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On Age Structures and Mortality

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Ageing in Advanced Industrial States

Part of the book series: International Studies in Population ((ISIP,volume 8))

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Comments by Jim Oeppen and Helge Brunborg, and research assistance by Petter Vegard Hansen are gratefully acknowledged.

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Notes

  1. 1.

    Lotka and Sharpe (1911). See also Lotka’s Analytical theory of biological populations. New York: Plenum Press, 1998 (Plenum Series on Demographic Methods and Population Analysis). This is an English translation of the work that Lotka published in the two-part Théorie Analytique des Associations Biologiques in 1934 and 1939, and represents Lotka’s contributions to the field of demographic analysis.

  2. 2.

    In practice one does not work with the age distribution c(a), but with the cumulative distribution \( C(a) = \int_0^a {c(\alpha )d\alpha.} \) This way one avoids problems caused by irregularities in the empirical age structure due to digit preference, age heaping and shifting. Probably this is an important reason why the regression approach is not widely used.

  3. 3.

    When the reduction of the death rates varies by age, the age distribution of the stable population is changed in such a way that age segments with the strongest mortality reduction get more weight. The typical mortality decline has been strongest below age five. As a result, mortality declines have, throughout human history, tended to make populations younger (Preston et al. 2001, p. 160).

  4. 4.

    Expression (5) can be generalized to include migration, by incorporating an age-specific net migration rate. The net migration rate is the difference of the immigration rate and the emigration rate. Note that the immigration rate is not a rate in the demographic (occurrence-exposure) sense, as the population exposed to the risk of immigration to the country is not included in the immigration rate.

  5. 5.

    This is exactly the reason why the starting age structure of IP is not critical. For example, starting from two very different stable populations (female, North, e 0 = 47.5, r = 0; and female, North, e 0 = 27.5, r = 0.01) for the case of England in the period 1540 to 1871, Lee (1985) finds converging IP-results after a few decades already.

  6. 6.

    Generously provided by Jim Oeppen (2001) (personal communication).

  7. 7.

    There is a printing error in Oeppen’s Table 2.1: growth rates are too low by a factor ten.

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Authors and Affiliations

  1. Department of Economics, University of Oslo, 1095, Blindern, N-0317, Oslo, Norway

    Nico Keilman

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  1. Dept. Biology, Stanford University, Herrin Labs 454, Stanford, 94305-5020, USA

    Shripad Tuljapurkar

  2. Population Research Institute, Nihon University Tokyo, Misaki-cho 1-3-2, Tokyo, 101-8360, Japan

    Naohiro Ogawa

  3. Canada Research Chair in Comparative, Public Policy, University of Calgary, University Dr. NW., 2500, Calgary, T2N 1N4, Canada

    Anne H. Gauthier

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Keilman, N. (2010). On Age Structures and Mortality. In: Tuljapurkar, S., Ogawa, N., Gauthier, A. (eds) Ageing in Advanced Industrial States. International Studies in Population, vol 8. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3553-0_2

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