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describe the experience of an actual birth co- hort—that is, a group of individuals who are born within a (narrowly) specified interval of time. If we wished to portray the mortality history of the birth cohort of 2000, for example, we would have to wait until the last individual of that cohort has died, or beyond the year 2110, before we would be able to calculate all of the values that comprise the life table. In such a life table, called a generation or cohort life table, we can explicitly obtain the probability of individuals surviving to a given age. As is intuitively clear, however, a generation life table is suitable primarily for historical analyses of cohorts now extinct. Any generation life table that we could calculate would be very much out of date and would in no way approximate the present mortality experience of a population. Thus, we realize the need for the period life table, which

treats a population at a given point in time as a synthetic or hypothetical cohort. The major drawback of the period life table is that it refers to no particular cohort of individuals. In an era of mortality rates declining at all ages, such a life table will underestimate true life expectancy for any cohort.

The most fundamental data that underlie the formation of a period life table are the number of deaths attributed to each age group in the population for a particular calendar year (nDx), where x refers to the exact age at the beginning of the age interval and n is the width of that interval, and the number of individuals living at the midpoint of that year for each of those same age groups (nPx).

To begin the life table’s construction, we take the ratio of these two sets of input data—nDx and nPx—to form a series of age-specific death rates, or

nMx:

For each death rate, we compute the corresponding probability of dying within that age interval, given that one has survived to the beginning of the interval. This value, denoted by nqx, is computed using the following equation:

where nax is the average number of years lived by those who die within the age interval x to x+n.

(Except for the first year of life, it is typically assumed that deaths are uniformly distributed within an age interval, implying that nax=n/2.)

Given the values of q and a, we are able to generate the entire life table.

The life table may be thought of as a tracking device, by which a cohort of individuals is followed from the moment of their birth until the last surviving individual dies. Under this interpretation, the various remaining columns are defined in the following manner: lx equals the number of individuals in the life table surviving to exact age x.

We arbitrarily set the number ‘‘born into’’ the life

table, lo, which is otherwise known as the radix, to some value—most often, 100,000. We generate all subsequent lx values by the following equation:

ndx equals the number of deaths experienced by the life table cohort within the age interval x to x+n. It is the product of the number of individuals alive at exact age x and the conditional probability of dying within the age interval:

The concept of ‘‘person-years’’ is critical to understanding life table construction. Each individual who survives from one birthday to the next contributes one additional person-year to those tallied by the cohort to which that person belongs. In the year in which the individual dies, the decedent contributes some fraction of a person-year to the overall number for that cohort.

nLx equals the total number of person-years experienced by a cohort in the age interval, x to x+n. It is the sum of person-years contributed by those who have survived to the end of the interval

and those contributed by individuals who die within that interval:

Tx equals the number of person-years lived beyond exact age x:

a=x,n

ex equals the expected number of years of life remaining for an individual who has already survived to exact age x. It is the total number of person-years experienced by the cohort above that age divided by the number of individuals starting out at that age:

x

The nLx and Tx columns are generated from the oldest age to the youngest. If the last age category is, for example, eighty-five and above (it is typically ‘‘open-ended’’ in this way), we must have an initial value for T85 in order to begin the process. This value is derived in the following fashion: Since for this oldest age group, l85=∞d85 (due to the fact that the number of individuals in a cohort who will die at age eighty-five or beyond is simply the number surviving to age eighty-five) and T85=∞L85, we have:

1≈ 1

From the life table, we can obtain mortality information in a variety of ways. In table 2, we see, for example, that the expectation of life at birth, e0, is 76.1 years. If an individual in this population survives to age eighty, then he or she might expect to live 8.4 years longer. We might also note that the probability of surviving from birth to one’s tenth birthday is l10/l0, or 0.99022. Given that one has already lived eighty years, the probability that one survives five additional years is l85/l80, or 33,629/ 49,276=0.68246.

