Estimating transition probabilities of age misstatement

This article outlines a method of estimating probabilities of gross transfers from one age to another due to misreporting of age. An essential ingredient in the computation is the information on the true age structure of the population, which may be estimated by using generalized stable population relationships. The method consists essentially of iteratively adjusting rows and columns of an initial guess matrix so that the application of the resultant transition matrix to the true age distribution produces the recorded age distribution. The initial guess matrix can be either empirically based or theoretically derived. The method is illustrated by using data on India, 1971-1981. The application reveals that in India, although the tendency to exaggerate age is strong at adult ages, the bias does not increase appreciably at older ages, as is commonly believed.     

Migrant cohort size,enforcement effort,and the apprehension of undocumented aliens

This article examines macro-structural conditions that affect time trends in aggregate probabilities of undocumented alien apprehension along the Mexico-US border. We show that the number of migrants attempting to cross the border illegally in a given period and the level of effort expended by the INS to apprehend undocumented migrants are principal determinants of apprehension probabilities. Our findings differ from those in earlier work by Donato, Durand, and Massey who argue that individual, household, and community factors are not significant predictors of apprehension probabilities and conclude that escaping INS detection at the border is essentially a random process unrelated to personal traits or to enforcement provisions of the 1986 Immigration Reform and Control Act. Although Donato et al. recognize that apprehension probabilities are affected by the size of the US Border Patrol budget and the number of personnel, they omit these larger structural factors from consideration. Instead, they introduce annual dummy variables to control for macro-structural forces. This approach is unsatisfactory because it confounds the effects of numerous explanatory factors. We conclude that one implication for future research is that it is worth modeling the effects of individuals' characteristics on apprehension probabilities by including as predictors an estimate of the flow of undocumented migrants and measures of INS border enforcement effort. Controlling explicitly for three macrostructural conditions may disclose the importance of some individual-level factors that would otherwise be obscured.     

Combining registration-system and survey data to estimate birth probabilities

With the widespread availability of event-history data, demographers have increasingly eschewed registration-system data in favor of survey data. We propose instead using survey and registration-system data in combination, via a constrained maximum-likelihood framework for demographic hazard modeling. As an application, we combine panel survey data and birth registration data to estimate annual birth probabilities by parity. The general fertility rate obtained from registration-system data constrains the weighted sum of parity-specific birth probabilities. The variances about the parity-specific birth probabilities are halved when registration-system data are used to constrain the estimates. Other demographic applications are discussed.     

Users and non-users of contraception: Tests of stationarity applied to members of a family planning programme

Abstract Regression analysis is used in examining the cumulative nature of contraceptive use among clients of a family planning programme. Markov chain analyses are performed on the data. χ(2) tests are used to test the stationarity of the transition probabilities from the state of user to non-user as well as from non-user to user over the period of operation of the programme. A good predictive equation is developed relating the cumulated number of users and the years of operation of the programme. The transition probabilities are not constant over the entire period of twelve years. The data are not homogeneous. When the twelve year-period is divided into three four-year periods, the transition probabilities are constant within each period. Each of these three periods coincides with a distinctive period in the development of the programme.     

Estimators for the Horvitz-Thompson Statistic Based on Some Posterior Distributions

The knowledge of first-order inclusion probabilities characterizing a sampling scheme is essential in design-based estimation of finite population totals. Sometimes the scheme is so complex that these probabilities cannot be computed exactly. Instead, both inclusion probabilities and corresponding sampling weights are simulated. One empirical Horvitz-Thompson estimator for a population total using simulation-based range-preserving estimates of sampling weights is obtained by applying the restricted maximum likelihood principle directly to each inclusion probability. The assumption of a prior distribution and the assessment of resulting posterior for a weight lead to two other estimators. One of them is the posterior mean estimator of the Horvitz-Thompson statistic. In a simulation involving Polish agricultural census data and a sequential fixed-cost sampling scheme, this estimator has attractive properties also from a frequentist point of view.     

