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 proba- bility 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 Any generation life table that we could calculate would be very much out of date and would in no way approximate the present mortality experience of a population.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 mor- tality 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 popula- tion for a particular calendar year ( n D x ), 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 ( n P x ). To begin the life table’s construction, we take the ratio of these two sets of input data— n D x and n P x —to form a series of age-specific death rates, or n M x : DEMOGRAPHIC METHODS 615 Abridged Life Table for the United States, 1996 Exact Age x n D xn P xn q x xn d xn L x T x e x (in 1,000s) 0 28,487 3,769 .00732 100,000 732 99,370 7,611,825 76.1 1 5,948 16,516 .00151 99,268 150 396,721 7,512,455 75.7 5 3,780 19,441 .00097 99,118 96 495,329 7,115,734 71.8 10 4,550 18,981 .00118 99,022 117 494,883 6,620,405 66.9 15 14,663 18,662 .00390 98,905 386 493,650 6,125,522 61.9 20 17,780 17,560 .00506 98,519 499 491,372 5,631,872 57.2 25 20,730 19,007 .00544 98,020 533 488,766 5,140,500 52.4 30 30,417 21,361 .00710 97,487 692 485,746 4,651,734 47.7 35 42,499 22,577 .00944 96,795 914 481,820 4,165,988 43.0 40 53,534 20,816 .01283 95,881 1,230 476,549 3,684,168 38.4 45 67,032 18,436 .01801 94,651 1,705 469,305 3,207,619 33.9 50 77,297 13,934 .02733 92,946 2,540 458,779 2,738,314 29.5 55 96,726 11,362 .04177 90,406 3,776 443,132 2,279,535 25.2 60 136,999 9,999 .06649 86,630 5,760 419,530 1,836,403 21.2 65 200,045 9,892 .09663 80,870 7,814 385,659 1,416,873 17.5 70 273,849 8,778 .14556 73,056 10,634 339,620 1,031,214 14.1 75 321,223 6,873 .21060 62,422 13,146 280,047 691,594 11.1 80 342,067 4,557 .31754 49,276 15,647 207,474 411,547 8.4 85 576,541 3,762 1.00000 33,629 33,629 204,073 204,073 6.1 Table 3 SOURCE : n D x and n P x values are obtained from Peters, Kochanek, and Murphy 1998, and from the web site, http://www.cdc.gov/ nchswww/datawh/statab/unpubd/mortabs/pop6096.htm, respectively. n M x = n D x n P x ( 3 ) For each death rate, we compute the correspond- ing probability of dying within that age interval, given that one has survived to the beginning of the interval. This value, denoted by n q x , is computed using the following equation: n q x = n . n M x 1 + (n– n a x ) . n M x ( 4 ) where n a x 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 n a x = 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 interpreta- tion, the various remaining columns are defined in the following manner: l x equals the number of individuals in the life table surviving to exact age x . We arbitrarily set the number ‘‘born into’’ the life table, l o , which is otherwise known as the radix , to some value—most often, 100,000. We generate all subsequent l x values by the following equation: x + n = x . [1– n q x ] ( 5 ) n d x 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: n d x = x . n q x ( 6 ) The concept of ‘‘person-years’’ is critical to understanding life table construction. Each indi- vidual 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 dece- dent contributes some fraction of a person-year to the overall number for that cohort. n L x 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 DEMOGRAPHIC METHODS 616 and those contributed by individuals who die with- in that interval: n L x = [n . x + n ] + [ n a x . n d x ] ( 7 ) T x equals the number of person-years lived beyond exact age x : T x = ∑ n L a = T x + n + n L x ∞ a=x,n ( 8 ) e x equals the expected number of years of life remaining for an individual who has already sur- vived 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: e x = T x x ( 9 ) The n L x and T x 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 T 85 in order to begin the proc- ess. This value is derived in the following fashion: Since for this oldest age group, l 85 = ∞ d 85 (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 T 85 = ∞ L 85 , we have: ( 10 ) e 85 = = 1 85 / T 85 = 11 ∞ d 85 / ∞ L 85 T 85 85 ≈ ∞ M 85 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, e 0 , 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 l 10 / l 0 , or 0.99022. Given that one has already lived eighty years, the probability that one survives five additional years is l 85 / l 80 , 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 n L x ’s and the T x ’s in the life table. We treat them as representing the age distri- bution of a stationary population —that is, a popula- tion having long been subject to zero growth. Thus, 5 L 20 , for example, represents the number of twenty- to twenty-four-year-olds in the life table ‘‘population,’’ into which l 0 , or 100,000, individu- als are born each year. (One will note by summing the n d x 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 mor- tality 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 fifty- to fifty-four-year-olds in 2006, we would take advantage of the following relation that is assumed to hold approximately: n P x + t ≈ τ + t n P x τ n L x + t τ + t n L x τ ( 11 ) 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 fifty- to fifty-four-year-olds in 2006, 5 P 50 2006 , is simply the number of forty-to forty-four-year- olds ten years earlier, 5 P 40 1996 , multiplied by the proportion of forty- to forty-four-year-olds in the life table surviving ten years, 5 L 50 / 5 L 40 . 