Formal demography, innovative methodologies, and their applications

The support ratio is a simple and intuitive indicator of the consequences of population aging, and its changes are interpreted as implying corresponding changes in per capita age adjusted consumption. However, this holds only when net consumers rely on transfers from net producers. If instead they rely on asset income, then support ratio variations have no effect on per capita consumption if the economy is open, and likewise across golden rule economies with different population growth rates. Here we reformulate the support ratio to include both asset income and transfers. In countries in which the elderly are funded heavily by public transfers as in Sweden or Austria, the new measure gives the same result as the old one. In countries like the US or Mexico where old age consumption is funded more heavily out of asset income, the new measures suggest that the effects of population aging will be muted.

Event history analyses make the explicit assumption of independence between censoring and event. Under this hypothesis right censoring due to survey time does not create a selection bias. However, when censoring is not independent from the event of interest (e.g. migration in relation to death) then results suffer from potential bias. This paper presents a model to deal with non-independent right- as well as left-censoring, when the same determinants may cause in-migration, out-migration and mortality. The model follows the rationale of two-stage regression models controlling for selection biases to control for both observed and unobserved heterogeneity in migration. The method is applied on longitudinal adult mortality data collected by the APHRC Nairobi Urban Health and Demographic Surveillance System (NUHDSS), situated in two Nairobi slums – Korogocho and Viwandani – where circular migration is high. Results confirm selection for both out- and in-migration. The method produces higher adult mortality rates than raw estimates. After controlling for migration effect, median age at death from age 15 would be 46 year old (against gross estimate of 70) for females, and 52 (against 70) for males. Migration is most likely an important strategy adopted by slum-dwellers to avoid health risks attached to slum environment.

Under natural circumstances, the ratio of the male to female under-five mortality rate is greater than one. However, deprivation of girls’ access to health care or proper nutrition could lead to distorted ratios of under-five mortality. Monitoring of mortality by sex is challenging because of issues with data availability and quality. Moreover, the sex ratio is expected to vary with under-five mortality, which makes it challenging to define "expected levels".
We present a Bayesian hierarchical model to estimate the sex ratio of under-five mortality for all countries. In addition, we estimate the relative difference between national sex ratios and expected sex ratios based on the global relation between under-five mortality and the sex ratio. All estimates include an uncertainty assessment to enable assessments of whether differences between countries or within countries over time are significant or highly uncertain. Preliminary results suggest that girls may be disadvantaged in several countries.

In this paper, we develop a Bayesian cohort population projection model that incorporates model uncertainty. We first argue that a Bayesian approach is a more natural framework for incorporating various forms of uncertainty in probabilistic projections. Second, we demonstrate the differences that arise from choosing different Lee-Carter type models for fertility, mortality, immigration and emigration in terms of forecasted age patterns and their associated measures of uncertainty. Third, we incorporate this information into a cohort component projection model and use Bayesian model averaging techniques to produce a model-averaged population forecast for the United Kingdom by age and sex. We end the paper by discussing the merits and flexibility of a Bayesian cohort component projection model and highlight some areas where this work could be extended.

Demographic events have characteristic age-specific patterns of occurrence. Finding model schedules to summarize the age-pattern of demographic rates has a long tradition, however, parametric models are predominantly used. Many demographic rates shows complex shape in their overall age-pattern. However such pattern can be attributed to different distinct components.

While some of the components can be described by a parametric model, such as the Gompertz hazard for adult mortality, many others cannot. Additional complication arises if data are provided in age groups, which is still the case in many official statistics and historical data.

In the article we propose a model that allows to specify rates across a wide range of ages as the sum of several components, which are modelled on the log scale and are assumed to be smooth, but do not have to follow a particular parametric form. A penalized composite link model is used to decompose complex trajectories into smooth additive components.

Parametric and non-parametric forms can be used. Data can be given in age-groups which can eventually be of variable lengths. Furthermore, monotonicity or shape constraints on the components can be incorporated and the model can cope with two-dimensional settings in which age-patterns change over time.

