Maximum likelihood estimates for the parameters of a continuous time model for first conception

The duration of time between two successive births or between marriage and first birth is an indicator of the level of fertility of a couple. Potter and Parker (1964) and Singh (1961, 1967) have suggested the Type I Geometric as a distribution appropriate for representing the length of interval to first conception leading to a live birth. Potter and Parker estimated the parameters of this distribution with the help of the first two moments. Majumdar and Sheps (1970) pointed out the limitations of these moment estimates and gave a method to obtain maximum likelihood estimates, based on formulas which are too involved for solution without the help of a computer. Singh proposed a continuous probability distribution based on another set of assumptions for the above situation. He outlined a method to obtain best asymptotically normal estimates of the parameters. These estimates are obtained after several iterations starting from any set of consistent estimates. The objective of this paper is to show that it is relatively easier to obtain maximum likelihood estimates of the parameters of the continuous model, which describes the data on duration to first conception as well as does the discrete model. Simple expressions for the moment and maximum likelihood estimates with the corresponding covariance matrices are obtained. Application is made to three sets of data.     

Age at marriage and timing of the first birth

Summary An attempt has been made to measure the effect of age at marriage of brides on the timing of the first birth. In Australian vital statistics, first nuptial confinements have been tabulated by age of mothers and by single years of marriage duration in single months for the first two years and by single years for all other durations since 1916. A simple technique has been used to link such data with marriage cohorts. The study briefly reviews the prevailing patterns of the timing of first births by mothers' age at marriage and changes in this pattern since the marriages of the 1925/9 period. The analysis shows that after a period of relative stability of family formation patterns in the 1950s and early 1960s, women married in the late 1960s started postponing the first birth beyond the first two years of marriage. It is suggested that a fraction of the decline in total births recorded in Australia since 1972 can be attributed to the postponement of first nuptial confinements by women married in the late 1960s and early 1970s.     

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.     

Toward a reappraisal of social indicators for housing in developing nations

The need for social indicators to monitor and evaluate progress in the achievement of certain predetermined goals is now very evident. However, the design and construction of these indiactors still leave much to be desired. This paper analyzes the application of social indicators for housing in the context of the developing nations. The problem of changing standards of acceptable housing over time and the different images and needs of the diverse inhabitants bring the validity of present indicators for housing into question and at least, point out the need for talking social and cultural variables into consideration.     

Fertility decline in Germany: An econometric appraisal

Summary A re-analysis of Knodel's data provides some new results for the fertility decline in Germany and a new approach to testing hypotheses about the demographic transition. Two formulations of transition theory are compared: one emphasizing the importance of changing social and economic structure for fertility decline; the other, the changing relationships between fertility and its determinants over time. To evaluate these formulations, multivariate time series cross-sectional models are developed. The statistical models permit the estimation of relationships both cross-sectionally and over time. As a consequence, the ability of the independent variables to explain cross-sectional as against temporal differences is evaluated. Industrialization, urbanization, religious composition, migration, infant mortality and marriage patterns satisfactorily explain the fertility decline once regional differences have been taken into account. Persisting characteristics of regional units account for much of the unexplained variance. Industrialization is the main explanatory variable of fertility decline in Germany. In the period considered, its impact on fertility increased substantially.     

Time series of growth in use of oral contraception and the differential diffusion of oral anovulents

Abstract Differential growth in the use of oral anovulents is explored through construction of separate time series for Canadian women classified by religion, education, and nativity. The series suggest that native-born Roman Catholic women are as likely as native-born Protestant women to be using oral contraceptives by the terminal point of our series in 1967. The period of very rapid growth in the use of orals appears to have come to an end. Differential patterns of diffusion of oral contraception shown by the categories of women discussed, suggest sources of bias in the profile of an aggregate time series.