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.     

Multiple paths in educational transitions: A multinomial transition model with unobserved heterogeneity

In many countries educational branching points consist of more than two qualitatively different alternatives, and only some alternatives provide the opportunity of continuing into higher education. I develop a multinomial transition model for modeling the effects of family background characteristics and individual characteristics on these complex educational careers. The model controls for unobserved heterogeneity that may, if ignored, result in biased estimates. Compared to previous research, I explicitly include instrumental variables that ensure identification of the unobserved component. I apply the model to the Danish case and analyze data which covers the educational careers of a cohort of Danes born around 1954. I find that the model brings forward non-trivial heterogeneity in the influence of family background and ability on qualitatively different choice alternatives both within and across transitions. I also find that not controlling for unobserved heterogeneity leads to marked underestimation of the family background effect on both early and late transitions in the educational career.     

Dealing with selection bias in educational transition models: The bivariate probit selection model

This paper proposes the bivariate probit selection model (BPSM) as an alternative to the traditional Mare model for analyzing educational transitions. The BPSM accounts for selection on unobserved variables by allowing for unobserved variables which affect the probability of making educational transitions to be correlated across transitions. We use simulated and real data to illustrate how the BPSM improves on the traditional Mare model in terms of correcting for selection bias and providing credible estimates of the effect of family background on educational success. We conclude that models which account for selection on unobserved variables and high-quality data are both required in order to estimate credible educational transition models.     

The consequences of unobserved heterogeneity in a sequential logit model

Cameron and Heckman (1998) established that a sequential logit model is more sensitive than many other models to the possible biasing influence of unobserved heterogeneity. This article proposes a method which allows researchers to find out how large this potential problem is for their data, their model, and their hypothesis of interest. This is done by proposing a set of scenarios for this unobserved heterogeneity, and showing how to estimate the effects of interest given these scenarios. The set of results from these scenarios give an indication of how sensitive the results are to assumptions regarding unobserved heterogeneity. This sensitivity analysis has been applied to a study of educational attainment in the Netherlands, and it showed that that the finding that the effect of father's education declined over transitions is quite sensitive to the assumptions made about unobserved heterogeneity, but that the finding that the effect of father's education declined over birth cohorts is more robust than is often feared.     

When studying schooling is not enough: Incorporating employment in models of educational transitions

Several recent studies have demonstrated the importance of incorporating qualitative differentiation within educational systems in the study of class inequality in student transitions. We extend these endeavors by broadening the definition of differentiation to include participation in the labor market. As increasing proportions of students continue their educational journeys beyond compulsory schooling, they are considering not only whether to stay in school but also whether to simultaneously enter the world of work. Using data from the National Longitudinal Survey of Youth of 1997 (NLSY97), we show that family background influences not only whether students make specific educational transitions but also whether they combine those educational transitions with work. Student trajectories are also path dependent, with employment during one educational transition being related to specific transition patterns at a later point in time. Considering how students combine school and work reveals another dimension of differentiation which can be exploited by socioeconomically advantaged families to “effectively maintain” inequality in educational outcomes.     

Unequal transitions: Selection bias and the compensatory effect of social background in educational careers

Previous studies have shown that social background inequality differs among educational transitions and it is stronger for those transitions that involve a higher risk of social demotion. This paper focuses on two processes that may account for part of the observed differences in social background inequality across educational transitions. First, it studies how the family of origin might compensate for a ‘false step’ in the early stage of young people's educational careers. This compensatory effect of social background can be described as the likelihood of having ‘a second chance’ for unsuccessful educational transitions. Second, it focuses on two unobserved factors that might potentially bias the effect of social background across educational transitions. These are the students’ unobserved cognitive and non-cognitive skills and their unobserved anticipated choices of dropping out of the education system. Two issues – the compensatory effect of social background and selection bias in educational transitions – are addressed by estimating a probit model with sample selection for the transition to post-compulsory education in Spain.     

Structural Change in Life Cycle Fertility During the Fertility Transition: France Before and After the Revolution of 1789

This paper explores the hypothesis that the fertility transition in France entailed a structural change in behaviour from natural to controlled fertility. We define the hypothesis in terms of an empirically estimable model of lifetime fertility. The model produces separate estimates of the three main proximate determinants: the hazard rate of conception for ovulating women, the timing of ovulation resumption after a birth, and permanent sterility. Fertility control is defined as responsiveness of the conception hazard to number of surviving children. We demonstrate key features of the model by simulated family histories. The historical application provides support for the transition hypothesis in the south of France, and mixed results for the north. We also find strong evidence of persistent couple-specific heterogeneity even after controlling for unobserved heterogeneity in fecundability. We suggest how future research might improve the model.     