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 suffi- ciently 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 distribu- tion within that interval resembles closely enough the age distribution of the actual population. In other words, if the actual population’s age distri- bution within a broad age interval is significantly DEMOGRAPHIC METHODS 617 different from that within the corresponding in- terval of the life table population, then implicitly by using this projection device we are improperly weighing the component parts of the broad inter- val 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 phe- nomena, it is clear that several factors may affect whether an individual exits from a life table. Cer- tainly, it is well-established that a large number of socioeconomic variables simultaneously impinge on the marital dissolution process. In many popu- lations, 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 haz- ards 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 dissolu- tion at each marital duration, d , and we allow this duration-specific risk to depend on individual char- acteristics (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 propor- tional amount at all durations. Thus, for an indi- vidual i at duration d, with an observed set of characteristics represented by a vector of covariates, Z i , the hazard function, µ i ( d ), is given by: µ i (d) = exp [ λ (d) ] exp [Z i β ] ( 12 ) 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 Z i is multiplied by a factor equal to exp[ Z i ß ]. 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 exam- ple, 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: µ i (d) = exp [ λ (d) ] exp [Z i (d) β (d) ] ( 13 ) where λ ( d) is defined as in the proportional haz- ards model, Z i ( 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 pa- rameters can be estimated using the method of maximum likelihood. The estimation procedure assumes that the hazard, µ i ( 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 industrial- ized nations, we typically have access to data from rigorous registration systems that collect data on mortality, marriage, fertility, and other demograph- ic processes. However, when analyzing the demo- graphic 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 DEMOGRAPHIC METHODS 618 inadequate to be significantly misleading. For ex- ample, 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 substan- tially overestimate life expectancy in these popula- tions. In essence, we will incorrectly infer that people are dying at a slower rate than is truly the case. The Stable Population Model. Much demo- graphic estimation has relied on the notion of stability. A stable population is defined as one that is established by a long history of unchanging fertili- ty and mortality patterns. This criterion gives rise to a fixed proportionate age distribution, constant birth and death rates, and a constant rate of popu- lation growth (see, e.g., Coale 1972). The basic stable population equation is: c(a) = be -ra p(a) ( 14 ) 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 sta- ble population. This becomes clear when we multi- ply both sides of the equation by the total popula- tion size. Thus, we have: N(a) = Be -ra p(a) ( 15 ) 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 rela- tionships 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 esti- mates 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 mor- tality has been gradually changing. The Nonstable Population Model. Through- out much of the time span during which indirect estimation has evolved, there have been many countries where populations approximated sta- bility. 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. Con- sequently, 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 devel- oped 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: c(a) = b . exp [ - ∫ r (x) dx] . p (a) a 0 ( 16 ) 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 ac- commodate populations open to migration. The implied relationships among the age dis- tribution 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 METHODS 619 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 popula- tion using the following equation (Bennett and Horiuchi 1981): N(a) = ∫ D (x) exp [ ∫ r (u) du] dx x ∞ aa ~ ( 17 ) 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 popula- tion, 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: N (x) N (a) = x - a p a exp [ ∫ r (u) du] x a ( 18 ) where N ( x) and N ( a) are the number of people exact ages x and a , respectively, and x − a p a is the probability of surviving from age a to age x accord- ing to period mortality rates. By using variants of this equation, we can generate reliable population age distributions (e.g., in situations in which cen- suses 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 regu- lar pattern in the data. Countries differ with re- spect 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 mor- tality schedules from different times and regions of the world and found that they could be catego- rized 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 re- searcher 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 popu- lation under study. In less developed countries, model life tables are often used to estimate basic mortality parameters, such as e 0 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 