POPULATION PROJECTION

The life table, in addition, is often used to project either total population size or the size of specific age groups. In so doing, we must invoke a different interpretation of the nLx’s and the Tx’s in the life table. We treat them as representing the age distribution of a stationary population—that is, a population having long been subject to zero growth. Thus, 5L20, for example, represents the number of twentyto twenty-four-year-olds in the life table

‘‘population,’’ into which l0, or 100,000, individuals are born each year. (One will note by summing the ndx column that 100,000 die every year, thus giving rise to stationarity of the life table population.)

If we were to assume that the United States is a closed population—that is, a population whose net migration is zero—and, furthermore, that the mortality levels obtaining in 1996 were to remain constant for the following ten years, then we would be able to project the size of any U.S. cohort up to ten years into the future. Thus, if we wished to know the number of fiftyto fifty-four-year-olds in

2006, we would take advantage of the following relation that is assumed to hold approximately:

where is the base year of the projection (e.g.,

1996) and t is the number of years one is projecting the population forward. This equation implies that the fiftyto fifty-four-year-olds in 2006, 5P502006, is simply the number of forty-to forty-four-year- olds ten years earlier, 5P401996, multiplied by the proportion of fortyto forty-four-year-olds in the life table surviving ten years, 5L50/5L40.

In practice, it is appropriate to use the above relation in population projection only if the width of the age interval under consideration, n, is sufficiently narrow. If the age interval is very broad— for example, in the extreme case in which we are attempting to project the number of people aged ten and above in 2006 from the number zero and above (i.e, the entire population) in 1996—we cannot be assured that the life table age distribution within that interval resembles closely enough the age distribution of the actual population. In other words, if the actual population’s age distribution within a broad age interval is significantly

different from that within the corresponding interval of the life table population, then implicitly by using this projection device we are improperly weighing the component parts of the broad interval with respect to survival probabilities.

Parenthetically, if we desired to determine the size of any component of the population under t years old—in this particular example, ten years old—we would have to draw upon fertility as well as mortality information, because at time τ these individuals had not yet been born.

HAZARDS MODELS

Suppose we were to examine the correlates of marital dissolution. In a life table analysis, the break-up of the marriage (as measured, e.g., by separation or divorce) would serve as the analogue to death, which is the means of exit in the standard life table analysis.

In the study of many duration-dependent phenomena, it is clear that several factors may affect whether an individual exits from a life table. Certainly, it is well-established that a large number of socioeconomic variables simultaneously impinge on the marital dissolution process. In many populations, whether one has given birth premaritally, cohabited premaritally, married at a young age, or had little in the way of formal education, among a whole host of other factors, have been found to be strongly associated with marital instability. In such studies, in which one attempts to disentangle the intricately related influences of several variables on survivorship in a given state, we invoke a hazards model approach. Such an approach may be thought of as a multivariate statistical extension of the simple life table analysis presented above (for theoretical underpinnings, see, e.g., Cox and Oakes 1984 and Allison 1984; for applications to marital stability, see, e.g., Menken, Trussell, Stempel, and

Babakol 1981 and Bennett, Blanc, and Bloom 1988).

In the marital dissolution example, we would assume that there is a hazard, or risk, of dissolution at each marital duration, d, and we allow this duration-specific risk to depend on individual characteristics (such as age at marriage, education, etc.). In the proportional hazards model, a set of individual characteristics represented by a vector

of covariates shifts the hazard by the same proportional amount at all durations. Thus, for an individual i at duration d, with an observed set of characteristics represented by a vector of covariates,

Zi, the hazard function, µi(d), is given by:

where ß is a vector of parameters and λ(d) is the underlying duration pattern of risk. In this model, then, the underlying risk of dissolution for an individual i with characteristics Zi is multiplied by a factor equal to exp[Ziß].

We may also implement a more general set of models to test for departures from some of the restrictive assumptions built into the proportional hazards framework. More specifically, we allow for time-varying covariates (for instance, in this example, the occurrence of a first marital birth) as well as allow for the effects of individual characteristics to vary with duration of first marriage. This model may be written as:

µi(d) = exp [ λ (d) ] exp [Zi (d) β (d) ] (13)

where λ(d) is defined as in the proportional hazards model, Zi(d) is the vector of covariates, some of which may be time-varying, and ß(d) represents a vector of parameters, some of which may give rise to nonproportional effects. The model parameters can be estimated using the method of maximum likelihood. The estimation procedure assumes that the hazard, µi(d), is constant within duration intervals. The interval width chosen by the analyst, of course, should be supported on both substantive and statistical grounds.

