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Life Course and Event History Analysis
Life Course and Event History Analysis Hans-Peter Blossfeld, European University Institute, Fiesole (FI), Italy Gwendolin J Blossfeld, Nuffield College, Oxford, UK 2015 Elsevier Ltd. All rights reserved.
Abstract Life course analysis has become a very active research field. This article summarizes the main research questions of the life course paradigm and its most important theoretical concepts. It also reports some recent research findings of life course studies. Then, this article introduces the terminology and models of discrete and continuous event history analysis. A concrete event history analysis example is given in order to demonstrate the strength of life course studies.
Introduction Life course analysis has become a very active research field in the social sciences these last decades for good reasons. Large retrospective life history and prospective panel data sets are now available in most modern societies. Well-known examples are the National Longitudinal Surveys (NLS66, NLS79, NLS97, NLSW) or the Panel Study of Income Dynamics (PSID) in the United States, the Life History Study, the Socio-Economic Panel Study (SOEP), or the National Educational Panel Study (NEPS) in Germany, the National Cohort Studies (NSHD, NCDS, BCS70, MCS), the British Household Panel Study (BHPS), and its successor, the study Understanding Society, in the United Kingdom, or the Household, Income and Labour Dynamics in Australia (HILDA) Survey. Most of these data sets are nationally representative for the population or some selected birth cohorts. They provide longitudinal data on intergenerational relationships, educational histories, job trajectories, family careers, fertility events, changes in health status in the life course, and often also data on the life courses of other family and household members such as partners or spouses. Life course data explicitly recognize the dynamic nature of social roles and circumstances as men and women move through their life paths, the interdependence of lives and life choices, the situational imperatives confronting actors in various phases of the life course, and the accumulation of advantages and disadvantages experienced by the individual over the life course (Elder et al., 2003; Crosnoe and Elder, this volume). The dynamic analysis of life course data is a rewarding but formidable challenge. It has been made possible by the development of statistical methods such as event history and panel analysis. These methods do not only allow studying changes over time but also offer better opportunities for a more appropriate timerelated causal analysis (Blossfeld et al., 2007). This article focuses on the close interrelationship of life course and event history analysis. Event history analysis is the statistical study of processes that are characterized in the following general way: (1) there is a population of individuals, each moving among a finite (usually small) number of life course states; (2) these changes (or events) may occur at any point in time; and (3) there are time-constant and/or timevarying factors influencing the timing of these events. Examples are workers who move between unemployment and employment; men and women who enter into consensual
International Encyclopedia of the Social & Behavioral Sciences, 2nd edition, Volume 14
unions or marriages; people who are mobile between different regions or nation-states, and so on. This article first summarizes the main research questions of the life course paradigm and its most important theoretical concepts. It will also report some recent research findings of life course studies. Then, this article introduces the terminology and models of discrete and continuous event history analysis. Finally, a concrete event history analysis example is given in order to demonstrate the strength of life course studies.
Life Course Analysis In the last four decades, there have been great advances in the study of lives over time, and they extend across various disciplines such as sociology, developmental psychology, demography, or medical sciences (Carr, 2008). We limit ourselves to the literature in the social sciences (Elder and Giele, 2009). Here we identify at least five typical research questions of life course researchers.
Studying the Endogenous Logic of Trajectories in the Life Course A first aim of life course researchers is to study the endogenous (causal) logic of trajectories over the life course. In sociology, the concept of trajectory is often used to refer to an individual’s sequence of roles in one domain of life such as the education, work, or family career. The conceptual tool of trajectory encompasses both sequences of different qualitative states (e.g., being single, married, or divorced in a family career) and continuous increases or decreases in quantitative characteristics (e.g., such as income or competence trajectories). In this article, we limit our discussion to life course studies that record and analyze the sequence of qualitative states occupied by individuals over the life course and the timing of changes among these states. For example, an event history of job mobility consists of more or less detailed information about each of the jobs and the exact beginning and ending dates of each job. Data on trajectories are often collected retrospectively in socalled life history studies. Collecting retrospective data is cheaper than panel studies and has the advantage that they code the life course data into one framework of codes and meaning. But retrospective studies also suffer from several
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limitations (see Blossfeld et al., 2007). In particular, data concerning motivational, attitudinal, cognitive, or affective states are difficult (or even impossible) to collect retrospectively because the respondents can hardly recall the timing of changes in these states accurately. Also the retrospective collection of behavioral data has a high potential for bias because of its reliance on autobiographic memory. To reduce these kind of methodological problems, modern panel studies (e.g., the PSID in the United States, the BHPS and the Understanding Society study in the United Kingdom, or the SOEP and the NEPS in Germany) are using a mixed data collection design which combines traditional panel information (i.e., multiple observations on the same individuals at discrete panel waves) with retrospectively collected event history data for the period before the first panel wave and between the successive panel waves. This combined design also allows linking information about an individual’s prospective life planning (e.g., career or family planning) collected in earlier panel waves, with life course behavior recorded in later panel waves. Trajectories of individuals often depend strongly on the structural context and thus draw theoretical attention to societal traditions and norms, social institutions, and organizational structures shaping the careers of individuals. For example, institutions such as the educational system define the times of possible school transitions in the life course and structure the school options available to individuals at certain points in their careers. For example, Shavit and Blossfeld (1993) have found declining effects of family background on successive educational transitions over the educational career for a broad selection of modern societies. It is, however, still an open question, whether the empirical pattern of declining social background effects across successive educational school transitions is (1) a life course effect because the students get increasingly independent from their families of origin, or (2) a selection effect since at each transition only the most competent students from lower social classes make it to the next level while also mediocre students from the upper social classes enter the higher level (Cameron and Heckman, 1998). Thus, as long as it is not possible to control for the unobserved competence development of individuals in educational transition studies, this issue cannot be decided. Life course researchers have been particularly interested to study whether and to which extent events and states at earlier stages of a trajectory have consequences for its later outcomes (Mayer and Tuma, 1990). Dannefer (1987) introduced the socalled Matthew effect into the literature on the life course. The Matthew effect means that small initial inequalities in a trajectory become magnified over the life span. For example, in modern societies there seems to be a general logic in educational careers that the ‘already educated get even more education in the next step’ while the ‘poorly educated at the same time get less,’ so that the difference in education between the two groups gradually increases. The Matthew effect is sometimes also referred to as the cumulative disadvantage/advantage hypothesis (O’Rand and Henretta, 1999). It offers a cumulative explanation of how intracohort inequality is increased over the life course in many life domains. The life course literature also suggests a ‘status maintenance’ and a ‘status leveling’ hypothesis. The first one contends that initial inequalities are carried along as
individuals move through their life course. The second one points to the possibility of a narrowing of the inequality gap (O’Rand and Henretta, 1999).
Studying the Timing of Transitions in the Life Course Transitions in the life course often represent discrete changes in states, for example starting a new job or getting married. The timing of these transitions in the life course is often characterized by inertia effects. Inertia is the increasing resistance of an individual to change its position with increasing duration in a state (duration dependence). For example, it is well-known that with increasing job-specific experience the job mobility rate of an individual is generally declining or with increasing time of living in a particular place, the rate of spatial mobility is generally decreasing. The mechanisms responsible for this life course patterns are often cumulative investments into job- or firm-specific human capital or into local ‘social capital’ (one’s social ties) which make it increasingly costly for the individual to become a mover. Sometimes the time dependence in a state has a nonmonotonic shape. For example, it is well-known that the rate of entry into first motherhood has a nonmonotonic pattern across age in modern societies. As women’s age increases, the rate of entry into motherhood initially rises, reaches a peak, and then decreases. This bell-shaped rate is often explained by two competing mechanisms: (1) the increasing readiness of individuals to enter into motherhood and (2) the probability of the individual to meet a single partner of the opposite sex. At younger ages, there are many unmarried singles on the marriage market in the relevant age range. Then, some of these young men and women marry as they are getting older. With increasing age, however, it is also increasingly difficult to meet an unmarried individual of the opposite sex at the relevant age band. Thus, the marriage rate is at first increasing with an increasing readiness, reaching a peak, and then decreasing with an increasingly difficult marriage market (Blossfeld and Huinink, 1991).
Studying the Effects of Early and Late Life Course Transitions Life transitions often are associated with societal age norms that create expectations when a life course transition ought to occur in an individual’s life (Carr, 2008). They provide a kind of social clock or timetable for important life events (such as the age of completing education, entering the labor market, or having a first child, etc.). With regard to certain life transitions, individuals might be ‘early,’ ‘on-time,’ or ‘late.’ Age norms, connected with social rewards and punishments, exert pressure on individuals to hasten or delay a certain transition and thus encourage age conformity of life course transitions.
Studying the Sequence of Multiple Life Course Transitions Life course studies indicate that normative sequences exist with regard to various life course transitions. For example, Hogan (1981) argued that as a result of general societal norms, individuals move from school to work and then to marriage as well as parenthood. In order to satisfy this sequencing norm, young adults will be less likely to enter
Life Course and Event History Analysis parenthood before they have finished schooling. In addition, individuals enrolled in education may consider themselves not economically ready for marriage and motherhood. Thus, the completion of education is expected to count as an important prerequisite for entering into parenthood. Indeed, many life course studies document that women’s increasing delays of entry into first marriage and motherhood are to a large extent connected with their longer educational participation (Blossfeld and Huinink, 1991).
