There is a long debate in the literature about the best way to measure segregation, and the only fact that is widely agreed upon is that there is no single best method for measuring segregation.13 While potentially cumbersome in practice, good practice is to report several measures of segregation. This is useful in checking the robustness of the findings, but different measures also tend to pick up slightly different dimensions of segregation, which can enrich the analysis. Most of this analysis relies on the dissimilarity index (also known to as the ID-index) developed by Duncan and Duncan (1955), but I supplement the analysis with other measures of segregation. In particular, I divide industries into male and female dominated industries following Hakim (1993). In Appendix A I also use the IP-index (Karmel and MacLachlan, 1988) as an alternative to the dissimilarity index. In this section I start by describing the dissimilarity index, before I discuss its advantages and
12This definition of compulsory and secondary education is different from that of Statistics Norway, who define individuals with two years of high school as high school graduates. The definition used here is consistent with that in international work, see e.g., Education at a Glance (OECD, 2014) or the Survey of Adult Skills (OECD, 2013).
13The literature is reviewed and discussed in detail by Grusky and Charles (1998), Watts (1998), Anker (1998) and Bridges (2003) among others.
wheremit(fit) is the percentage of male (female) workers employed in industry i in year t. This index takes a value between 0 and 100 and is interpreted as the percentage of women (or men) who would have to change industries in order to reach an equal distribution of males and females across industries. An index of zero means that the female share in each industry is identical to the overall female share in the labor force (i.e., full integration), while an index of 100 means that men and women work in different industries (i.e., that there is complete segregation).
The dissimilarity index is by far the most commonly used measure of segregation in the literature, which is partly explained by its simplicity. It is easy to calculate and to interpret, but it has some drawbacks. As many segregation indices, it is sensitive to the number of industries in the analysis. The level of the index mechanically increases when the number of industries increases.14 The relationship between the level of the dissimilarity index and the number of industries is not linear, however. Anker (1998) shows that the increase in the dissimilarity index is much smaller when moving from 2-digit to 3-digit data than when moving from 1-digit to 2-digit occupational data.
Carrington and Troske (1997) show that the dissimilarity index is sensitive to the size of the industry cells and to the minority share (in this case the female share of total employment). When the industry cells are small, random allocation of workers can in itself lead to considerable deviation from evenness. This leads to a segregation index that is higher than the true level of segregation. Similarly, Carrington and Troske also show that the dissimilarity index tends to be too high when the female share of total employment is low. Therefore, one has to be careful when using the dissimilarity index to study time trends in segregation in time periods when female labor force participation increases. To work around these issues, the authors propose calculating an alternative dissimilarity index that measures the distance from randomness rather than evenness and compare this to the standard dissimilarity index. If the two differ substantially, using the
14To illustrate: if everybody worked in one industry, the index would be zero, and if everybody worked in their own industry the segregation index would be 100.
The main critique of the dissimilarity index is that changes in the dissimilarity index over time can stem either from changes in the within industry gender composition, or from changes in the relative size of industries. Watts (1998) and Grusky and Charles (1998), among others, have argued that a good measure of segregation should only pick up changes in segregation that stem from the changes in the distribution of males and females within industries.
To get around this critique, many researchers (Blau, Simpson, and Anderson, 1998; Blau, Brummund, and Liu, 2013) have used a decomposition technique introduced by Fuchs (1975) that decomposes the change in the dissimilarity index between two points in time into a sex component and an industry mix component.16 The sex component refers to the part of the change in the index that happened because the distribution of men and women within industries changed keeping industry composition fixed. The industry mix component is interpreted as the part of the change in the segregation index that is explained by changes in the relative size of industries keeping the distribution of males and females within industries constant. The decomposition is easily computed by first noting that Mit (Fit) is the number of males (females) in industry i in year t and that Tit =Mit+Fit, and by rewriting Equation 3.1 as industry. The sex composition and industry mix components are then defined as:
Ssex =
15Female labor force participation increased rapidly in the first half of the period of this study (see Figure 3.2). To study whether this is a problem, I calculated the alternative measure of segregation proposed by Carrington and Troske. The results suggest that there is very little bias in the dissimilarity index. In other words, neither changes in the female participation rate nor in the size or number of industries is a problem in this setting. Nonetheless, I have also calculated the dissimilarity index at different levels of aggregation, and by excluding industries with industries with less than 50 and 100 individuals to make sure that the results are not driven by small industries. The results are robust to all of these changes.
16An alternative to decomposing the dissimilarity index is to size-standardize it, which in practice means giving the same weight to all industries. The changes in the standardized index indicates how the level of segregation would have changed if there had been no change in the relative size of the industries (Jacobs, 1989). This method is not very commonly used in the literature since it has the drawback that it gives large weight to small industries (Anker, 1998).
decomposition has two weaknesses. First, the results may depend on the set of weights used, and second, in order for the two effects to the sum to the total effect inconsistent weights must be used. Alternatively, one can use consistent weights and allow for an interaction term.
Bertaux (1991) noted that since the sex and industry mix components (Ssex
and Sind) are simply the sums of the industry specific components, it is possible to study the influence of the specific industries on the dissimilarity index by disaggregating the sex and industry mix components. I use this approach to study which industries contributed the most to changes in segregation over time.
When interpreting the sex and industry mix components of specific industries, it is helpful to be understand a few things about how the decomposition of the segregation index works in practice.17 First, in any given year, an industry where the female share of employment is equal to the female employment share in the labor force will have a sex component of zero. The sex component of an industry increases in absolute size as the deviation from the overall female employment share increases. Further, an increase in the sex component can occur for two reasons; either because the female share in a female dominated industry increases, or because the female share in a male dominated industry decreases.
It is important to note that in periods where the female share of employment increases, the point of comparison for the dissimilarity index is moving. If the female share in a female dominated industry increases by less than the female share in the labor force, the sex component will be negative as the distance to the comparison point decreases. Second, the contribution of an industry to the dissimilarity index, and to the sex and industry mix components, depends on its size. When calculating the sex component, industry size is held constant, but a given change in the female employment share will be assigned more weight if the initial size of the industry is larger. The same is true for the industry mix components.
Based on the discussion above, it is clear that the dissimilarity index has its flaws, but so have many other indices of segregation. I have chosen to use
17This is also explained in Blau et al. (1998).
despite the issues mentioned above for four reasons. First, the fact that is it so commonly used makes the results comparable to those in other studies. Second, it is very easy to calculate and interpret. Third, while some researchers argue that is it a weakness that the dissimilarity index depends on changes in the industry structure, I find this useful. Since the 1970s, the industry structure has undergone large changes, as will be clear in subsequent sections, and ignoring this would not give a truthful picture of what happened in this period. Fourth, while the dissimilarity index is not very well suited for studying time trends in segregation in periods where female labor force participation is increasing, my view is that at least it does better than the IP-index, which is sometimes used as alternative to the dissimilarity index.18 The problem with the IP-index is that the maximum value of the index in a given year is dependent on the female share of employment, and so the index has a tendency to show an increasing trend in segregation in periods of increasing female labor force participation simply because the maximum value of the index is increasing. This is explained in more detail in Appendix A and also shown in Figure 3.A.1.