The use of fourier analysis to express the relation between time variations in fertility and the time sequence of births in a closed human population

A fundamental theorem of mathematical demography states that two closed populations sharing the same extended history of net fertility, no matter how variable, have the same age composition. In consequence, when in any population net fertility has long followed a purely repetitive cycle, age composition must also be repetitive with the same cycle length. Under these conditions annual births follow a path that is an exponential multiplied by a periodic time-function. If the time variation of fertility is a small amplitude sinusoidal oscillation, the periodic component of the birth sequence is also sinusoidal. The relative amplitude and timing of fertility oscillations and the consequent birth fluctuations are functions of the duration (or frequency) of the fertility cycle; the nature of the functions is determined by the age structure of net fertility.Any time sequence of fertility variation over an extended period of time can be treated as if part of a repetitious cycle of very long duration. By Fourier analysis the fertility sequence can be expressed as the sum of a series of sinusoidal terms; and finally the sinusoidal components of the resultant birth sequence can be derived. The calculated birth sequence closely approximates the actual.     

The analysis of sex segregation: When is index measurement not index measurement

In their paper in this issue. Grusky and Charles (1998) make a number of dubious claims about the measurement and interpretation of sex segregation. First, they incorrectly claim that only log-odds measures yield margin-free measures of segregation. Second. the estimation and testing of a limited class of log-linear models does not provide an independent test of the appropriateness of a log-odds ratio index to measure segregation. Their estimation informs them of the statistically justifiable degree of occupational disaggregation, not whether a log-odds ratio is superior to, say, a linear index in the measurement of segregation. Finally, their index A is beset with problems of interpretation. not withstanding their arguments. and their additional measures, A_w and A_B, suffer similar problems. Grusky and Charles are. however, correct in arguing that measurement procedures should be margin-free. Further, I concur with the view that the adoption of a single annual summary measure of segregation cannot be justified. because it is premised on the assumption that individual occupations, or groups of occupations. exhibit similar trends in sex segregation.     

The analysis and measurement of happiness as a sense of well-being

General happiness is philosophically construed as a sense of well-being which in turn has been defined either as a complete and lasting satisfaction with life-as-a-whole or as a preponderance of positive over negative feelings. A factor analysis of thirteen well-being scales shows that these two definitions coalesce into a single general well-being factor which is distinguishable only from an independent stress/worries factor. Further evidence shows that familiar scales of neuroticism, depression and trait anxiety measure the same well-being dimension if only in the negative half-range. So does a list of somatic complaints. Various two-factor models of well-being that treat positive and negative affect as independent processes, or that distinguish between affective and cognitive components, are challenged on the grounds that they depend on the properties of Bradburn's affect scales which are found to be highly dependent on methodological parameters. Attention is drawn here to the role of test method effects and curvilinearities as factors influencing inter-scale correlations and structural models. It is concluded that well-being is a robust, primary dimension of human experience and that happiness research is alive and well in psychology.     

Guidelines for time use data collection

Growing and widespread interest in time begs the need for time use data collection and reporting standards. Initial guidance for comparative work was provided by the Multinational Time Use Project. However, changing technologies, methodologies, and divergent data needs have given rise to the need for updated guidance. This paper, prepared with input from members of the International Association for Time Use Research, examines the history and applications of time use data, identifies and evaluates methodological options for time use studies, recommends options facilitating cross-national and cross-temporal comparability and identifies methodological challenges facing time use researchers. The study concludes that alternative collection methods appear to make little difference in the resulting activity and time use estimates at customary levels of reporting.     

The use of mortality time series data to produce hypothetical morbidity distributions and project mortality trends

It is difficult to obtain direct empirical estimates of chronic disease prevalence in the U.S. population. The available estimates are usually derived from epidemiological studies of selected populations. In this paper we present strategies for estimating morbidity distributions in the national population using auxiliary biomedical evidence and theory to estimate transitions to morbidity states from a cohort mortality time series. We present computational methods which employ these estimates of morbid state transitions to produce life table functions for both primary (morbidity) and secondary (mortality) decrements. These methods are illustrated using data on stomach cancer mortality for nine white male cohorts, aged 30 to 70 in 1950, observed for a 28-year period (1950 to 1977).     

