Constructing fertility tables for Soviet populations

Because the 1970 Soviet Union census does not provide information on the age structure of men and women separately by sex and according to their ethnic affiliation, the 1959 USSR census data serve as the basis to infer knowledge about ethnic fertility. The model takes into account (1) the total number of births in 1960, estimated from the child-woman ratio in 1959, (2) the age structure of women in 1959, and (3) the assumed pattern of age-specific birth rates structured in terms of the modal age at childbearing and the length of the fertility age span. The results show that Ukrainians among the Slav populations ranked as the lowest with 2.07 children born per woman. Their total fertility contrasts with that of Kazakhs native to Central Asia, who reportedly according to Soviet sources had 7.46 children per woman in 1958-1959, and whose estimated rate is around 8.59 children. Extreme variations appear in the estimates of fertility among nationalities of the Caucasus region, Volga Basin, and to a lesser degree in Siberia. Official Soviet calculations of crude birth rates and age-specific rates for 15 Union Republics in 1967-1968 are transcribed and compared with the estimates for nationalities in 1959-1960. The same theoretical model used to generate the Soviet rates may be adapted under different assumptions to non-Soviet populations in other situations where the data are scanty or incomplete.     

On model life tables]

A comparative study and detailed analysis of various standard model life tables are presented. After examining the development of various methods by which demographic factors and weighting techniques are applied, the reasons for the existence of vast discrepancies among the model life tables for various world regions are discussed. It is argued that the 1955 UN model life tables and others developed in Europe and in the United States theoretically apply to Western populations, thus the so-called Chilean, Far East, Southern Asia, and Latin American models, all of which are extensions of Western models, are not totally applicable. Nonetheless, it is concluded that the UN's model population tables 90, 95, and 100 (published in 1955) closely approximate China's 1982 census statistics for life expectancy.     

A reducible four-parameter system of model life tables

Abstract In this paper a four-parameter extension of Brass's relational system of model life tables is suggested that (1) matches a wide range of empirical age patterns of mortality, (2) is easy to apply, especially to partial life tables, and (3) contains demographically meaningful parameters. A test of the model on a set of 62 empirical life tables indicates that four parameters are necessary and sufficient for fitting a wide range of mortality patterns. A further test on an historical series of Swedish life tables reveals a consistent pattern of mortality change. Examination of the parameters for a set of geographicallyrelated life tables suggests a way to define families of life tables. Identification of such temporal and spatial relationships allows the model to be reduced to a form with twoor three-parameters for application to incomplete or inaccurate data.     

Repeated resuscitation: How lifesaving alters life tables

How does saving lives affect the force of mortality and life table statistics? How can the progress being made in reducing the force of mortality be interpreted in terms of lifesaving? How many times can a person expect to have his or her life saved as a result of this progress? We develop a model to answer these questions and illustrate the results by using mortality rates for the United States in 1900 and 1980 and as projected for 2050.     

[Mortality distribution factors and life tables].]

This is an introduction to life table methodology. Particular attention is given to problems concerning the calculation of the distribution of deaths by age and their impact on estimates of life expectancy. Problems are illustrated using data from the abbreviated life tables of China for 1982.     

Labor force status life tables for the United States, 1972

As an ordinary life table follows a closed group from birth to the death of its last member, a labor force status life table follows a closed group through life and through the statuses “in the labor force” and “not in the labor force.” Using data from the January 1972 and January 1973 Current Population Surveys, two types of labor force status life tables were calculated for the United States, 1972. One type was a conventional working life table (for males) which started with an ordinary life table and partitioned the life table population into labor force statuses using age-specific proportions in the labor force. The other type was an increment-decrement table, prepared for both males and females, which was calculated so as to be consistent with the rates of labor force accession and separation implied by the data. Increment-decrement labor force status life tables are generally preferable to conventional working life tables. They reflect the implications of a clearly specified set of behavioral rates, provide detailed measures of the flows between labor force statuses, do not introduce seriously biasing approximations into the calculation of summary measures of labor force experience, and can be applied to female data as easily as male data. In practice, incrementdecrement labor force status life tables can be calculated from current and retrospective data generated by a single labor force survey. The increment-decrement labor force status life tables for the United States, 1972 reflected the extent to which the labor force participation of males exceeded that of females, but indicated that, on the average, half a woman’s lifetime between the ages of 16 and 65 was spent in the labor force. There were marked differences in the proportions, by age, of males and females in the labor force, with the male pattern rising to a single, flat peak and the female pattern being bimodal. Nonetheless, the two sexes shared similar age patterns in the proportions changing, or not changing, their labor force status.     

