Gini coefficient as a life table function

This paper presents a toolkit for measuring and analyzing inter-individual inequality in length of life by Gini coefficient. Gini coefficient and four other inequality measures are defined on the length-of-life distribution. Properties of these measures and their empirical testing on mortality data suggest a possibility for different judgements about the direction of changes in the degree of inequality by using different measures. A new computational procedure for the estimation of Gini coefficient from life tables is developed and tested on about four hundred real life tables. The estimates of Gini coefficient are precise enough even for abridged life tables with the final age group of 85+. New formulae have been developed for the decomposition of differences between Gini coefficients by age and cause of death. A new method for decomposition of age-components into effects of mortality and composition of population by group is developed. Temporal changes in the effects of elimination of causes of death on Gini coefficient are analyzed. Numerous empirical examples show: Lorenz curves for Sweden, Russia and Bangladesh in 1995, proportional changes in Gini coefficient and four other measures of inequality for the USA in 1950-1995 and for Russia in 1959-2000. Further shown are errors of estimates of Gini coefficient when computed from various types of mortality data of France, Japan, Sweden and the USA in 1900-95, decompositions of the USA-UK difference in life expectancies and Gini coefficients by age and cause of death in 1997. As well, effects of elimination of major causes of death in the UK in 1951-96 on Gini coefficient, age-specific effects of mortality and educational composition of the Russian population on changes in life expectancy and Gini coefficient between 1979 and 1989. Illustrated as well are variations in life expectancy and Gini coefficient across 32 countries in 1996-1999 and associated changes in life expectancy and Gini coefficient in Japan, Russia, Spain, the USA, and the UK in 1950-1999. Variations in Gini coefficient, with time and across countries, are driven by historical compression of mortality, but also by varying health and social patterns.inequality, life expectancy, mortality, variability

Algorithm for decomposition of differences between aggregate demographic measures and its application to life expectancies, healthy life expectancies, parity-progression ratios and total fertility rates

A general algorithm for the decomposition of differences between two values of an aggregate demographic measure in respect to age and other dimensions is proposed. It assumes that the aggregate measure is computed from similar matrices of discrete demographic data for two populations under comparison. The algorithm estimates the effects of replacement for each elementary cell of one matrix by respective cell of another matrix. Application of the algorithm easily leads to the known formula for the age-decomposition of differences between two life expectancies. It also allows to develop new formulae for differences between healthy life expectancies. In the latter case, each age-component is split further into effects of mortality and effects of health. The application of the algorithm enables a numerical decomposition of the differences between total fertility rates and between parity progression ratios by age of the mother and parity. Empirical examples are based on mortality data from the USA, the UK, West Germany, and Poland and on fertility data from Russia.healthy life expectancy, life expectancy, parity progression

Estimates of mortality and population changes in England and Wales over the two World Wars

Almost one million soldiers from England and Wales died during the First and Second World War whilst serving in the British Armed Forces. Although many articles and books have been published that commemorate the military efforts of the British Armed Forces, data on the demographic aspects of British army losses remain fragmentary. Official population statistics on England and Wales have provided continuous series on the civilian population, including mortality and fertility over the two war periods. The combatant population and combatant mortality have not been incorporated in the official statistics, which shows large out-migration at the beginning and large in-migration towards the end of the war periods. In order to estimate the dynamics of the total population and its excess mortality, we introduce in this paper a model of population flows and mortality in times of war operations. The model can be applied to a detailed reconstruction of war losses, using various shapes of the input data. This enables us to arrive at detailed estimates of war-related losses in England and Wales during the two world wars. Our results agree with elements of data provided by prior studies.England, First World War, population estimates, Second World War, Wales

Algorithm for decomposition of differences between aggregate demographic measures and its application to life expectancies, Gini coefficients, health expectancies, parity-progression ratios and total fertility rates

A general algorithm for the decomposition of differences between two values of an aggregate demographic measure in respect to age and other dimensions is proposed. It assumes that the aggregate measure is computed from similar matrices of discrete demographic data for two populations under comparison. The algorithm estimates the effects of replacement for each elementary cell of one matrix by respective cell of another matrix. Application of the algorithm easily leads to the known formula for the age-decomposition of differences between two life expectancies. It also allows to develop new formulae for differences between Gini coefficients (measures of inter-individual variability in age at death) and differences between health expectancies. In the latter case, each age-component is split further into effects of mortality and effects of health. The application of the algorithm enables a numerical decomposition of the differences between total fertility rates and between parity progression ratios by age of the mother and parity. Empirical examples are based on mortality data from the USA, the UK, West Germany, and Poland and on fertility data from Russia.

