Some demographic consequences of changing cohort fertility patterns: An investigation using the Gompertz function

Abstract In this paper are formulated some convenient summary measures of fertility patterns. These measures, which are based on the Gompertz function, are total lifetime fertility, median age of mothers at childbirth, and inter-quartile range of age of mothers at childbirth. Estimates of the parameters of Gompertz function, based on Canadian data, are used to derive, for each of the summary measures, values which reflect historical fertility experience, and thus give an impression about the range of realistic values for these measures. A simple model of demographic activity which includes the Gompertz function is also considered, and this model is used in computer simulation experiments to determine the macro-demographic effects of changes in each of the three summary measures.     

On the pattern of cohort fertility

Abstract An examination of the patterns of cohort fertility rates in a number of populations revealed the existence of a common pattern showing how mean family sizes of the different age-at-marriage groups of a given marriage cohort are built up over the reproductive span. Standard schedules of fertility patterns are generated by the use of the Gompertz function which defines the distribution of cumulative fertility rates of a given marriage cohort by marriage duration by means of only three parameters. The generated system is tested with the historical series for England and Wales and Sweden and is found adequate to describe widely different childbearing patterns. Some of the demographic implications of the existence of common fertility patterns are examined and the usefulness of the generated system in projecting future fertility trends is briefly discussed.     

Education and survival: Birth cohort,period, and age effects

Previous studies have found that educational differences in mortality are weaker among the elderly. In this study I examine whether either cohort or period effects may have influenced the interpretation of age effects. Six 10-year birth cohorts are followed over 30 years through decennial censuses. Differential survival is inferred from changes in the relative proportions of a cohort in each education category as the cohort ages. In cross-section, younger persons generally show stronger education effects on survival, although this pattern is clearer for women than for men. There is evidence of period effects. Within cohorts, relative survival tends to increase with age.     

Intergenerational patterns of teenage fertility

One of the frequently cited consequences of teen childbearing is the repetition of early births across generations, which thereby perpetuates a cycle of poverty and disadvantage. We use data from the 1988 National Survey of Family Growth (NSFG), Cycle IV, to examine trends and determinants of the intergenerational teen fertility link for women who reached adolescence between the 1950s and the 1980s. We find that daughters of both white and black teen mothers face significantly higher risks of teen childbearing than daughters of older mothers. We also find, more generally, that patterns of teenage family formation (i.e., both marriage and childbearing behaviors) tend to be repeated intergenerationally. The results suggest that the intrafamily propensity for early childbearing is not inherited biologically, at least not through factors related to the timing of puberty. Rather, the intergenerational patterns appear to operate at least in part through the socioeconomic and family context in which children grow up.     

Age,period, and cohort effects in demography: a review

This paper considers only the vital events of demographic measurement, the factors influencing the rate at which those events occur and then investigates the consequences of patterns of these events. It reviews the state of the art of age, period and cohort analysis for demographic dependent variables. Major examples of such analyses are given in both mortality and fertility studies. In the area of mortality the conventional approach to such analysis apears to be well suited to a wide range of applications yielding useful results. The reasons for this suitability are: early childhood experience is important in many major disease and death processes, so that cohorts are legitimately viewed as acquiring early on a certain fixed susceptibility; data sometimes stretch back far enough that stationary standards of age patterns can be developed empirically, and applied to later experience; and, logarithmic or logistic transformations linearize comparisons of age schedules or mortality so that standard statistical procedures are suitable. Applications of age, period, and cohort analysis are not always routine; external constraints are required, in the form of theoretically based and mathematically expressed age patterns of mortality, in order to distinguish effectively between period and cohort effects. A set of models of age patterns of mortality that are based on cohort as well as period experience could be constructed with useful applications. With fertility analysis the conventional approach is much less suitable. Once goal directed behavior is introduced, empirical examinations must be based on theories or assumptions about how such goals are formulated and pursued. Conventional analysis might suffice only if one is prepared to accept the assumption that all pertinent goals and strategies are formulated before the initiation of childbearing and remain unaffected by subsequent events. This assumption is untenable for modern developed populations and the forms of analysis appropriate to age period cohort investigations of fertility will have to develop along with theories of reproductive behavior.     

Timing effects and the interpretation of period fertility

Low fertility levels and later childbearing in many developed countries have reinvigorated the debate between period and cohort perspectives on fertility and on the meaningfulness of the period total fertility rate (TFR). Here, fertility-timing effects are defined as level changes in period fertility that do not reflect level changes in the completed fertility of cohorts. That definition leads to the average cohort fertility (ACF) as a measure of period fertility adjusted for timing effects. In an influential paper, Bongaarts and Feeney (1998) presented an alternative approach and a different measure, TFR*, to adjust for timing effects. Here, the two measures are compared. In the context of model populations, the ACF performs well, reflecting an average of the fertility of the active cohorts. The Bongaarts-Feeney TFR*, however, is frequently unreliable and can be erratic when there are cycles in period timing. When applied to twentieth-century U.S. experience, the TFR* behaves like a period measure and yields adjustments that are often wide of the mark. The ACF shows the stability associated with cohort measures and quantifies the substantial impact that timing effects had during the "birth dearth" of the 1970s. The period TFR reached a low of 1.74 in 1976, but the ACF never went below 2.06 during the 1970s.     