Studying the Effects of Parallel and Interdependent Processes on the Life Course From a causal-analytical point of view, the dynamic study of parallel and interdependent processes is one of the most important advances of life course research (Blossfeld et al., 2007). These parallel and interdependent processes can operate (1) at the level of individual’s different domains of life (e.g., one may ask how an individual’s job career influences his/her family trajectory; see Blossfeld et al., 2005); (2) there may be parallel processes at the level of some few individuals interacting with each other (e.g., one might study the effect of husband’s career events on his wife’s labor force participation); (3) there may be parallel processes at the intermediate level (e.g., one can analyze how organizational growth of a firm influences career advancement or how changing household structure determines women’s labor force participation; see Blossfeld and Hofmeister, 2006); (4) there may be parallel processes at the macro level (e.g., one may be interested in the effect of changes in the business cycle on family formation or individual career advancement); and (5) there may be any combination of such processes of type (1)– (4). For example, in the study of life course, cohort, and period effects, processes at different levels can be measured and included simultaneously in a multilevel analysis (Blossfeld, 1986).
Interdependent Trajectories at the Level of the Individual At the level of the individual, events in one trajectory are often presumed to influence the transitions in other domains of life and vice versa (e.g., Blossfeld et al., 2007). For example, the economic theory of the family expects that women’s rising educational attainment levels and better career resources affect their rate of entry into first marriage and first motherhood (opportunity cost hypothesis). However, life course analyses demonstrated that changes in the level of educational attainment or changes in career resources had little or no effect on women’s marital timing. The higher-educated women only marry later because they stay longer in school and therefore delay entry into marriage (sequence norm). Yet, there is an effect of women’s educational and career investments on entry into first birth. Because women, and not men, still take primary responsibility for child care in most modern societies. Women therefore work less or even interrupt their careers when a child is born. Therefore, women who have accumulated a high stock of human capital in their life course tend to gradually postpone or even avoid the birth of a first child. This effect is especially pronounced in traditional family systems, where insufficient child care facilities are available, such as those in Southern Europe (Blossfeld, 1995).
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Interdependencies in the Process of Spouse Selection (Educational Homogamy) In most modern societies the participation in higher education has increased dramatically in recent decades – and more so for women than for men. Life course researchers therefore have been especially interested to explore the role of the educational system as a marriage market and to analyze the changes in educational assortative mating induced by educational expansion (Blossfeld, 2009). In their longitudinal analyses they reconstructed the processes of spouse selection in the life courses of single men and women step by step and compared the results across birth cohorts and various countries (Blossfeld and Timm, 2003). These life course studies tried to take into account the dynamic opportunity structures to meet potential partners in the various parts of the educational system. One finding of these longitudinal analyses has been that with increasing duration in the educational system the rate of homogamous marriage is indeed rising. Increasing rates of educational homogamy across cohorts, however, means that social networks are closing to outsiders and that the opportunities of the generation of children are gradually segmenting.
Interdependencies of the Careers of Spouses Life course researchers have been particularly interested to study linked lives (Elder et al., 2003). For example, they analyzed the effect of husbands’ careers on their wives’ labor force participation. A comparative analysis of spouses in 13 countries provided evidence that despite substantial improvements in wives’ educational attainment and career opportunities, the change in gender specialization within dual-earner couples has been rather modest (Blossfeld and Drobnic, 2001). Gender role change within the family to a large extent has been asymmetric almost everywhere: Housework and child care primarily remained ‘women’s work,’ and husband’s participation in housework and child care has not increased substantially (Baxter et al., 2013). The result is often a double burden on women (Evans and Baxter, 2013). Regardless of wife’s job status, husbands in general pursue a life-long continuous employment career. Even in dual-earner marriages, men still tend to define themselves as primary breadwinners, even in cases where their female partners have a similar or even higher occupational status (Blossfeld and Drobnic, 2001). Thus, the career patterns of (married) men are to a large extent independent of career patterns of their partners. Such independence generally does not apply when (married) women’s employment trajectories are analyzed in dependence of their husbands. Male partners tend to exhibit a significant influence on their female partners’ career patterns in many countries (Blossfeld and Drobnic, 2001). For example, Germany stands out as a country with a particularly traditional division of labor in married couples. In this country, the analysis shows that high career resources of the husband can even suppress wife’s career potentials and drive her out of the labor market.
Interdependencies at an Intermediate Level At the intermediate level, life course researchers might examine how the changing household or organizational structure of a firm determines women’s labor force participation in different countries. For example, in modern societies there is
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very often a complex association between the age of the youngest child and female labor force participation (Blossfeld and Hakim, 1997; Blossfeld and Drobnic, 2001). The common interpretation is that the care of young children tends to keep mothers at home in conservative welfare states. However, it is also plausible that the lack of jobs encourages women to enter into a stay-at-home marriage. Event history analysis is able to shed light into this complex interdependence.
Dependencies of Life Courses on Processes at the Macro and Global Level At the macro level of society, life course researchers have been interested, for instance, in the effect of changes in the business cycle on family formation (e.g., Blossfeld and Huinink, 1991). In these studies often effects at different levels are jointly examined. For instance, in the study of life course, cohort, and period effects, processes at the individual level (accumulation of career resources) have been jointly analyzed with two kinds of processes at the macro level: (1) variations in economic entry conditions specific for certain (birth, marriage, etc.) cohorts (cohort effects); and, (2) changes in particular historical conditions affecting all cohorts in the same way (period effects) (Blossfeld, 1986). More recent studies have also demonstrated that similar processes at the global level have diverse effects on individual life courses in various countries (Mayer, 1997). In all modern countries, the effect of globalization is ‘filtered’ by domestic institutions and shaping the life course transitions in countryspecific ways (Blossfeld, 2009). The globalization impact is most important at the transition from youth to adulthood (e.g., at entry into the labor market and the phase of family formation, Blossfeld et al., 2005). In particular the growing economic and temporal uncertainties lead young people to postpone or even forgo family formation (Blossfeld et al., 2005). Established men in their midlife career, however, are remarkably unaffected by globalization (Blossfeld et al., 2006a). The kind of labor market participation and the different welfare regimes are very important, if the impact of globalization on women’s midlife transitions between employment and family are considered in modern societies (Blossfeld and Hofmeister, 2006). Finally, the effects of globalization on late job careers of men and women and their transition into retirement in modern societies are shaped by different pension systems (Blossfeld et al., 2006b).
Event History Analysis Event history analysis provides an appropriate statistical framework for investigating the various dimensions of life course processes just described.
Basic Terminology Event history analysis studies transitions across a set of discrete life course states, including the length of time intervals between entry to and exit from these states. The basic analytical framework is a state space and a time axis. The choice of the time axis or clock (e.g., age, experience, marriage duration, etc.) used in
the life course analysis must be based on theoretical considerations. An episode, spell, waiting time, or duration–terms that are used interchangeably in the literature–is the time span an individual spends in a specific state. The states are discrete and usually small in number (e.g., single, married, divorced, remarried). The definition of a set of possible states, called the state space, is also dependent on substantive considerations. Thus, a careful, theoretically driven choice of the time axis and design of state space are crucial for a successful life course analysis. These issues are often serious sources of misspecification (Blossfeld et al., 2007). The most restricted event history model is based on a process with only a single episode and two states (one origin and one destination state) (see Blossfeld et al., 2007: 38pp.). An example may be the duration (or episode) of first marriage until the end of the marriage (for whatever reason). In this case, each individual who entered into first marriage (origin state) started an episode, which could be terminated by a transition to the destination state ‘not married anymore.’ If more than one destination state exists, these models are called multistate models. They are also referred to as models with competing events or competing risks. For example, the first marriage might be terminated by the event ‘death’ or the event ‘divorce.’ If there are repeated events over the life course, these models are called multiepisode models. For example, if we analyze not only first marriages but all marriages of individuals over the life course at once. The individual then moves repeatedly between different states. Thus, in event history analysis, we have often a sample of i ¼ 1,.,N multistate-multiepisode data. A complete description of the data is given by ðui ; mi ; oi ; di ; si ; ti ; xi Þ i ¼ 1; .; N where ui is the identification number of the individual; mi is the serial number of the episode; oi is the origin state, the state held during the episode until the ending time of the episode; di is the destination state defined as the state reached at the ending time of the episode; si and ti are the starting and ending times, respectively. In addition, there is a covariate vector xi with timeconstant and/or time-changing factors associated with the episode. We always assume that the starting and ending times are coded such that the difference ti si is the duration of the episode, which is positive and greater than zero.
Censoring Observations of event histories are often censored. Censoring occurs when the information about the duration in the origin state is incompletely recorded. If the length of time an individual has already spent in the origin state is unknown, the episode is censored on the left. This kind of censoring should be avoided because it is not easy to handle in methodological terms (see Blossfeld et al., 2007: 39pp.). Most life course studies are designed in a way that the processes are observed right from the beginning. Right-censoring on the other hand, is very common. This type of censoring typically occurs in life course studies at the time of the retrospective interview, or in panel studies at the time of the last panel wave. For example, if one is interested in entry into first motherhood, women who are still in their fertile years and have not had a first baby until the interview, have a right-censored episode. This means that
Life Course and Event History Analysis these women might get a first baby later, but we do not know. Because the timing of the interview is normally independent of the timing of the substantive processes under study, this type of right censoring is unproblematic. It can easily be handled with event history methods.
