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Introduction to fertility analysis


In most settings and in the long term, fertility is the single most important determinant of population dynamics and growth. This section gives an overview of the classes of methods available for the measurement of fertility. The methods themselves are described in other sections.

Sources of data

Broadly speaking, data for the measurement of fertility come from three sources.

The first of these is information collected as part of an ongoing vital registration system. For the most part, the registration of births in developing countries is incomplete: parents often lack incentives to register births; babies who die shortly after birth may not be registered either as a birth or as a death; and late registration of births (for example, when the child attains school-going age) may mean that there is a delay of several years before all the survivors of the cohort born in a given year have their births registered.

The second source of data is the answers to questions on fertility collected in a census. These questions are typically asked of all women of childbearing age (12, or 15 and older, often with an upper age limit of 49). Due to the complexity of the census exercise, and the need to attempt to enumerate every individual, it is not feasible to ask detailed questions on fertility. In practice, the census questions seek summary information about lifetime fertility (the number of children ever born, and still alive) and fertility in a narrowly defined period of time before the census. From the latter, demographers seek to estimate current fertility rates. Due to the abridged nature of the questions asked, the scope for internal validation and cross-checking of the answers given is limited.

Furthermore, as described in greater detail in the section on the evaluation of fertility data, data on fertility collected in censuses commonly suffer from two errors. First, data on lifetime fertility tend to be increasingly poorly reported with increasing age of the mother. Often the omissions are of children who have died or who are no longer living with the mother. Second, data on recent fertility tend to be systematically underreported by all women (similar to the widespread under-enumeration of the youngest children in the household head-count). Over-enumeration of recent births is also a possibility, occasioned by misunderstandings related to the reference period used, or shifting of the most recent births into the reference period. The methods used to estimate fertility from census data explicitly seek to take these errors into account.

Third, as well as asking these summary questions on fertility, surveys often collect a detailed birth history from mothers. Such histories ask about each child’s date of birth, vital status (whether the child is still living) and – if the child is dead – date of death. The data obtained can be used to make detailed estimates of fertility. On the downside, however, the effort expended on such detailed data collection frequently limits the sample sizes of the investigations. In such cases, variability in the estimated rates, and the inability to investigate finely-grained spatial or other differentials in fertility are an inherent weakness of this approach.

Classes of methods to estimate fertility

The methods available to estimate fertility are closely aligned with the type of data available.

Direct estimation

Three possible approaches to measuring fertility directly exist, depending on the data available.

The first approach uses data from a vital registration system in conjunction with estimates of the population by age and sex (from a population register, for example, or from mid-year population estimates). If data for the numerator and denominator are both complete and unbiased, and the denominator appropriately reflects the population exposed to risk of giving birth by age, the calculation of fertility rates is straightforward.

The second approach makes use of the full birth history data collected in a survey and the various validation checks that can be built into the survey instrument. Detailed information on the birth of each child, as well as the mother’s age, is obtained. Accordingly, the age of the mother at the birth of each child can be determined exactly, and births and exposure-to-risk can be allocated to particular calendar years or other time periods. This approach is described in greater detail in the section on direct estimation of fertility from survey data.

The third approach uses the summary fertility measures routinely collected in censuses to estimate recent fertility. Methods for doing so are described in the section on evaluation of fertility data from censuses. Of course, if the data suffer from the common problem of under-reporting of recent births in censuses, the resulting estimates of fertility will be too low.

Indirect estimation

Indirect estimation of fertility makes use of the direct estimates of fertility derived from the summary information on recent births, but – recognizing that recent births tend to be misreported in censuses – uses information on the lifetime fertility of younger women reported in the same census to adjust the direct estimates. The earliest such method is the Brass P/F method, first set out by Brass (1964). The method was written up in Manual X (UN Population Division 1983), along with a number of variants for extending the method depending on exactly what data are available. A brief description of the P/F method is given in the section on fertility estimation methods based on the P/F ratio. A refinement to the P/F method – the relational Gompertz model – was mentioned in passing in Manual X but much of the development of the relational Gompertz model occurred after Manual X was published. This manual presents several extensions to the relational Gompertz model (the basic version of which is presented in section on the relational Gompertz model) that emulate the extensions to the P/F method presented in Manual X. These include extensions to situations where:

In this manual all methods of fertility estimation that make use of the P/F ratio method are recast here to use the relational Gompertz model.

Further analysis of fertility

Finally, there are several other methods that may shed light on fertility trends and dynamics.

Using census data, one can calculate both conventional and projected parity progression ratios. These measures indicate the propensity of women in a population to bear further children contingent on the number of children that they have already borne. Projected parity progression ratios indicate the possible future evolution of parity progression for younger women, taking into account current fertility and the women’s childbearing history to date.

Second, methods exist  (P/F ratio methods with survey data) for the calculation of cohort-period fertility rates from detailed birth history data. These rates not only provide information on trends in fertility, but can also be used to assess the quality of the birth history data.

Third, a method exists for estimating fertility measures based on reverse survival of the enumerated population of children and adults.

All the above-mentioned methods are described and discussed in this manual.

References and further reading

The best earlier description of approaches to estimating fertility indirectly is contained in Chapter 2 of Manual X (UN Population Divison 1983). The manual written by the Centre for Population Studies for the UN Statistical Institute for Asia and the Pacific (Sloggett, Brass, Eldridge et al. 1994) offers a simple exposition of evaluation of fertility data, the use of the relational Gompertz model in fertility estimation, and the calculation of projected parity progression ratios. The paper by Brass (1964) has been superseded by more recent developments, but is still instructive in its exposition of the approach which has shaped almost all subsequent methods for measuring fertility from limited and defective data.


Brass W. 1964. Uses of census or survey data for the estimation of vital rates. Paper prepared for the African Seminar on Vital Statistics, Addis Ababa 14-19 December 1964. Document No. E/CN.14/CAS.4/V57. New York: United Nations.

Sloggett A, W Brass, SM Eldridge, IM Timæus, P Ward and B Zaba (eds). 1994. Estimation of Demographic Parameters from Census Data. Tokyo: Statistical Institute for Asia and the Pacific.

UN Population Division. 1983. Manual X: Indirect Techniques for Demographic Estimation. New York: United Nations, Department of Economic and Social Affairs, ST/ESA/SER.A/81.