Lee, R.D. "Target Fertility, Contraception, and Aggregate Rates: Toward a Formal Synthesis." Demography, 14, no. 4 (November 1977): 455-79.
This paper develops a stock adjustment model relating total expected births to conventional aggregate fertility rates for married women over 25. Each year, cohorts bear about 20 percent of their additional expected births. Aggregate U.S. rates have been consistent with expectations as expressed in surveys between 1955 and 1975; indeed, total expected births may be inferred from aggregate fertility behavior. A peculiar empirical finding is that the additional expected fertility of nonterminators has not changed since 1955, despite the dramatic decline in total expected and actual fertility. The model leads to a dynamic expression for the duration pattern of current and cumulative fertility and for the proportion of couples who have terminated childbearing. The model is also used to analyze the effects of changing contraceptive failure rates on fertility patterns. For example, a decline in "timing" failure rates increases duration-specific fertility five years later.