Whelpton’s age-order specific fertility rates

A first indication of tempo distortions in the period TFR comes from computing the period TFR by birth order or parity (i) (Whelpton 1945):

 

$$TFR={\displaystyle \sum _{i}TF{R}^i}$$ $$TF{R}^i=n*{\displaystyle \sum _{x-\alpha }^{\beta -n}{}_{n}ASF{R}_x^i}$$

In these calculations, we compute age-parity specific fertility rates. Summed over the reproductive age range spanning from menarche (α) to menopause (β), gives the total number of i^th births a woman would have in her lifetime provided that she survives to age 50 (TFRⁱ). An intuitively more appealing interpretation of TFRi is the fraction or proportion of women who achieve parity i in their lifetime provided that they were subject to the current age and parity-specific fertility rates.

The example of Tanzania (1996) below demonstrates, however, that there may be problems with that interpretation. The last row in the table with rates (Table 1b) are the age-specific fertility rates (summed over parity) that we recognize as the building blocks for the conventional period TFR; the last column in the table are the parity specific fertility rates (summed over age). Summation of row totals or the column totals produces the period TFR (here 7.30).

Roll your mouse over the table below to reveal the table with rates (Table 1b).

 The parity-specific fertility rates sometimes exceed 1 (at parity 1, 2, and 10+), and that violates the interpretation of TFRⁱ as the proportion women who would have a first, second, …n^th  birth at current rates. This should not be a surprise for parity 10+ because the category collapses several higher order parities.

For parities 1 and 2, however, this is clearly not plausible and indicative of a conceptual flaw in the definition of period fertility rates. Critical observers might contend that these aberrations could be due to age-misreporting or other problems in the Tanzanian data, but there are other examples where these inconsistencies arise and where data problems are not likely.

Shortly after WWII, for example, the TFR¹ in the U.S. exceeded 1 and that resulted from the postponement of childbearing during the war years and the recuperation of births foregone immediately after the war. The recovery of births by older women in combination with younger cohorts of women reverting to a ‘normal’ age schedule of fertility produced an artificial peak in first births and thus TFR¹. In other words, conventional period fertility measures are affected by the parity distribution of women due to past changes in the tempo of childbearing.