proba- bilities (i.e., the vector of l x values, given a radix of one). Thus, one may generate a life table by apply- ing 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. DEMOGRAPHIC METHODS 620 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 popula- tions 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: ( 20 ) g (a) = 1.2813 exp { –1.145 ( + E σ a– µ σ 0.805) – exp[ –1.896 ( +0.805)] } a– µ σ 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 rela- tionship between the parameters of the model distribution and a set of covariates. This may be specified as follows: µ i = X i ′ α ′ σ i = Y i ′ β ′ Ε i = Z i ′ Y ′ ( 20 ) where X i , Y i , and Z i are the vector values of charac- teristics of an individual that determine, respec- tively, µ i , σ i , and E i , 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 child- bearing activity. When fitted to an observed age pattern of fertility, the model’s two parameters describe the overall level of fertility in the popula- tion and the degree to which their fertility within marriage is controlled by some means of contra- ception. 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 demo- graphic 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 ap- plied to the development of model migration sched- ules. 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 avail- able to demographers and to social scientists, in general. Some of these methods are more readily applicable than others to fields outside of demog- raphy. 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 meth- ods. 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. DEMOGRAPHIC TRANSITION 621 REFERENCES Allison, Paul D. 1984 Event History Analysis . Beverly Hills, Calif.: Sage Publications. Bennett, Neil G., Ann K. Blanc, and David E. Bloom 1988 ‘‘Commitment and the Modern Union: Assess- ing the Link between Premarital Cohabitation and Subsequent Marital Stability.’’ American Sociological Review 53:127–138. Bennett, Neil G., and Lea Keil Garson 1983 ‘‘The Cente- narian 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 Universi- ty 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 Fertili- ty Schedules: Variations in the Age Structure of Childbearing in Human Populations.’’ Population In- dex 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 Mod- els: 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 Migra- tion Schedules.’’ (Research Report 81–30) Laxenburg, Austria: International Institute for Applied Systems Analysis. N EIL G. B ENNETT 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 un- dergone 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 tran- sition 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 popula- tion 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 mortali- ty, 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. DEMOGRAPHIC TRANSITION 622 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 over- seas European settlement in the nineteenth centu- ry, 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 reach- ing into the mid- and 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 coun- tries 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 experi- ence 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 twen- ty years), although the amount of change was quite variable. Suddenly in the 1960s, fertility transi- tions emerged in a small number of societies, especially in the Caribbean and Southeast Asia, to be followed in the last part of the twentieth centu- ry 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 coun- tries 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 oc- curred during the past few decades. Sweden, a model example of the nineteenth century Europe- an 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 stan- dards 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 in- cluded increased agricultural productivity and im- provements in transportation infrastructure which enabled more efficient food distribution and, there- fore, greater nutrition to ward off disease. The European mortality transition was also probably influenced by improvements in medical knowl- edge, 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 in- fants, most susceptible to infectious and environ- mental diseases, have showed the greatest gains in life expectancy. The more recent and rapid mortality transi- tions in the rest of the world have mirrored the European change with a movement from infec- tious/environmental causes to cancers and cardio- vascular problems. In addition, the greatest bene- ficiaries have been children and infants. These transitions result from many of the same factors as the European case, generally associated with eco- nomic development, but as Preston (1975) out- lines, 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 in- expensive vaccines are now available throughout the world for immunization against many infec- tious diseases. In addition, airborne sprays have been distributed at low cost to combat widespread DEMOGRAPHIC TRANSITION 623 diseases such as malaria. Even relatively weak na- tional governments have instituted major improve- ments 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) ob- serves 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 rela- tionship between diarrheal diseases, poverty, and ignorance—and therefore a nation’s level of so- cioeconomic 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 equita- ble treatment of women may enhance life expect- ancy 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 high- ly variable. Of all the countries, 29.7 percent actu- ally 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 repre- sents a country and shows the level of life expect- ancy 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 econom- ic development, the points on the graph generally form a continuum from low to high life expectan- cy. 