Age intervals and time intervals

Reply to Kim

Bibliographic Data

ID10969166
AuthorsH Preston (0000-0001-7038-9689, University of Pennsylvania, corresponding author), Samuel H Preston (Population Studies Center, University of Pennsylvania, 3718 locust Walk, Philadelphia, Pennsylvania 19104), Ansley J Coale (Office of Population Research, 21 Prospect Avenue, Princeton University, Princeton, New Jersey 08540)
Year1986
Volume23
Issue3
Pages463-465
Publication date1986-08-01
Peer ReviewedYes
Open AccessYes
TypeARTICLE
VenueDemography (JOURNAL)
Journal identifiersISSN: 0070-3370 • E-ISSN: 1533-7790
PublisherDuke University Press (PUBLISHER • US)
DOI10.2307/2061442
OpenAlexW2077809940
LanguageEN
Citations received5
References cited5

Professor Kim has performed a valuable service in deriving certain discrete analogs to many of the equations presented in our paper (Preston and Coale 1982). She is correct that, when the time interval separating two data sets that are arrayed by age or by duration in a state is equal to the age or duration interval in which the data are presented, there is no value for demographic estimation in resorting to equation (1) of her paper. Standard procedures for intercensal survival analysis provide much the same answers, and with less effort. In this circumstance, using equation (1) is like counting sheep by adding up the number of feet and dividing by four. We and our collaborators have stressed in a series of papers (e.g., ]3ennett and Horiuchi 1981; Preston and Bennett 1983) that equation (1) and its offshoots are valuable precisely because they can be used when age intervals are not equal to time intervals, which is probably the most common circumstance facing the analyst. Consider the problem of constructing a life table from two single-year age distributions separated by an arbitrary time interval, say 8 years. If the age distributions are accepted as accurate (and if the population is a closed one), then the single-year population at age a in the first census minus the single-year population at age a + 8 in the second census equals the number of deaths experienced by this cohort over the 8-year interval. By intra-cohort interpolation it is possible to estimate the number of persons crossing each exact age from a + 1 to a + 8, to estimate the number of deaths experienced by the cohort within each single-year age interval, and to estimate the number of person-years lived in each single-year age interval from a to a + 8. By combining such estimates it is possible to construct a life table. For example, the deaths at each age divided by the person-years lived at each age yield a schedule of age-specific mortality rates that can be converted into the probability of dying in each age interval and then into a q, function. Intra-cohort interpolation was used by Coale (1984) to estimate the number of persons crossing each birthday in intercensal periods in China from 1953 to 1964 and from 1964 to 1982. Interpolation factors were obtained by two procedures, an iterative process that begins with linear interpolation, and model interpolation factors. The total number attaining each exact age in the intercensal period was then converted into a life table by a formula using the calculated age-specific growth rate in each single-year age interval. A life table could equally well have been calculated by an analogous interpolation procedure establishing the number of deaths and the number of person-years lived in each age interval. Kim's examples, using as they do a single-year age distribution at a time interval of only one year, are not analogous to the example just described. Her identities apply only if the data from the two censuses are grouped into age intervals equal to the duration of the intercensal period. For censuses in 1953 and 1964, her procedure permits the calculation only of 11L11111L0L 11L22111L11, etc

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