A Family of Flexible Parametric Duration Functions & their Applications to Modelling Child-Spacing in Sub-Saharan Africa

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. This paper focuses on the latter where covariates act, multiplicatively, on the duration itself to accelerate or decelerate the transition time between successive births. We demonstrate how a number of common parametric duration models may be embedded in a single parametric framework, and how each competing model may be assessed relative to a more comprehensive one. These models are applied to data from Eritrea, Ghana, & Kenya. The results show that the flexible parametric approach provides an alternative to the usually untenable quantum-based proportional hazards modelling of birth interval data. Further, it is demonstrated that the distributional shape of birth intervals depends on the birth order of the index child and/or the subset of children under study. It is also shown that inferences concerning covariate effects on birth intervals are sensitive model choice.