INDIRECT DEMOGRAPHIC ESTIMATION

Unfortunately, many countries around the world have poor or nonexistent data pertaining to a wide array of demographic variables. In the industrialized nations, we typically have access to data from rigorous registration systems that collect data on mortality, marriage, fertility, and other demographic processes. However, when analyzing the demographic situation of less developed nations, we are often confronted with a paucity of available data on these fundamental processes. When such data are in fact collected, they are often sufficiently

inadequate to be significantly misleading. For example, in some countries we have learned that as few as half of all actual deaths are recorded. If we mistakenly assume the value of the actual number to be the registered number, then we will substantially overestimate life expectancy in these populations. In essence, we will incorrectly infer that people are dying at a slower rate than is truly the case.

The Stable Population Model. Much demographic estimation has relied on the notion of stability. A stable population is defined as one that is established by a long history of unchanging fertility and mortality patterns. This criterion gives rise to a fixed proportionate age distribution, constant birth and death rates, and a constant rate of population growth (see, e.g., Coale 1972). The basic stable population equation is:

where c(a) is the proportion of the population exact age a, b is the crude birth rate, r is the rate of population growth, and p(a) is the proportion of the population surviving to exact age a. Various mathematical relationships have been shown to obtain among the demographic variables in a stable population. This becomes clear when we multiply both sides of the equation by the total population size. Thus, we have:

where N(a) is the number of individuals in the population exact age a and B is the current annual number of births. We can see that the number of people aged a this year is simply the product of the number of births entering the population a years ago—namely, the current number of births times a growth rate factor, which discounts the births according to the constant population growth rate, r (which also applies to the growth of the number of births over time)—and the proportion of a birth cohort that survives to be aged a today. Note that the constancy over time of the mortality schedule, p(a), and the growth rate, r, are crucial to the validity of this interpretation.

When we assume a population is stable, we are imposing structure upon the demographic relationships existing therein. In a country where data

are inadequate, indirect methods allow us—by drawing upon the known structure implied by stability—to piece together sometimes inaccurate information and ultimately derive sensible estimates of the population parameters. The essential strategy in indirect demographic estimation is to infer a value or set of values for a variable whose elements are either unobserved or inaccurate from the relationship among the remaining variables in the above equation (or an equation deriving from the one above). We find that these techniques are robust with respect to moderate departures from stability, as in the case of quasi-stable populations, in which only fertility has been constant and mortality has been gradually changing.

The Nonstable Population Model. Throughout much of the time span during which indirect estimation has evolved, there have been many countries where populations approximated stability. In recent decades, however, many countries have experienced rapidly declining mortality or declining or fluctuating fertility and, thus, have undergone a radical departure from stability. Consequently, previously successful indirect methods, grounded in stable population theory, are, with greater frequency, ill-suited to the task for which they were devised. As is often the case, necessity is the mother of invention and so demographers have sought to adapt their methodology to the changing world.

In the early 1980s, a methodology was developed that can be applied to populations that are far from stable (see, e.g., Bennett and Horiuchi

1981; and Preston and Coale 1982). Indeed, it is no longer necessary to invoke the assumption of stability, if we rely upon the following equation:

where r(x) is the growth rate of the population at exact age x. This equation holds true for any closed population, and, indeed, can be modified to accommodate populations open to migration.

The implied relationships among the age distribution of living persons and deaths, and rates of growth of different age groups, provide the basis for a wide range of indirect demographic methods that allow us to infer accurate estimates of basic

demographic parameters that ultimately can be used to better inform policy on a variety of issues. Two examples are as follows.

