1. Demographic Analysis and Evaluation
Workshop on
Demographic Analysis and Evaluation 1

2. Fertility: The Own-children Technique A. Introduction

3. The Own-children Method
In this part of the workshop we will cover:
The own-children fertility estimation technique
The East-West Center's program FERT, which performs the calculations
The own-children technique is described in Population Analysis with Microcomputers, chapter 4 (pp and appendix IV-4). The FERT manual may be downloaded from the website of the East-West Population Institute.
overview/population-and-health/demographic-software-available- from-the-east-west-center/ 3

4. The Own-children Method
This technique estimates age-specific fertility rates based on a current age structure of the population and mortality estimates for the past. The time reference of the estimates runs from the year prior to the census to about 15 years back in time.

5. The Own-children Method
If the current age of the mother and of her children is known, it is possible to calculate not only the year of birth of each child, but also the age of the mother at the birth of the child. With this information, an estimate of the number of births for each year prior to the census can be obtained, as well as the distribution of births by age of mother.
With data on children by age of their mothers and females by single ages for several years prior to the census, age- specific fertility rates can be calculated. The method takes into account mortality of both women and children during the rejuvenation period.

6. The Own-children Method
Data required:
Census information that matches each child to its mother – either relationship to head of household for both women and children in the household or a code “mother's person number” for each child.
A distribution of the population by single years of age
Mortality estimates for a 15-year period prior to the census.

7. The Own-children Method
Data required:
A distribution of the population by single years of age
The number of children under 15 years of age living with their own mothers ("matched children"), classified by both their own single years of age and their mothers' single years of age.
The number of children under 15 years of age not living with their own mothers ("unmatched children"), classified by their own single years of age.
The total number of women, by single years of age.

8. The Own-children Method
Assumptions:
Census coverage is the same for children as for women. The completeness of census enumeration is the same for all ages.
There is no migration.
There is no age misreporting.
The age distribution of mothers of unmatched children is the same as the age distribution of mothers of matched children.

9. The Own-children Method
Procedure, step-by-step:
Matching of children with their natural mothers by age of child and age of mother.
Adjustment of numbers of children for “non-own children” (children who cannot be matched)
Rejuvenation (reverse-survival) of mothers to birth year of each child and rejuvenation of each child to its birth year based on its age at interview.
Calculation of age-specific fertility rates using rejuvenated children and rejuvenated women for each year over the past 15 years or so.

10. The Own-children Method
Procedure:
The technique requires special tabulations matching children with their natural mothers. Once children and mothers are matched, the number of children and the female population are rejuvenated in such a way that children are continuously linked to their mothers, by age. This procedure allows the estimation of the number of births, by age of mother, for each year. Based on the number of births by age of mother and the female population, age-specific fertility rates are calculated.

11. The Own-children Method
Advantages:
The technique provides estimates of the total fertility rate as well as age-specific fertility rates without requiring any assumptions concerning the pattern of fertility.
Own-children fertility estimates can be calculated from any survey, not just a demographic survey, if the requisite household composition information is collected.

12. The Own-children Method
Limitations:
Fertility estimates are based on the assumption that completeness of enumeration was the same for all ages. However, the completeness of enumeration for ages under 5 years is often lower than for other age groups. This produces biased estimates, since the number of births estimated based on the youngest ages is too small. As a result, the trend of the fertility estimates shows a decline for 2 or 3 years prior to the census.
ASFR estimates are affected by age-misstatement.

13. The Own-children Method and the East-West Center Program FERT
Stage 1
Working from a person record file, FERT’s MATCHTAB program creates a mother-child matrix.
The person record file reflects data collected using a questionnaire such as the 1974 American Samoa census questionnaire reproduced on the next page.
Questions highlighted include (1) person’s relationship to head, (2) sex, (3) date of birth, (10) mother’s person number, and (11) employment status.

14. Preliminary Steps

15. Rules for Matching Children to Mothers
Note: The rules have been created to be flexible enough to adapt to the particular country’s situation.
Relationship to Head
If the mother is the spouse of the head, then the child must be the child of the head.
If the mother is the child of the head, then the child must be the grandchild of the head.
If the mother is the mother of the head, then the child must be either the head or the sister or brother of the head.

16. Rules for Matching Children to Mothers (cont.)
Age
The mother must be between 15* and 65 years old.
The child must be between 0 and 14 years old.
Age Difference
The mother must be at least 14* years older than the child.
The mother must be no more than 50* years older than the child.
* Age limits may change, depending on the country being analyzed.

17. Rules for Matching Children to Mothers (cont.)
Children Living (or children living at home, if available)
A mother may not have more children assigned to her than she has children living.
If information on the sex of children living is available, this information can also be used in matching.

18. Cumulative Proportions Of Own Children (Ages 0-14)
Proportions matched by age of mother for various methods of matching, American Samoa, 1974

19. Percentage of Own-children (Under Age 15)

20. Percentages of Non-own Children Using Different Matching Procedures
Alternative non-own children estimates for American Samoa 1974

21. TFRs with Different Matching Procedures
TFR estimates for American Samoa 1974

22. The Own-children Method and the East-West Center Program FERT
Stage 3
Reverse survival- based fertility estimation using OWNCH3

23. Reverse Survival
Reverse survival adjusts numbers of children and numbers of mothers for mortality over a period of years matching the ages of the children.
Children must be adjusted for:
Non-own children factor
Underenumeration
Women must be adjusted for:

24. Reverse Survival
For a census in 1974, to calculate an age-specific- fertility rate for women who were age 25 in 1969:
where C is children, W is women, B is births, and F is age-specific fertility

25. To Determine a Non-own Factor
For each child age group, the non-own factor is calculated as the ratio of total to own-children. It is then multiplied by the number of births to women of each age, inflating the number or births to account for all births.

26. Calculation of Age-specific Fertility Rates/
So, for example:

27. Dating the Estimates
On average, children under age 1 were born half a year prior to date of the interview, children age 1 were born 1.5 years prior to date of interview, and so on.
For this reason, ASFRs from FERT should be dated 6 months prior to the survey date (which we might approximate as the midpoint of the fieldwork period).

28. Graph the Single-year ASFRs to Check for Own-children Estimates Consistency across Sources
Three censuses, Kenya

29. Graph the Single-year ASFRs to Check for Consistency across Methods
Own-children and birth history-based estimates, Philippines

30. For More Detail
Michael Levin, “Own Children Fertility Estimates
Using Demographic Health Survey Data: Methodology and Comparisons.” Combined with the East-West Center’s manual EASWESPOP: Fertility Estimate Programs in your workshop handout. Or, see Levin-OwnChildrenExtract.pdf on your workshop CD.

31. References
Cho, Lee-Jay, "The own-children approach to fertility estimation: an elaboration," in Proceedings of the International Population Conference, Liège 1973, International Union for the Scientific Study of Population. Liège.
Grabill, Wilson, 1942a. "A method for calculating growth and net reproduction rates from census data," Master's dissertation submitted to the American University. Washington D.C.

32. References
Grabill, Wilson and Lee-Jay Cho, "Methodology for the measurement of current fertility from population data on young children," in Demography, vol. 2, pp
Retherford, R. and L. J. Cho, "Age-parity-specific birth rates and birth probabilities from census or surveys data on own children," in Population Studies, vol. 32, pp