Age patterns of chinese marital fertility, 1950–1981

Coale and Trussell’s model of marital fertility is used to analyze data from China’s National One-per-Thousand Fertility Survey. Rural China experienced a regime of natural fertility until 1970, after which levels of fertility control rose with unprecedented speed and with an age pattern starkly dissimilar from that observed in other populations. Urban marital fertility was apparently under a modest level of deliberate control in the 1950s, with a sustained rise in control beginning in 1963. Natural fertility was low relative to other populations, with the urban level exceeding the rural.     

Forecasting cohort incomplete fertility: A method and an application

Drawing on insights from previous work on fertility forecasts, we develop a method for forecasting incomplete cohort fertility. Our approach involves two basic steps. First, we use a singular-value-decomposition (SVD) model to establish a relationship between the level and the age pattern of fertility for completed cohorts. This relationship is then applied to incomplete cohorts to obtain forecast fertility. We propose techniques to evaluate model assumptions and illustrate our method using cohort data from Canada, the USA, Norway, and Japan. With the exception of Japan, our results show that the model fits the data well, and that the youngest cohort whose total fertility can be reliably forecast is age 25 for Canada, the USA, and Norway. Our method is less applicable to Japan, where the youngest cohort whose total fertility could be forecast was age 35 or older. We discuss the limitations of our method in the context of model assumptions.     

A sequential probability model of fertility patterns

The present paper analyses the fertility histories of a sample of women within a stochastic framework. Recognising the sequential nature of reproductive decisions, the probability that a birth will occur at any given date is related to the realisations of past decisions and to all new information accrued since the last decision date, as well as to the characteristics of the potential mother. Time series are combined with survey data to provide information about the changing economic environment facing all women in the sample. The results of the analysis show the effects of wage rates, child benefits and various personal characteristics on birth probability profiles. The conclusions of the econometric analysis are related to existing theory and to the results of other empirical studies of the economic factors affecting the timing and spacing of births.Thanks are due to Ermisch, Jurgen Doornik and anonymous referees for helpful comments, to Mrs Su Spencer for careful typing and also to the ESRC Data Archive for making available the data. All errors are, of course, ours.     

Marriage patterns and fertility of the world population]

Marriage patterns of the world population may be divided into two major categories; i.e., the traditional marriage pattern, and the European marriage pattern. Characteristics of the traditional marriage pattern are: early marriage, a high percentage of married people, and a low percentage of people who remain single during their lifetime. Characteristics of the European marriage pattern include: late marriage and a higher percentage of females who do not marry in their lifetime. In most parts of Asia and Africa and some Latin American countries, the traditional marriage pattern is dominant, and the birth rate in these countries has remained very high. Most countries in Europe show the characteristics of the European marriage pattern, and the fertility rate in these countries is comparatively low. Some other countries, such as Sri Lanka, are in a process of transformation in their marriage pattern, and their fertility level also shows a transition from a high fertility rate to a lower fertility rate. There is a close relationship between marriage patterns and the level of fertility.     

Religion and fertility in the United States: New patterns

In the United States, the baby boom-era pattern of high Catholic and low Protestant fertility has ended. Among non-Hispanic whites in the 1980s, Catholic total fertility rates (TFRs) were about one-quarter of a child lower than Protestant rates (1.64 vs. 1.91). Most of the Protestant-Catholic difference is related to later and less frequent marriage among Catholics. Future research on the demography of religious groups should focus on explaining the delayed marriage pattern of Catholics, the high fertility of Mormons and frequently attending Protestants, and the very low fertility of those with no religious affiliation.     

Proximate determinants of Philippine fertility: 1983 levels and patterns

Data from the 1983 National Demographic Survey are used to analyze the proximate determinants of Philippine fertility in each of the 3 stages of family formation and to identify all of the direct and indirect factors affecting fertility levels and trends. 10,843 ever-married women and 12,771 children were included. The analysis pertains first to the starting patterns of family formation, the age at first birth, and the proximate determinants (age at menarche, age at first marriage/union, conception before first birth, fetal wastage first birth, interval between first marriage and first birth). Further analysis examines birth spacing patterns including the postpartum nonsusceptible period, the exposure interval and stopping patterns. Almost all births occur within marriage, and childbearing begins late at 22.5 years. However, 15.4% of first births are conceived premaritally. The mean age at first birth increases from younger to older cohorts. Urban women were slightly older (23.0 years) at the birth of their first child. Those with education below the 4th grade had first births 3.5 years earlier. Contraceptive use was low at 1.8% before first birth. Younger cohorts were more likely to use birth control and urban wives were more likely to use it than rural wives. 6.4% reported a first pregnancy ending in nonlive births, which were primarily spontaneous abortions (5.2%), stillbirths (1.0%), and induced abortions (.2%). 5.8% report never having been pregnant and 1.1% never having given birth to a live-born child. 20.4% were childless between the ages of 15-24 years, and 4.6% between 25-34 years. Childlessness was slightly higher among urban women (7.1%) than rural women (6.7%). A decreasing age at menarche has appeared; i.e., 13.6 years for the cohort 15-24 years, and 14.0 for the oldest cohort. By age 15, 82.9% had begun menstruating. The mean age at marriage is early at 20.7 years, and older cohorts tended to marry later at 21.4 years. Urban women marry a year later (21.4 years) than rural women. Lower educated women marry 4 years earlier. The mean length between first marriage and first birth was 18.4 months. In the younger cohorts, spacing patterns are shorter. Postpartum susceptibility is short. Return to sexual relations after a birth occurred at 2.8 months. The exposure time required to conceive is fairly long at 16.6 months and is attributed to contraceptive use, since coital frequency is high and temporary separation is infrequent. The average age at last birth is late at 37.6 years.     

