The Use of Flexible Parametric Duration Functions in Modelling the Tempo of Fertility: Applications to the Analysis of Birth Intervals in Rural China

The birth-interval approach to the study of fertility reflects two aspects of the process of reproduction: (1) the quantum of fertility as indicated by the proportion of women who move to the next higher parity; and (2) the tempo of fertility, as measured by the time it takes to make the transition for those women who continue reproduction. In most previous empirical analyses, the focus has been on the quantum of fertility using proportional hazard models for the intensity of birth. That is, the rates at which children are born to a defined set of women within a specified unit of time is modelled as a function of covariates such that the effect of covariates is to increase or decrease such intensity relative to that of a reference category. This paper focuses on the tempo of fertility where covariates act multiplicatively on the duration itself so that their effect is to accelerate or decelerate the transition time between successive births relative to that of a reference category. We utilize the flexibility of a family of parametric duration models to select a statistically appropriate model for a given birth interval using data from rural China. The results show that the distributional shape of birth intervals depends on the birth order of the index child and that inferences concerning covariate effects on birth intervals are sensitive to model choice. The flexible parametric approach suggested in this paper provides a statistically well grounded, theoretically appropriate, and empirically evident alternative to the usually untenable quantum-based proportional hazards modelling of birth interval data.