Defining a sub-Saharan Fertility Pattern and a Standard for use with the Relational Gompertz Model

Type Thesis or Dissertation - Master of Philosophy
Title Defining a sub-Saharan Fertility Pattern and a Standard for use with the Relational Gompertz Model
Publication (Day/Month/Year) 2009
The relational Gompertz model is often used to obtain fertility estimates for sub-Saharan Africa
populations. This indirect estimation technique is dependent on a fertility standard - the Booth
standard. This standard was developed in 1979 using a selection of 33 Coale-Trussell schedules
congruent with high fertility patterns. However, evidence from 61 Demographic and Health Surveys
of sub-Saharan countries shows that fertility has decreased to levels that were considered medium
fertility at the time the standard was developed. This raises concerns about the continued relevance
of the (high fertility) Booth standard. In particular, the standard would appear to consistently
underestimate fertility among African women aged 45-49. This understatement occurs irrespective
of the level of total fertility and suggests that fertility may be generally higher at the older ages in
Africa than can be constructed with the Coale-Trussell schedules. In addition, further investigation
of the understatement highlighted that the patterns of fertility for 61 African DHS are broadly
similar. This result has two important implications: First, a pattern of fertility that is distinctly
African can be identified. Second, it suggests that an African standard be developed to utilize with
the relational Gompertz model in the analysis of fertility data. To this end a number of alternatives
are considered: 1) Two reworks of the Coale-Trussell model, 2) the Brass polynomial and 3) the
Hadwiger function. Of these, the two restatements of the Coale-Trussell model are dismissed due to
a continued misfit in the 45-49 age group. The appropriateness of the two remaining alternatives is
assessed using least squares methodology and graphical graduation and both yield apparently
reasonable results. However, the Brass polynomial has the advantage of being simpler than the
Hadwiger function and allows the direct calculation of cumulative fertility rates. Furthermore,
statistical tests show that the Brass polynomial is superior to the Hadwiger function, since the latter
fails both the smoothness and goodness-of-fit graduation tests. As a result, the Brass polynomial is
deemed to be the most suitable to model the African fertility pattern and is used to develop an
African fertility standard.

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