# Momentum of Population Growth

# MOMENTUM OF POPULATION GROWTH

Population momentum is the tendency for changes in population growth rates to lag behind changes in childbearing behavior and mortality conditions. Momentum operates through the population age distribution. A population that has been growing rapidly for a long time, for example, acquires a *young* age distribution that will result in positive population growth rates for many decades even if childbearing behavior and mortality conditions imply zero population growth in the very long run. Population momentum is important because of the magnitude and duration of its effects.

## An Example

Consider the population of Nigeria, estimated at 114 million persons at mid-year 2000. Life expectancy rose from 36 to 51 years over the preceding half century, while completed family size remained at around six children per woman. In consequence, population grew very rapidly, with an average annual growth rate of 2.7 percent. (Statistics here and below are from United Nations 2000 projection series unless otherwise indicated.)

Rapid population growth implies a young age distribution because larger numbers of persons were born in the recent past than in the more distant past. During the period 1995 to 2000, for example, 22 million children were born in Nigeria, as compared with only 8 million from 1950 to 1955. Even if everyone in the earlier cohort had survived, there would have been far fewer persons aged 45 to 49 years than persons aged 0 to 4 in the year 2000.

Because of this young age distribution, the population of Nigeria will tend to grow rapidly in the future even if fertility declines rapidly to replacement level. The relatively large numbers of women and female children in and approaching reproductive age will generate large numbers of births, while the smaller numbers of persons at older ages will generate small numbers of deaths. The resulting population growth will slow as the population ages, but this will occur only over the many decades it takes for young persons to become old.

The United Nation's "instant replacement" population projections show that even with two-child families from the year 2000 forward, the population of Nigeria would grow from 114 million in 2000 to 183 million persons in 2050, an increase of 60 percent. The same projections show that the less developed world as a whole would grow from 4.9 to7.1 billion persons, an increase of 2.2 billion persons, even with an immediate fall of fertility to replacement level in 2000.

## Momentum and World Population Growth

The importance of momentum as a cause of future world population growth has increased as fertility levels throughout the world have declined. In 1994, John Bongaarts estimated that population growth due to momentum could account for nearly half of world population increase during the twenty-first century. He pointed out that this growth could be reduced without any change in completed fertility by raising the average age of childbearing. This is a consequence of the *tempo effect* identified by Norman Ryder, whereby shifts in the timing of births result in a bunching up or thinning out of births during the years in which the shifts occur.

For populations with very young age distributions, however, reducing population growth due to momentum may lead to undesirable changes in the population age distribution. The *constant stream of births* model proposed by Li Shaomin in 1989 is useful in this connection. Fertility declines that produce a constant stream of births will result in age distributions for which numbers of persons decline slowly with increasing age through old age. More rapid fertility declines will result in age distributions in which numbers of young persons in younger age groups are lower than numbers of persons in older age groups.

Returning to the example of the population of Nigeria, suppose that fertility declines after 2005 in such a way as to maintain numbers of births constant at the level observed during the period 2000 to 2005. On this assumption, the population would grow from 114 million persons in 2000 to 250 million in 2050. The later number is not much less than the United Nations medium-variant projection of 279 million. Further reduction in population growth would require more rapid fertility decline.

To eliminate growth during the period 2005 to 2010, for example, it would be necessary to reduce the number of births from the 26 million projected in the medium variant to 8.4 million, the projected number of deaths. This precipitous decline in births would be followed by similarly precipitous falls in the numbers of persons entering primary school (after a delay of 5 or 6 years), in numbers of persons entering the labor force (after a delay of 15 or 20 years), and so on through the life cycle.

Some decline in numbers in these age groups might be advantageous, but such extreme declines would be problematic. Any sustained fertility decline will yield an age distribution with a larger proportion of old persons relative to those at working ages, but the momentum effect–although ultimately transient–will greatly accentuate this dependency burden for a period of many decades.

## Generality of the Momentum Concept

Population momentum is most often thought of in the context of fertility declining to replacement level, but the concept applies to all changes in childbearing behavior and mortality conditions. Consider for example a population that has a very old age distribution as a result of an extended period of population decline resulting from below replacement fertility. Should fertility rise to and remain at replacement level, population decline would nevertheless continue for many decades. Large numbers of persons in post-reproductive ages would generate relatively large numbers of deaths, because death rates in old age are high, but no births. Population decline would slow only as the large cohorts of older persons die out, so that the population age distribution ceases to be old.