Model-based Clustering of Sequential Data with an Application to Contraceptive Use Dynamics

ABSTRACT

Multi-state models describe the transitions people experience as life unfolds. The transition probabilities depend on sex, age, and attributes of the person and the context. Empirical evidence suggests that attributes that cannot be measured directly may at most be inferred from a long list of observable characteristics. A cluster-based, discrete-time multi-state model is presented, where transition probabilities are estimated simultaneously for several subpopulations of a heterogeneous population. The subpopulations are not defined a priori but are determined on the basis of similarities in behavior in order to determine which women exhibit similar characteristics with respect to method choice, method switch, discontinuation and subsequent resumption of contraceptive use. The data are from the life history calendar based on the Brazilian Demographic and Health Survey 1996. The parameters of the model are estimated using the EM algorithm. Seven subpopulations with heterogeneous transition probabilities are identified.     

Learning about migration decisions from the migrants: Using complementary datasets to model intra-regional migrations in Spain

We investigate the determinants of the remarkable increase in intra-regional migrations since the 1980's in Spain, using a large administrative micro dataset on migrants. Conditional migration probabilities are identified by comparing the migrants' joint distribution of characteristics to the corresponding distribution from the Spanish Labour Force Survey. The proportion of employment in the service industry, unemployment, house prices and education, all have an important positive effect on the individual probabilities of intra-regional migration. Received: 16 May 1999/Accepted: 26 September 2000     

A semi‐Markovian approach to using event history data in multiregional demography

As a first step towards infusing event‐history analysis into multiregional demography, this paper introduces a semi‐Markovian framework and outlines its salient features as differentiated from a pure Markovian framework. Specifically, what differentiates the former from the latter is an explicit consideration of duration‐dependence in migrating from one region to another. This duration‐dependence is one of the complexities involved in using event‐history data in multiregional demography. The use of event‐history data lends itself easily to defining basic probabilities involved in a semi‐Markovian framework directly on sample paths of individuals. The underlying concepts of a semi‐Markov process in the special case of time‐homogeneity or age‐independence of transition probabilities are given in a coherent and concise form. Illustrations of empirical applications to the event‐history data on migration as provided by the Korean National Migration Survey conducted in 1983, and of distinct features of the semi‐Markovian analysis through a parametrization of the basic probabilities are also given in this paper.     

Survivorship Of Sons Under Conditions Of Improving Mortality

The strong desire of fathers to be assured that at least one son will outlive them, coupled with the traditional belief in a high probability of sons predeceasing their father, is often a deterrent to restriction of family size. A calculation of the probabilities of survivorship of sons on the basis of the United Nations Model Life Tables, however, shows that the probabilities of a father being outlived by even one son are remarkably high, particularly after that son has survived the first two years of life. When cohort tables are used, reflecting expected mortality improvements, the probabilities are even higher. In general, it is found that the probability that a two-year-old son will outlive his father is 80% or better, subject to the current mortality level and the age of the father.Finally, this paper examines (1) probabilities of a father being outlived by at least one of two or three sons, (2) probabilities of a mother or of both parents being outlived by a son, and (3) the probability that at least one of two sons will outlive a father when allowance is made for the fact that mortality probabilities of the sons are not independent of one another.     

Comment on “compromised birth outcomes and infant mortality among racial and ethnic groups”

Frisbie, Forbes, and Pullum (1996) show that it is meaningful to account for low birth weight, preterm delivery, and intrauterine growth-retardation when analyzing differences in compromised birth outcomes and infant mortality among racial and ethnic groups. I compare their findings for the 1987 U.S. birth cohort with findings for the 1988 U.S. birth cohort, using linked birth and infant death vital statistics from the National Center for Health Statistics. I focus on their calculation of fetal growth curves, which are highly at odds with the curves commonly used in the obstetric and pediatric literature. I compare birth outcome distributions and infant death probabilities using Frisbie et al. 's method and other standards. I conclude that Frisbie et al. 's method is not suited for the study of intrauterine growth-retardation at the population level because of the major flaws in gestational age measurement that exist in the type of data they use. An appropriate alternative is to apply a standard of normal intrauterine growth derived from antenatal estimation of fetal weight-for-gestational-age to the vital statistics data.     

