The effect of standardization and rate decomposition in population analysis]

Two alternative ways of distinguishing between the vital rates of two distinct populations are introduced. In the first method, called direct standardization, the effect of other factors is held constant when the effect of one factor is estimated. The second method, indirect standardization, involves choosing an approximate standard to estimate a specific rate. A method of rate decomposition is also presented.     

A general method of decomposing a difference between two rates into several components

In her work on the components of a difference between two rates, Kitagawa (1955) was successful in dividing the difference into the rate effect and the effect of the factor, for data classified by one factor. Her formulation for data classified by two factors, however, involves an interaction term which is difficult to interpret. Retherford and Cho (1973) devised a method that does not include any interaction terms. However, their method has other limitations, such as the dependence of the results on the order in which the effects of the factors are computed. In this paper, we provide a general method capable of handling any number of factors, which is developed along the lines suggested by Kitagawa and by Retherford and Cho but without the limitations of their methods.     

Estimation of contemporaneous mortality factors

Summary We present methods for solving and making statistical inferences about marginal attack rates based on observed death rates for contemporaneous mortality factors. The general method of solution involves solving a system of nonlinear equations which depend in part on competition coefficients that express the outcome when more than one agent attacks the same host individual. For two factors, we present a detailed analysis of the effect of varying this competition coefficient. Statistical inferences are illustrated using standard large sample approximations (the delta method) and the bootstrap, which is a resampling technique. We also extend the results to allow inferences fork-values.     

Combining pheromone-baited and food-baited traps for insect pest control: Effects of developmental period

Summary An age-structured population dynamics model is presented that incorporates pheromone-trapping and food-trapping as control methods for an insect pest. The model yields the following results. Low rates of pest survivorship allow lower trapping rates for control. Species with long developmental periods are easier to control than those with shorter developmental periods (other factors being equal) due to lower net survival. The rates of pheromone trapping alone for effective control are usually very high. The combination of pheromone and food trapping allows control with much lower trapping rates than either method alone. Even small amounts of immigration of adult pests into the control area renders pheromone control ineffective, whereas food traps suppress both the immigrants and the resident population. Food- (or odor-) baited traps which attract both males and females are only somewhat more efficient than those which attract females alone. The existence of density-dependent population regulation assists the control program substantially, but this assistance declines as food trapping becomes a more important part of the control program. Larval competition strongly affects the required trapping rates for eradication; species in which all larvae exert strong competition are much easier to control than those in whic the younger larvae contribute little to the total competitive depression.     

A Flexible Approach for the Decomposition of Rate Differences

Conventional methods of decomposing the difference between two rates, such as Kitagawa's classic component analysis, are confined to taking the average of compositional differences. I propose a more general modeling approach involving three steps: (1) A system of equations with the various additive components of the rate difference is set up; (2) unknowns (refined rate differences) are estimated with Clogg's purging method; (3) the components are calculated. I use an example of U.S. mortality data to compare the proposed method with the conventional ones. The method can be generalized to decompositions for multiple groups and for multiple confounding factors. Kitagawa's method is a special case of this general approach.     

The Cause-Deleted Index: Estimating Cause of Death Contributions to Mortality

Causes underlying mortality disparities are often determined by causal decomposition. This method is based on the decomposition of differences in mortality or life expectancy into parameters representing the contribution of underlying causes. It quantifies disparities as differences in mortality rates and does not account for the fact that many underprivileged groups are more likely to die from nearly all causes. Results are driven by the frequency of cause of death. Alternatively, the cause deleted index quantifies the role of underlying causes in mortality disparities as the change in the relative risk of dying that is related to deleting a specific cause. The consistency between the methods in estimating cause of death contributions is analyzed using 2000 U.S. mortality data and simulated mortality profiles. The two methods often produce divergent results because causal decomposition relies on the prevalence of causes of death.     