The concept and measurement of child dependency: An approach to family formation analysis

Abstract Two distinctions appear crucial in the study of human fertility: (1) aggregate versus individuallevel analysis; and (2) true explanations versus 'demographic explanations', using Stinchcombe's terminology. Social demographers analysing fertility have been accustomed to using fertility measurements derived from aggregative population analyses, and have largely terminated their analytic efforts at the level of a 'demographic explanation'. The failure to arrive at a social analysis of the process of fertility decision-making may in part to be due to this measurement heritage, which may be inappropriate for individual-level analyses. As a first step in the direction of creating measurement suitable for such analyses, fertility decision-making is labelled as family formation decision-making, and this is linked to the concept of child dependency. Measures of child-years-of-dependency (CYD) are proposed for use in family formation analysis. These integrate current quantity and tempo measures, and have greater potential for use at the level ofthe family. They require no additional data beyond fertility histories, are flexible in terms of non-modal family situations (e.g. divorce, infant or child mortality) and may be indicators of criteria used by couples in planning their fertility. Refinements of the basic CYD measures are explored. These include analyses of average versus marginal costs of child-rearing, age gradients of costs and social class differentials in costs. All of these are intended to make CYD measures more useful in individual cost-benefit analyses of child-bearing and child-rearing.     

The use of multiple regression analysis in employment discrimination cases

This paper explores the use of multiple regression in employment discrimination cases brought under the Equal Pay Act of 1963 or Title VII of the Civil Rights Act of 1964. Through examining the outcomes of the cases and judicial commentary about regression analyses as evidence, the paper concludes that plaintiffs are most likely to prevail in cases where both the plaintiffs and defendants utilize regression. Plaintiffs who do not present regression analyses as evidence are at a distinct disadvantage when defendants do so. However, defendants are not similarly disadvantaged when responding to a plaintiffs regression analysis without their own statistical showing. Finally, plaintiffs who support their regression analyses with witness testimony of discriminatory employer acts appear to be more likely to prevail than plaintiffs who do not present such witnesses.     

Australians' changing use of time, 1974–1987

This paper examines various scenarios of social change in industrialised societies. Amongst the ideas considered are: the post-industrial society thesis; reduction of (paid) work time; the leisure revolution; the self-provisioning of services; and the growth of the “symmetrical family”. These propositions are tested by comparing data gathered in the 1974 Cities Commission study of time use in Melbourne (N=717) with data collected by the Australian Bureau of Statistics Pilot Study of Time Use conducted in Sydney, 1987 (N=1611). Analysis of time spent on leisure, paid and unpaid work. The results of this analysis indicate a significant modification of the ideas about the probable future of industrial societies is needed.     

Intergenerational relations and time use in urban black South African households

Intergenerational relations is a critical issue in South Africa's transition to democracy. Harsh apartheid laws as well as rapid urbanization have divided families and weakened the traditional mutual intergenerational support system. Earlier research indicated signs of alienation and conflict between the generations, particularly among urban black families (Ferreira et al., 1992). The paper reports on the role of everyday life in promoting solidarity in families and the well-being of members. A weekday time-use study was conducted among 300 multigeneration urban black households in two metropolitan areas. A time budget and questionnaire were administered to a high school pupil, a parent and a grandparent in each of the households (n900). Motivations underlying activities of the diary day were examined using the method developed by Elchardus and Glorieux (1992). Results suggest that generational norms exist regarding the allocation of time to social, physiological and personal gratification needs. Signs of alienation were found only among a minority of the oldest generation who gave a negative evaluation of their daily round of activities and reported depressed well-being. Results supported the idea that the urban black three-generation household represents a special case of family solidarity. Further research is needed to identify generational norms of time use in a wider range of South African family situations.     

Spare time use and perceived well-being among black South African youth

Leisure opportunities for urban black South Africans are limited but there is little evidence which documents the experience of disadvantage or its significance for retarded advancement and depressed quality of life. An exploratory questionnaire study, conducted in 1989 in three metropolitan areas among black township youth (age 15–25 years, predominantly Zulu-and Xhosa-speakers) of both sexes, inquired into spare time habits and activities, participation rates, leisure aspirations, satisfactions, preferences, and barriers. Each subject also kept activity diaries for a specific weekday and a weekend day. Preliminary results from the time budget data are discussed with reference to subjects' overall life satisfaction and outlook on the future. Findings have policy implications for reducing inequalities in a socially divided society.The University of Natal rejects apartheid. It is an equal opportunities, affirmative action University.     

Changes of time use of the town population in Latvia

The first study of weekly time budgets of the republic population was performed in 1971–1973 to ascertain the expenditure of working and non-working time for different kinds of activities concerning qualitative and quantitative reproduction of the population. A repeated study was performed in 1987 to determine changes in time use and ways to improve socio-economic conditions in order to optimize the structure of activities. This article discusses ways in which the two studies varied, with regard to the questions asked and the results obtained.     

