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# FERTILITY MEASUREMENT

This article provides a nontechnical account of the principal indexes used by demographers to gauge the level of fertility of a population. For each measure the main advantages and disadvantages are also noted.

## Crude Birth Rate

The simplest indicator of the fertility of a population in a given year is the number of births that year divided by the average size of the population during the year. There is nothing special about the one-year period, but if births are measured over a different period (still in units of years), consistency in comparisons requires that the denominator be the average population over the period times the length of the period–more strictly, the number of "personyears" lived by the population during the period. By convention, the resulting fraction is applied to a standard-sized population of 1,000. The result is the crude birth rate: the number of births per 1,000 population per year. The adjective crude is used because none of the structural characteristics of the population that might affect the number of births that occur in the time period, such as the age distribution or the composition by sex, is taken into account, only the total population size. The rate can be simply calculated as a fraction in which the numerator is the number of live births in the population in a year–say, beginning January 1–and the denominator is the midyear (July 1) population, approximating the "average" size of the population over the year.

Thus, from the Institut de la Statistique et des Études Économiques, for France in 2000, see Item 1 from the Formula Table.

The crude birth rate is most often calculated for a single year, although in order to smooth out year-to-year fluctuations published estimates often give an average rate over several years–typically a five-year period. Crude birth rates below about 15 per 1,000 are usually regarded as low; those above about 35 are high. Examples of extreme values are 9 for Spain in 2000 and 52 for Kenya in the 1970s.

Pros. The crude birth rate requires less detailed data than other fertility measures and data that are more likely to be available for a very recent period. It is needed for the calculation of the rate of natural increase (the crude birth rate minus the crude death rate) and the population growth rate (the rate of natural increase plus the net migration rate).

FORMULA TABLE

Cons. The crude birth rate is affected by vagaries in the age and sex distribution and by other structural characteristics of the population, such as those resulting from a past baby boom or particularly heavy immigration. An example of such a country would be a Gulf state of the Middle East that has experienced significant immigration of males of working age. In such a case the crude birth rate may be artificially low because the total population contains an unusually high number of males. In addition, the crude birth rate does not provide any insight into individual-level childbearing behavior.

## General Fertility Rate

The general fertility rate is similar to the crude birth rate except that it uses a more restricted denominator, the female population of childbearing age, ages 15 to 49. For Turkey in 1998, see Item 2 in the Formula Table.

Pros. The general fertility rate provides a somewhat more refined measure of fertility than the crude birth rate and requires knowledge of only the total number of births and the total female population, ages 15 to 49. In most countries, the female population of childbearing age is about one-fourth of the country's total population, so that the advantage over the crude birth rate is not a great one. When the age-sex structure of the population has been skewed in some way, such as by migration, however, the general fertility rate is often preferable.

Cons. This rate will be skewed somewhat by the distribution of women within the childbearing ages, affecting country-to-country comparisons slightly. As with the crude birth rate, it provides no insight into childbearing behavior. The general fertility rate is not as widely used as other measures.

## Age-Specific Fertility Rates

Age-specific fertility rates (also called age-specific birth rates) are similar to the crude birth rate but are calculated for specific age groups of women of childbearing age. The range of childbearing ages is conventionally considered to be ages 15 to 49 (sometimes 15 to 44 is used), and a full set of age-specific fertility rates would span this interval–usually either in single-year age groups or, more commonly, in five-year groups: 15 to 19, 20 to 24, …, 45 to 49. (Rarely, age-specific fertility rates are also calculated for men.) The numerator of the rate is the number of live births to women in the specific age or age group during a given period and the denominator is the average population of women in that age or age group during the same period. For convenience, age-specific fertility rates are usually presented as rates per 1,000. See Item 3 in the Formula Table for an explanation of the calculations.

Pros. Age-specific fertility rates enable analysis of the pattern of fertility by age of women and analysis of changes in the timing of childbearing. Comparisons between consecutive years may, for example, indicate that women are delaying childbearing and the onset of family formation. Age-specific fertility rates are required for calculation of fertility measures such as the total, gross, and net reproduction rates. They are also required as an input in cohort-component population projections.

Cons. Age-specific fertility rates require detailed data on the number of births by age or age group of mother and data on the number of women of childbearing age by age or age group, data that are seldom available in developing countries. Age-specific fertility rates cannot be directly used to calculate population growth rates or natural increase rates.