A decomposition method based on a model of continuous change

A demographic measure is often expressed as a deterministic or stochastic function of multiple variables (covariates), and a general problem (the decomposition problem) is to assess contributions of individual covariates to a difference in the demographic measure (dependent variable) between two populations. We propose a method of decomposition analysis based on an assumption that covariates change continuously along an actual or hypothetical dimension. This assumption leads to a general model that logically justifies the additivity of covariate effects and the elimination of interaction terms, even if the dependent variable itself is a nonadditive function. A comparison with earlier methods illustrates other practical advantages of the method: in addition to an absence of residuals or interaction terms, the method can easily handle a large number of covariates and does not require a logically meaningful ordering of covariates. Two empirical examples show that the method can be applied flexibly to a wide variety of decomposition problems. This study also suggests that when data are available at multiple time points over a long interval, it is more accurate to compute an aggregated decomposition based on multiple subintervals than to compute a single decomposition for the entire study period.     

Demographic Conditions Responsible for Population Aging

This article develops and applies two expressions for the rate of change of a population's mean age. In one, aging is shown to be negatively related to contemporary birth rates and death rates. In a general sense, aging occurs when vital rates are too low, as illustrated through applications to the United States, the Netherlands, and Japan. The other expression relates the rate of aging to a population's demographic history, in particular to changes in mortality, migration, and the annual number of births. Applications to the United States and Sweden show that the dominant factor in current aging in these countries is a history of declining mortality. Migration also contributes significantly but in opposite directions in the two countries. The two approaches are integrated after recognizing that the rate of change in the mean age is equal to the covariance between age and age-specific growth rates. A decomposition of this covariance shows that the two seemingly unrelated expressions contain exactly the same information about the age pattern of growth rates.     

Methods of adjusting the stable estimates of fertility for the effects of mortality decline

Summary The paper shows how stable population methods, based on the age structure and the rate of increase, may be used to estimate the demographic measures of a quasi-stable population. After a discussion of known methods for adjusting the stable estimates to allow for the effects of mortality decline two new methods are presented, the application of which requires less information. The first method does not need any supplementary information, and the second method requires an estimate of the difference between the last two five-year intercensal rates of increase, i.e. five times the annual change of the rate of increase during the last ten years. For these new methods we do not need to know the onset year of mortality decline as in the Coale-Demeny method, or a long series of rates of increase as in Zachariah's method.     

On the derivation of a two-sex stable population model

It is well known that the intrinsic rates of growth derived separately for the males and females in a population, when one assumes the continuation of their respective mortality and fertility experiences, usually turn out to be different. Noting that the phenomenon of human reproduction is a product of the cooperation between the two sexes, we have attempted in this paper to define the sex-age-specific fertility rates as a function not only of age but also of time, where the latter is implicitly introduced in the model through the sex composition of the reproductive population. It has been shown that a stable model can then be defined based on such changing sex-age-specific fertility rates and given sets of unchanging mortality rates. The fertility rates stabilize with time, and the common intrinsic rates of growth for the two sexes are found to lie in the interval generated by the corresponding rates of the two one-sex models. Several other interesting relationships among the parameters of this model have been presented in the paper. Among other alternatives, a least square solution has been presented for the values of sex-age-specific fertility rates that are minimally discrepant with the observed rates but are consistent in terms of the parametric estimates they generate. It is interesting to note that a relatively modest adjustment in the sex-age-specific fertility rates is all that it takes to eliminate the inconsistencies generated by the separate one-sex models.     

Methods for the analysis of mortality risks across heterogeneous small populations: examination of space-time gradients in cancer mortality in North Carolina counties 1970–75

A method of analyzing mortality rates in heterogeneous populations is presented. This method, appropriate for the investigation of mortality rates in small geographic areas (e.g., counties) where the forces of mobility operate to selectively “package” persons, is applied to the determination of whether a spatial west-east gradient in cancer mortality rates existed in North Carolina over the period 1970 to 1975. A significant gradient (as well as a significant temporal trend) is determined to exist in the data, though only for particular race, age and sex-specific demographic groups. Several alternate hypotheses are presented to explain the existence of the spatial gradient in these particular demographic groups.     