The Dependent Variable Event history models can be formulated in continuous-time (Blossfeld et al., 2007) or discrete-time (Mills, 2011; Yamaguchi, 1991; Vermunt, 1997). For each point in time (continuous-time models) or for each time interval (discretetime models), they predict future levels or changes of the transition rate of the dependent process on the basis of states and/or events of other processes in the past. The central concept of event history analysis is the transition rate. Because of the various origins of event history analysis in the different disciplines, the transition rate is also called the hazard rate, intensity rate, failure rate, transition intensity, risk function, or mortality rate. The transition rate describes in detail how the dependent process evolves over time. If time can be considered to be (approximately) continuous, i.e., when events at least in principle can happen at any point in time, the transition rate r(t) can be interpreted as the propensity (or intensity) to change from an origin state to a destination state, at time t (Blossfeld et al., 2007: p. 36): Prðt T < t 0 jT tÞ=ðt 0 tÞ with t < t 0 rðtÞ ¼ lim 0 t /t
It is important to note that the propensity r(t) is defined in relation to a risk set (T t) at t, i.e., the set of units that still can experience the event because they have not yet had the event before t. In other words, the transition rate is a conditional density function, that is, the density function f(t) divided by the survivor function G(t) rðtÞ ¼ f ðtÞ=GðtÞ Pr (t T < t0 )/(t0 t) with t < t0 and where f(t) ¼ lim t 0 /t G(t) ¼ Pr(T t). If events can only happen within fixed time-intervals, the continuous time axis is arbitrarily split into a series of time intervals s0 < s1 < s2 < . < sq, with s0 ¼ 0. The number of the time interval then becomes a discrete random variable T* ¼ t 5 T* ˛ (st1, st), with t ¼ 1, ., q. T* denotes the time interval, where an event happens. The discrete-time transition rate is then a (conditional) probability, r ðtÞ ¼ PrðT ¼ tjT tÞ with 0 r ðtÞ 1 r*(t) is the probability that the dependent variable changes from an origin state to a destination state in time interval t under the condition that the event did not yet happen until the beginning of that interval. In the discrete-time model the transition rate r*(t) is therefore a conditional probability function, where the probability function f*(t) is divided by the survivor function G*(t) r ðtÞ ¼ f ðtÞ=G ðtÞ where f ðtÞ ¼ PrðT ¼ tÞ
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and G ðtÞ ¼ PrðT tÞ For small time intervals (e.g., when life histories are recorded on the basis of months) continuous-time models can be approximated by discrete-time models (Blossfeld et al., 2007: p. 37). The estimation results of equivalent time-continuous and time-discrete event history models Pr(T* ¼ t) then yield very similar coefficients.
Statistical Models The central idea in event history analysis is to make the continuous-time transition rate r(t) or the discrete-time transition rate r*(t) dependent on concepts of time (e.g., duration t) and on a set of time-constant x or time-dependent x(t) covariates: rðtÞ ¼ g½t; x; xðtÞ or r ðtÞ ¼ g½t; x; xðtÞ The causal interpretation of the transition rate requires that we take the temporal order in which the processes evolve very seriously. In the continuous-time mode, at any given point in time t, the transition rate r(t) can be made dependent on conditions that happened to occur in the past (i.e., before t), but not on what is the case at t or in the future after t. Equivalently, in the discrete-time model, in any given time interval t, the discrete-time transition rate r*(t) can be made dependent on conditions that happened to occur before the beginning of interval t, but not on what is the case in time interval t or after time interval t. There are several possibilities to specify the functional relationship g(.) between covariates and the transition rate in continuous-time event history analysis (see Blossfeld et al., 2007). First, the ‘exponential model,’ which normally serves as a kind of baseline model, assumes that the transition rate can vary with different constellations of time-constant covariates, so that the rates are time-constant, too (see Blossfeld et al., 2007: 87pp.) rðtÞ ¼ expðb0 þ b1 x1 þ b2 x2 þ . þ bn xn Þ ¼ expðXbÞ where b0 is a constant, X is the row vector of covariates, and b is a corresponding column vector of coefficients. In most life course applications of transition rate models, the assumption that the forces of change are constant over time is, however, not justified. This is particularly true, if we are interested in causal relationships which relate changes (or events) in some (explaining) processes to changes (or events) in a dependent life course process. In our view, the most important step forward in event history analysis has been to explicitly measure and include time-dependent covariates in transition rate models. In such cases, covariates can change their values over process time. Time-dependent covariates can be qualitative or quantitative, and may stay constant for finite periods of time or change continuously (see Blossfeld et al., 2007: p. 128). Time-dependent covariates can be included (1) by using a piecewise constant exponential model, (2) by applying the method of episode splitting in parametric or semiparametric transition rate models, and (3) by specifying the distributional form of the time-dependence and directly estimating its parameters using maximum likelihood method.
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A first simple and very useful generalization of the ‘exponential model’ is the so-called ‘piecewise constant exponential model.’ It allows the transition rate to vary across fixed time periods with period-constant or period-specific effects of covariates (see Blossfeld et al., 2007: 116pp.). The piecewise constant model is particularly helpful when researchers are not in a position to measure and include important causal factors (time-dependent covariates) explicitly or when they do not have a clear idea about the form of the time-dependence of the process, after controlling for important covariates. The basic idea of the piecewise constant exponential model is to split the duration into L time periods. It ¼ ftjs1 < t slþ1 g
1 ¼ 1; .; L
based on arbitrary split points on the time axis 0 ¼ s1 < s2 < . < sL, with sL ¼ N. The transition rate can then vary over the l ¼ 1, ., L time periods based on the changing period-specific constants bl (baseline hazard rate) rðtÞ ¼ expfb1 þ Xbg if t ε I1 where X is a (row) vector of covariates, and b is an associated vector of coefficients. Note that in this model there is no additional constant in X. Since causal relationships relate changes (or events) in explaining processes to changes (or events) in a dependent life course process, it is very important to be able to represent the changes of the causal forces in event history models directly. An easy way to do this is to include time-varying covariates x(t) in the ‘exponential model’ via the method of episode splitting. rðtÞ ¼ exp b1 x1 þ b2 x2 þ . þ bn xn þ bnþ1 xnþ1 ðtÞ þ bnþ2 xnþ2 ðtÞ þ . þ bnþp xnþp ¼ exp½XðtÞb
[1]
where b1 is the regression constant (x1 ¼ 1). The transformation of the person-spell file into a person-period file through episode splitting is described in detail in Blossfeld et al. (2007: 135pp.). Another model is the so-called Cox (1972) model, where the baseline hazard rate h(t) is left unspecified. Thus, it is only possible to estimate the effects of the time-constant or/and time-varying covariates, controlling for an unknown baseline hazard rate. This model is also called semiparametric model, since only part of the rate function is parametrically specified, or partial likelihood model, because only part of the likelihood function is maximized (see Blossfeld et al., 2007: 216pp.), rðtÞ ¼ hðtÞexp b1 x1 þ b2 x2 þ . þ bn xn þ bnþ1 xnþ1 ðtÞ þ bnþ2 xnþ2 ðtÞ þ . þ bnþp xnþp ðtÞ ¼ hðtÞexp XðtÞb Note that in this model there is again no regression constant in X(t). However, in some applications in life course research, substantive theory or previous empirical research may suggest a specific shape of time or duration dependence of the transition rate. However, time itself is no causal factor. Rather measures of time may serve as proxies for time-changing causal factors that could not be observed directly (see Blossfeld et al.,
2007: 182pp.). For example, duration might serve as a proxy for ‘the changing amount of marriage-specific investments’ in divorce studies. There are different parametric models which are based on specific shapes of the time-dependence. For example, the Gompertz(-Makeham) and Weibull models are able to specify monotonically increasing or monotonically decreasing shapes of the hazard rate. Further parametric models such as the Sickle, the Log-logistic, and the Log-normal models allow to estimate a (at first increasing and then decreasing) nonmonotonic time-dependency (see for more details Blossfeld et al., 2007: 204pp.). Finally, an important problem of event history analysis is also the issue of unobserved heterogeneity. In this case, the transition rate that is estimated for a population can be the result (a mixture) of quite different transition rates in the subpopulations (see Blossfeld et al., 2007: 247pp.). There have been several proposals to deal with unobserved heterogeneity in time-continuous transition rate models. The basic idea is to incorporate an ‘error term’ into the model specification. For example, the continuous-time transition rate can be made dependent on an exponential model, the observed (timedependent) covariates X(t) and a stochastic error term n, which is e.g., Gamma distributed (see Blossfeld et al., 2007: 256pp.) rðtjnÞ ¼ exp½XðtÞbn
with n 0
[2]
A likelihood ratio test can then be used to test, whether the transition rate models with and without this unobserved heterogeneity term differ. In the case of discrete-time models, the estimation of covariate parameters is normally achieved by preparing a periodperson data file and then estimating a simple logit model: r ðtÞ ¼
expða1 x1 þ a2 x2 þ . þ an xn Þexp½bðtÞ 1 þ expða1 x1 þ a2 x2 þ . þ an xn Þexp½bðtÞ
[3]
or r ðtÞ ¼
abðtÞ 1 þ abðtÞ
with a ¼ expða1 x1 þ a2 x2 þ . þ an xn Þ and bðtÞ ¼ exp½bðtÞ
If b(t) ¼ exp(b0), the logit model estimates an exponential model, if b(t) ¼ exp(b0 þ b1t) it estimates a Gompertz model, if b(t) ¼ exp(b0 þ b1lnt) it estimates a Weibull model. A piecewise constant model is estimated for b(t) ¼ exp(b1) if t ε I1 where changing period-specific constants b1 can vary over the l ¼ 1,., L time periods.