The impact of war, famine, and economic decline on marital fertility in ethiopia

We examine recent fertility trends in Ethiopia for evidence of short- and long-term responses to famine, political events, and economic decline. We use retrospective data on children ever born from the 1990 National Family and Fertility Survey to estimate trends in annual marital conception probabilities, controlling for women's demographic and socioeconomic characteristics. The results of our analysis provide evidence of significant short-term declines in conception probabilities during years of famine and major political and economic upheaval. In the longer term, marital fertility in both urban and rural areas declined in the 1980s after increasing moderately in the 1970s.     

Ethnic variations in the relationship between income and fertility

The effects of husband'spotential andrelative incomes on completed fertility, as well as their effects on certain parity progression probabilities, are examined within samples of Anglos, Blacks and Mexican Americans. Relationships are estimated using data from the one-percent 1960 and 1970 U.S. Public Use Samples. The results reveal different patterns of relationship by ethnicity between the measures of income and the measures of fertility. The effects on completed fertility of the income measures are positive for Anglos and negative for Blacks, while in the case of Mexican Americans the effect ofpotential income is negative and that ofrelative income is positive. Income effects on the parity progression probabilities are similar in pattern to those from the analyses using completed fertility, although somewhat different patterns tend to appear at different birth orders, especially among Anglos.     

Lifetime probability of additional births by age and parity for American women, 1935–1968: A new measurement of period fertility

A new fertility measurement, probability that a woman of specified parity and age will bear a given number of births in her remaining lifetime, is proposed in this article. The measurement is a summary index of a set of age-parity-specific birth probabilities and in a particular case it is conceptually analogous to the total fertility by birth order but free from the influence of the parity distribution. Fertility of American women for the period 1935-1968 was studied by use of such lifetime probabilities. It appears that the trend of fertility of high birth orders has been parallel with that of low orders. Initiation of the recent decline in fertility depends on parity and age of woman.     

Modeling and Forecasting Health Expectancy: Theoretical Framework and Application

Life expectancy continues to grow in most Western countries; however, a major remaining question is whether longer life expectancy will be associated with more or fewer life years spent with poor health. Therefore, complementing forecasts of life expectancy with forecasts of health expectancies is useful. To forecast health expectancy, an extension of the stochastic extrapolative models developed for forecasting total life expectancy could be applied, but instead of projecting total mortality and using regular life tables, one could project transition probabilities between health states simultaneously and use multistate life table methods. In this article, we present a theoretical framework for a multistate life table model in which the transition probabilities depend on age and calendar time. The goal of our study is to describe a model that projects transition probabilities by the Lee-Carter method, and to illustrate how it can be used to forecast future health expectancy with prediction intervals around the estimates. We applied the method to data on the Dutch population aged 55 and older, and projected transition probabilities until 2030 to obtain forecasts of life expectancy, disability-free life expectancy, and probability of compression of disability.     

Reproduction in upheaval: ethnic-specific fertility responses to societal turbulence in Kazakhstan

This study contributes to the literature on demographic adjustments to societal crises by examining ethnic-specific probabilities of having first, second, and third marital births in late-twentieth-century Kazakhstan. Discrete-time logit models, employing data from the 1995 and 1999 Kazakhstan Demographic and Health Surveys, are fitted. The results show that the probability of a first birth responded to societal cataclysms of the post-Soviet transition, but this response was most manifest and enduring in the ethnic group that had been most demographically advanced and that also found itself most politically and economically vulnerable. While ethnic differences in the probability of second and third births were generally more pronounced than in the probabilities of first birth, the pace of their post-Soviet decline was relatively uniform across all ethnic groups.     

Computer Models of Social Processes: The Case of Migration

The demographic model is a program for representing births, deaths, migration, and social mobility as social processes in a non-stationary stochastic process (Markovian). Transition probabilities for each age group are stored and then retrieved at the next appearance of that age cohort. In this way new transition probabilities can be calculated as a function of the old transition probabilities and of two successive distribution vectors.Transition probabilities can be calculated to represent effects of the whole age-by-state distribution at any given time period, too. Such effects as saturation or queuing may be represented by a market mechanism; for example, migration between metropolitan areas can be represented as depending upon job supplies and labor markets. Within metropolitan areas, migration can be represented as invasion and succession processes with tipping points (acceleration curves), and the market device has been extended to represent this phenomenon.Thus, the demographic model makes possible the representation of alternative classes of models of demographic processes. With each class of model one can deduce implied time series (varying parame-terswithin the class) and the output of the several classes can be compared to each other and to outside criteria, such as empirical time series.     