Empirical analysis of the contribution of age composition to population growth

The method of decomposition is applied to rates of natural increase in order to elucidate the role played by age composition in the growth of populations. A population’s age distribution and fertility schedule are contrasted to those in a "stationary" population having the same mortality rates and having a fertility schedule equal to that of the observed population divided by its net reproduction rate. In this manner it is shown that about one-quarter to one-third of the growth of most current high-growth populations can be attributed to non-stationarity of their age distributions. This fraction will rise, as it has in most industrialized countries, if fertility is reduced and age distributions become middle-heavy. In projections of the 1963 Venezuelan female population with fertility rates declining by 20/0 and 1% annually, more than half of the growth (in numbers) that occurs prior to zero-growth attainment is contributed by non-stationarity of its intervening age distributions.

     

Child poverty and changes in child poverty

This article offers a cross-country overview of child poverty, changes in child poverty, and the impact of public policy in North America and Europe. Levels and changes in child poverty rates in 12 Organisation for Economic Co-operation and Development (OECD) countries during the 1990s are documented using data from the Luxembourg Income Study project, and a decomposition analysis is used to uncover the relative role of demographic factors, labor markets, and income transfers from the state in determining the magnitude and direction of the changes. Child poverty rates fell noticeably in only three countries and rose in three others. In no country were demographic factors a force for higher child poverty rates, but these factors were also limited in their ability to cushion children from adverse shocks originating in the labor market or the government sector. Increases in the labor market engagement of mothers consistently lowered child poverty rates, while decreases in the employment rates and earnings of fathers were a force for higher rates. Finally, there is no single road to lower child poverty rates. Reforms to income transfers intended to increase labor supply may or may not end up lowering the child poverty rate.     

A decomposition of trends in the nonmarital fertility ratios of blacks and whites in the united states, 1960–1992*

We use a method of standardization and decomposition developed by Das Gupta to update Smith and Cutright’s analysis of demographic factors responsible for increases in the nonmarital fertility ratio (illegitimacy ratio) among blacks and whites in the United States. We create standardized rates for each year between 1960 and 1992, and consistent, exhaustive decompositions of the nonmarital fertility ratio for any interval during this period in terms of four components: (1) the age distribution of women of reproductive age, (2) the proportion of women unmarried at each age, (3) the age-specific birth rates of married women, and (4) the age-specific birth rates of unmarried women. Nonmarital fertility ratios are much higher among blacks than among whites, but both increased monotonically from 1960 to 1992. During the last 10 years, each increased by nearly 10 percentage points. Increases in the proportion of women not married, at all ages, account for the preponderance of the increase in black nonmarital fertility ratios. Increasing rates of unmarried childbearing, however, have played a role during the most recent decade (1983–1992). For whites, from 1960 until 1975, declines in marital fertility were most important in producing increases in the proportion of children born out of wedlock. Since then, these proportions have increased primarily because of increases in unmarried women s birth rates, and secondarily because of declines in the proportion of women who are married. These trends are consistent with arguments that emphasize declining economic incentives to marry and reduced access to, and acceptability of, abortion.     

Revisiting das gupta: Refinement and extension of standardization and decomposition

Standardization and decomposition are established and widely used demographic techniques for comparing rates and means between groups with differences in composition. The difference in rates and means has heretofore been resolved in terms of the contribution of variables to compositional effects for each variable and an overall rate effect. This study demonstrates that the resolution of differences is attainable at the categorical level for both compositional effects and rate effects. Refinements to Das Gupta’s equations yield a complete decomposition because of the additivity of categorical compositional and rate effects. Other refinements allow the decomposition of polytomous variables. Extensions to the method provide for the decomposition of the standard deviation and the multivariate index of dissimilarity.     

