Effect of adjustment for sex composition in the measurement of fertility on intrinsic rates

The inconsistencies inherent in the one-sex models created a need for the construction of what are known as marriage functions, especially for the measurement of fertility. But attempts to develop marriage functions have been frustrated by the inability of the proposed functions to meet certain consistency conditions and also by difficulties in empirically determining function parameters. Among several functions proposed so far, Das Gupta’s (1972) “effective population” deserves special mention. He uses both sexes in its formulation, and has shown that the constancy of fertility rates based on such a function together with the constancy of survivorship probabilities of both sexes would result in a stable population. It is suggested in this article that the major source of the problem in a two-sex model seems to be the requirement that the model has to be specific both for sex and age. The idea of incorporating the relative composition of one sex in the age-specific rates of the other, thereby creating a function dependent on both sexes, is advanced in this article. Such functions, defined explicitly for births, can be easily translated into age-specific birth rates. In addition to simplicity in the definition and form, the conditions leading toward stability can also be established. Interestingly enough, the intrinsic rate for this two-sex model lies in the interval determined by the rates obtained from the two one-sex models.