What is natural fertility? The remodeling of a concept

This paper applies three log-linear models to Louis Henry's original 1961 natural fertility data in order to test various assumptions leading to ways of obtaining a standard natural fertility schedule through explicit modeling. "The models specify that births follow an independent Poisson distribution for each age interval of each population. All parameters are estimated through an iterative maximum-likelihood procedure." The author suggests that the model selected provides better estimates of the standard natural fertility function than previous models.     

A method of estimating the time of marital fertility decline and associated parameters

Significant research attention has been given to historical patterns of marital fertility transitions in currently industrialized countries. Specifically, studies consider the time of the onset of fertility decline and its distribution among populations or population subgroups; the distribution of pre-decline parital fertility levels; and/or the rate of marital fertility decline. Analyses of pre-decline fertility level and its rate of decline, however, depend upon the procedure used to estimate the time of fertility decline. The Princeton European Fertility Project is the most prominent historical fertility study ever conducted. The procedure employed to estimate the timing parameter in these Princeton studies is described. An alternative statistical procedure is then proposed for detecting the onset of the transition from high to low marital fertility; the method may also be used to find the termination point of decline where the sequence of fertility variables is long enough. Both methods produce maximum likelihood least squares estimates, but the form proposed in the text has conceptual advantages.     

A comparison and latent variable test of two fertile ideas

Perhaps the two most important recent strands in the economics of fertility have been developed by Becker and Easterlin. Both suggest possible biases due to unobserved variables. Becker earlier emphasized changing shadow prices for child quantity and quality and, more recently, intergenerational serially-correlated endowments, all with given preferences. Easterlin has focused on intergenerational serially-correlated preferences. Some demographers have suggested that the Becker and Easterlin approaches are converging and may not be identified from each other.We demonstrate that while the Becker endowment and Easterlin taste models can be expressed in terms of the same variables, it is possible to identify each of the models because of different signs in a latent variable system that uses information from individuals, siblings, and cousins. Estimates of this model are consistent with the Easterlin, but not the Becker formulation. But neither model results in significant income coefficient estimates.The authors thank NIH for research support and Alan Mathios for excellent research assistance. The usual disclaimer applies.     

Accounting for dynamic selection bias in educational transitions: The Cameron-Heckman latent class estimator and its generalizations

The sequential logit model of educational transitions has long been the dominant modeling framework for the study of inequality of educational opportunity ever since the seminal works of [Mare, 1980] and [Mare, 1981]. But conventional applications of the model are known to be biased by the ubiquitous presence of unobserved heterogeneity. Cameron and Heckman (1998) propose a logit model that allows for two or three latent classes if the selection bias is solely generated by a person-specific component of stable unobserved heterogeneity. To evaluate the latent class logit regression estimator, this study makes use of simulated data to eliminate the influences of other problems of transition modeling. The simulation is based on five independent pairs of large samples generated from standard distributional assumptions of transition modeling. The new estimator appears to be an effective way to adjust for dynamic selection bias when family background effects are transition-invariant and sample size is in the order of ten thousand or above. By contrast, the conventional sequential logit model produces results that are very different from the data generating models. This study also considers two alternative ways to improve statistical efficiency: (1) incorporate a crude indicator of stable unobserved heterogeneity; (2) pool the effect estimates across transitions, background variables, and alternative estimators to smooth out noise under the null hypothesis of transition invariance. In addition, this study examines the impact of indicator reliability and sample size on the performance of the latent class regression models and suggests practical guidelines.     

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.     

The determinants of marital fertility in the united states, 1968–1970: Inferences from a dynamic model

Criticizing the static assumptions of previous socioeconomic and microeconomic models of marital fertility, particularly regarding the sequential and stochastic facets of family building, this paper advocates a dynamic perspective. Of particular concern is the assumption of equilibrium family size made by those who employ the static perspective. The equilibrium family size assumption implies that the parameters relating social and economic variables to fertility will be similar for all births, regardless of order. To test this assumption of constancy, a two-equation model of fertility and female employment is introduced. Contrary to the static perspective’s implication of constant effects, substantial parity differences in the estimates of parameters for both equations are reported, as are several differences between blacks and whites. On the basis of this evidence, I conclude that the static decision-making framework should be replaced by a dynamic approach to marital fertility.     