Application Example In order to demonstrate the strength of life course analysis with event history models in a substantive context, we estimate the rate of dissolution of first marriage for East and West German women. Using a subsample of retrospective life histories of 3957 married women born in East and West Germany from the NEPS, we estimate a period-specific discrete-time event history logit model with time-constant and time-varying covariates. The NEPS collects dates of transitions and events on a monthly basis. For our analysis, we define for each woman a spell starting at entry into first marriage and ending at the time of its dissolution. For women, who do not experience a marital dissolution until the time of the interview, we censor the spells
Life Course and Event History Analysis
on the right. The spells are also right-censored for women whose husband passed away. This leads to a person-oriented spell data set, where each married woman in the sample has exactly one record of data. We have then transformed this person-level data set into a person-period data set using the method of episode splitting (Blossfeld et al., 2007), in which each woman has multiple records – one for each month. Such a person-period data set allows an easy integration of timevarying covariates because the covariates can change their values across each of the person-month records. In our longitudinal analysis, we are using the following covariates: 1. Duration of marriage (time-dependent covariate). We include dummy variables distinguishing eight periods of marriage duration; 2. Place of birth (time-constant covariate). We use the dummy variable ‘East Germany’ to identify women born in East Germany, women born in West Germany are the reference category; 3. Historical periods (time-dependent covariates). To distinguish the periods before and after unification in our analysis, we use the dummy variable ‘Period after 1990.’ The reference category is the ‘Period until 1990.’ We include also an interaction dummy variable ‘East*Period after 1990’ to estimate the effect of the ‘German unification’ on East German women; 4. Husband’s educational attainment (time-constant covariate). In order to model husband’s highest educational attainment, we distinguish seven educational degrees. We then attach the average number of years that are necessary to achieve these degrees; 5. Wife’s educational attainment (time-dependent covariate). Each time when a woman attains a higher level of education, the educational attainment level is adjusted. We distinguish seven educational attainment levels and express each degree as the average number of years necessary to achieve it; 6. Partner’s relative levels of education (time-dependent covariates). In order to model the relative resources of partners, we introduce two dummy variables indicating whether a woman has a higher or lower level of education than her partner (ref. category: both partners have the same educational attainment level); 7. Premarital states (time-constant covariates). We introduce three dummy variables to control if women cohabited with their husband at the time of marriage (ref. category: women who did not cohabit with their husband at the time of marriage), were pregnant at the time of marriage (ref. category: women who were not pregnant at the time of marriage), or have had a child before marriage (ref. category: women who had no child before marriage); 8. Age at first marriage (time-constant covariates). To include the age at first marriage into our analysis we distinguish five age categories; 9. Age of the youngest child (time-dependent covariate). We include the age of the youngest child by distinguishing seven time-dependent dummy variables. Table 1 shows the results of our discrete event history analysis of women’s dissolution of first marriage in Germany including time-varying and time-constant variables. In order to
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Table 1 Estimation results of a discrete-time event history model for the dissolution of women’s first marriage in Germany Covariate Duration (in years) 0–1 2–3 4–5 6–7 8–10 11–15 16–20 20þ Place of birth East Germany Historical Period Period after 1990 East*Period after 1990 Education Husband’s education Wife’s education Partner’s relative levels of education Woman higher Both equal (ref.) Woman lower Premarital states Cohabitation at time of marriage Pregnancy at the time of marriage Birth of a child before marriage Age at first marriage Under 20 (ref.) 20–22 23–25 26–28 >28 Age youngest child (years) No child (ref.) <1 1–2 3–5 6–10 11–14 >14 Log likelihood Number of events Number of subepisodes Chi2 Degrees of freedom
Coefficient 9.286 7.328 6.957 7.149 7.349 7.700 7.675 7.950
c c c c c c c c
0.214 0.142 0.562
b
0.095 0.096
c
0.378
c
0.268
a
0.511 0.052 0.237
c
0.250 0.484 0.771 0.800
a
0.222 0.259 0.701 0.645 0.806 0.516 5902.277 742 959 259 36140.81 28
a
c
a
c c c
c c c b
a
p < 0.05. p < 0.01. p < 0.001. n ¼ 3957. Source: Own computations based on the NEPS data. b c
test whether the duration of the first marriage has an effect on divorce, we include information on the duration of first marriage into our analysis. The results show a nonmonotonic bell-shaped pattern of the duration of marriage on divorce. In other words, the rate of dissolution increases up to the fifth year and then decreases. To analyze the divorce rate in East and West Germany before and after German unification, we include dummy variables to control the place of birth (East vs West Germany), historical periods (before and after German unification), and
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an interaction term ‘East*Period after 1990.’ The results show that there is a declining divorce rate in East Germany after the German unification because of the high level of uncertainty in the transition process from socialism to capitalism. Table 1 also shows that a higher educational attainment level of the husband stabilizes the marriage, while a higher educational attainment level of the wife has a destabilizing effect. If we compare the relative resources of husband and wife, we find that only homogamous marriages are more stable. If we include information on premarital cohabitation, childbirth before marriage and pregnancy at the time of marriage into our model, our results show that premarital cohabitation and childbirth before marriage have a destabilizing effect on marriages. Being pregnant at the time of marriage has no effect. We also include information on the age at first marriage. The result shows that marriages are more stable the older the woman is at entry into first marriage. Finally, we include information whether a couple has children and the age of the youngest child into our example analysis. Couples who have a baby younger than 1 year have the lowest divorce rate. The divorce rate then increases with the age of the youngest child and rises above the divorce rate of couples without children. If we control for unobserved heterogeneity, the results of this analysis do not change.
See also: Age Stratification; Age, Sociology of; Aging, Theories of; Assortative Mating in the Marriage Market; Capitalism: Global; Cohabitation: United States; Demographic Models; Demographic Techniques: LEXIS Diagram; Divorce, Sociology of; Family Theory: Economics of Childbearing; Family Theory: Economics of Marriage and Divorce; Fertility Change: Quantum and Tempo; Fertility Theory; Fertility of Single and Cohabiting Women; Labor, Division of; Life Course: Sociological Aspects; Life Table; Lifespan Development, Theory of; Lifespan Development: Evolutionary Perspectives; Linked Lives; Marriage and the Dual-Career Family; Multistate Transition Models in Demography; Period and Cohort Analysis in Demography; Retirement and Encore Adulthood: The New Later Life Course; Social Stratification; Transition to Adulthood.
Bibliography Baxter, J., Hewitt, B., Haynes, M., Western, M., 2013. Pathways through the life course: the effect of relationship and parenthood transition on domestic labour. In: Evans, A., Baxter, J. (Eds.), Negotiating the Life Course. Stability and Change in Life Pathways. Springer, Dordrecht, pp. 145–159. Blossfeld, H.-P., 2009. Educational assortative marriage in comparative perspective. Annual Review of Sociology 35, 513–530. Blossfeld, H.-P., 1995. The New Role of Women. Family Formation in Modern Societies. Westview Press, Boulder, CO.