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, prob- ably a consequence of their struggles with ac- quired immune deficiency syndrome (AIDS), mal- nutrition, 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 coun- tries 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 deteriorat- ed 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 DEMOGRAPHIC TRANSITION 624 Life Expectancy Patterns Life Expecenty in Years, 1986 Life Expecenty in Years, 1998 50 7060 804030 30 40 50 60 70 80 90 Figure 1 societies due to factors (Bongaarts 1975) that have little relationship to conscious desires such as prolonged breastfeeding which supresses repro- ductive ovulation in women, the effectiveness of birth control methods, and the amount of involun- tary foetal abortion. As a result of these analytic ambiguities, scholars seem to have less consensus on the social factors that might produce fertility than mortality decline (Hirschman 1994; Ma- son 1997). Coale (1973), in an attempt to reconcile the diversity of circumstances under which fertility declines have been observed to occur, identified three major conditions for a major fall in fertility: 1. Fertility must be within the calculus of conscious choice. Parents must consider it an acceptable mode of thought and form of behavior to balance the advantages and disadvantages of having another child. 2. Reduced fertility must be viewed as so- cially or economically advantageous to couples. 3. Effective techniques of birth control must be available. Sexual partners must know these techniques and have a sustained will to use the them. Beyond Coale’s conditions, little consensus has emerged on the causes of fertility decline. There are, however, a number of major ideas about what causes fertility transitions that may be summarized in a few major hypotheses. A major factor in causing fertility change may be the mortality transition itself. High-mortality societies depend on high fertility to ensure their survival. In such circumstances, individual couples will maximize their fertility to guarantee that at least a few of their children survive to adulthood, to perpetuate the family lineage and to care for DEMOGRAPHIC TRANSITION 625 them in old age. The decline in mortality may also have other consequences for fertility rates. As mortality declines, couples may perceive that they can control the survival of family members by changing health and living practices such as clean- liness and diet. This sense of control may extend itself to the realm of fertility decisions, so that couples decide to calculate consciously the num- ber of children they would prefer and then take steps to achieve that goal. Another major factor may be the costs and benefits of children. High-mortality societies are often characterized by low technology in produc- ing goods; in such a situation (as exemplified by many agricultural and mining societies), children may be economically useful to perform low-skilled work tasks. Parents have an incentive to bear children, or, at the minimum, they have little incentive not to bear children. However, high- technology societies place a greater premium on highly-skilled labor and often require extended periods of education. Children will have few eco- nomic benefits and may become quite costly as they are educated and fed for long periods of time. Another major factor that may foster fertility decline is the transfer of functions from the family unit to the state. In low-technology societies, the family or kin group is often the fundamental unit, providing support for its members in times of economic distress and unemployment and for older members who can no longer contribute to the group through work activities. Children may be viewed as potential contributors to the unit, either in their youth or adulthood. In high-tech- nology societies, some of the family functions are transferred to the state through unemployment insurance, welfare programs, and old age retire- ment systems. The family functions much more as a social or emotional unit where the economic benefits of membership are less tangible, thus decreasing the incentive to bear children. Other major factors (Hirschman 1994; Mason 1997) in fertility declines may include urbaniza- tion and gender roles. Housing space is usually costly in cities, and the large family becomes un- tenable. In many high-technology societies, wom- en develop alternatives to childbearing through employment outside their homes, and increasing- ly assert their social and political rights to partici- pate equally with men in the larger society. Be- cause of socialization, men are generally unwilling to assume substantial child-raising responsibilities, leaving partners with little incentive to participate in sustained childbearing through their young adult lives. No consensus exists on how to order these theories in relative importance. Indeed, each theo- ry may have more explanatory power in some circumstances