Modeling household fertility decisions with generalized Poisson regression

This paper models household fertility decisions by using a generalized Poisson regression model. Since the fertility data used in the paper exhibit under-dispersion, the generalized Poisson regression model has statistical advantages over both standard Poisson and negative binomial regression models, and is suitable for analysis of count data that exhibit either over-dispersion or under-dispersion. The model is estimated by the method of maximum likelihood. Approximate tests for the dispersion and goodness-of-fit measures for comparing alternative models are discussed. Based on observations from the Panel Study of Income Dynamics of 1989 interviewing year, the empirical results support the fertility hypothesis of Becker and Lewis (1973). Received January 7, 1997 /Accepted April 3, 1997     

Population Density is a Key Factor in Declining Human Fertility

In studying the complex determinants of human fertility, social scientists have given little attention to population density, although reproduction has been shown to be density-dependent for a wide variety of other species. Using fixed effects models on the time series of 145 countries and controlling for key social and economic variables, we find a consistent and significant negative relationship between human fertility and population density. Moreover, we find that individual fertility preferences also decline with population density. These findings suggest that population density should be included as a variable in future studies of fertility determinants.

Cointegration modeling of fertility in the United States

This paper presents estimates of a multiple time series model of fertility, female labor force participation, women's wages, and the relative cohort size of younger to older adult males. Cointegration methods permit modeling of these nonstationary variables, yielding estimates of the long-run relation among the variables, and the dynamic response of each variable to displacements from the steady state. The estimated steady state relation between fertility and the other variables is consistent with economic models of fertility, with fertility negatively related to female wages and male relative cohort size. Fertility responds to cohort size in a manner that is consistent with Easterlin's relative income model of household behavior. Finally, both female labor market variables adjust significantly to departures from the steady state relation, implying that they cannot be treated as exogenous in time series models of fertility.     

The effects of teenage fertility on young adult childbearing

Numerous studies of fertility behavior find that an early age at first birth increases the rate of subsequent childbearing. Typically, however, these studies do not account for the possibility of serial correlation in the unobserved determinants of fertility. Using 1979–1992 individual-level data from the National Longitudinal Survey of Youth, this paper employs the Method of Simulated Moments to estimate panel probit models of annual birth outcomes. The panel probit models account for several alternative sources of serial correlation. Estimation reveals that once serial correlation is taken into account, the subsequent fertility effects of early childbearing are either statistically eliminated or reversed. JEL classification: J13 Received March 3, 1995 / Accepted February 23, 1996     

Determinants of Korean Birth Intervals: The Confrontation of Theory and Data

In this analysis, data from the Korean National Fertility Survey of 1974 are used to seek to explain differences in the pace of fertility in terms of differences in contraception, breastfeeding and other intermediate variables. Strong effects are found for these variables, particularly contraception. Nonetheless, virtually none of the effects of the socio-economic variables can be explained in our full model. Overall, our first models, which included only the socio-economic variables, contained 44 significant coefficients. With the introduction of the intermediate variables, only eleven of these coefficients became non-significant (while six others became significant). Thus, though using excellent data, we cannot begin to reproduce what theory predicts. The analysis suggests that this is a consequence of both measurement error and omitted intermediate variables, such as coital frequency. There are strong theoretical reasons for attempting to elucidate the mediating role of proximate variables by using individual data. Nonetheless, these findings, together with similar results obtained by others, strongly suggest that this is not likely to be a fruitful line of future endeavour.     