First, suppose we have the age distribution for a country at each of two points in time, in addition to the age distribution of deaths occurring during the intervening years. We may then estimate the completeness of death registration in that population using the following equation (Bennett and Horiuchi 1981):

where (a) is the estimated number of people at exact age a, D(x) is the number of deaths at exact age x and r(u) is the rate of the growth of the number of persons at exact age u between the two time points. By taking the ratio of the estimated number of persons with the enumerated population, we have an estimate of the completeness of death registration in the population relative to the completeness of the enumerated population. This relative completeness (in contrast to an ‘‘absolute’’ estimate of completeness) is all that is needed to determine the true, unobserved age-specific death rates, which in turn allows one to construct an unbiased life table.

A second example of the utility of the nonstable population framework is shown by the use of the following equation:

where N(x) and N(a) are the number of people exact ages x and a, respectively, and x−apa is the probability of surviving from age a to age x according to period mortality rates. By using variants of this equation, we can generate reliable population age distributions (e.g., in situations in which censuses are of poor quality) from a trustworthy life table (Bennett and Garson 1983).

MORTALITY MODELING

The field of demography has a long tradition of developing models that are based upon empirical regularities. Typically in demographic modeling, as in all kinds of modeling, we try to adhere to the

principle of parsimony—that is, we want to be as efficient as possible with regard to the detail, and therefore the number of parameters, in a model.

Mortality schedules from around the world reveal that death rates follow a common pattern of relatively high rates of infant mortality, rates that decline through early childhood until they bottom out in the age range of five to fifteen or so, then rates that increase slowly through the young and middle adult years, and finally rising more rapidly during the older adult ages beyond the forties or fifties. Various mortality models exploit this regular pattern in the data. Countries differ with respect to the overall level of mortality, as reflected in the expectation of life at birth, and the precise relationship that exists among the different age components of the mortality curve.

Coale and Demeny (1983) examined 192 mortality schedules from different times and regions of the world and found that they could be categorized into four ‘‘families’’ of life tables. Although overall mortality levels might differ, within each family the relationships among the various age components of mortality were shown to be similar.

For each family, Coale and Demeny constructed a ‘‘model life table’’ for females that was associated with each of twenty-five expectations of life at birth from twenty through eighty. A comparable set of tables was developed for males. In essence, a researcher can match bits of information that are known to be accurate in a population with the corresponding values in the model life tables, and ultimately derive a detailed life table for the population under study. In less developed countries, model life tables are often used to estimate basic mortality parameters, such as e0 or the crude death rate, from other mortality indicators that may be more easily observable.

Other mortality models have been developed, the most notable being that by Brass (1971). Brass noted that one mortality schedule could be related to another by means of a linear transformation of the logits of their respective survivorship probabilities (i.e., the vector of lx values, given a radix of one). Thus, one may generate a life table by applying the logit system to a ‘‘standard’’ or ‘‘reference’’ life table, given an appropriate pair of parameters that reflect (l) the overall level of mortality in the population under study, and (2) the relationship between child and adult mortality.

MARRIAGE, FERTILITY, AND

MIGRATION MODELS

Coale (1971) observed that age distributions of first marriages are structurally similar in different populations. These distributions tend to be smooth, unimodal, and skewed to the right, and to have a density close to zero below age fifteen and above age fifty. He also noted that the differences in age- at-marriage distributions across female populations are largely accounted for by differences in their means, standard deviations, and cumulative values at the older ages, for example, at age fifty. As a basis for the application of these observations, Coale constructed a standard schedule of age at

first marriage using data from Sweden, covering the period 1865 through 1869. The model that is applied to marriage data is represented by the following equation:

where g(a) is the proportion marrying at age a in the observed population and µ, σ, and E are, respectively, the mean and the standard deviation of age at first marriage (for those who ever marry), and the proportion ever marrying.

The model can be extended to allow for covariate effects by stipulating a functional relationship between the parameters of the model distribution and a set of covariates. This may be specified as follows:

where Xi, Yi, and Zi are the vector values of characteristics of an individual that determine, respectively, µi, σi, and Ei, and α, ß, and Y are the associated parameter vectors to be estimated.

Because the model is parametric, it can be applied to data referring to cohorts who have yet to complete their marriage experience. In this fashion, the model can be used for purposes of projection (see, e.g., Bloom and Bennett 1990).