Reproduction measures were most popular between the two World Wars, before various methodological remarks produced a general negative opinion about them. Those measures were essentially developed from one-sex population models with no migration; however, since the second half of past century, immigration has become a relevant component of population change in Europe, and nowadays is the most important one in several European countries. With the acknowledged primary contribution of migration to the population dynamics, scholars have tried to incorporate its effects in the traditional reproduction measures, or they have proposed new indicators, which were then taking more a wider meaning of measures of population replacement. This study makes a comparative assessment, both analytically and empirically, of old and new measures proposed in literature. Further, it uses these demographic tools for a revision of the population replacement dynamics in Europe over the last 50 years. It is shown the similarity between some of the existing measures, as well as their different sensitivity to migration changes. A few additional measures of population replacement, variation of existing indicators, are also proposed for illustrative purposes.

Short Abstract: The role of random error in age on estimate of malnutrition measured by anthropometric indicators of nutritional status for young children is not clear. This study demonstrates statistically and empirically that random error can over estimate severe malnutrition and at the same time it can underestimate severe and moderate malnutrition combined. But this depends on the level of malnutrition in the population. If malnutrition in the population is less than 50%, random error in age overestimates malnutrition; if it is more than 50%, it underestimates malnutrition; and if it is 50%, there will be no effect. Both bias and random error in age deserve attention in estimating malnutrition for young children using anthropometric indices.

**This tiny paper (having only 10 pages with statistical derivation, figures and references) is ready for submission, if needed.

During last two decades India has moderate reduction of child mortality which is an important measure of population health. It is frequently watched by demographers to determine how rapidly moving. However, most of its projection techniques are still based on conventional approach which ignores prior information. This suggests performing Bayesian analysis for projecting Indian child mortality rate to incorporate prior information. Our method of illustration includes dynamic linear models based on state space prior and known demographic information from National Family Health Survey (NFHS) data. In order to evaluate the accuracy of estimates, we compare our estimates with conventional estimates.

We show that Bayesian population reconstruction, a recent method for estimating past populations by age, works in a very wide variety of data quality contexts. To date, it has been shown to work only in a single case (i.e., Burkina Faso). Bayesian reconstruction simultaneously estimates age-specific population counts, fertility rates, mortality rates and net international migration flows from fragmentary data while formally accounting for measurement error. As inputs, Bayesian reconstruction takes initial bias-reduced estimates of age-specific population counts, fertility rates, survival proportions and net international migration. Here, we show that the method performs well when applied in a range of data quality contexts by reconstructing the female populations of Laos, a country with little vital registration data where population estimation depends largely on surveys, Sri Lanka, a country with some vital registration data, and New Zealand, a country with a highly developed statistical system and high-quality vital registration data. In addition, we extend the method to apply to countries without censuses at regular intervals. We also develop a method for using it to assess the consistency between model life tables and available census data, and hence to compare different model life table systems.

Event-history demography is concerned with statistical individuals, whose life courses can be inferred from empirical information. In contrast, agent-based models study simulated individuals, for whom certain behavioural rules are assumed. We wish to bring these two approaches closer together by proposing a method to analyse the rule-based outcomes statistically. We present a Semi-Artificial Model of Population (SAMP), which augments the Wedding Ring agent-based model of partnership formation by statistical data on natural population change in the United Kingdom. We utilise a Gaussian process emulator - a statistical model of the SAMP - to analyse the impact of selected parameters on two key model outputs: population size and share of agents with partners. Emulators permit a statistical analysis of model properties and help select plausible parameter values, despite the non-linearities and feedback loops present in agent-based models. A sensitivity analysis is also attempted, aiming to assess the relative importance of different parameters. The resulting multi-state model of population dynamics has an enhanced predictive capacity, but with some trade-offs between the outputs considered. The proposed methods allow for generating coherent, multi-level agent-based scenarios aligned with selected aspects of the demographic reality.