Parental underinvestment: A link in the fertility-mortality continuum

Selective parental investment in siblings has been used to describe differential mortality rates. Using data from 986 Filipino women who had an average of 4.8 live births, a LISREL and six sets of regression models support the hypothesis that fertility is linked to underinvestment and that mortality, as a consequence, is linked to high birth order. The analysis also identifies intervening factors associated with this relationship. Age of mother at childbirth showed a strong influence on the relationship of birth order and infant and child mortality; correlations are stronger among older than youger mothers. However, even after the effect of age of mother at childbirth was partialled out, the effect of birth order on infant and child mortality remained significant and substantial. The conclusion is that parental underinvestment represents a link between fertility and mortality during infancy and early childhood that has not been described previously. Policy makers appear to have overlooked parental underinvestment in favor of more obvious economic and health mediators.     

Risk, uncertainty and family formation: The social context of poverty groups

Abstract Despite the assumptions of many demographers that the net returns from children for non-elite groups in underdeveloped areas are likely to be negative, high fertility persists in most of these societies. Both cultural and institutional explanations have been proposed to account for this. We attempt to provide some mediation between these competing models, by introducing the elements of risk and uncertainty as factors likely to induce poverty and lead works to opt for the 'high fertility, low quality' pattern of investment of time and money in family formation. Drawing upon the work of Wharton in subsistence agriculture practices, several alternative decision-making models are proposed to account for both the persistence of high fertility, and the declines that have been registered in selected areas, such as Taiwan and perhaps China. The empirical work of Mueller on Taiwanese expectations of returns on children and the concomitant variation in family-size preferences is consistent with the models proposed. Some implications for uncertainty and risk-reduction strategies in family planning and other social welfare programmes are drawn.     

An Assessment and Extension of the Mechanism-Based Approach to the Identification of Age-Period-Cohort Models

Many methods have been proposed to solve the age-period-cohort (APC) linear identification problem, but most are not theoretically informed and may lead to biased estimators of APC effects. One exception is the mechanism-based approach recently proposed and based on Pearl’s front-door criterion; this approach ensures consistent APC effect estimators in the presence of a complete set of intermediate variables between one of age, period, cohort, and the outcome of interest, as long as the assumed parametric models for all the relevant causal pathways are correct. Through a simulation study mimicking APC data on cardiovascular mortality, we demonstrate possible pitfalls that users of the mechanism-based approach may encounter under realistic conditions: namely, when (1) the set of available intermediate variables is incomplete, (2) intermediate variables are affected by two or more of the APC variables (while this feature is not acknowledged in the analysis), and (3) unaccounted confounding is present between intermediate variables and the outcome. Furthermore, we show how the mechanism-based approach can be extended beyond the originally proposed linear and probit regression models to incorporate all generalized linear models, as well as nonlinearities in the predictors, using Monte Carlo simulation. Based on the observed biases resulting from departures from underlying assumptions, we formulate guidelines for the application of the mechanism-based approach (extended or not).     

Antecedents to contraceptive innovation: Evidence from rural Northern Thailand

A number of different causal mechanisms have been proposed to explain the onset of fertility declines in populations with previously uncontrolled fertility, but they have never been adequately tested. The present study identifies and tests five antecedents to family limitation practices in a sample of 755 currently married couples resident in rural Northern Thailand. The loglinear multiple regression models estimated indicate that couples in more developed districts, more modern couples, couples in which wives have more equal roles, couples believing that intergenerational wealth transfers favor children rather than their parents, and more wealthy couples, were all significantly more likely to be early adopters of contraception. Local development levels appeared to have the greatest net effects on the timing of adoption of fertility control. In addition, couples in areas where contraceptive services were more readily available were also significantly more likely to be contraceptive innovators, net of these five variables.     