Blossfeld, H.-P., 1986. Career opportunities in the Federal Republic of Germany: a dynamic approach to the study of life course, cohort, and period effects. European Sociological Review 2, 208–225. Blossfeld, H.-P., Buchholz, S., Hofäcker, D., 2006b. Globalization, Uncertainty and Late Careers in Society. Routledge, London and New York. Blossfeld, H.-P., Drobnic, S., 2001. Careers of Couples in Contemporary Societies. From Male Breadwinner to Dual-Earner Families. Oxford University Press, Oxford. Blossfeld, H.-P., Golsch, K., Rohwer, G., 2007. Event History Analysis with Stata. Lawrence Erlbaum, Mawah, NJ. Blossfeld, H.-P., Hakim, C., 1997. Between Equalization and Marginalization. Women Working Part-Time in Europe and the United States of America. Oxford University Press, New York and Oxford. Buchholz, S., Hofäcker, D., Mills, M., Blossfeld, H.-P., Kurz, K., Hofmeister, H., 2009. Life courses in the globalization process: the development of social inequalities in modern societies. A summary of findings from the GLOBALIFE project. European Sociological Review 25, 53–72. Blossfeld, H.-P., Hofmeister, H., 2006. Globalization, Uncertainty and Women’s Careers in International Comparison. Edward Elgar, Cheltenham, UK and Northampton, MA, USA. Blossfeld, H.-P., Huinink, J., 1991. Human capital investments or norms of role transition? How women’s schooling and career affect the process of family formation. American Journal of Sociology 97, 143–168. Blossfeld, H.-P., Mills, M., Klijzing, E., Kurz, K., 2005. Globalization, Uncertainty and Youth in Society. Routledge, London and New York. Blossfeld, H.-P., Mills, M., Bernardi, F., 2006a. Globalization, Uncertainty and Men’s Careers in International Comparison. Edward Elgar, Cheltenham, UK and Northampton, MA,USA. Blossfeld, H.-P., Timm, A., 2003. Who Marries Whom? Educational Systems as Marriage Markets in Modern Societies. Kluwer Academic Publishers, Dordrecht. A Comparison of Thirteen Countries, European Studies of Population. Cameron, S.V., Heckman, J.J., 1998. Life cycle schooling and dynamic selection bias. models and evidence for five cohorts of American males. Journal of Political Economy 106, 262–333. Carr, D., 2008. Encyclopedia of the Life Course and Human Development, 3 vols. Gale, Detroit. Cox, D.R., 1972. Partial likelihood. Biometrika 62, 269–276. Dannefer, D., 1987. Aging as intercohort differentiation. Accentuation, the Matthew Effect, and the life course. Sociological Forum 2, 211–236. Elder, G.H., Kirkpatrick, J.M., Crosnoe, R., 2003. The emergence and development of life course theory. In: Mortimer, J.T., Shanahan, M.J. (Eds.), Handbook of the Life Course. Springer, New York, pp. 3–19. Elder, G.H., Giele, J.Z., 2009. Life course studies: an evolving field. In: Elder, G.H., Giele, J.Z. (Eds.), The Craft of Life Course Research. The Guilford Press, New York, pp. 1–24. Evans, A., Baxter, J., 2013. Negotiating the Life Course. Stability and Change in Life Pathways. Springer, Dordrecht. Hogan, D.P., 1981. Transitions and Social Change: The Early Lives of American Men. Academic Press, New York. Mayer, K.U., 1997. Notes on a comparative political economy of life courses. Comparative Social Research 16, 203–226. Mayer, K.U., Tuma, N.B., 1990. Event History Analysis in Life Course Research. University of Wisconsin Press, Madison. Mills, M., 2011. Introducing Survival and Event History Analysis. Sage, London. O’Rand, A.M., Henretta, J.C., 1999. Age and Inequality: Diverse Pathways through Later Life. Westview Press, Boulder, CO. Shavit, Y., Blossfeld, H.-P., 1993. Persistent Inequality. Changing Educational Attainment in Thirteen Countries. Westview Press, Boulder, CO. Vermunt, J.K., 1997. Log-linear Models for Event Histories. Sage, Newbury Park, CA. Yamaguchi, K., 1991. Event History Analysis. Sage, Newbury Park, CA.
Abstract Life course analysis has become a very active research field. This article summarizes the main research questions of the life course paradigm and its most important theoretical concepts. It also reports some recent research findings of life course studies. Then, this article introduces the terminology and models of discrete and continuous event history analysis. A concrete event history analysis example is given in order to demonstrate the strength of life course studies.
Introduction Life course analysis has become a very active research field in the social sciences these last decades for good reasons. Large retrospective life history and prospective panel data sets are now available in most modern societies. Well-known examples are the National Longitudinal Surveys (NLS66, NLS79, NLS97, NLSW) or the Panel Study of Income Dynamics (PSID) in the United States, the Life History Study, the Socio-Economic Panel Study (SOEP), or the National Educational Panel Study (NEPS) in Germany, the National Cohort Studies (NSHD, NCDS, BCS70, MCS), the British Household Panel Study (BHPS), and its successor, the study Understanding Society, in the United Kingdom, or the Household, Income and Labour Dynamics in Australia (HILDA) Survey. Most of these data sets are nationally representative for the population or some selected birth cohorts. They provide longitudinal data on intergenerational relationships, educational histories, job trajectories, family careers, fertility events, changes in health status in the life course, and often also data on the life courses of other family and household members such as partners or spouses. Life course data explicitly recognize the dynamic nature of social roles and circumstances as men and women move through their life paths, the interdependence of lives and life choices, the situational imperatives confronting actors in various phases of the life course, and the accumulation of advantages and disadvantages experienced by the individual over the life course (Elder et al., 2003; Crosnoe and Elder, this volume). The dynamic analysis of life course data is a rewarding but formidable challenge. It has been made possible by the development of statistical methods such as event history and panel analysis. These methods do not only allow studying changes over time but also offer better opportunities for a more appropriate timerelated causal analysis (Blossfeld et al., 2007). This article focuses on the close interrelationship of life course and event history analysis. Event history analysis is the statistical study of processes that are characterized in the following general way: (1) there is a population of individuals, each moving among a finite (usually small) number of life course states; (2) these changes (or events) may occur at any point in time; and (3) there are time-constant and/or timevarying factors influencing the timing of these events. Examples are workers who move between unemployment and employment; men and women who enter into consensual
International Encyclopedia of the Social & Behavioral Sciences, 2nd edition, Volume 14
unions or marriages; people who are mobile between different regions or nation-states, and so on. This article first summarizes the main research questions of the life course paradigm and its most important theoretical concepts. It will also report some recent research findings of life course studies. Then, this article introduces the terminology and models of discrete and continuous event history analysis. Finally, a concrete event history analysis example is given in order to demonstrate the strength of life course studies.
Life Course Analysis In the last four decades, there have been great advances in the study of lives over time, and they extend across various disciplines such as sociology, developmental psychology, demography, or medical sciences (Carr, 2008). We limit ourselves to the literature in the social sciences (Elder and Giele, 2009). Here we identify at least five typical research questions of life course researchers.
Studying the Endogenous Logic of Trajectories in the Life Course A first aim of life course researchers is to study the endogenous (causal) logic of trajectories over the life course. In sociology, the concept of trajectory is often used to refer to an individual’s sequence of roles in one domain of life such as the education, work, or family career. The conceptual tool of trajectory encompasses both sequences of different qualitative states (e.g., being single, married, or divorced in a family career) and continuous increases or decreases in quantitative characteristics (e.g., such as income or competence trajectories). In this article, we limit our discussion to life course studies that record and analyze the sequence of qualitative states occupied by individuals over the life course and the timing of changes among these states. For example, an event history of job mobility consists of more or less detailed information about each of the jobs and the exact beginning and ending dates of each job. Data on trajectories are often collected retrospectively in socalled life history studies. Collecting retrospective data is cheaper than panel studies and has the advantage that they code the life course data into one framework of codes and meaning. But retrospective studies also suffer from several
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limitations (see Blossfeld et al., 2007). In particular, data concerning motivational, attitudinal, cognitive, or affective states are difficult (or even impossible) to collect retrospectively because the respondents can hardly recall the timing of changes in these states accurately. Also the retrospective collection of behavioral data has a high potential for bias because of its reliance on autobiographic memory. To reduce these kind of methodological problems, modern panel studies (e.g., the PSID in the United States, the BHPS and the Understanding Society study in the United Kingdom, or the SOEP and the NEPS in Germany) are using a mixed data collection design which combines traditional panel information (i.e., multiple observations on the same individuals at discrete panel waves) with retrospectively collected event history data for the period before the first panel wave and between the successive panel waves. This combined design also allows linking information about an individual’s prospective life planning (e.g., career or family planning) collected in earlier panel waves, with life course behavior recorded in later panel waves. Trajectories of individuals often depend strongly on the structural context and thus draw theoretical attention to societal traditions and norms, social institutions, and organizational structures shaping the careers of individuals. For example, institutions such as the educational system define the times of possible school transitions in the life course and structure the school options available to individuals at certain points in their careers. For example, Shavit and Blossfeld (1993) have found declining effects of family background on successive educational transitions over the educational career for a broad selection of modern societies. It is, however, still an open question, whether the empirical pattern of declining social background effects across successive educational school transitions is (1) a life course effect because the students get increasingly independent from their families of origin, or (2) a selection effect since at each transition only the most competent students from lower social classes make it to the next level while also mediocre students from the upper social classes enter the higher level (Cameron and Heckman, 1998). Thus, as long as it is not possible to control for the unobserved competence development of individuals in educational transition studies, this issue cannot be decided. Life course researchers have been particularly interested to study whether and to which extent events and states at earlier stages of a trajectory have consequences for its later outcomes (Mayer and Tuma, 1990). Dannefer (1987) introduced the socalled Matthew effect into the literature on the life course. The Matthew effect means that small initial inequalities in a trajectory become magnified over the life span. For example, in modern societies there seems to be a general logic in educational careers that the ‘already educated get even more education in the next step’ while the ‘poorly educated at the same time get less,’ so that the difference in education between the two groups gradually increases. The Matthew effect is sometimes also referred to as the cumulative disadvantage/advantage hypothesis (O’Rand and Henretta, 1999). It offers a cumulative explanation of how intracohort inequality is increased over the life course in many life domains. The life course literature also suggests a ‘status maintenance’ and a ‘status leveling’ hypothesis. The first one contends that initial inequalities are carried along as
individuals move through their life course. The second one points to the possibility of a narrowing of the inequality gap (O’Rand and Henretta, 1999).