Comparative analysis of the index of our population life quality]

A comprehensive method of calculating and measuring a country's or an area's health and literacy levels is examined. The method, known as population quality life inference (PQLI), was used to determine which of China's provinces has the highest and the lowest degree of population quality. The PQLI indicates infant mortality, average life expectancy of 1 year olds, and literacy rates of those 15 years and older. Because developing countries traditionally have high rates of infant mortality and illiteracy and low life expectancy rates during their industrialization, measuring the degree of population quality of life improvement of such countries during this period was found to be significant. These factors (infant mortality, illiteracy, and life expectancy) will improve substantially as industrialization continues. In order to compare various areas, these 3 factors must be changed into "inferences" 0-100, "0" representing the lowest population quality and "100" the highest. These 3 inferences must then be averaged in order to calculate the PQLI. For example: life expectancy value 77 (highest in the world) minus 38 (lowest)/100 = .39. In order to measure the value of India's life expectancy: value of 1-year-old's life expectancy = 56 (1-year-old's life expectancy in India) minus 38/.39 = 46. The value of adult illiteracy does not need to be changed. Thus, the actual comparison will be based on the values of the 3 inferences. Using this method of calculation, it is concluded that the PQLI analysis indicated that Peking (93.04) is the highest in China and Yumnan Province (60.72) is the lowest.     

Age patterns of mortality for older women: an analysis using the age-specific rate of mortality change with age

"In this paper we propose a mortality measure that seems useful in analyzing age patterns of death rates. The measure, which will be denoted by k(x), indicates the proportional increase or decrease with age in the risk of death at a given age x, and is called the age-specific rate of mortality change with age." Estimations are presented for women in 10 countries. "Eight of the selected sets of data are for developed nations in the 1960s and 1970s, and the other two sets of data, for Taiwan, 1931-35, and for Germany, 1910-11, represent relatively high mortality. For France and West Germany, three different periods are included for an investigation of cohort effects on the observed age patterns." Other mathematical models of age-specific mortality rates are discussed and compared. (SUMMARY IN FRE)     

What Explains the Rural-Urban Gap in Infant Mortality: Household or Community Characteristics?

The rural-urban gap in infant mortality rates is explained by using a new decomposition method that permits identification of the contribution of unobserved heterogeneity at the household and the community level. Using Demographic and Health Survey data for six Francophone countries in Central and West sub-Saharan Africa, we find that differences in the distributions of factors that determine mortality-not differences in their effects-explain almost the entire gap. Higher infant mortality rates in rural areas mainly derive from the rural disadvantage in household characteristics, both observed and unobserved, which explain two-thirds of the gap. Among the observed characteristics, environmental factors-a safe source of drinking water, electricity, and quality of housing materials-are the most important contributors. Community characteristics explain less than onequarter of the gap, with about two-thirds of this coming from community unobserved heterogeneity and one-third from the existence of a health facility within the community. The effect of disadvantageous environmental conditions-such as limited electricity and water supply-derives both from a lack of community-level infrastructure and from the inability of some households to exploit it when available. Policy needs to operate at both the community and household levels to correct such deficiencies.     

Examination of the generalized age distribution

The formula for the age distribution and other relationships that follow from it for any (non-stable) population presented by Preston and Coale are significant contributions to demography. The formulas summarize the relationships among various demographic measures precisely, and are formally analogous to the relationships that hold for stable populations. The significance of these formulas cannot be overstated; they allow us to understand clearly the relationships among demographic measures in any arbitrary population. However, when it comes to using them for estimating demographic measures when census data are defective, the method of estimation is still affected by defective data. The reason is that the series of age-specific growth rates reflects the observed census age distributions exactly so that any defects in the census data are summarized in the growth rates. This paper begins with the formulation of the discrete version of the "new synthesis" developed by Preston and Coale. With the discrete formulation, the three kinds of errors introduced when the continuous time formulas are applied to real data can be avoided. Then it is pointed out that when two accurate census data are available, the Preston-Coale procedure of "estimating" the age distribution at the second census is equivalent to checking the identity of the age distribution formula. Also "estimating" mortality by the procedure of Preston-Coale is shown to be equivalent to obtaining mortality directly from intercensal survival rates. That the procedure which involves the age-specific growth rates is equivalent to those that involve the intercensal survival rates may have escaped notice because there are no a priori constraints for patterns of age-specific growth rates to follow. The irregularity in growth rates due to defective data are not distinguishable from true irregularity that exists in the population, contrary to the well-known regularity in the pattern of survival rates in human populations.