variation in the age structure of the female population (see the population pyramid for more), and considerable variation in the age-specific fertility rates.

Note also that, whereas TFR numbers are scaled to 1 (i.e., they represent actual numeric values), GFR numbers are scaled to a denominator of 1000. If the GFR numbers were not scaled to a denominator of 1000, they would be much smaller than TFR values. Both the above points about the relationship in special cases become valid *only after we rescale the GFR and ASFR values to a denominator of 1.*

## What does it take to compute TFR?

### Accurate measurement of TFR

Accurately measuring TFR requires the following:

- The recording and collation of all birth events in the current year
*along with*the recording of the date of birth of the mother at the time the birth event took place. - A complete record of the total female population at a given age (for all ages within the range of childbearing ages) in a given year. Note that knowing the total population does not suffice: one also needs to know the distribution of the population by age and sex (or rather, one needs information on the female subpopulation).

### Estimation of TFR via proxies

Measurement of the TFR requires a lot of data collection, and such data is not available for all populations. The following are some proxies:

Proxy | What we have in place of the record of birth events with the mother's date of birth | What we have in place of the record of the age distribution of the whole population | Qualitative nature of additional data needed to estimate TFR | Empirical estimate of correlation with TFR | Empirical estimate of conversion factor to multiply by this to estimate TFR (slope for linear regression) |
---|---|---|---|---|---|

general fertility rate | record of birth events only, without necessarily having data on the mother's age or date of birth | the total number of females who are in their childbearing years (no age distribution necessary) | age distribution of women within childbearing years (rather than just the population total) plus distribution of births by mother's age. | ||

crude birth rate | record of birth events only, without necessarily having data on the mother's age or date of birth | the total population | age-sex distribution of the entire population, plus distribution of births by the age of the mother. | According to Gapminder documentation, Page 17, a correlation of 0.989 in a UN cross-country dataset. | According to Gapminder documentation, Page 18, a value of 0.134 (default), but when available, use a country-specific regression to estimate the conversion factor. |

child-woman ratio | record of the total number of children under age 5. This can be done using a census and does not require recording events. | record of the total number of women of childbearing age. | age distribution of women within childbearing years (rather than just the population total), distribution of births by mother's age, and age-specific mortality rates of children. | Value unavailable, but correlation of 0.979 between CWR and CBR and 0.989 between CBr and TFR, so assuming multiplicatively, correlation of 0.968 between CWR and TFR (see Gapminder documentation, Pages 17 and 27) |

## What do TFR values look like?

### Gapminder data

- Gapminder data: Download, View online
- Gapminder data: Download, View online

### Historical data

Historical TFR data extends back to 1800, but for the initial period, such data was not collected every year but rather based on occasional census estimates. In 1800, the mean TFR (unweighted) of all countries was about 6.1, and the standard deviation was about 0.8, with very few countries having values significantly higher than 7. The United States had among the higher TFRs of the world, at slightly over 7, reflecting the very low population density relative to the size of the land. There is good reason to believe that TFR values had remained in this range for large parts of human history, because a fertility rate higher than 6 would be biologically relatively difficulty, and also because the other related indicators had not changed much in human history until 1800.

Proper data collection around the world began in 1950, with the United Nations playing an important coordinating role. In 1950, the unweighted mean of the TFR values of all countries recorded was about 5.4. It stayed steady at that level until about 1965, at which point it started seeing a steady decline with the decline initially being 0.1/year (for the first decade), then slowing down to 0.08/year (for the next decade), then slowing down to about 0.05/year. In the entire period from 1950 to 2012, the standard deviation remained study at about 1.5, suggesting that "all fertilities were coming down together." The current unweighted mean of TFR values across all countries is 2.83.