The model has also been found to replicate well

the first birth experience of cohorts (see, e.g., Bloom 1982).

Coale and Trussell (1974), recognizing the empirical regularities that exist among age profiles of fertility across time and space and extending the work of Louis Henry, developed a set of model fertility schedules. Their model is based in part on a reference distribution of age-specific marital fertility rates that describes the pattern of fertility in a natural fertility population—that is, one that exhibits no sign of controlling the extent of childbearing activity. When fitted to an observed age pattern of fertility, the model’s two parameters describe the overall level of fertility in the population and the degree to which their fertility within marriage is controlled by some means of contraception. Perhaps the greatest use of this model has been devoted to comparative analyses, which is facilitated by the two-parameter summary of any age pattern of fertility in question.

Although the application of indirect demographic estimation methods to migration analysis is not as mature as that to other demographic processes, strategies similar to those invoked by fertility and mortality researchers have been applied to the development of model migration schedules. Rogers and Castro (1981) found that similar age patterns of migration obtained among many different populations. They have summarized these regularities in a basic eleven-parameter model, and, using Brass and Coale logic, explore ways in which their model can be applied satisfactorily to data of imperfect quality.

The methods described above comprise only a small component of the methodological tools available to demographers and to social scientists, in general. Some of these methods are more readily applicable than others to fields outside of demography. It is clear, for example, how we may take advantage of the concept of standardization in a variety of disciplines. So, too, may we apply life table analysis and nonstable population analysis to problems outside the demographic domain. Any analogue to birth and death processes can be investigated productively using these central methods. Even the fundamental concept underlying the above mortality, fertility, marriage, and migration models—that is, exploiting the power to be found in empirical regularities—can be applied fruitfully to other research endeavors.

Bennett, Neil G., Ann K. Blanc, and David E. Bloom 1988 ‘‘Commitment and the Modern Union: Assessing the Link between Premarital Cohabitation and Subsequent Marital Stability.’’ American Sociological Review 53:127–138.

Bennett, Neil G., and Lea Keil Garson 1983 ‘‘The Centenarian Question and Old-Age Mortality in the Soviet Union, 1959–1970.’’ Demography 20:587–606.

Bennett, Neil G., and Shiro Horiuchi 1981 ‘‘Estimating the Completeness of Death Registration in a Closed Population.’’ Population Index 47:207–221.

Bloom, David E. 1982 ‘‘What’s Happening to the Age at First Birth in the United States? A Study of Recent Cohorts.’’ Demography 19:351–370.

———, and Neil G. Bennett 1990 ‘‘Modeling American Marriage Patterns.’’ Journal of the American Statistical Association 85 (December):1009–1017.

Coale, Ansley J. 1972 The Growth and Structure of Human Populations. Princeton, N.J.: Princeton University Press.

——— 1971 ‘‘Age Patterns of Marriage.’’ Population Studies 25:193–214.

———, and Paul Demeny 1983 Regional Model Life Tables and Stable Populations, 2nd ed. New York: Academic Press.

Coale, Ansley J., and James Trussell 1974 ‘‘Model Fertility Schedules: Variations in the Age Structure of Childbearing in Human Populations.’’ Population Index 40:185–206.

Cox, D. R., and D. Oakes 1984 Analysis of Survival Data. London: Chapman and Hall.

Menken, Jane, James Trussell, Debra Stempel, and Ozer Babakol 1981 ‘‘Proportional Hazards Life Table Models: An Illustrative Analysis of Sociodemographic Influences on Marriage Dissolution in the United States.’’ Demography 18:181–200.

Peters, Kimberley D., Kenneth D. Kochanek, and Sherry L. Murphy 1998 ‘‘Deaths: Final Data for 1996.’’

National Vital Statistics Reports, vol. 47, no. 9. Hyattsville, Md.: National Center for Health Statistics.

Preston, Samuel H., and Ansley J. Coale 1982 ‘‘Age Structure, Growth, Attrition, and Accession: A New Synthesis.’’ Population Index 48:217–259.

