On the Quantum and Tempo of Fertility
The standard measure of the total fertility rate (TFR) used in demographic measure is a summary measure that can change for a variety of reasons. The TFR is composed of birth-order components, such as the first-order component (TFR1), which gives the average number of first births women would have by age 50 if they were to bear first births at the age-specific rates observed in a given year or period. The sum of all of the order components equals the total TFR. During the late 1940s and early 1950s the TFR1 exceeded 1, which would imply that women on average had more than one first birth, which is impossible. This above effect is caused by changes in the tempo of childbearing. During years in which women delay childbearing, fertility rates are depressed; and in years when childbearing is accelerated, fertility is raised. The TFR therefore, incorporates not only changes in the number of children that women have, but also the rate at which women have children. These changes are primarily period, rather than cohort based changes in fertility. They affect childbearing at all ages. Quantum effects often affect childbearing at the higher ages, because cohorts generally reduce their fertility by reducing childbearing at higher birth orders and therefore at higher ages. Bongaarts and Feeney assume that fertility may be influenced by period, age, parity, and duration since last birth, but not by cohort. Under this condition, the TFR that would be observed in a given year had there been no change in the timing of births during that year may be estimated by the following equation: TFR`i = TFRi /(1 ri) Where TFRi is the observed TFR in any given year, ri is the change in the mean age at childbearing at order i between the beginning and end of the year, and TFR`i is the TFR that would have been observed had there been no change in the timing of births. The adjusted TFR is given by: TFR` = Ó TFR`i Bongaarts and Feeney test their formula on data from the U.S. and Taiwan. In the U.S. between 1950 and 1962, declining age at childbearing pushed the unadjusted total fertility well above the adjusted values. From 1963 through 1987, increasing age at childbearing pushed unadjusted total fertility below the adjusted values. The age of childbearing is a weighted average of the mean age at childbearing for different parities, i. In Taiwan, from the mid-1970s to the early 1990s, the mean age at birth of all orders was rising, so that the tempo effects in the 1970s and 1990s amounted to about 0.25 births per woman, and 0.4 births in the 1980s. Absent of tempo changes, fertility would have been close to replacement level. A comparison between the cohort fertility rates and the adjusted TFR shows that they do follow each other closely, implying that the adjusted TFR is a good measure.