To illustrate momentum resulting from changes in mortality conditions, imagine a hypothetical population in which 1,000 children are born every year and in which everyone dies on reaching their 60th birthday. Total population is the product of the annual number of births and life expectancy at birth, 60,000 persons. Suppose that at some time *t* mortality conditions change in such a way that persons alive at time *t* die only when they reach their 70th birthday. Then no deaths will occur for 10 years, during which period the population will grow from 60,000 to 70,000 persons. This growth is due to population momentum.

The constant-stream-of-births model may be used to generalize the concept of momentum to populations that do not reproduce biologically. Consider for example the population of PhD degree holders in the United States, for which new PhDs constitute "births" and "age" may be understood as time since PhD. According to the U.S. Bureau of the Census, the number of degrees granted annually grew from 1 in 1870 to just under 30,000 in 1970, with an average annual growth rate of 7 percent. Because of this very rapid growth, the population of PhD holders in 1970 had a very young age distribution, and therefore a strong tendency to future growth. On the assumption that there were 330,000 PhD holders in 1970 (the precise number is not pertinent for this example), holding the annual number of degrees constant at 30,000 after 1970 would result in a population of about 1.2 million PhD holders in 2010, an increase of over 360 percent.

## Definition of Population Momentum

The definition of population momentum requires three concepts from stable population theory. First, a population that experiences fixed age schedules of fertility and mortality will over time approach a stable state in which the age composition (the proportions of persons in each age group) and the population growth rate (which may be positive, zero, or negative) are constant. Second, this age composition and growth rate are determined by the age schedules of fertility and mortality. They do not depend on the initial population age distribution. Third, two age distributions (giving numbers of persons in each age group) are *asymptotically equivalent* with respect to given age schedules of fertility and mortality if the ratio *P*_{1}*(t)/P*_{2}*(t)* approaches 1 as *t* gets large, where *P*_{1}*(t)* and _{2} are the total populations projected from the two age distributions.

Given any age distribution and any age schedules of fertility and mortality, two stable age distributions may be calculated, both with the age composition implied by the age schedules of fertility and mortality, but with different total populations. Let the total population for the first stable distribution equal the total population for the given age distribution, and denote this number by *P*_{1}. Let the total population for the second stable distribution be chosen so that the second stable distribution is asymptotically equivalent to the given age distribution. Let this population be denoted *P*_{2}. The *momentum* of the given age distribution with respect to the given age schedules of fertility and mortality is the ratio *P*_{2}*/P*_{1}. This formulation was first stated by Paul Vincent in 1945, following Alfred Lotka's seminal 1939 monograph on stable population theory.

A necessary condition for momentum effects to exist is that risks of birth or death vary with age. If age schedules of birth and death are constant over age, the age distribution does not influence numbers of births and deaths and population dynamics are fully described by crude birth and death rates. The population growth rate will equal zero (assuming no migration) for any period in which birth and deaths rates are equal.

**See also:** *Keyfitz, Nathan*; *Population Dynamics*; *Projections and Forecasts, Population*; *Renewal Theory and Stable Population Model*.

## bibliography

Bongaarts, John. 1994. "Population Policy Options in the Developing World." *Science* 263: 771–776.

Keyfitz, Nathan. 1971. "On the Momentum of Population Growth." *Demography* 8(1): 71–80.

Li, Shaomin. 1989. "China's Population Policy: A Model of a Constant Stream of Births." *Population Research and Policy Review* 8: 279–300.

Lotka, Alfred J. 1939. *Théorie Analytique des Associations Biologiques.* Paris: Hermann et Cie.

Preston, Samuel H., Patrick Heuveline, and Michel Guillot. 2001. *Demography: Measuring and Modeling Population Processes.* Oxford: Blackwell.

Ryder, Norman B. 1983. "Cohort and Period Measures of Changing Fertility." In *Determinants of Fertility in Developing Countries,* Vol. 2, ed. Rudolfo Bulatao and Ronald D. Lee. New York: Academic Press.

United Nations. 2001. *World Population Prospects: The 2000 Revision.* CDROM. New York: United Nations. Sales No. E.01.XIII.13

United States Department of Commerce. 1975. *Historical Statistics of the United States, Colonial Times to 1970.* Part I. Washington, D.C.: U.S. Government Printing Office.

Vincent, Paul. 1945. "Potentiel d'accroissement d'une population." *Journal de la Société de Statistique de Paris* 86(1–2): 16–39.

Griffith Feeney

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