Griffith Feeney and John Bongaarts
1999-05-24
Our proposal for adjusting the total fertility rate for distortions due to changes in timing of childbearing (Bongaarts and Feeney 1998) has been criticized by Kim and Schoen (no date). Their conclusions are based on two misunderstandings: (i) that our adjustment attempts to estimate completed cohort fertility and (ii) that we assume linear change in fertility over an extended period. Both statements are wrong and render their criticisms irrelevant. We welcome critical scrutiny of our work and have no desire to defend it against valid objections. This note attempts to clarify the points at issue in the hope that future criticism may be more productive.
Suppose that circumstances in some year cause women to postpone births, pushing some births that would have occurred in the given year into the following year. Since there are fewer births in the given year, but no change in numbers of women, age-specific birth rates and the total fertility rate (TFR) will be lower than they would have been if the postponement had not occurred.
By assumption, however, nothing has happened to the “level of fertility,” if by this we understand the behavior of women as regards the number of children they have, as distinct from when they have these children. The total fertility rate therefore fails in its appointed task: to say what level of fertility would be observed in the population in future years if womens' propensity for having various numbers of children were to remain unchanged.
Similar observations apply in the case of circumstances that cause women to advance births during a given year. Some births that would have occurred during the following year are pulled into the given year, whence numbers of births, age-specific birth rates and the TFR are higher during the given year than they would otherwise have been.
The adjustment procedure described in our paper aims to answer the counterfactual question of what TFR would have been observed if births had not been postponed or advanced. We do not attempt to estimate the completed fertility of any actual birth cohort, nor do we attempt any prediction of future fertility. Both the data used and the question posed refer strictly to the time period during which the change in timing of births occurs.
Obviously it is impossible to answer the question without making some assumptions about possible patterns of change in childbearing. Our main assumption is that the shape of the age-schedule of fertility at each birth order does not change over time. That is, changes in these schedules are limited to multiplication by a constant factor to change the level of age-specific birth rates and translation to lower or higher ages to change the timing of childbearing. This implies that postponement or advancing of births occur uniformly over all ages. Kim and Schoen consider this assumption to be “not unreasonable” and we agree.
As is customary in analyses of this kind, we do not imagine these assumptions to hold absolutely, only that they are sufficiently reasonable approximations that the analysis advances our understanding.
Demography owes an enormous debt to the work of Norman Ryder in this area. We gratefully acknowledge this debt and influence, but our formulation of quantum and tempo departs radically from Ryder’s. In Ryder's work quantum refers to the completed fertility of cohorts, tempo to the age distribution of births within these cohorts. In our paper quantum and tempo are components of the TFR observed during any given year. The quantum component is what the TFR would have been if there were no tempo effects. The tempo component is the difference between the quantum component and the observed TFR.
In Ryder's formulation, quantum and tempo are observable quantities, if only after the cohorts in question have completed their childbearing years. In our formulation quantum and tempo are quantities that have meaning and can be calculated only on the basis of a conceptualization that allows us to answer the counterfactual question of what the TFR would have been in a given year if there had been no changes in the timing of childbearing.
Kim and Schoen have misread our paper on several key points. The root of the misunderstanding appears to be that they have incorrectly imputed Ryder's concepts of quantum and tempo to our work. The first paragraph of their paper notes, for example, that “When cohorts of women delay childbearing, the TFR is depressed; when cohort childbearing is accelerated, it is elevated.” This is true but irrelevant to our formulation of the problem, which focuses solely on what happens during a specific time period, not on what happens within birth cohorts. Our paper states explicitly that “our formulation of quantum and tempo effects is a period formulation” and that “No reference is needed to anything that happens before or after the period with which we are concerned” (p. 278).
In discussing our adjustment Kim and Schoen state (p. 7): “The initial question that must be asked is how the Bongaarts-Feeney measure can capture aspects of completed cohort fertility behavior from the experience of a single period. After all, mathematical demography does not enable analysts to predict the future.”
Our adjustment procedure does not attempt to estimate completed cohort fertility behavior for actual cohorts. The question is mis-put.
Further in the same discussion Kim and Schoen state that we make three assumptions (pp. 7-8 of their note): “First, the shape of the age schedule of fertility is assumed to be fixed over time; however, the level may rise or fall, and the schedule itself might shift up or down the age range. This is not [an] unreasonable simplifying assumption. Second, the pattern of change is assumed to shift up (or down) by a fixed number of years. Third, this pattern is assumed to be in place for a sufficient number of years so that all of the period fertility rates in the year being examined are generated by cohorts following that pattern of linearly shifting fertility.” Our paper makes only the first assumption. Scenario 2 in the Appendix to our paper considers the case in which age age childbearing rises linearly over an extended period, but the first sentence of the following Scenario 3 states explicitly that “We do not expect ever to observe Scenario 2. It is rather a conceptual stepping stone to a more general result.” Our results, given Scenarios 3 and 4 of the Appendix, assume only piecewise linearity, i.e., that the rate of postponement or advancing of births is constant within any given year but may change from one year to the next. This is of course a far weaker assumption.
Kim and Schoen state that (p. 8) “A crucial test for the applicability of the Bongaarts-Feeney measure to actual populations is whether their measure is robust to violations of the second and third assumptions.”
As already indicated, we do not make the assumptions they claim we make, so there is, in this respect, nothing to test.
Because of these misunderstandings, Kim and Schoen's model calculations have no bearing on the validity or invalidity of our proposed adjustment procedure. What our paper shows is that, subject to certain assumptions, it is possible to infer (i) the TFR that would have been observed in a population during a given year from (ii) observed levels of the birth order components of the TFR and (iii) changes in mean age at childbearing for births of each order. This is at heart a proposition in mathematics, which we claim to have demonstrated, and which Kim and Schoen do not claim to refute. If the proposition is in fact true and our demonstration valid, as we believe, model calculations of the type they present are superfluous.
We welcome critical scrutiny of our work, for we believe it is only a beginning. Unfortunately, Kim and Schoen have misunderstood our paper and their criticism is therefore not constructive.
Bongaarts, John, and Griffith Feeney. 1998. On the quantum and tempo of fertility. Population and Development Review 24(2):271-291.
Kim, Young J., and Robert Schoen. No date. Changes in timing and the measurement of fertility. Typescript, Department of Population and Family Health Services, Johns Hopkins University, Baltimore MD 21205.