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MATHEMATICAL POPULATION STUDIES, 2000, Vol. 7, No. 4
LI, Nan; TULJAPURKAR, Shripad.
The solution of time-dependent population models.
We analyze the dynamics of age-structured population renewal when vital rates make a transition in a finite time interval from arbitrary initial values to any specified final values. The general solution to the renewal equation in such cases is obtained. This solution describes the birth sequence explicitly, and also leads to a general formula for population momentum. We show that the duration of the transition determines the complexity of the solution for the birth sequence. For transitions that are completed in a time smaller than the maximum age of reproduction, we show that the classical Lotka solution found in every textbook also applies, with a small modification, to the time-dependent case. Our results substantially extend previous work that has often focused on instantaneous transitions or on slow and infinitely persistent change in vital rates.
(MATHEMATICAL DEMOGRAPHY, MATHEMATICAL MODELS, DEMOGRAPHIC MODELS, DEMOGRAPHIC TRANSITION).
English - pp. 311-329.
Nan Li and S. Tuljapurkar, Mountain View Research, 2251 Grant Road, Los Altos, CA 94204, U.S.A.
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KOSTAKI, Anstasia; LANKE, Jan.
Degrouping mortality data for the elderly.
Proposed in this paper is a technique for estimating, from coarsly grouped empirical death data, the age-specific numbers of deaths for the elderly population. This question is primarily of interest in countries where the empirical data are available only in a grouped form, given usually in quinquennial age groups and in a large open-ended interval for the ages 85 and over. The main reason that the official data are given in such a form in some countries of Southern Europe and in the Third World is the existence of heaping in the empirical data, i.e. misstatements in age recording, usually rounding to the nearest integer divisible with five. Our evaluation of the method on Swedish mortality data shows that the technique proposed can be efficiently applied to period mortality data.
(MATHEMATICAL DEMOGRAPHY, METHODOLOGY, AGED, MORTALITY, AGE GROUPS, DATA ADJUSTMENT, DIGIT PREFERENCE).
English - pp. 331-341.
A. Kostaki, Department of Statistics, Athens University of Economics and Business, Patission 74, 104 34, Athens, Greece; J. Lanke, Department of Statistics, University of Lund, Box 743, S-220 07, Lund, Sweden.
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PRSKAWETZ, A.; STEINMANN, G.; FEICHTINGER, G.
Human capital, technological progress and the demographic transition.
We emphasize the importance to consider components of population growth -- fertility and mortality -- separately, when modeling the mutual interaction between population and economic growth. Our model implies that two countries with the same population growth will not converge towards the same level of per capita income. The country with the lower level of birth and death rates will be better off in the long run. Introducing a spill over effect of average human capital on total productivity our model implies multiple equilibria as illustrated in Becker et al. (1990) and Strulik (1999). Besides the existence of a low and high level equilibrium -- as characterized by low and high levels of per capita output respectively -- we show the existence of multiple low level (Malthusian) equilibria. Initial conditions and parameters of technological progress and human capital investment determine whether an economy is capable to escape the low level equilibrium trap and to enjoy sustained economic growth.
(ECONOMIC MODELS, DEMOGRAPHIC TRANSITION, ECONOMIC GROWTH, TECHNOLOGICAL CHANGE, HUMAN RESOURCES).
English - pp. 343-363.
A. Prskawetz, Max Planck Institute for Demographic Research, Rostock, Germany; G. Steinmann, Department of Economics, University Halle-Wittenberg, Germany; G. Feichtinger, Institute for Econometrics, Operations Research and Systems Theory, Technical University of Vienna, Austria.
Fuernkranz@demogr.mpg.de.
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Persistent age distributions for an age-structured two-sex population model.
In this paper we formulate an age-structured two-sex population model which takes into account a monogamous marriage rule and the duration of marriage. We are mainly concerned with the existence of exponential solutions with a persistent age distribution. First we provide a semigroup method to deal with the time-evolution problem of our two-sex population model. Next, by constructing a fixed point mapping, we prove the existence of exponential solutions under homogeneity conditions.
(MATHEMATICAL DEMOGRAPHY, DEMOGRAPHIC MODELS, AGE-SEX DISTRIBUTION).
English - pp. 365-398.
H. Inaba, Department of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba Meguro-ku, Tokyo 153-8914, Japan.
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