## Marital Fertility Rates

Marital fertility rates can be calculated either for the full range of reproductive ages (15 to 49 or 15 to 44) or as age-specific rates. The numerator is usually taken as the total number of births to women in the specified age range, regardless of the marital status of the mother; the denominator is the number of currently married women in the specified age range. With the large increase in fertility outside of legal marriage that has occurred in many industrialized countries (with many births occurring in consensual unions or to cohabiting couples), the usefulness of marital fertility rates may be seriously compromised. For that reason, it may be desirable to restrict the numerator to births that occur within legal marriage and to also calculate complementary nonmarital fertility rates. The calculated example is, in fact, based on marital births only. See Item 4 in the Formula Table, using data for the United States in 2000.

Pros. Marital fertility rates enable analysis of marital fertility and the pace and timing of childbearing that occurs within formal marriage, analysis that cannot be performed with other fertility measures.

TABLE 1

Cons. Marital fertility rates require detailed data on births by age group of mother and possibly by marital status of mother, and on women by age and marital status, data that are seldom available in developing countries. While this rate provides the ability to analyze marital fertility, increases in nonmarital fertility result in only a partial picture of childbearing trends.

## Total Fertility Rate

The total fertility rate (TFR) at a given time (technically referred to as the period total fertility rate) is the average number of children a woman would bear in her life if she experienced the age-specific fertility rates prevailing at that time. A closely related measure is the cohort total fertility rate–the average number of children borne by women in an actual birth cohort over their reproductive lives. The period total fertility rate is used much more frequently than the cohort total fertility rate and is always meant when the abbreviation TFR is used without further specification.

Period total fertility rate. The TFR for a given year is calculated by summing the age-specific fertility rates for that year over the range of reproductive ages. Each single-year age-specific fertility rate measures the "risk" that a woman of that age would have a child during the year in question; the sum of those risks equals the number of children a hypothetical woman experiencing those risks would have at the end of her reproductive life. If the age-specific rates are averages for five-year age groups of women, the sum of the age-specific rates must be multiplied by five, as in the example, for Ethiopia in 2000, in Table 1.

The TFR is often discussed in terms of "replacement-level" fertility, or the number of children that women, on average, must produce in order for a population to ultimately reach a stationary state ("zero population growth" position)–neither growing nor declining in size. A value of 2.1 is often cited as replacement-level fertility. The ".1" is required because there are approximately 5 percent more boys born than girls and because not all women survive throughout their childbearing years. The value of 2.1, however, is valid only for countries with low mortality (high life expectancy). In countries with high mortality, that is, when survival rates from birth to maturity are low, a replacement-level TFR is much higher; it can be as high as 3.0.

Pros. The TFR has the immediate intuitive interpretation as the number of children that the average woman will bear in her lifetime. That number can be gleaned only very roughly from other measures. (For example, a crude birthrate of 50 per 1,000 in a country with a normal age-sex distribution means that women on average bear about seven children each; a crude birthrate of 15 would mean about two children.)

Cons. The TFR for a given year does not indicate how many additional children an average woman of any selected age will actually have over her remaining reproductive lifetime. It would do so only if the age-specific fertility rates of that year remained constant over the woman's lifetime. When age-specific fertility rates are changing, such as when women are delaying births from their 20s to their 30s, age-specific fertility rates–and thus the TFR–would be depressed for a time and then rise again when women begin to have children at the older age. Hence the TFR may be a poor measure of the completed fertility of women at or near the end of their

TABLE 2

childbearing years and also a poor predictor of the completed fertility of women at early phases of their reproductive career.

Cohort total fertility rate. The cohort total fertility rate can be calculated in a manner similar to the period total fertility rate, but the calculation can be completed only for women who have already passed through their childbearing years. This rate is based on the actual fertility of an age cohort of women–that is, a group of woman born in the same period, usually a five-year period. (For example, women who were born from 1975 to 1980 are the 1975–1980 cohort.) Cohort fertility rates can be calculated for each five-year period as women pass through their childbearing years and summed to give their completed cohort fertility up to particular ages, such as 20, 25, 30, and so on. For the 1975–1980 birth cohort, the cohort total fertility rate could be calculated only when the youngest of the group pass 50, in the year 2030.

Pros. The cohort total fertility rate allows a precise description of the actual childbearing experience of specific birth cohorts of women. As a measure of reproduction it is superior to estimates made from questions on "children ever born" in censuses and

TABLE 3

surveys because it does not omit the childbearing experience of women who died before the time of the census or survey.