A cohort perspective of the effect of unemployment on fertility

This work offers an explanation for the apparent contradiction between empirical work that finds a negative relationship between unemployment and fertility, and theoretical work that emphasizes the lower opportunity cost of childbearing while unemployed. I reconcile these perspectives by distinguishing between two forms of unemployment. The first form is structural unemployment, while the second form is cyclical unemployment, a less permanent component of unemployment that is linked to the economic cycle. I apply a cohort-based model to study both effects over the life cycle using panel data methods applied to a sample of developed countries. My results show that higher levels of structural unemployment decrease fertility, but that the effects of cyclical variations in unemployment depend to a large extent on the age at which they are experienced. Cyclical reductions in the unemployment level mostly result in increases in fertility rates. However, for some age groups, positive variations in the cyclical component of unemployment can also have a positive impact on fertility.     

Family limitation and the fertility transition: Evidence from the age patterns of fertility in Europe and Asia

Summary The age patterns of marital fertility levels and decline in modern Asia and historical Europe are analysed in order to answer two questions: (1) How closely do the age patterns of marital fertility in both areas prior to a systematic fertility decline conform to the age pattern of natural fertility? (2) How similar are the age patterns of the fertility transition experienced in Europe in the past, and the age pattern of fertility decline now under way in a number of Asian populations? The answers have important implications for our understanding of the fertility transition. They suggest that modern family limitation (i.e. parity-specific fertility control) was largely absent prior to a secular decline in marital fertility in both Europe and Asia. Furthermore, the evidence indicates that once the practice of family limitation starts to spread among the broader strata of the population, it seems almost inevitably to increase until it becomes a common behavioural norm. In this respect, the modern fertility transition appears to result from the spread of innovative behaviour and cannot be viewed simply as an adjustment to new socio-economic circumstances based on previously established behavioural mechanisms.     

Relationships between period and cohort life expectancy: gaps and lags

This paper offers an empirical and analytic foundation for regarding period life expectancy as a lagged indicator of the experience of real cohorts in populations experiencing steady improvement in mortality. We find that current period life expectancy in the industrialized world applies to cohorts born some 40-50 years ago. Lags track an average age at which future years of life are being gained, in a sense that we make precise. Our findings augment Ryder's classic results on period-cohort translation.     

Relationships between period and cohort life expectancy: Gaps and lags

This paper offers an empirical and analytic foundation for regarding period life expectancy as a lagged indicator of the experience of real cohorts in populations experiencing steady improvement in mortality. We find that current period life expectancy in the industrialized world applies to cohorts born some 40–50 years ago. Lags track an average age at which future years of life are being gained, in a sense that we make precise. Our findings augment Ryder's classic results on period–cohort translation.     

Low fertility due to delay in -- not dearth of -- births

Population Council demographer John Bongaarts and his colleague Griffith Feeney argue that recent concern about a lack of births overlooks the fact that many women in developed countries are simply choosing to bear children later than women used to. So-called birth dearths are often caused by temporary delays in childbearing. The two demographers have designed a new way for demographers to account for the timing, or tempo, of childbearing in estimates of fertility. Their tempo-adjusted total fertility rate (TFR) allows demographers to correct skewed fertility trends, such as those leading to projections of birth dearths. The new measure provides a better indication of women's true propensity to bear children. Standard measures of fertility are distorted by changes in tempo. Such changes occur when large numbers of couples delay or accelerate their initiation of family building. The authors used historical data and theoretical arguments to validate the tempo-adjusted TFR, which improves upon the two common measures of fertility. Flaws in the TFR and the completed fertility rate (CFR) are corrected by Bongaarts and Feeney's new measure. To demonstrate their new tool, they examined the below-replacement fertility seen in recent decades in the US. By the mid-1990s, the TFR in almost every developed country had fallen below the replacement level of 2.1 births/woman, and in Italy, Spain, and Germany it fell below 1.5. If such fertility persists, declining population size, extreme population aging, and financial pressure upon social security systems may result. However, if fertility preferences hold at current levels, the very low fertility rates observed in the developed world will approach 2 children/couple.