Rogers, Andrei, and Luis J. Castro 1981 ‘‘Model Migration Schedules.’’ (Research Report 81–30) Laxenburg,

NEIL G. BENNETT

DEMOGRAPHIC TRANSITION

The human population has maintained relatively gradual growth throughout most of history by high, and nearly equal, rates of deaths and births. Since about 1800, however, this situation has changed dramatically, as most societies have undergone major declines in mortality, setting off high growth rates due to the imbalance between deaths and births. Some societies have eventually had fertility declines and emerged with a very gradual rate of growth as low levels of births matched low levels of mortality.

There are many versions of demographic transition theory (Mason 1997), but there is some consensus that each society has the potential to proceed sequentially through four general stages of variation in death and birth rates and population growth. Most societies in the world have passed through the first two stages, at different dates and speeds, and the contemporary world is primarily characterized by societies in the last two stages, although a few are still in the second stage.

Stage 1, presumably characterizing most of human history, involves high and relatively equal birth and death rates and little resulting population growth.

Stage 2 is characterized by a declining death rate, especially concentrated in the years of infancy and childhood. The fertility rate remains high, leading to at least moderate population growth.

Stage 3 involves further declines in mortality, usually to low levels, and initial sustained declines in fertility. Population growth may become quite high, as levels of fertility and mortality increasingly diverge.

Stage 4 is characterized by the achievement of low mortality and the rapid emergence of low fertility levels, usually near those of mortality. Population growth again becomes quite low or negligible.

While demographers argue about the details of demographic change in the past 200 years, clearcut declines in birth and death rates appeared on the European continent and in areas of overseas European settlement in the nineteenth century, especially in the last three decades. By 1900, life expectancies in ‘‘developed’’ societies such as the United States were probably in the mid-forties, having increased by a few years in the century (Preston and Haines 1991). By the end of the twentieth century, even more dramatic gains in mortality were evident, with life expectancies reaching into the midand high-seventies.

The European fertility transition of the late 1800s to the twentieth century involved a relatively continuous movement from average fertility levels of five or six children per couple to bare levels of replacement by the end of the 1930s. Fertility levels rose again after World War II, but then began another decline about 1960. Some countries now have levels of fertility that are well below long-term replacement levels.

With a few exceptions such as Japan, most other parts of the developing world did not experience striking declines in mortality and fertility until the midpoint of the twentieth century. Gains in life expectancy became quite common and very rapid in the post-World War II period throughout the developing world (often taking less than twenty years), although the amount of change was quite variable. Suddenly in the 1960s, fertility transitions emerged in a small number of societies, especially in the Caribbean and Southeast Asia, to be followed in the last part of the twentieth century by many other countries.

Clear variations in mortality characterize many parts of the world at the end of the twentieth century. Nevertheless, life expectancies in countries throughout the world are generally greater than those found in the most developed societies in 1900. A much greater range in fertility than mortality characterizes much of the world, but fertility declines seem to be spreading, including in ‘‘laggard’’ regions such as sub-Saharan Africa.

The speed with which the mortality transition was achieved among contemporary lesser-devel- oped countries has had a profound effect on the magnitude of the population growth that has occurred during the past few decades. Sweden, a

model example of the nineteenth century European demographic transition, peaked at an annual rate of natural increase of 1.2 percent. In contrast, many developing countries have attained growth rates of over 3.0 percent. The world population grew at a rate of about 2 percent in the early 1970s but has now declined to about 1.4 percent, as fertility rates have become equal to the generally low mortality rates.

CAUSES OF MORTALITY TRANSITIONS

The European mortality transition was gradual, associated with modernization and raised standards of living. While some dispute exists among demographers, historians, and others concerning the relative contribution of various causes (McKeown 1976; Razzell 1974), the key factors probably included increased agricultural productivity and improvements in transportation infrastructure which enabled more efficient food distribution and, therefore, greater nutrition to ward off disease. The European mortality transition was also probably influenced by improvements in medical knowledge, especially in the twentieth century, and by improvements in sanitation and personal hygiene.

