Some methodological issues in estimating demographic parameters in Southern Africa Centre for Actuarial Research (CARe) A Research Unit of the University of Cape Town

Overview  Child mortality  Adult mortality Orphanhood method Methods using deaths and population  GGB vs SEG methods  Deaths reported by households vs vital registration Use of deaths reported by households  Fertility Brass P/F and variants Relational Gompertz models

Child mortality: 5 q 0  The rule of 60  If … 30% prevalence among women /3 maternal transmission 60% of children infected die before age 5  Then … Increase in child mortality must be > 60 per mille  So… Can’t use CEB/CS

Orphanhood  Problems Correlation of mortality of child with mother/parents Life table  AIDS  Not a single table  Bias apparently not too significant (Timæus and Nunn – 4%?)  Confine to older age women – but then of limited use

Generalized Growth Balance and Synthetic Extinct Generations  Methods based on census counts alone can’t be used (inaccuracies in counts, no model life tables)  Constant-r methods (Growth Balance (Brass) and Preston-Coale method) not applicable  GGB (Hill), SEG (Bennett and Horiuchi)  Hill and Choi recommended GGB+SEG, BUT  SEG+delta on their dataset better, BUT  Not necessarily in Africa with AIDS, BUT  The real problem…

Proportionate error in estimate of 45 q 15 : African hypothetical data set

Deaths reported by households vs vital registration of deaths  Virtually no countries with adequate vital registration systems (South Africa = 85% adult completeness)  Otherwise ask households to report on deaths in household in “the last 12 months”  Problem: Potential biases  Problem: How complete is the reporting? Only 1 year deaths but censuses 10+ years apart

Potential biases  Two underlying assumptions of methods of estimating rates adjusted for completeness deaths represent the population completeness the same for all ages  Deaths reported by households represent only those in households – the bulk of the population  Completeness is unlikely to be the same for children as adults, and may not be the same for all adult ages

Potential for bias  Under-reporting (as a result of): failure to report a recent death; confusion around the length of the reference period; *non-coverage of specific areas/populations; *disintegration of the household on the death; or, for completeness, *the institutionalising of segments of the population (e.g. the aged)  Over-reporting (as a result of): confusion around the length of the reference period; or people seen as belonging to more than one household)  Age misreporting (either age heaping or *age exaggeration)

Method – Data situations  Two censuses and data on deaths from both censuses Estimate the deaths in the intercensal period by assuming exponential growth/change in the number of deaths over time GGB and SEG+delta to intercensal period  Two censuses and data on deaths from the latter census Estimate the population one year prior to the second census Apply GGB and SEG+delta to the year prior to the second census  Single census with data on deaths Use Growth Balance as a diagnostic

Zimbabwe – males ( )

Zimbabwe – females ( )

Zimbabwean adult mortality ( 45 q 15 )

Best of both vital registration + deaths reported by households  Problem with vital registration sub-nationally  Dorrington, Moultrie and Timaeus monograph  Use vital registration to estimate completeness and hence expected number of deaths by sex and age nationally  Derive factors by sex and age to adjust the deaths reported by households for misreporting  Assume misreporting by households in the census is independent by sub-population  Correct deaths reported by households sub- nationally

Fertility: Brass P/F methods  Results from a simulation exercise 200 year projections starting / ending with stable populations; systematically introducing fertility decline; mortality decline; mortality rise due to HIV (with associated fertility impacts)  What is the best of the existing methods for adapting the P/F method for declining fertility?

Declining fertility and declining mortality

Declining fertility and rising AIDS mortality

Fertility: Relational Gompertz models  Model is designed for medium-high fertility populations Booth standard is based on 33 Coale-Trussell high fertility schedules  What if the schedules are not appropriate for use in Africa? Fertility patterns no longer typical of the 33 Particular problem at the oldest age group, where the C-T force estimated fertility to be low … ongoing research work with Reinier van Gijsen (M student)

Relational Gompertz models