than others, and their relative im- portance may vary over time. For instance, de- clines in mortality may be crucial in starting fertili- ty transitions, but significant alterations in the roles of children may be key for completing them. Even though it is difficult to pick the ‘‘best’’ theory, every country that has had a sustained mortality decline of at least thirty years has also had some evidence of a fertility decline. Many countries seem to have the fertility decline precondition of high life expectancy, but fewer have achieved the possible preconditions of high proportions of the population achieving a secondary education. EUROPEAN FERTILITY TRANSITION Much of what is known about the process of fertility transition is based upon research at Prince- ton University (known as the European Fertility Project) on the European fertility transition that took place primarily during the seventy-year peri- od between 1870 and 1940. Researchers used aggregate government-collected data for the nu- merous ‘‘provinces’’ or districts of countries, typi- cally comparing birth rates across time and provinces. In that almost all births in nineteenth-century Europe occurred within marriage, the European model of fertility transition was defined to take place at the point marital fertility was observed to fall by more than 10 percent (Coale and Treadway 1986). Just as important, the Project scholars iden- tified the existence of varying levels of natural fertility (birth rates when no deliberate fertility control is practiced) across Europe and through- out European history (Knodel 1977). Comparative use of natural fertility models and measures de- rived from these models have been of enormous use to demographers in identifying the initiation and progress of fertility transitions in more con- temporary contexts. DEMOGRAPHIC TRANSITION 626 Most scholars have concluded that European countries seemed to start fertility transitions from very different levels of natural fertility but moved at quite similar speeds to similar levels of con- trolled fertility on the eve of World War II (Coale and Treadway 1986). As the transition progressed, areal differences in fertility within and across coun- tries declined, while the remaining differences were heavily between countries (Watkins 1991). Although some consensus has emerged on descriptive aspects of the fertility transition, much less agreement exists on the social and economic factors that caused the long-term declines. Early theorists of fertility transitions (Notestein 1953) had posited a simple model driven by urban-indus- trial social structure, but this perspective clearly proved inadequate. For instance, the earliest de- clines did not occur in England, the most urban- industrial country of the time, but were in France, which maintained a strong rural culture. The simi- larity of the decline across provinces and countries of quite different social structures also seemed puzzling within the context of previous theorizing. Certainly, no one has demonstrated that varia- tions in the fertility decline across countries, either in the timing or the speed, were related clearly to variations in crude levels of infant mortality, litera- cy rates, urbanization, and industrialization. Oth- er findings from recent analysis of the European experience include the observation that in some instances, reductions in fertility preceded reduc- tions in mortality (Cleland and Wilson 1987), a finding that is inconsistent with the four-stage theory of demographic transition. The findings of the European Fertility Project have led some demographers (Knodel and van de Walle 1979) to reformulate ideas about why fertili- ty declined. They suggest that European couples were interested in a small family well before the actual transition occurred. The transition itself was especially facilitated by the development of effective and cheap birth control devices such as the condom and diaphragm. Information about birth control rapidly and widely diffused through European society, producing transitions that seemed to occur independently of social structural factors such as mortality, urbanization, and educational attainment. In addition, these scholars argue that ‘‘cultural’’ factors were also important in the de- cline. This is based on the finding that provinces of some countries such as Belgium differed in their fertility declines on the basis of areal religious composition (Lesthaeghe 1977) and that, in other countries such as Italy, areal variations in the nature of fertility decline were related to political factors such as the Socialist vote, probably reflect- ing anticlericalism (Livi-Bacci 1977). Others (Lesthaeghe 1983) have also argued for ‘‘cultural’’ causes of fertility transitions. While the social causes of the European fertili- ty transition may be more complex than originally thought, it may still be possible to rescue some of the traditional ideas. For instance, mortality data in Europe at the time of the fertility transition were often quite incomplete or unreliable, and most of the studies focused on infant (first year of life) mortality as possible causes of fertility decline. Matthiessen and McCann (1978) show that mor- tality data problems make some of the conclusions suspect and that infant mortality may sometimes be a weak indicator of child survivorship to adult- hood. They argue that European countries with the earliest fertility