Social inequality of reading literacy: A longitudinal analysis with cross-sectional data of PIRLS 2001 and PISA 2000 utilizing the pair wise matching procedure

In accordance to Boudon's structural-individualistic action model, it is the aim of this paper to investigate the casual effects of individual abilities, resources of the parental home, socially selective educational transitions as well as teaching and learning conditions in schools on the development of reading literacy and its dispersion in respect of social origin. It is assumed that the socially selective transition into the secondary school tracks contributes to the general deterioration of the mean reading literacy when controlling for social origin and individual achievement. The socially selective transition from primary to secondary school contributes to the increase of social inequality of reading literacy existing already since the start of the pupils’ schooling. Since it is not possible to isolate these causes with comparative-static cross-sectional data like PIRLS or PISA empirically, we use a design of generating quasi-longitudinal data with three time references, namely reading literacy at the point of enrolment into elementary school, at the age of 9–10 years, and at the age of 15 years by the pair wise matching of “synthetic twins” with identical status criteria. The empirical analysis of the German data of PISA 2000 and PIRLS 2001 confirm the effects of the individual abilities depending on social origin, the social selectivity of transition into the secondary schools, the sorting and selection performances of the school system, the allocation of children into different learning contexts, and the schooling of both the individual development of reading competences and the social inequality of reading literacy.     

The Interrelations Between Cohabitation,Marriage and First Birth in Germany and Sweden

We study the interrelationships between union-formation forms and fertility in Swedish and West German female cohorts born in 1949–1971. We apply simultaneous hazard models, permitting the presence of correlated unobserved heterogeneity. This method allows us to control for country-specific composition of the population with respect to several socio-economic variables, as well as with respect to unobserved factors jointly affecting childbearing and union formation behavior. Our results confirm that partnership formation and the transition to parenthood are partially interchangeable. Net of those selection effects, we find that the impact of being in a union on first birth is higher in Sweden than in Germany, in particular for cohabitation.     

Transitions in welfare participation and female headship

This study uses data from the 1990, 1992, 1993 and 1996 panels of the Survey of Income and Program Participation to examine how welfare policies and local economic conditions contribute to women's transitions into and out of female headship and into and out of welfare participation. It also examines whether welfare participation is directly associated with longer spells of headship. The study employs a simultaneous hazards approach that accounts for unobserved heterogeneity in all of its transition models and for the endogeneity of welfare participation in its headship model. The estimation results indicate that welfare participation significantly reduces the chances of leaving female headship. The estimates also reveal that more generous welfare benefits do not directly contribute to headship but rather contribute indirectly to headship by increasing the chances that a mother will enter welfare and consequently remain a single mother for longer. More generous Earned Income Tax Credit benefits are associated with more stable arrangements for both headship and welfare participation. Other measures of welfare policies, including indicators for the adoption of welfare waivers and the implementation of Temporary Assistance for Needy Families programs, are generally not significantly associated with headship or welfare receipt. Better economic opportunities are estimated to increase headship but reduce welfare participation among unmarried mothers.     

The dynamics of immigrant welfare and labor market behavior

This paper analyzes transitions into and out of social assistance, unemployment, and employment. We estimate a dynamic multinomial logit model, controlling for endogenous initial condition and unobserved heterogeneity, using a large representative Swedish panel data set. The empirical results suggest that particularly refugee immigrants display a greater degree of “structural” state dependence than natives. The high welfare participation rates among refugee immigrants may be due to the existence of a “welfare trap”, while participation among natives and non-refugee immigrants is largely due to permanent unobserved characteristics. These results suggest that welfare reforms may have differential effects on refugee immigrants and natives.

Demographic change,attendance area adjustment and school system impacts

In the extensive litigation over school board liability for segregated schools, a great deal of attention has been focused on changes in school attendance areas. Evidence presented in several trials suggested that school boards have gerrymandered boundaries to keep some schools black and others white. Even though both district and appeal courts have found violations in attendance zone changes, there has been little other than anecodotal evidence to support these findings. In many cases the areas with the most changes in attendance boundaries are also the areas of rapid racial transition, but correlation does not necessarily mean causation. This case study examines boundary changes in Topeka and suggests that racial change in schools is more directly attributable to demographic shifts than to attendance boundary changes.     

Child labour or school attendance? Evidence from Zambia

In this paper we investigate what affects school attendance and child labour in an LDC, using data for Zambia. Since the data comes from a household survey with information on all household members it allows us to take account of unobserved household effects by introducing household-specific effects in a logit model. The empirical analysis suggests that both economic and sociological variables are important determinants for the choice between school attendance and child labour. In particular, we find some support for the hypothesis that poverty forces households to keep their children away from school. JEL classification: J24, I21, O15 Received May 20, 1996/Accepted January 2, 1997     

Methods for combining ancillary data in stochastic compartment models of cancer mortality: Generalization of heterogeneity models∗

In analyzing mortality data there may be available information from survey and other sources that describe the marginal distribution of risk factors. We present a mortality model where nationally representative survey data on risk factor distributions are combined with data on cohort mortality rates to increase information, i.e., a fixed marginal risk factor distribution is combined with a cohort model representing unobserved individual risk heterogeneity. The model is applied to lung cancer mortality in nine U.S. white male cohorts aged 30 to 70 in 1950 and followed 38 years. Estimates of the cohort specific proportions of smokers were made from the National Health Interview Survey. Comparisons are made for models with different patterns of changes with age of individual heterogeneity.     

