Chapter 4
Illustration Using Employment Trajectories
Texte intégral
I. Context and Data
1In this application, we will look at employment trajectories. Specifically, we want to identify regularities in careers—that is, the main types of trajectories.
2The data used here are drawn from the Biographies et entourage survey, carried out by the French National Institute for Demographic Studies (INED) in 2001.1 The survey traces the family, residential, and occupational trajectories of 2,830 residents of the Île-de-France region (which includes Paris), born between 1930 and 1950, as well as those of their close relations (Bonvalet & Lelièvre, 2016; Lelièvre & Vivier, 2001). Building on INED’s previous survey research (Lelièvre, 1999), Biographies et entourage sits at the confluence of two of its long-standing lines of investigation. The first investigates networks of family and close relations, with the Réseaux familiaux (Family relations; INED, 1976) and Proches et parents (Close relations and family; INED, 1990) surveys. The second group covers family, occupational, and residential mobility, with the Peuplement de Paris (Settlement of Paris: INED, 1961), Triple Biographie (INED, 1981),2 and Peuplement et dépeuplement de Paris (Population and depopulation of Paris; INED, 1986)3 surveys. By collecting information on generations ranging from the respondents’ grandparents to their grandchildren, the observations in these successive surveys, thus, achieve exceptional historical depth, covering a period ranging from the late 19th century to the late 20th. The occupational component of the survey reconstructs the succession of the respondents’ activities over their life course—from their first job up to the time of the survey. Information on their various occupations, including inactivity, was collected at the annual level through a retrospective calendar.
II. The Choices
1. Study Population and Period
3We randomly selected a sample of 500 trajectories. As the observation of individuals’ life courses stops at the time of the survey, the data are right-censored. While event history models can control for censoring, the descriptive methods that we are applying here cannot. We, thus, make the choice to analyze individual careers observed over an identical period, delimited by the same boundaries. We will focus on employment trajectories between ages 14 (the end of obligatory schooling for the cohorts we will look at) and 50 (the age of the youngest respondents at the time of the survey). We could continue the analysis beyond this age by focusing on a subpopulation of respondents, but this would be of little interest, since the number of respondents decreases rapidly with age. At age 55, we would be working with only 65.3% of the population; at 60, 40.7%; at 65, 20.7%; and at 70, we would be left with only 4.8%. In any case, most occupational transitions happen before age 50.
2. The State Variable
4We will be describing the different activity situations that make up the trajectories in our sample. By construction, the sample does not include any retirees, as the description ends at age 50. We, thus, code six states: education, full-time employment, part-time employment, odd jobs, military service, and other inactivity.
5Our sample consists of 500 employment trajectories, observed annually between ages 14 and 50. They, thus, include 37 successive observations, each of which takes one of the six states just defined as its value. From a purely theoretical point of view, then, there are 637 possible distinct trajectories. Empirically, some respondents have identical trajectories but, nonetheless, there are a large number of distinct trajectories. In our sample of 500 careers, we observe 377 distinct sequences. The diversity of the trajectories is clearly too great for us to classify them “by hand.” We must resort to more sophisticated methods.
3. Implementing the Method
6We will use optimal matching, given that our objective is to differentiate trajectories characterized by mobility (with changes in employment and activity or time) from more stable trajectories, as well as the timing of individuals’ entry into the labor market and, more broadly, the principal situations. Experience tells us that this dissimilarity measure offers a good compromise between the different temporal dimensions of trajectories.
7Having made this choice, the next step is to choose the costs for the substitution and insertion-deletion (indel) operations. We do not want to impose a theoretical hypothesis about a possible hierarchy of states in advance and, as we saw above, building substitution costs on transition rates is not of particular use. We, thus, set a single substitution cost with a value of 2. We set the indel cost at three-quarters of this value (1.5), an intermediate solution between the Hamming distance (which emphasizes contemporaneity) and the longest common subsequence (which emphasizes the order of events).
8For clustering, we will make the most “classical” choice, using agglomerative hierarchical clustering and Ward’s criterion.
III. Results
9Next, we examine different typologies of trajectories, starting with two clusters and then gradually increasing the number. On a first pass, a typology with five clusters seems satisfactory. With this number, the clusters seem at once relatively homogeneous and clearly distinct from each other (Figure 4).4
Figure 4. State Distribution Plots of a Five-Cluster Typology

Coverage: A sample of 500 individuals.
Source: Biographies et entourage survey (INED, 2001).
10The trajectories in the first cluster, which includes more than two-thirds (69%) of individuals, consist predominantly of full-time employment (Table 9). The four other clusters seem to be characterized by the following: full-time employment with a period of inactivity (8%); career start in full-time employment, followed by inactivity (15%); career start in full-time employment, followed by part-time employment (3%); and odd jobs (4%). While an entire career of full-time employment seems to be the norm (at least statistically), there are still three out of every 10 individuals whose trajectory took a different path.
Table 9. Five-Cluster Typology of Employment Trajectories