The allocation and value of time assigned to housework and child-care: An analysis for Switzerland

In this paper, data from the 1997 Swiss Labour Force Survey are used to analyse the allocation and value of time assigned to housework and child-care. It is shown that men's allocation of time to housework and child-care is largely invariant to changes in socio-economic factors. Women's allocation of time to housework and child-care, on the other hand, is shown to depend on several social, economic, and demographic factors. The value of time assigned to housework and child-care is calculated with two market replacement cost methods and three opportunity cost methods. The results show that the value of time assigned to housework and child-care ranges from 27% to 39% and from 5% to 8% of GDP (in 1997), respectively. The value of time assigned to housework and child-care is also calculated for different household structures. Received: 15 April 1999/Accepted: 5 May 2000     

Concept,measurement, and data in migration analysis

Two methods of computing migration rates-one relating moves to population at risk in place of origin and the other using as a denominator the cross-product of population in places of origin and destination-are discussed. It is concluded that the second assumes implicitly that moves originate and terminate as a random population variable.Some difficulties with this particular model are pointed out and the author suggests that other analytical approaches to migration data be sought and in this connection refers to the literature on the mathematical theory of epidemics.     

Systematic error in behavioural measurement: Comparing results from interview and time budget studies

Data collected by survey methodology are sensitive to measurement errors. Factors of memory, understanding, and willingness to respond truthfully, distort the quality of results. In this paper, time diaries were used as a quality check for results obtained by direct interviews and questionnaires. Data is based on surveys carried out by Statistics Finland. Comparison showed that measurement error varied considerably between population groups, influencing dependencies and interpretations of the results. Activities clearly distinctive from other activities, such as gainful employment outside the home, produced the most accurate data in direct survey questions. Everyday activities that don't clearly stand out from other uses of time, such as home based employment, are difficult to recall and produce a lot of biasing measurement errors.     

The economic measurement and determinants of diversity

This paper has a 2-fold objective: (1) To introduce a measure that would be of general applicability in measuring diversity in different institutions. (2) To identify the determinants of diversity in child-care centers and, in particular, to examine whether the for-profit sector is less diverse than the not-for-profit sector in the child-care industry as the statistics suggest. Using our measure, we isolate factors that significantly influence diversity by using an economic model that makes diversity a decision variable of a firm. Two measures of diversity are suggested: absolute diversity and relative diversity (diversity relative to the surrounding community). To select a suitable index, the Herfindahl measure of concentration is considered relative to several suitable ecological indices measuring species diversity, and found to be virtually identical to such indices. Thus theH-index is used in both absolute and relative measures. Empirical estimation of both absolute and relative diversity equations use probability models and isolate factors that significantly influence both absolute diversity of child-care centers as well as their diversity relative to their respective counties. The data used is the recently released Profile of Child-Care Settings collected by the Mathematica Policy Research.     

The end of rapid increase in the use of oral anovulants? Some problems in the interpretation of time series of oral use among married women

Several problems in the interpretation of time series of oral anovulant usage are discussed, among them the shifting marriage-duration distribution over time. Standardization fails to negate the conclusion that the rate of increase in the proportion of women using orals has slackened since January 1966. Separate analyses by duration-specific rates of use and by marriage cohorts show that the two factors sustaining the initial spectacular growth rate in the use of orals-the ever—higher initial use rates of new marriage cohorts and the rapid adoption of orals among earlier cohorts at later durations—have lost their sustaining force. Further analysis indicates that concern over the pill as a health hazard is a major deterrent to substantial increase in oral usage. A final distribution of women by risk status with respect to oral use, and current and prospective oral use, shows that under present circumstances the maximum oral use rate will be considerably less than unity.     

The measurement of social well-being

This paper provides a conceptual framework for viewing social well-being as composed of two elements: social adjustment and social support. Social adjustment is a combination of satisfaction with relationships, performance in social roles and adjustment to one's environment. Social support is composed of the number of contacts in one's social network and satisfaction with those contacts. Through the pioneering work of McDowell and Newell, comparative ratings of measures of social adjustment and social support are available. It appears that Weissman's Social Adjustment Scale and Sarason's Social Support Scale are currently the best measures in terms of validity and reliability. But, they are merely starting points for future measurement of these concepts.Prepared for delivery at the American Public Health Association meeting in Atlanta, Georgia November 1991.     

Time use studies for leisure analysis

There is a growing interest in, time allocation research. Particularly by government statistical bodies. Papers in this issue, briefly highlighted in this introduction, make a small contribution to fulfilling a need for wider exposure of time use literature. The included papers do two things. First, they identify issues related to the collection and analysis of time use data. Second, they show how time use data can be effectively applied to improve one's understanding of significant issues.