declines may have been charac- terized by more impressive declines in post-infant (but childhood) mortality than infant mortality. Conclusions about the effects of children’s roles on fertility decline have often been based on rates of simple literacy as an indicator of educa- tional system development. However, basic litera- cy was achieved in many European societies well before the major fertility transitions, and the ma- jor costs of children would occur when secondary education was implemented on a large scale basis, which did not happen until near the end of the nineteenth century (Van de Walle 1980). In a time- series analysis of the United States fertility decline from 1870 to the early 1900s, Guest and Tolnay (1983) find a nearly perfect tendency for the fertili- ty rate to fall as the educational system expanded in terms of student enrollments and length of the school year. Related research also shows that edu- cational system development often occurred some- what independently of urbanization and industri- alization in parts of the United States (Guest 1981). An important methodological issue in the study of the European transition (as in other transitions) is how one models the relationship between social structure and fertility. Many of the research re- ports from the European Fertility Project seem to assume that social structure and fertility had to be DEMOGRAPHIC TRANSITION 627 closely related at all time points to support various theories about the causal importance of such fac- tors as mortality and children’s roles, but certain lags and superficial inconsistencies do not seem to prove fundamentally that fertility failed to respond as some of the above theories would suggest. The more basic question may be whether fertility even- tually responded to changes in social structure such as mortality. Even after admitting some problems with pre- vious traditional interpretations of the European fertility transition, one cannot ignore the fact that the great decline in fertility occurred at almost the same time as the great decline in mortality and was associated (even if loosely) with a massive process of urbanization, industrialization, and the expan- sion of educational systems. FERTILITY TRANSITIONS IN THE DEVELOPING WORLD The great majority of countries in the developing world have undergone some fertility declines in the second half of the twentieth century. While the spectacularly rapid declines (Taiwan, South Ko- rea) receive the most attention, a number are also very gradual (e.g. Guatemala, Haiti, Iraq, Cambo- dia), and a number are so incipient (especially in Africa) that their nature is difficult to discern. The late twentieth century round of fertility transitions has occurred in a very different social context than the historical European pattern. In the past few decades, mortality has declined very rapidly. National governments have become very attuned to checking their unprecedented national growth rates through fertility control. Birth con- trol technology has changed greatly through the development of inexpensive methods such as the intrauterine device (IUD). The world has become more economically and socially integrated through the expansion of transportation and developments in electronic communications, and ‘‘Western’’ prod- ucts and cultural ideas have rapidly diffused throughout the world. Clearly, societies are not autonomous units that respond demographically as isolated social structures. Leaders among developing countries in the process of demographic transition were found in East Asia and Latin America, and the Carribbean (Coale 1983). The clear leaders among Asian na- tions, such as South Korea and Taiwan, generally had experienced substantial economic growth, rap- id mortality decline, rising educational levels, and exposure to Western cultural influences (Freed- man 1998). By 1998, South Korea and Taiwan had fertility rates that were below long-term replace- ment levels. China also experienced rapidly declin- ing fertility, which cannot be said to have causes in either Westernization or more than moderate eco- nomic development, with a life expectancy esti- mated at seventy-one years and a rate of natural increase of 1.0 percent (PRB 1998). Major Latin American nations that achieved substantial drops in fertility (exceeding 20 per- cent) in recent decades with life expectancies sur- passing sixty years include Argentina, Brazil, Chile, Columbia, the Dominican Republic, Jamaica, Mexi- co, and Venezuela. All of these have also experi- enced substantial changes in mortality, education, or both, and economic development. Unlike the European historical experience, fertility declines in the post-1960 period have not always sustained themselves until they reached near replacement levels. A number of countries have started declines but then leveled off with three or four children per reproductive age wom- an. For instance, Malaysia was considered a ‘‘mira- cle’’ case of fertility decline, along with South Korea and Taiwan, but in recent years its fertility level has stabilized somewhat above the replace- ment level. Using the PRB data for 1986 and 1998, we can trace recent changes for 166 countries in estimat- ed fertility as measured by the Total Fertility Rate (TFR), an indicator of the number of children typically born to a woman during her lifetime. Some 80.1 percent of the countries showed de- clines in fertility. Of all the