# Tempo effect

## Definition

The term tempo effect is a loose term encompassing many phenomena that relate to how differences over time or between demographic groups in the age at which women have children (at various birth orders) affect demographic variables.

## Particular aspects

### Secular changes in childbearing age leading to a disparity between TFR and CFR

The total fertility rate of a population in a given year is the sum of the age-specific fertility rates for females at all age levels within that population. The TFR is an attempt to extrapolate from current data to paint a picture of how many children a hypothetical female would have if she conformed to the age-specific fertility patterns of the current year when she is of the relevant age.

The completed fertility rate, measured for females who are in a birth cohort that has completed its childbearing years, is the average of the values of completed fertility (total number of live births in the childbearing years) of the females.

If the age-specific fertility rates of the population were to remain constant with time, then TFR would equal CFR (this is the type of behavior that we expect to see in a stable population). In particular, TFR can be used to predict later CFR values.

If, however, the age-specific fertility rates of the population are changing with time, then TFR does not accurately measure CFR. In the case that there is a steady directional effect on age-specific fertility rates, we call it a tempo effect. Explicitly:

• In the case that women's age of having children at each birth order is increasing with time, TFR would underestimate CFR.
• In the case that women's age of having children at each birth order is decreasing with time, TFR would overestimate CFR.

### Relation between fertility and population growth

For societies with above-replacement fertility, the same value of completed fertility rate (and even the same value of total fertility rate) could mean a higher population growth rate if the average age of having children is lower. For instance, a society where all women have five children between the ages of 15-25 (a completed fertility rate of 5) would multiply in size by 2.5 roughly ever 20 years (even ignoring issues of changes to life expectancy). A society where all women have five cildren between the ages of 25-35 (a completed fertility rate of 5) would multiply in size by 2.5 every 30 years.

Note that for societies that have fertility at replacement, tempo effects do not matter (this is more or less by definition, but more concretely, if all parents have 2 children who survive to adulthood and have their own children, then it does not matter when they have these children, assuming that life expectancy is constant). In particular, we can imagine stable populations with many different possibilities for the age of childbearing.

For societies that have fertility below replacement, tempo effects can still matter, but not in the usual way. The mathematics is somewhat complicated, but the upshot is that tempo effects, either in isolation or combined with life expectancy changes, can forestall population decline and cause population growth, but there is a hard upper bound on what population can become.