Estimating internal migration from incomplete data using model multiregional life tables

A principal feature of current methods of estimating demographic measures from incomplete data is the use of model life tables that approximate the mortality of a region for which reliable mortality data are unavailable. Observed decennial rates of survivorship may be used to identify out of a set of such model life tables one that best matches the observed data. This paper introduces the concept of a modelmultiregional life table and outlines a procedure for selecting an appropriate one using place-of-birth-by-residence data.     

Revised regional model life tables at very low levels of mortality

This paper presents and discusses new model life tables at very low mortality, which make use of age-specific death rates from the 1960s, 1970s, and 1980s. These life tables fit recorded death rates in very low mortality populations better than do the existing ones at expectations of life of 77.5 and 80 years. The old tables incorporate too-high mortality at the higher ages and in infancy and they incorporate regional differences that no longer exist. The new tables "close out" the mortality schedules above age 80 more realistically. The convergence of age patterns of mortality at very high life expectancies in populations that used to conform to different families is in itself of demographic interest. Some convergence may perhaps be expected. Sullivan (1973) found that, in Taiwan, the comparison of mortality at ages 1-5 to mortality at 5-35 in the late 1950s showed higher mortality at the younger ages relative to the ensuing 30-year age interval than was found in any of the models, including the South model, which has the highest relative mortality from ages 1-5 among the 4 regional patterns. Then, in the late 1960s, the relation of mortality at 1-5 to mortality at 5-35 in Taiwan fell to a position intermediate between the West and South tables. Sullivan found in data on mortality by cause of death a large reduction in mortality from diarrhea and enteritis, no doubt as a result of environmental sanitation. Mortality from these causes is concentrated among young children, and reduction in deaths from these causes would naturally diminish the excess mortality in this age interval. The East pattern, characterized by very high mortality in infancy (but not from 1-5), may be the result of the prevalence of early weaning or avoidance of breast feeding altogether in the populations characterized by this pattern. As health conditions have improved, evidenced by the overall design of mortality, these special factors are diminished or erased. Model life tables at these very low mortality levels have different uses from most applications of model life tables at higher mortality. The use of model tables to estimate accurate schedules of mortality when the basic data are incomplete or inaccurate is less relevant in this range of mortality levels.     

A simple model for linking life tables by survival mortality ratios

Patterns of variation in mortality can be studied by measuring changes in selected life table functions. A model is proposed in which the rate of change over time in the life table survivorship probability at any age has been assumed as proportional to the product of its own value and its complementary probability or the probability of dying by that age, where the proportion is the same for all ages and depends only on the time duration between successive life tables. The end result is that the logit functions of the survivorship probabilities at two points in time are linearly related with a slope of one. The projecting power of the model has been tested by using U.S. life tables for the years 1950 and 1970 as well as Coale and Demeny's regional model life tables. In the latter case, the model produced surprisingly close matches even when the expectations of life differed by as much as 20 years.     

Calculation of life tables from survey data: A technical note

Life table calculations from survey data are frequently based on events for which exact dates are not available. When these dates are coded in monthly form (e.g., century months), estimates should take into account the fact that the first duration interval—the interval which captures events occurring in the first month of exposure—is half the length of all remaining intervals. Although failure to do so has a trivial effect on many demographic calculations, estimates which are based on events which occur with high frequency in the first few months of exposure can be substantially biased. Estimates offecundability for four countries in the World Fertility Survey are used to illustrate this bias.     