countries, 37.3 percent had a decline of at least one child per woman, and 9.0 percent had a decline of at least two children per woman. The region that encompasses countries hav- ing the highest rates of population growth is sub- Saharan Africa. Growth rates generally exceed 2 percent, with several countries having rates that clearly exceed 3 percent. This part of the world has been one of the latest to initiate fertility declines, but in the 1986–1998 period, Botswana, Kenya, DEMOGRAPHIC TRANSITION 628 and Zimbabwe all sustained fertility declines of at least two children per woman, and some neighbor- ing societies were also engaged in fertility transi- tion. At the same time, many sub-Saharan coun- tries are pre-transitional or only in the very early stages of a transition. Of the twenty-five countries that showed fertility increases in the PRB data, thirteen of them were sub-Saharan nations with TFRs of at least 5.0. In general, countries of the Middle East and regions of Northern Africa populated by Moslems have also been slow to embark on the process of fertility transition. Some (Caldwell 1976) found this surprising since a number had experienced substantial economic advances and invited the benefits of Western medical technology in terms of mortality reduction. Their resistance to fertility transitions had been attributed partly to an alleged Moslem emphasis on the subordinate role of wom- en to men, leading them to have limited alterna- tives to a homemaker role. However, the PRB data for 1986–1998 indicate that some of these coun- tries (Algeria, Bangladesh, Jordan, Kuwait, Moroc- co, Syria, Turkey) are among the small number that achieved reduction of at least two children per woman. The importance of the mortality transition in influencing the fertility transition is suggested by Figure 2. Each dot is a country, positioned in terms of graphical relationship in the PRB data between life expectancy in 1986 and the TFR in 1998. The relationship is quite striking. No country with a life expectancy less than fifty has a TFR below 3.0. Remember that before the twentieth century, vir- tually all countries had life expectancies below fifty years. In addition, the figure shows a very strong tendency for countries with life expectancies above seventy to have TFRs below 2.0. For a number of years, experts on population policy were divided on the potential role of contra- ceptive programs in facilitating fertility declines (Davis 1967). Since contraceptive technology has become increasingly cheap and effective, some (Enke 1967) argue that modest international ex- penditures on these programs in high-fertility coun- tries could have significant rapid impacts on re- production rates. Others (Davis 1967) point out, however, that family planning programs would only permit couples to achieve their desires, which may not be compatible with societal replacement level fertility. The primary implication was that family planning programs would not be effective without social structures that encouraged the small family. A recent consensus on the value of family planning programs relative to social structural change seems to have emerged. Namely, family planning programs may be quite useful for achiev- ing low fertility where the social structure is consis- tent with a small family ideal (Mauldin and Berelson 1978). While the outlook for further fertility declines in the world is good, it is difficult to say whether and when replacement-level fertility will be achieved. Many, many major social changes have occurred in societies throughout the world in the past half- century. These changes have generally been unprecented in world history, and thus we have little historical experience from which to judge their impact on fertility, both levels and speed of change (Mason 1997). Some caution should be excercised about fu- ture fertility declines in some of the societies that have been viewed as leaders in the developing world. For instance, in a number of Asian socie- ties, a strong preference toward sons still exists, and couples are concerned as much about having an adequate number of sons survive to adulthood as they are about total sons and daughters. Since pre-birth gender control is still difficult, many couples have a number of girl babies before they are successful in bearing a son. If effective gender control is achieved, some of these societies will almost certainly attain replacement-level fertility. In other parts of the world such as sub-Saharan Africa, the future of still-fragile fertility transitions may well depend on unknown changes in the organization of families. Caldwell (1976), in a widely respected theory of demographic transition that incorporates elements of both cultural innovation and recognition of the role of children in tradi- tional societies in maintaining net flows of wealth to parents, has speculated that the traditional ex- tended kinship family model now predominant in the region facilitates high fertility. Families often form economic units where children are impor- tant work resources. The extended structure of the household makes the cost of any additional member low relative to a nuclear family structure. Further declines in fertility will depend on the DEMOGRAPHIC TRANSITION 629 Mortality and Fertility Life Expecenty in Years, 1986 Total Fertility Rate, 1998 50 7060 804030 1 2 3 4 5 6 7 8 Figure 2 degree to which populations adopt the ‘‘