Studying the Timing of Transitions in the Life Course Transitions in the life course often represent discrete changes in states, for example starting a new job or getting married. The timing of these transitions in the life course is often characterized by inertia effects. Inertia is the increasing resistance of an individual to change its position with increasing duration in a state (duration dependence). For example, it is well-known that with increasing job-specific experience the job mobility rate of an individual is generally declining or with increasing time of living in a particular place, the rate of spatial mobility is generally decreasing. The mechanisms responsible for this life course patterns are often cumulative investments into job- or firm-specific human capital or into local ‘social capital’ (one’s social ties) which make it increasingly costly for the individual to become a mover. Sometimes the time dependence in a state has a nonmonotonic shape. For example, it is well-known that the rate of entry into first motherhood has a nonmonotonic pattern across age in modern societies. As women’s age increases, the rate of entry into motherhood initially rises, reaches a peak, and then decreases. This bell-shaped rate is often explained by two competing mechanisms: (1) the increasing readiness of individuals to enter into motherhood and (2) the probability of the individual to meet a single partner of the opposite sex. At younger ages, there are many unmarried singles on the marriage market in the relevant age range. Then, some of these young men and women marry as they are getting older. With increasing age, however, it is also increasingly difficult to meet an unmarried individual of the opposite sex at the relevant age band. Thus, the marriage rate is at first increasing with an increasing readiness, reaching a peak, and then decreasing with an increasingly difficult marriage market (Blossfeld and Huinink, 1991).
Studying the Effects of Early and Late Life Course Transitions Life transitions often are associated with societal age norms that create expectations when a life course transition ought to occur in an individual’s life (Carr, 2008). They provide a kind of social clock or timetable for important life events (such as the age of completing education, entering the labor market, or having a first child, etc.). With regard to certain life transitions, individuals might be ‘early,’ ‘on-time,’ or ‘late.’ Age norms, connected with social rewards and punishments, exert pressure on individuals to hasten or delay a certain transition and thus encourage age conformity of life course transitions.
Studying the Sequence of Multiple Life Course Transitions Life course studies indicate that normative sequences exist with regard to various life course transitions. For example, Hogan (1981) argued that as a result of general societal norms, individuals move from school to work and then to marriage as well as parenthood. In order to satisfy this sequencing norm, young adults will be less likely to enter
Life Course and Event History Analysis parenthood before they have finished schooling. In addition, individuals enrolled in education may consider themselves not economically ready for marriage and motherhood. Thus, the completion of education is expected to count as an important prerequisite for entering into parenthood. Indeed, many life course studies document that women’s increasing delays of entry into first marriage and motherhood are to a large extent connected with their longer educational participation (Blossfeld and Huinink, 1991).
Studying the Effects of Parallel and Interdependent Processes on the Life Course From a causal-analytical point of view, the dynamic study of parallel and interdependent processes is one of the most important advances of life course research (Blossfeld et al., 2007). These parallel and interdependent processes can operate (1) at the level of individual’s different domains of life (e.g., one may ask how an individual’s job career influences his/her family trajectory; see Blossfeld et al., 2005); (2) there may be parallel processes at the level of some few individuals interacting with each other (e.g., one might study the effect of husband’s career events on his wife’s labor force participation); (3) there may be parallel processes at the intermediate level (e.g., one can analyze how organizational growth of a firm influences career advancement or how changing household structure determines women’s labor force participation; see Blossfeld and Hofmeister, 2006); (4) there may be parallel processes at the macro level (e.g., one may be interested in the effect of changes in the business cycle on family formation or individual career advancement); and (5) there may be any combination of such processes of type (1)– (4). For example, in the study of life course, cohort, and period effects, processes at different levels can be measured and included simultaneously in a multilevel analysis (Blossfeld, 1986).
Interdependent Trajectories at the Level of the Individual At the level of the individual, events in one trajectory are often presumed to influence the transitions in other domains of life and vice versa (e.g., Blossfeld et al., 2007). For example, the economic theory of the family expects that women’s rising educational attainment levels and better career resources affect their rate of entry into first marriage and first motherhood (opportunity cost hypothesis). However, life course analyses demonstrated that changes in the level of educational attainment or changes in career resources had little or no effect on women’s marital timing. The higher-educated women only marry later because they stay longer in school and therefore delay entry into marriage (sequence norm). Yet, there is an effect of women’s educational and career investments on entry into first birth. Because women, and not men, still take primary responsibility for child care in most modern societies. Women therefore work less or even interrupt their careers when a child is born. Therefore, women who have accumulated a high stock of human capital in their life course tend to gradually postpone or even avoid the birth of a first child. This effect is especially pronounced in traditional family systems, where insufficient child care facilities are available, such as those in Southern Europe (Blossfeld, 1995).
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Interdependencies in the Process of Spouse Selection (Educational Homogamy) In most modern societies the participation in higher education has increased dramatically in recent decades – and more so for women than for men. Life course researchers therefore have been especially interested to explore the role of the educational system as a marriage market and to analyze the changes in educational assortative mating induced by educational expansion (Blossfeld, 2009). In their longitudinal analyses they reconstructed the processes of spouse selection in the life courses of single men and women step by step and compared the results across birth cohorts and various countries (Blossfeld and Timm, 2003). These life course studies tried to take into account the dynamic opportunity structures to meet potential partners in the various parts of the educational system. One finding of these longitudinal analyses has been that with increasing duration in the educational system the rate of homogamous marriage is indeed rising. Increasing rates of educational homogamy across cohorts, however, means that social networks are closing to outsiders and that the opportunities of the generation of children are gradually segmenting.
Interdependencies of the Careers of Spouses Life course researchers have been particularly interested to study linked lives (Elder et al., 2003). For example, they analyzed the effect of husbands’ careers on their wives’ labor force participation. A comparative analysis of spouses in 13 countries provided evidence that despite substantial improvements in wives’ educational attainment and career opportunities, the change in gender specialization within dual-earner couples has been rather modest (Blossfeld and Drobnic, 2001). Gender role change within the family to a large extent has been asymmetric almost everywhere: Housework and child care primarily remained ‘women’s work,’ and husband’s participation in housework and child care has not increased substantially (Baxter et al., 2013). The result is often a double burden on women (Evans and Baxter, 2013). Regardless of wife’s job status, husbands in general pursue a life-long continuous employment career. Even in dual-earner marriages, men still tend to define themselves as primary breadwinners, even in cases where their female partners have a similar or even higher occupational status (Blossfeld and Drobnic, 2001). Thus, the career patterns of (married) men are to a large extent independent of career patterns of their partners. Such independence generally does not apply when (married) women’s employment trajectories are analyzed in dependence of their husbands. Male partners tend to exhibit a significant influence on their female partners’ career patterns in many countries (Blossfeld and Drobnic, 2001). For example, Germany stands out as a country with a particularly traditional division of labor in married couples. In this country, the analysis shows that high career resources of the husband can even suppress wife’s career potentials and drive her out of the labor market.
Interdependencies at an Intermediate Level At the intermediate level, life course researchers might examine how the changing household or organizational structure of a firm determines women’s labor force participation in different countries. For example, in modern societies there is
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very often a complex association between the age of the youngest child and female labor force participation (Blossfeld and Hakim, 1997; Blossfeld and Drobnic, 2001). The common interpretation is that the care of young children tends to keep mothers at home in conservative welfare states. However, it is also plausible that the lack of jobs encourages women to enter into a stay-at-home marriage. Event history analysis is able to shed light into this complex interdependence.
Dependencies of Life Courses on Processes at the Macro and Global Level At the macro level of society, life course researchers have been interested, for instance, in the effect of changes in the business cycle on family formation (e.g., Blossfeld and Huinink, 1991). In these studies often effects at different levels are jointly examined. For instance, in the study of life course, cohort, and period effects, processes at the individual level (accumulation of career resources) have been jointly analyzed with two kinds of processes at the macro level: (1) variations in economic entry conditions specific for certain (birth, marriage, etc.) cohorts (cohort effects); and, (2) changes in particular historical conditions affecting all cohorts in the same way (period effects) (Blossfeld, 1986). More recent studies have also demonstrated that similar processes at the global level have diverse effects on individual life courses in various countries (Mayer, 1997). In all modern countries, the effect of globalization is ‘filtered’ by domestic institutions and shaping the life course transitions in countryspecific ways (Blossfeld, 2009). The globalization impact is most important at the transition from youth to adulthood (e.g., at entry into the labor market and the phase of family formation, Blossfeld et al., 2005). In particular the growing economic and temporal uncertainties lead young people to postpone or even forgo family formation (Blossfeld et al., 2005). Established men in their midlife career, however, are remarkably unaffected by globalization (Blossfeld et al., 2006a). The kind of labor market participation and the different welfare regimes are very important, if the impact of globalization on women’s midlife transitions between employment and family are considered in modern societies (Blossfeld and Hofmeister, 2006). Finally, the effects of globalization on late job careers of men and women and their transition into retirement in modern societies are shaped by different pension systems (Blossfeld et al., 2006b).
Event History Analysis Event history analysis provides an appropriate statistical framework for investigating the various dimensions of life course processes just described.