Cons. This measure requires detailed data on births by age of mother and data on women by birth cohort over a long period, data not often readily available for developing countries. Total cohort fertility can be calculated, by definition, only at the conclusion of a cohort's childbearing years.

## Gross Reproduction Rate

The gross reproduction rate (GRR) for a particular year is the average number of daughters that a woman would have if she experienced over her lifetime the age-specific fertility rates of that year. In that it refers only to the number of daughters born to women, not the total number of children, it is a special case of the (period) total fertility rate; in most circumstances (unless the sex ratio at birth is highly unequal) the GRR equals roughly half the TFR.

An example–for Ethiopia in 2000–is given in Table 2.

Pros. The gross reproduction rate, like the total fertility rate, translates other measures of fertility into a clear result: in this case, the number of daughters that a cohort of women is likely to produce in their lifetimes.

Cons. This rate adds little information to the TFR, which is a more widely used measure. The GRR, like the TFR, may be affected by changes in the timing of births even when the total number of lifetime births per woman is not changing.

## Net Reproduction Rate

The net reproduction rate (NRR) measures the effective fertility in a population, taking account not only of births but also of the fact that not all women born will survive to their own reproductive years. The NRR is the average number of daughters of reproductive age that a woman would have if she experienced over her lifetime the prevailing age-specific rates of fertility and if her daughters experienced the prevailing rates of mortality. If the age schedules of both fertility and mortality for a population remained constant, the net reproduction rate would be a measure of generational replacement. For example, if NRR = 1.5, the next generation would be 50 percent larger than the present generation; if NRR = 0.8, it would be 20 percent smaller. For any population, therefore, the NRR can be taken to indicate the underlying tendency of the population to increase or decrease based on its current fertility and mortality patterns, abstracting from the effects of its current age structure.

An NRR = 1.0 means that each woman in a population will, on average, replace herself exactly in the next generation. For the existing level of mortality, fertility would be precisely at replacement level.

Calculation of the net reproduction rate requires estimates of the female survival rate from birth to each reproductive age or age group, values that would be given in the appropriate female life table. In life-table notation, the average survival rate from birth to age x is Lx / l0 or, for survival to a five-year age group, 5Lx/ 5 l0. An example for Ethiopiais given in Table 3.

Pros. The NRR precisely measures the reproductivity of a population by taking into account the level of fertility and the likelihood that women will survive from birth to each childbearing age.

Cons. The NRR requires detailed data on fertility and female life-table values up to age 50.

## Parity Progression Ratios

A parity progression ratio is the proportion of women of a given "parity" (i.e., who have had that

TABLE 4

particular number of live births) who go on to have at least one additional child during the course of their remaining childbearing years. This measure is often calculated for married women only.

In the example shown in Table 4, the first parity progression ratio, P1 (indicating the probability of progressing from parity 0 to parity 1) is calculated by dividing the total number of married women who had at least one child (901,785) by the total number of married women (1,094,294).

Pros. The parity progression ratio allows detailed analysis of family formation and childbearing patterns for a given cohort of women. It is useful for comparisons with other birth cohorts or between the same birth cohorts in different countries.

Cons. The parity progression ratio can be used only to study childbearing patterns among women who have completed their childbearing years and requires detailed data on children ever born from a census or survey.

## bibliography

Bogue, Donald J., Eduardo E. Arriaga, and Douglas L. Anderton, eds. 1993. Readings in Population Research Methodology, Volume 3. Fertility Research. Chicago: United Nations Population Fund and Social Development Center.

Coale, Ansley J., and Paul Demeny. 1983. Regional Model Life Tables and Stable Populations, 2nd edition. New York: Academic Press.

Council of Europe. 2000. Recent Demographic Developments in Europe 2000. Strasbourg: Council of Europe.

National Center for Health Statistics and U.S. Census Bureau. 2002. Births: Final Data for 2000. Hyattsville, MD: National Center for Health Statistics and U.S. Census Bureau.

Pressat, Roland. 1972. Demographic Analysis: Methods, Results, Applications. Chicago: Aldine Atherton, Inc.

Shryock, Henry S., Jacob S. Siegel, et al.. 1976. The Methods and Materials of Demography, Condensed Edition. New York: Academic Press.

Weeks, John R. 2002. Population, an Introduction to Concepts and Issues. Belmont, CA: Wadsworth Publishing Company.

Carl Haub