Determinants of infant and child mortality in Kenya: an analysis controlling for frailty effects

In this paper, Weibull unobserved heterogeneity (frailty) survival models are utilized to analyze the determinants of infant and child mortality in Kenya. The results of these models are compared to those of standard Weibull survival models. The study particularly examines the extent to which child survival risks continue to vary net of observed factors and the extent to which nonfrailty models are biased due to the violation of the statistical assumption of independence. The data came from the 1998 Kenya Demographic and Health Survey. The results of the standard Weibull survival models clearly show that biodemographic factors are more important in explaining infant mortality, while socioeconomic, sociocultural and hygienic factors are more important in explaining child mortality. Frailty effects are substantial and highly significant both in infancy and in childhood, but the conclusions remain the same as in the nonfrailty models.     

The impact of family structure transitions on youth achievement: Evidence from the children of the NlSY79

We investigated the sensitivity of measures of cognitive ability and socioemotional development to changes in parents' marital status using data from the National Longitudinal Survey of Youth, 1979. We used several scores for each assessment, taken at different times relative to parents' marital transitions, which allowed us to trace the effects starting up to five years before a parent's change in marital status and continuing for up to six years afterward. It also allowed us to correct for the unobserved heterogeneity of the transition and nontransition samples by controlling for the child's fixed effect in estimating the time path of his or her response to the transition. We found that children from families with both biological parents scored significantly better on the BPI and the PIAT-math and PIAT-reading assessments than did children from nonintact families. However, much of the difference disappeared when we controlled for background variables. Furthermore, when we controlled for child fixed effects, we did not find significant longitudinal variation in these scores over long periods that encompass the marital transition. This finding suggests that most of the variation is due to cross-sectional differences and is not a result of marital transitions per se.     

Transitions in welfare participation and female headship

This study uses data from the 1990, 1992, 1993 and 1996 panels of the Survey of Income and Program Participation to examine how welfare policies and local economic conditions contribute to women's transitions into and out of female headship and into and out of welfare participation. It also examines whether welfare participation is directly associated with longer spells of headship. The study employs a simultaneous hazards approach that accounts for unobserved heterogeneity in all of its transition models and for the endogeneity of welfare participation in its headship model. The estimation results indicate that welfare participation significantly reduces the chances of leaving female headship. The estimates also reveal that more generous welfare benefits do not directly contribute to headship but rather contribute indirectly to headship by increasing the chances that a mother will enter welfare and consequently remain a single mother for longer. More generous Earned Income Tax Credit benefits are associated with more stable arrangements for both headship and welfare participation. Other measures of welfare policies, including indicators for the adoption of welfare waivers and the implementation of Temporary Assistance for Needy Families programs, are generally not significantly associated with headship or welfare receipt. Better economic opportunities are estimated to increase headship but reduce welfare participation among unmarried mothers.     

Parental income and the fruits of labor: Variability in homework efficacy in secondary school

Research in the sociology of education has shown that noncognitive traits are important predictors of educational outcomes and a mechanism of the intergenerational transmission of status. However, previous research on this topic typically posits that there is a constant effect of these traits with variable prevalences of these traits by socioeconomic status. Using time spent on homework as an example, I analyze income-based heterogeneity in homework efficacy, defined as the individual effect of study time on academic achievement, using a national U.S. probability sample of secondary students. Higher income students gain more knowledge from their homework time than their counterparts in all grades and all subjects except history, with greater group differences for math than for science and reading. These results are confirmed by models accounting for time-invariant unobserved heterogeneity in the 8th–10th, but not 10th–12th, grade windows. These results imply that increases in the amount of homework assigned may increase the socioeconomic achievement gap in math, science, and reading in secondary school.     

Methods for combining ancillary data in stochastic compartment models of cancer mortality: generalization of heterogeneity models

"We present a mortality model where nationally representative survey data on risk factor distributions are combined with data on cohort mortality rates to increase information, i.e., a fixed marginal risk factor distribution is combined with a cohort model representing unobserved individual risk heterogeneity. The model is applied to lung cancer mortality in nine U.S. white male cohorts aged 30 to 70 in 1950 and followed 38 years. Estimates of the cohort specific proportions of smokers were made from the National Health Interview Survey. Comparisons are made for models with different patterns of changes with age of individual heterogeneity." (SUMMARY IN FRE)