Basic Terminology Event history analysis studies transitions across a set of discrete life course states, including the length of time intervals between entry to and exit from these states. The basic analytical framework is a state space and a time axis. The choice of the time axis or clock (e.g., age, experience, marriage duration, etc.) used in
the life course analysis must be based on theoretical considerations. An episode, spell, waiting time, or duration–terms that are used interchangeably in the literature–is the time span an individual spends in a specific state. The states are discrete and usually small in number (e.g., single, married, divorced, remarried). The definition of a set of possible states, called the state space, is also dependent on substantive considerations. Thus, a careful, theoretically driven choice of the time axis and design of state space are crucial for a successful life course analysis. These issues are often serious sources of misspecification (Blossfeld et al., 2007). The most restricted event history model is based on a process with only a single episode and two states (one origin and one destination state) (see Blossfeld et al., 2007: 38pp.). An example may be the duration (or episode) of first marriage until the end of the marriage (for whatever reason). In this case, each individual who entered into first marriage (origin state) started an episode, which could be terminated by a transition to the destination state ‘not married anymore.’ If more than one destination state exists, these models are called multistate models. They are also referred to as models with competing events or competing risks. For example, the first marriage might be terminated by the event ‘death’ or the event ‘divorce.’ If there are repeated events over the life course, these models are called multiepisode models. For example, if we analyze not only first marriages but all marriages of individuals over the life course at once. The individual then moves repeatedly between different states. Thus, in event history analysis, we have often a sample of i ¼ 1,.,N multistate-multiepisode data. A complete description of the data is given by ðui ; mi ; oi ; di ; si ; ti ; xi Þ i ¼ 1; .; N where ui is the identification number of the individual; mi is the serial number of the episode; oi is the origin state, the state held during the episode until the ending time of the episode; di is the destination state defined as the state reached at the ending time of the episode; si and ti are the starting and ending times, respectively. In addition, there is a covariate vector xi with timeconstant and/or time-changing factors associated with the episode. We always assume that the starting and ending times are coded such that the difference ti si is the duration of the episode, which is positive and greater than zero.
Censoring Observations of event histories are often censored. Censoring occurs when the information about the duration in the origin state is incompletely recorded. If the length of time an individual has already spent in the origin state is unknown, the episode is censored on the left. This kind of censoring should be avoided because it is not easy to handle in methodological terms (see Blossfeld et al., 2007: 39pp.). Most life course studies are designed in a way that the processes are observed right from the beginning. Right-censoring on the other hand, is very common. This type of censoring typically occurs in life course studies at the time of the retrospective interview, or in panel studies at the time of the last panel wave. For example, if one is interested in entry into first motherhood, women who are still in their fertile years and have not had a first baby until the interview, have a right-censored episode. This means that
Life Course and Event History Analysis these women might get a first baby later, but we do not know. Because the timing of the interview is normally independent of the timing of the substantive processes under study, this type of right censoring is unproblematic. It can easily be handled with event history methods.
The Dependent Variable Event history models can be formulated in continuous-time (Blossfeld et al., 2007) or discrete-time (Mills, 2011; Yamaguchi, 1991; Vermunt, 1997). For each point in time (continuous-time models) or for each time interval (discretetime models), they predict future levels or changes of the transition rate of the dependent process on the basis of states and/or events of other processes in the past. The central concept of event history analysis is the transition rate. Because of the various origins of event history analysis in the different disciplines, the transition rate is also called the hazard rate, intensity rate, failure rate, transition intensity, risk function, or mortality rate. The transition rate describes in detail how the dependent process evolves over time. If time can be considered to be (approximately) continuous, i.e., when events at least in principle can happen at any point in time, the transition rate r(t) can be interpreted as the propensity (or intensity) to change from an origin state to a destination state, at time t (Blossfeld et al., 2007: p. 36): Prðt T < t 0 jT tÞ=ðt 0 tÞ with t < t 0 rðtÞ ¼ lim 0 t /t
It is important to note that the propensity r(t) is defined in relation to a risk set (T t) at t, i.e., the set of units that still can experience the event because they have not yet had the event before t. In other words, the transition rate is a conditional density function, that is, the density function f(t) divided by the survivor function G(t) rðtÞ ¼ f ðtÞ=GðtÞ Pr (t T < t0 )/(t0 t) with t < t0 and where f(t) ¼ lim t 0 /t G(t) ¼ Pr(T t). If events can only happen within fixed time-intervals, the continuous time axis is arbitrarily split into a series of time intervals s0 < s1 < s2 < . < sq, with s0 ¼ 0. The number of the time interval then becomes a discrete random variable T* ¼ t 5 T* ˛ (st1, st), with t ¼ 1, ., q. T* denotes the time interval, where an event happens. The discrete-time transition rate is then a (conditional) probability, r ðtÞ ¼ PrðT ¼ tjT tÞ with 0 r ðtÞ 1 r*(t) is the probability that the dependent variable changes from an origin state to a destination state in time interval t under the condition that the event did not yet happen until the beginning of that interval. In the discrete-time model the transition rate r*(t) is therefore a conditional probability function, where the probability function f*(t) is divided by the survivor function G*(t) r ðtÞ ¼ f ðtÞ=G ðtÞ where f ðtÞ ¼ PrðT ¼ tÞ
55
and G ðtÞ ¼ PrðT tÞ For small time intervals (e.g., when life histories are recorded on the basis of months) continuous-time models can be approximated by discrete-time models (Blossfeld et al., 2007: p. 37). The estimation results of equivalent time-continuous and time-discrete event history models Pr(T* ¼ t) then yield very similar coefficients.
Statistical Models The central idea in event history analysis is to make the continuous-time transition rate r(t) or the discrete-time transition rate r*(t) dependent on concepts of time (e.g., duration t) and on a set of time-constant x or time-dependent x(t) covariates: rðtÞ ¼ g½t; x; xðtÞ or r ðtÞ ¼ g½t; x; xðtÞ The causal interpretation of the transition rate requires that we take the temporal order in which the processes evolve very seriously. In the continuous-time mode, at any given point in time t, the transition rate r(t) can be made dependent on conditions that happened to occur in the past (i.e., before t), but not on what is the case at t or in the future after t. Equivalently, in the discrete-time model, in any given time interval t, the discrete-time transition rate r*(t) can be made dependent on conditions that happened to occur before the beginning of interval t, but not on what is the case in time interval t or after time interval t. There are several possibilities to specify the functional relationship g(.) between covariates and the transition rate in continuous-time event history analysis (see Blossfeld et al., 2007). First, the ‘exponential model,’ which normally serves as a kind of baseline model, assumes that the transition rate can vary with different constellations of time-constant covariates, so that the rates are time-constant, too (see Blossfeld et al., 2007: 87pp.) rðtÞ ¼ expðb0 þ b1 x1 þ b2 x2 þ . þ bn xn Þ ¼ expðXbÞ where b0 is a constant, X is the row vector of covariates, and b is a corresponding column vector of coefficients. In most life course applications of transition rate models, the assumption that the forces of change are constant over time is, however, not justified. This is particularly true, if we are interested in causal relationships which relate changes (or events) in some (explaining) processes to changes (or events) in a dependent life course process. In our view, the most important step forward in event history analysis has been to explicitly measure and include time-dependent covariates in transition rate models. In such cases, covariates can change their values over process time. Time-dependent covariates can be qualitative or quantitative, and may stay constant for finite periods of time or change continuously (see Blossfeld et al., 2007: p. 128). Time-dependent covariates can be included (1) by using a piecewise constant exponential model, (2) by applying the method of episode splitting in parametric or semiparametric transition rate models, and (3) by specifying the distributional form of the time-dependence and directly estimating its parameters using maximum likelihood method.