Differential Survival in Europe and the United States: Estimates Based on Subjective Probabilities of Survival

Cross-country comparisons of differential survival by socioeconomic status (SES) are useful in many domains. Yet, to date, such studies have been rare. Reliably estimating differential survival in a single country has been challenging because it requires rich panel data with a large sample size. Cross-country estimates have proven even more difficult because the measures of SES need to be comparable internationally. We present an alternative method for acquiring information on differential survival by SES. Rather than using observations of actual survival, we relate individuals’ subjective probabilities of survival to SES variables in cross section. To show that subjective survival probabilities are informative proxies for actual survival when estimating differential survival, we compare estimates of differential survival based on actual survival with estimates based on subjective probabilities of survival for the same sample. The results are remarkably similar. We then use this approach to compare differential survival by SES for 10 European countries and the United States. Wealthier people have higher survival probabilities than those who are less wealthy, but the strength of the association differs across countries. Nations with a smaller gradient appear to be Belgium, France, and Italy, while the United States, England, and Sweden appear to have a larger gradient.     

Computing a population budget from sequentially sacrificed, replicated cultures

Summary When a population budget must be obtained from censuses based on replicated, sacrificed cultures, it is difficult to obtain estimates of transition probabilities and of the errors of such estimates, because there is no logical basis for pairing successive census counts. In a study of this nature estimating a population budget of immature stages of the housefly, the problem was solved by a randomization treatment of the original census results obtained at two densities. One hundred randomly generated census matrices over all census times for each density were smoothed to remove the effects of sampling error and a population budget constructed according to defined rules. Transition probabilities computed from the population budget were plotted on triangular coordinate paper and mean probabilities, 95% confidence regions for these means, and 95% equal frequency ellipses computed. All computations and the graphing of the results were carried out on a digital computer. The computer program, available from the authors, is written in FORTRAN IV and could be easily modified for similar studies. Contribution No. 1364 from the Department of Entomology, The University of Kansas. This study has been supported by the Medical Research and Development Command of the Office of the Surgeon General of the Army under contract No. DA-49-007-MD-738, U.S.A. and by a Public Health research career program award (No. 3-K3-GM-22, 021-01S1) from the National Institute of General Medical Sciences, U.S.A. to RobertR. Sokal. It was carried out during the tenure of a National Science Foundation predoctoral fellowship by EdwinH. Bryant. The authors appreciate the help of Dr.F.J. Rohlf with computational aspects.     

Combining forward and backward mortality estimation

Demographers often form estimates by combining information from two data sources—a challenging problem when one or both data sources are incomplete. A classic example entails the construction of death probabilities, which requires death counts for the subpopulations under study and corresponding base population estimates. Approaches typically entail ‘back projection', as in Wrigley and Schofield's seminal analysis of historical English data, or ‘inverse’ or ‘forward projection’ as used by Lee in his important reanalysis of that work, both published in the 1980s. Our paper shows how forward and backward approaches can be optimally combined, using a generalized method of moments (GMM) framework. We apply the method to the estimation of death probabilities for relatively small subpopulations within the United States (men born 1930–39 by state of birth by birth cohort by race), combining data from vital statistics records and census samples.     

Employing the Components of the Human Development Index to Drive Resources to Educational Policies

A new form of composition of the indicators employed to generate the United Nations Human Development Index (HDI) is presented here. This form of composition is based on the assumption that random errors affect the measurement of each indicator. This assumption allows for replacing the vector of evaluations according to each indicator by vectors of probabilities of being the best or the worst according to such attribute. The probabilistic composition of such probabilities of preference according to each indicator into probabilities of being the best or the worst according to all of them generates indices that may unveil, on one hand, performances to be followed and, on the other hand, extreme conditions that an additive composition would hide. Differences between the results of application of the diverse forms of composition are examined in the case of the HDI and in the case of the districts version of the HDI employed to compare Brazilian municipalities. It is verified that the smallest correlation between the education enrolment rate and the other indicators in the Brazilian case enlarges such differences.