11A way to “flesh out” this typology is to embody the clusters by describing the trajectory of the medoid—that is, the individual who is closest to the center of the cluster. In practical terms, we do this using the distance matrix, by identifying the person with the lowest mean distance from the other members of their cluster. We can then draw a “portrait” of these individuals on the basis of the survey data.
12Cluster 1: After graduating from secondary school, Martine began work at age 19 as a shorthand typist in Paris. At 30, she became a technical and financial assistant and continued in this role until the time of the survey.
13Cluster 2: After a few years working as a salesperson, Geneviève left the labor market at age 22, when her first child was born. Five years later, she returned to employment as a salesperson once again.
14Cluster 3: Josiane started her first job at age 16, as an unskilled laborer in a textile factory. Six years later, when her first child was born, she left her job. She, then, had a second child and remained a homemaker over the subsequent years.
15Cluster 4: On her arrival in France, Rafika began work as a housekeeper in the suburbs of Paris. Having a child meant she had to switch to part-time work, a situation that she remained in up to the time of the survey.
16Cluster 5: Moussa immigrated to France at age 20 and found a job as an unskilled laborer in the automotive sector. A year and a half later, his contract was not renewed. From that moment on, he did many types of odd jobs (e.g., masonry, carpentry, moving).
17Using indicators to examine the clusters in more detail sheds further light on the typology (Table 10). The indicators of the mean duration of states—or of their occurrence (at least one episode in a given state)—offer a characterization of the clusters in terms of the main employment situations—those the respondents were in during most of their trajectory—that seems largely to confirm our interpretation of the graphs. But we can also see that the duration of studies is markedly higher in Cluster 5 and, to a lesser extent, in Cluster 4. In addition, full-time work is totally absent from the trajectories of 20–30% of the individuals in clusters 3 and 4, despite the fact that looking at the state distribution plots suggested that we should consider it a central characteristic. In addition, more than half of the trajectories in Cluster 4 include at least one episode of inactivity, which is not apparent from looking at the graph. However, the mean amount of time spent in inactivity in this cluster is low (1.8 years). Finally, clusters 2 and 3 are by far the most heterogeneous, as indicated by the intracluster distances.
Table 10. Description of the Five-Cluster Typology Through Indicators

18These different ways of describing the typology clarify the characteristics of the different clusters. But we must always keep in mind that there is some heterogeneity within each one. This is often very visible in sorted index plots (Figure 5). Here, we can see, for example, that the age at which respondents in Cluster 1 completed their studies varies widely and that the inactivity seen in the trajectories in Cluster 3 may or may not have been preceded by a period of full-time employment. To bring out these differences, it is imperative to analyze the data at a finer-grained level. In other words, we need to increase the number of clusters in the typology.
Figure 5. Index Plot of the Five-Cluster Typology

Coverage: A sample of 500 individuals.
Source: Biographies et entourage survey (INED, 2001).
19Constructing a typology with eight clusters instead of five brings out new patterns (Table 11). The main cluster splits into two subclusters depending on the timing of their entry into the labor market: relatively earlier for the first and later for the second. Cluster 3 is subdivided into three subclusters. Trajectories featuring a single, permanent transition from full-time work to inactivity make up only one of the three. One of the other subclusters consists of individuals who were inactive throughout their entire trajectory and the other of individuals whose transition from full-time work to inactivity was followed by a return to employment in part-time roles. A finer-grained partition of the data, thus, brings to light new distinctions in terms of timing, order, and duration. We can also see—through the example of the initial cluster of “full-time > inactive” trajectories—that the precise measurement of the proportion of trajectories that are of a given type can be tenuous, depending closely on the level of partition that we choose. We, thus, have every reason to explore multiple partitions before moving on to the next phase in our analyses.
Table 11. Typologies of Careers with Five and Eight Clusters

Table 12. Typology of Careers with Five Clusters, by Gender (%)

20Here, we will not continue on with in-depth analyses based on our typologies. But we know that inactivity and part-time employment have historically been characteristic of women’s careers. We can check the consistency of the typology with this fact by looking at the distribution of women and men across the different clusters (Table 12). Unsurprisingly, we see that clusters 2, 3, and 4—which are marked by inactivity or part-time employment—consist overwhelmingly of women, while the other two clusters are relatively more balanced (albeit with substantially more men in full-time careers).
Notes de bas de page
4 At this step, we could have chosen to inspect the dendrogram (clustering tree) and look at the changes in inertia between different levels of partition (see the vignette for the R package seqhandbook). When there is a substantial difference in inertia between two neighboring levels of partition, that tells us that adding an additional cluster to the typology provides significant additional information. Conversely, when the difference in inertia is low, the added value of increasing the number of clusters in the typology is itself statistically low.
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