56
Life Course and Event History Analysis
A first simple and very useful generalization of the ‘exponential model’ is the so-called ‘piecewise constant exponential model.’ It allows the transition rate to vary across fixed time periods with period-constant or period-specific effects of covariates (see Blossfeld et al., 2007: 116pp.). The piecewise constant model is particularly helpful when researchers are not in a position to measure and include important causal factors (time-dependent covariates) explicitly or when they do not have a clear idea about the form of the time-dependence of the process, after controlling for important covariates. The basic idea of the piecewise constant exponential model is to split the duration into L time periods. It ¼ ftjs1 < t slþ1 g
1 ¼ 1; .; L
based on arbitrary split points on the time axis 0 ¼ s1 < s2 < . < sL, with sL ¼ N. The transition rate can then vary over the l ¼ 1, ., L time periods based on the changing period-specific constants bl (baseline hazard rate) rðtÞ ¼ expfb1 þ Xbg if t ε I1 where X is a (row) vector of covariates, and b is an associated vector of coefficients. Note that in this model there is no additional constant in X. Since causal relationships relate changes (or events) in explaining processes to changes (or events) in a dependent life course process, it is very important to be able to represent the changes of the causal forces in event history models directly. An easy way to do this is to include time-varying covariates x(t) in the ‘exponential model’ via the method of episode splitting. rðtÞ ¼ exp b1 x1 þ b2 x2 þ . þ bn xn þ bnþ1 xnþ1 ðtÞ þ bnþ2 xnþ2 ðtÞ þ . þ bnþp xnþp ¼ exp½XðtÞb
[1]
where b1 is the regression constant (x1 ¼ 1). The transformation of the person-spell file into a person-period file through episode splitting is described in detail in Blossfeld et al. (2007: 135pp.). Another model is the so-called Cox (1972) model, where the baseline hazard rate h(t) is left unspecified. Thus, it is only possible to estimate the effects of the time-constant or/and time-varying covariates, controlling for an unknown baseline hazard rate. This model is also called semiparametric model, since only part of the rate function is parametrically specified, or partial likelihood model, because only part of the likelihood function is maximized (see Blossfeld et al., 2007: 216pp.), rðtÞ ¼ hðtÞexp b1 x1 þ b2 x2 þ . þ bn xn þ bnþ1 xnþ1 ðtÞ þ bnþ2 xnþ2 ðtÞ þ . þ bnþp xnþp ðtÞ ¼ hðtÞexp XðtÞb Note that in this model there is again no regression constant in X(t). However, in some applications in life course research, substantive theory or previous empirical research may suggest a specific shape of time or duration dependence of the transition rate. However, time itself is no causal factor. Rather measures of time may serve as proxies for time-changing causal factors that could not be observed directly (see Blossfeld et al.,
2007: 182pp.). For example, duration might serve as a proxy for ‘the changing amount of marriage-specific investments’ in divorce studies. There are different parametric models which are based on specific shapes of the time-dependence. For example, the Gompertz(-Makeham) and Weibull models are able to specify monotonically increasing or monotonically decreasing shapes of the hazard rate. Further parametric models such as the Sickle, the Log-logistic, and the Log-normal models allow to estimate a (at first increasing and then decreasing) nonmonotonic time-dependency (see for more details Blossfeld et al., 2007: 204pp.). Finally, an important problem of event history analysis is also the issue of unobserved heterogeneity. In this case, the transition rate that is estimated for a population can be the result (a mixture) of quite different transition rates in the subpopulations (see Blossfeld et al., 2007: 247pp.). There have been several proposals to deal with unobserved heterogeneity in time-continuous transition rate models. The basic idea is to incorporate an ‘error term’ into the model specification. For example, the continuous-time transition rate can be made dependent on an exponential model, the observed (timedependent) covariates X(t) and a stochastic error term n, which is e.g., Gamma distributed (see Blossfeld et al., 2007: 256pp.) rðtjnÞ ¼ exp½XðtÞbn
with n 0
[2]
A likelihood ratio test can then be used to test, whether the transition rate models with and without this unobserved heterogeneity term differ. In the case of discrete-time models, the estimation of covariate parameters is normally achieved by preparing a periodperson data file and then estimating a simple logit model: r ðtÞ ¼
expða1 x1 þ a2 x2 þ . þ an xn Þexp½bðtÞ 1 þ expða1 x1 þ a2 x2 þ . þ an xn Þexp½bðtÞ
[3]
or r ðtÞ ¼
abðtÞ 1 þ abðtÞ
with a ¼ expða1 x1 þ a2 x2 þ . þ an xn Þ and bðtÞ ¼ exp½bðtÞ
If b(t) ¼ exp(b0), the logit model estimates an exponential model, if b(t) ¼ exp(b0 þ b1t) it estimates a Gompertz model, if b(t) ¼ exp(b0 þ b1lnt) it estimates a Weibull model. A piecewise constant model is estimated for b(t) ¼ exp(b1) if t ε I1 where changing period-specific constants b1 can vary over the l ¼ 1,., L time periods.
Application Example In order to demonstrate the strength of life course analysis with event history models in a substantive context, we estimate the rate of dissolution of first marriage for East and West German women. Using a subsample of retrospective life histories of 3957 married women born in East and West Germany from the NEPS, we estimate a period-specific discrete-time event history logit model with time-constant and time-varying covariates. The NEPS collects dates of transitions and events on a monthly basis. For our analysis, we define for each woman a spell starting at entry into first marriage and ending at the time of its dissolution. For women, who do not experience a marital dissolution until the time of the interview, we censor the spells
Life Course and Event History Analysis
on the right. The spells are also right-censored for women whose husband passed away. This leads to a person-oriented spell data set, where each married woman in the sample has exactly one record of data. We have then transformed this person-level data set into a person-period data set using the method of episode splitting (Blossfeld et al., 2007), in which each woman has multiple records – one for each month. Such a person-period data set allows an easy integration of timevarying covariates because the covariates can change their values across each of the person-month records. In our longitudinal analysis, we are using the following covariates: 1. Duration of marriage (time-dependent covariate). We include dummy variables distinguishing eight periods of marriage duration; 2. Place of birth (time-constant covariate). We use the dummy variable ‘East Germany’ to identify women born in East Germany, women born in West Germany are the reference category; 3. Historical periods (time-dependent covariates). To distinguish the periods before and after unification in our analysis, we use the dummy variable ‘Period after 1990.’ The reference category is the ‘Period until 1990.’ We include also an interaction dummy variable ‘East*Period after 1990’ to estimate the effect of the ‘German unification’ on East German women; 4. Husband’s educational attainment (time-constant covariate). In order to model husband’s highest educational attainment, we distinguish seven educational degrees. We then attach the average number of years that are necessary to achieve these degrees; 5. Wife’s educational attainment (time-dependent covariate). Each time when a woman attains a higher level of education, the educational attainment level is adjusted. We distinguish seven educational attainment levels and express each degree as the average number of years necessary to achieve it; 6. Partner’s relative levels of education (time-dependent covariates). In order to model the relative resources of partners, we introduce two dummy variables indicating whether a woman has a higher or lower level of education than her partner (ref. category: both partners have the same educational attainment level); 7. Premarital states (time-constant covariates). We introduce three dummy variables to control if women cohabited with their husband at the time of marriage (ref. category: women who did not cohabit with their husband at the time of marriage), were pregnant at the time of marriage (ref. category: women who were not pregnant at the time of marriage), or have had a child before marriage (ref. category: women who had no child before marriage); 8. Age at first marriage (time-constant covariates). To include the age at first marriage into our analysis we distinguish five age categories; 9. Age of the youngest child (time-dependent covariate). We include the age of the youngest child by distinguishing seven time-dependent dummy variables. Table 1 shows the results of our discrete event history analysis of women’s dissolution of first marriage in Germany including time-varying and time-constant variables. In order to
57
Table 1 Estimation results of a discrete-time event history model for the dissolution of women’s first marriage in Germany Covariate Duration (in years) 0–1 2–3 4–5 6–7 8–10 11–15 16–20 20þ Place of birth East Germany Historical Period Period after 1990 East*Period after 1990 Education Husband’s education Wife’s education Partner’s relative levels of education Woman higher Both equal (ref.) Woman lower Premarital states Cohabitation at time of marriage Pregnancy at the time of marriage Birth of a child before marriage Age at first marriage Under 20 (ref.) 20–22 23–25 26–28 >28 Age youngest child (years) No child (ref.) <1 1–2 3–5 6–10 11–14 >14 Log likelihood Number of events Number of subepisodes Chi2 Degrees of freedom
Coefficient 9.286 7.328 6.957 7.149 7.349 7.700 7.675 7.950
c c c c c c c c
0.214 0.142 0.562
b
0.095 0.096
c
0.378
c
0.268
a
0.511 0.052 0.237
c
0.250 0.484 0.771 0.800
a
0.222 0.259 0.701 0.645 0.806 0.516 5902.277 742 959 259 36140.81 28
a
c
a
c c c
c c c b
a
p < 0.05. p < 0.01. p < 0.001. n ¼ 3957. Source: Own computations based on the NEPS data. b c
test whether the duration of the first marriage has an effect on divorce, we include information on the duration of first marriage into our analysis. The results show a nonmonotonic bell-shaped pattern of the duration of marriage on divorce. In other words, the rate of dissolution increases up to the fifth year and then decreases. To analyze the divorce rate in East and West Germany before and after German unification, we include dummy variables to control the place of birth (East vs West Germany), historical periods (before and after German unification), and
58
Life Course and Event History Analysis
an interaction term ‘East*Period after 1990.’ The results show that there is a declining divorce rate in East Germany after the German unification because of the high level of uncertainty in the transition process from socialism to capitalism. Table 1 also shows that a higher educational attainment level of the husband stabilizes the marriage, while a higher educational attainment level of the wife has a destabilizing effect. If we compare the relative resources of husband and wife, we find that only homogamous marriages are more stable. If we include information on premarital cohabitation, childbirth before marriage and pregnancy at the time of marriage into our model, our results show that premarital cohabitation and childbirth before marriage have a destabilizing effect on marriages. Being pregnant at the time of marriage has no effect. We also include information on the age at first marriage. The result shows that marriages are more stable the older the woman is at entry into first marriage. Finally, we include information whether a couple has children and the age of the youngest child into our example analysis. Couples who have a baby younger than 1 year have the lowest divorce rate. The divorce rate then increases with the age of the youngest child and rises above the divorce rate of couples without children. If we control for unobserved heterogeneity, the results of this analysis do not change.
See also: Age Stratification; Age, Sociology of; Aging, Theories of; Assortative Mating in the Marriage Market; Capitalism: Global; Cohabitation: United States; Demographic Models; Demographic Techniques: LEXIS Diagram; Divorce, Sociology of; Family Theory: Economics of Childbearing; Family Theory: Economics of Marriage and Divorce; Fertility Change: Quantum and Tempo; Fertility Theory; Fertility of Single and Cohabiting Women; Labor, Division of; Life Course: Sociological Aspects; Life Table; Lifespan Development, Theory of; Lifespan Development: Evolutionary Perspectives; Linked Lives; Marriage and the Dual-Career Family; Multistate Transition Models in Demography; Period and Cohort Analysis in Demography; Retirement and Encore Adulthood: The New Later Life Course; Social Stratification; Transition to Adulthood.
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