Binary outcomes and endogenous explanatory variables: Tests and solutions with an application to the demand for contraceptive use in tunisia

Many demographic studies examine discrete outcomes, and researchers often suspect that some of the explanatory variables may be influenced by the same unobserved factors that determine the discrete outcome under examination. In linear models, the standard solution to this potential endogeneity bias is an estimator such as two-stage least squares. These methods have been extended to models with limited dependent variables, but there is little information on the performance of the methods in the types of data sets typically used in demographic research. This paper helps to fill this gap. It describes a simple analytic framework for estimating the effects of explanatory variables on discrete outcomes, which controls for the potential endogeneity of explanatory variables. It also discusses tests for exogeneity and joint determination of the outcomes and the explanatory variables. It summarizes the results of a Monte Carlo study of the performance of these techniques and uses these results to suggest how researchers should approach these problems in practice. We apply these methods to the examination of the impact of fertility intentions on contraceptive use, based on data from the 1988 Tunisia Demographic and Health Survey.     

Immigration to the UK from High‐Fertility Countries: Intergenerational Adaptation and Fertility Convergence

The fertility of immigrants' children increasingly shapes the ethnic diversity of the population in Western Europe. However, few data are available on the fertility patterns of immigrants and their offspring. This article provides new fertility estimates of immigrants and immigrants' children by ethnic group in the United Kingdom that may provide better‐informed fertility assumptions for future population projection models. The impact of migration‐specific tempo effects on the period TFR of immigrants is analyzed. Among the results, intergenerational fertility transitions strongly contribute both to fertility convergence between ethnic groups and to fertility “assimilation” or “intergenerational adaptation” to the UK mainstream childbearing behavior. Ethnic fertility convergence, particularly marked for populations originating from high‐fertility countries, reflects in part decreasing fertility in sending countries and in part intergenerational adaptation to the UK mainstream. Higher educational enrollment of the daughters of immigrants may partly explain their relatively lower fertility.     

Biodemographic modeling of the links between fertility motivation and fertility outcomes in the NLSY79

In spite of long-held beliefs that traits related to reproductive success tend to become fixed by evolution with little or no genetic variation, there is now considerable evidence that the natural variation of fertility within populations is genetically influenced and that a portion of that influence is related to the motivational precursors to fertility. We conduct a two-stage analysis to examine these inferences in a time-ordered multivariate context. First, using data from the National Longitudinal Survey of Youth, 1979, and LISREL analysis, we develop a structural equation model in which five hypothesized motivational precursors to fertility, measured in 1979–1982, predict both a child-timing and a child-number outcome, measured in 2002. Second, having chosen two time-ordered sequences of six variables from the SEM to represent our phenotypic models, we use Mx to conduct both univariate and multivariate behavioral genetic analyses with the selected variables. Our results indicate that one or more genes acting within a gene network have additive effects that operate through child-number desires to affect both the timing of the next child born and the final number of children born, that one or more genes acting through a separate network may have additive effects operating through gender role attitudes to produce downstream effects on the two fertility outcomes, and that no genetic variance is associated with either child-timing intentions or educational intentions.     

Do fertility transitions influence infant mortality declines? Evidence from early modern Germany

The timing and sequencing of fertility transitions and early-life mortality declines in historical Western societies indicate that reductions in sibship (number of siblings) may have contributed to improvements in infant health. Surprisingly, however, this demographic relationship has received little attention in empirical research. We outline the difficulties associated with establishing the effect of sibship on infant mortality and discuss the inherent bias associated with conventional empirical approaches. We offer a solution that permits an empirical test of this relationship while accounting for reverse causality and potential omitted variable bias. Our approach is illustrated by evaluating the causal impact of family size on infant mortality using genealogical data from 13 German parishes spanning the sixteenth, seventeenth, eighteenth, and nineteenth centuries. Overall, our findings do not support the hypothesis that declining fertility led to increased infant survival probabilities in historical populations.     

Intergenerational effects on fertility Theory and evidence from Israel

On the assumption that genetic inheritage and experience during adolescence influence the taste for children, the characteristics of a couple's parents may be used to improve on the explanation of fertility which can be obtained from variables that only refer to the couple itself. We find that in Israel fertility depends positively on the mother's siblings and negatively on the grandfathers' wage, but apparently does not depend on the father's siblings. Since fertility also depends positively on the mother's predicted wage, the number of children is positively related to improvements in the economic achievements from one generation to the next.We wish to thank the referees and the managing editor for helpful suggestions.