Infectious and environmental diseases especially have declined in importance relative to cancers and cardiovascular problems. Children and infants, most susceptible to infectious and environmental diseases, have showed the greatest gains in life expectancy.

The more recent and rapid mortality transitions in the rest of the world have mirrored the

European change with a movement from infectious/environmental causes to cancers and cardiovascular problems. In addition, the greatest beneficiaries have been children and infants. These transitions result from many of the same factors as the European case, generally associated with economic development, but as Preston (1975) outlines, they have also been influenced by recent advances in medical technology and public health measures that have been imported from the high- ly-developed societies. For instance, relatively inexpensive vaccines are now available throughout the world for immunization against many infectious diseases. In addition, airborne sprays have been distributed at low cost to combat widespread

diseases such as malaria. Even relatively weak national governments have instituted major improvements in health conditions, although often only with the help of international agencies.

Nevertheless, mortality levels are still higher than those in many rich societies due to such factors as inadequate diets and living conditions, and inadequate development of health facilities such as hospitals and clinics. Preston (1976) observes that among non-Western lesser-developed countries, mortality from diarrheal diseases (e.g., cholera) has persisted despite control over other forms of infectious disease due to the close relationship between diarrheal diseases, poverty, and ignorance—and therefore a nation’s level of socioeconomic development.

Scholars (Caldwell 1986; Palloni 1981) have warned that prospects for future success against high mortality may be tightly tied to aspects of social organization that are independent of simple measures of economic well-being: Governments may be more or less responsive to popular need for improved health; school system development may be important for educating citizens on how to care for themselves and their families; the equitable treatment of women may enhance life expectancy for the total population.

Recent worldwide mortality trends may be charted with the help of data on life expectancy at age zero that have been gathered, sometimes on the basis of estimates, by the Population Reference Bureau (PRB), a highly respected chronicler of world vital rates. For 165 countries with relatively stable borders over time, it is possible to relate estimated life expectancy in 1986 with the same

figure for 1998. Of these countries, only 13.3 percent showed a decline in life expectancy during the time period. Some 80.0 percent had overall increasing life expectancy, but the gains were highly variable. Of all the countries, 29.7 percent actually had gains of at least five years or more, a sizable change given historical patterns of mortality.

An indication of the nature of change may be discerned by looking at Figure 1, which shows a graph of the life expectancy values for the 165 countries with stable borders. Each point represents a country and shows the level of life expectancy in 1986 and in 1998. Note the relatively high

levels of life expectancy by historical standards for most countries in both years. Not surprisingly, there is a strong tendency for life expectancy values to be correlated over time. A regression straight line, indicating average life expectancy in 1998 as a function of life expectancy in 1986 describes this relationship. As suggested above, the levels of life expectancy in 1998 tend to be slightly higher than the life expectancy in 1986. Since geography is highly associated with economic development, the points on the graph generally form a continuum from low to high life expectancy. African countries tend to have the lowest life expectancies, followed by Asia, Oceania, and the Americas. Europe has the highest life expectancies.

The African countries comprise virtually all the countries with declining life expectancies, probably a consequence of their struggles with acquired immune deficiency syndrome (AIDS), malnutrition, and civil disorder. Many of them have lost several years of life expectancy in a very short period of time. However, a number of the African countries also have sizeable increases in life expectancies.

Asian and American countries dominate the mid-levels of life expectancy, with the Asian countries showing a strong tendency to increase their life expectancies, consistent with high rates of economic development.

Unfortunately, Figure 1 does not include the republics of the former Soviet Union, since exactly comparable data are not available for both time points. Nevertheless, there is some consensus among experts that life expectancy has deteriorated in countries such as Russia that have made the transition from communism to economically-un- stable capitalism.

WHAT DRIVES FERTILITY RATES?

The analysis of fertility decline is somewhat more complicated analytically than mortality decline. One may presume that societies will try, if given resources and a choice, to minimize mortality levels, but it seems less necessarily so that societies have an inherent orientation toward low fertility, or, for that matter, any specific fertility level. In addition, fertility rates may vary quite widely across