Calculating life tables by estimating Chiang’s a from observed rates

A simple, accurate method of life table construction is advanced based upon a new way to estimate Chiang’s _n a _x (the average number of years lived in the x to x + n age interval by those dying in the interval). The estimate for _n a _x leads immediately to an expression for l _x+n (the survivors to age x + n) in terms of l _x and the known mortality rates for the interval x to x+n and the two adjacent intervals. The complete solution for the basic life table is given. The proposed method and five other easily applied methods are then compared against the standard provided by the U.S. life tables for 1969–1971. The results attest to the excellent performance and high degree of accuracy of the proposed method. Finally, extensions of the method to multiple decrement and associated single decrement life tables are briefly described.     

Voting status life tables for the United States, 1968–1980

Using current and retrospective voting data from the November Current Population Surveys of Presidential election years, this study modifies and applies demographic accounting and increment-decrement life table methods to construct voting status life tables for three recent election periods. The paper shows how to combine a continuously occurring process (mortality) with a process that is active only at discrete times (voting transitions) within a multistate life table. Empirical results pertain to the number of Presidential elections an individual is expected to vote in at ages 0 and 18, the typical life course pattern of transitions between voting and not voting statuses, sex and race differentials, changes across the three election periods, and cohort effects.     

Parental survival data: Some results of the application of Ledermann's model life tables

Summary Ledermann's one- and two-parameter model life tables are used in order to summarize and compare adult mortality estimates derived from parental survival data, and also to link parental survival with child survival data. The Ledermann models provide an alternative to the logit model used by Brass and Hill. Examination of life tables derived from actual child and adult mortality estimates reveals that although the two types of models yield similar overall levels of mortality, they show marked differences in the estimated patterns by sex and age. It has not been possible to disentangle completely how much of this divergence is due to the models themselves and how much to inadequacies in the data available. Finally, we question whether it is always wise to establish a full life table from child and adult mortality estimates when these are based on data which refer to different periods of exposure to the risk of dying, without allowance for possible distortions resulting from mortality change.     

Model life tables: An empirical test of their applicability to less developed countries

Model life tables are commonly used for estimating various parameters of mortality of populations in developing countries with limited data. The application of the models is based on the assumption that the agemortality pattern of the population under consideration resembles one of the life tables in the models. The analysis in this paper tests the validity of this assumption for developing countries with data usable for the purpose. The major conclusion is that infant mortality in the populations analyzed is higher than predicted by the models corresponding to the levels of adult mortality of these populations. The observed discrepancy is ascribed to the selectivity involved in the construction of model life tables, which are primarily derived from the historical experience of Western countries. Populations in the currently developing countries apparently differ in the process of mortality change from those used in the models. Though the analysis is limited to a few countries and may not necessarily be true for all the less developed countries, it suggests the need for caution in the use of conventional model life tables.     

The calculation of mortality-rates in the construction of life tables. A mathematical statistical study

Official life tables are frequently calculated for a period of years, rather than for an individual year, and the question arises, how annual rates are to be combined, in order to give an indication of the average mortality of the period. The author examines this problem, and uses methods based on the binomial probability distribution to suggest a solution of the ‘weighting’ problem. Taking as his starting-point the work of the Dutch statistician Van Pesch, he modifies the latter's theory so as to make it applicable to the case, where mortality rates have a secular downward trend, and reaches the conclusion that the ‘most probable values for the mortality rates are not obtained by applying the weighted mean, but by the application of a weighted mean and a correction term. The inclusion of the correction term means that, practically speaking, the results do not differ from those obtained by the application of the unweighted mean. The unweighted mean, which has the advantage of requiring less computational work, may therefore be given preference over the theoretically more accurate method.’     

[Estimate of indicators of life tables in 1953-1964 and 1964-1982].]

The variable-r method is applied to data from the 1953, 1964, and 1982 censuses of China to produce life tables for 1953-1964 and 1964-1982. The tables are used to discuss a selection of mortality indicators, including infant mortality, age-specific mortality, and life expectancy by sex.