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Abstract
In their attempts to distinguish empirically between the innovation/diffusion and adaptation theories of fertility decline, researchers have pointed out that if indirect methods were able to detect fertility control practiced by a significant proportion of women in pretransition populations, it would be difficult to argue that fertility fell as a result of innovative behavior. Knodel and van de Walle have also argued that an absence of fertility control in pretransition populations would indicate that couples did not know how, or were unwilling because of cultural norms, to control fertility. That the Coale-Trussell index of fertility control, m, takes on small values in pretransition populations has therefore been taken as evidence in favor of the innovation/diffusion view; that Cohort Parity Analysis (CPA) has pointed to the existence of a significant minority of controllers in pretransition populations is evidence against that view.
This thesis suggests that neither the Coale-Trussell (M&m) method nor CPA can be relied on to identify accurately a minority of controllers. m takes on values very close to zero (e.g. less than 0.20) in simulated populations where as many as 40% of the population practice effective, parity-dependent control. Moreover, time series of m values estimated from historically realistic samples do a poor job of identifying the initial stages of fertility transitions characterized by increases in the proportion controlling.
Potentially more powerful than M&m in that it can detect minorities of controllers when its assumptions are not violated, CPA is extremely sensitive to misspecification of the standard population. For example, a difference in the median nonsusceptible period of just over one-half month causes significant bias in CPA measures--upward bias if breastfeeding is slightly more extensive in the target population than in the standard, and downward bias if breastfeeding is more extensive in the standard. Moreover, the bias is greater when a smaller proportion of the population are controllers. Thus, neither M&m nor CPA can be used reliably to test alternative theories of the fertility decline when, as is often the case, the tests revolve around identification of a minority of controllers.