On the Stability of Rod with Variable Cross-section

AbstractThere is a solution of the problem of the stability of a compressed rod with a variable cross-section. A rectangular cross-section with a variable width is selected as the section. The result is that the problem leads to a differential equation of the fourth order with variable coefficients. From the solution of this equation, a critical force for several particular cases. These cases reflect some different conditions fixing rod and function changes of the width of the cross-section

Long-term trends in the longevity of scientific elites: evidence from the British and the Russian academies of science.

National science academies represent intellectual elites and vanguard groups in the achievement of longevity. We estimated life expectancy (LE) at age 50 of members of the British Royal Society (RS) for the years 1670-2007 and of members of the Russian Academy of Sciences (RAS) for the years 1750-2006. The longevity of academicians was higher than that of their corresponding national populations, with the gap widening from the 1950s. Since the 1980s, LE in the RS has been higher than the maximum LE among all high-income countries. In each period, LE in the RS was greater than in the RAS, although since the 1950s it has risen in parallel in the two academies. This steep increase shared by academicians in Britain and Russia suggests that general populations have the potential for a substantial increase in survival to high ages

Pollen and Isotope Investigations of an Ice Core from Vavilov Ice Cap, October Revolution Island, Severnaya Zemlya Archipelago, Russia

The Vavilov Ice Cap (79°27'N, 95° 21'E) was cored during February and March of 1988. The corer passed through 457.18 m of glacier ice, 2.15 m of moraine-containing ice, and 2.28 m of underlying rocks. Structural-stratigraphical and isotope analysis show the glacier ice is of Holocene in age; the ice layer covered by frozen deposits is Pleistocene glacier ice; and the ground (ice wedge?) ice from underlying sediments was formed during the Last Interglacial. Palynological studies of this core, carried out for the first time in the Russian Arctic demonstrate that the pollen spectra have a unique pattern. It reduces the possibility of correlation between the Vavilov Ice Cape spectra and pollen spectra from other surficial deposits, because the ice retains pollen and spores brought from enormous distances. Only the upper 65 m of the core is easily dated, to the last millennium, by the presence of cereals, Plantago lanceolata, Centaurea cyanus, Cannabis pollen. That is in good agreement with the model of age distribution based upon depth. The presence of considerable amounts of Tilia cordifolia pollen, a West-European species in the upper layers suggests that summer air masses have been dominantly from the southwest during the last 500 years. The pollen data do not contradict the conclusion the Vavilov ice core is composed of a section of Holocene ice, moraine-containing ice representing the Pleistocene episode, and a ground ice formed during an earlier warm period (Last Interglacial?).Une carotte de glace prélevée en 1988 au sein de la calotte glaciaire de Vavilov (79°27'N, 95°21'E) a fait l'objet d'analyses isotopiques et palynologiques. Le sondage comprend 457,18 m de glace « pure », suivis de 2,15 m de glace chargée de sédiments et 2,28 m de roches gelés du socle. Les résultats des analyses structurales, stratigraphiques et isotopiques sont les suivants : la glace pure datée de l'Holocène, les 2,15 de la couche chargée de sédiments datent du Pléistocène, tandis que la glace présente dans les fentes du socle s'est formée au cours du dernier interglaciaire. Les spectres polliniques de cette carotte sont caractérisés par des grains de pollen d'origine lointaine préservés dans la glace. Cette constatation réduit grandement les possibilités de corrélation avec les données sédimentaires de la région, qui reflètent la composition de la végétation locale. Un âge inférieur à 1000 ans peut être attribué aux 65 m supérieurs de la carotte en raison de la présence de pollen de céréales, de Plantago lanceolata, Centaurea cyanus et de Cannabis. Cette interprétation concorde avec le modèle du taux d'accumulation de la glace. Dans la partie supérieure de la carotte, la présence en quantité considérable de Tilia cordifolia, une espèce de tilleul d'Europe de l'Ouest, laisse supposer que les masses d'air en provenance du sud-ouest ont prédominé au cours des étés des 500 dernières années. En conclusion, les données palynologiques ne contredisent pas les résultats antérieurs selon lesquels la carotte glaciaire étudiée couvre une partie de l'Holocène, que la glace contenant la moraine représente l'épisode du Pléistocène et que la glace du socle se soit formée pendant une période chaude (le dernier interglaciaire?)