Measures of generation length
Generation length is a slightly strange concept, and it is not clear how it should be measured. It can be approximated by using the mean age of childbearing: the average age of women at the birth of their children. This average age can be defined in various ways, as you can see below.
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If there was no mortality, the mean age at childbearing could be calculated as the mean of the age-specific fertility schedule. This measure corresponds to the GRR and is known as the mean age of the age-specific fertility schedule. In the formula. The mean age is therefore a weighted average in which the weights are the proportion of the fertility distribution spent in each age category.
For single-year age categories:
For multi-year age categories (a is the mid-point of the age group (i.e. 17.5, 22.5, 27.5 etc) and y is the number of years in the interval):
| μƒ |
= |
| ∑ a . y . 5 ƒx |
| ∑ y . 5 ƒx |
|
In the context of mortality, we would want to calculate a mean age of childbearing corresponding to the NRR. This is known as the mean age of childbearing in a cohort. In this case, the number of years spent in an interval is substituted by the number of person-years lived in the interval, i.e. the 5Lx function.
For single-year age categories:
| μc |
= |
| ∑( x + 0.5 ) ƒx Lx |
| ∑ ƒx Lx |
|
For multi-year age categories:
| μc |
= |
| ∑ a . 5 Lx . 5 ƒx |
| ∑ 5 Lx . 5 ƒx |
|
Both of the above measures refer to a cohort of women in a life table population with constant fertility and mortality schedules and where there is no growth. This is known as a stationary population (see PAPP101_s08 
for an overview of a stationary population). A stable population is like a stationary population, in that fertility and mortality are constant, but it may also be growing or declining. You will learn about stable populations in PAPP103_s07 . The mean age at childbearing in a stable population is:
For single-year age categories:
| μs |
= |
| ∑( x + 0.5 ) e -r (x+0.5) ƒx Lx |
| ∑ e -r (x+0.5) ƒx Lx |
|
For multi-year age categories:
| μs |
= |
| ∑ a . e -r.a 5 ƒx 5 Lx |
| ∑ e -r.a5 ƒx 5 Lx |
|
Finally, we could also calculate the mean age at childbearing in an observed population. In this case the weights are the actual numbers of births rather than the distribution of ASFRs (5Wx is the number of women aged x to x+5).
For single year age categories:
For multi-year age categories:
| μb |
= |
| ∑ a . 5 Wx . 5 ƒx |
| ∑ 5 Wx . 5 ƒx |
|