Labour market segmentation and the gender wage gap in Spain

1. Introduction

When economists wonder why men receive higher wages than women or try to analyse how this wage gap evolves over time or behaves within the wage distribution itself, they usually resort to the so-called decomposition methods. The driving authors of this methodology are Oaxaca (1973) and Blinder (1973) – both papers focus on the issue of wage discrimination. The basic idea of the Oaxaca–Blinder (OB) decomposition method consists of answering the following two questions: (1) How large is the part of the gender wage gap (GWG) that can be attributed to gender differences in those characteristics that are relevant to wages? This portion (due to the endowments of each one) is called the “explained” component of the gap. (2) How large is the part of the GWG which is due to differences in how those relevant characteristics are rewarded in the labour market for men and women? This second part of the gap (due to the coefficients/returns of each one) is called the “unexplained” component. In the context of the GWG, this second component is often interpreted as “discrimination,” at least partially (Jann, 2008) though there is not always discrimination behind it.

Although the Spanish labour market is showing a positive evolution after the COVID-19 pandemic, with 21 million employed people and an unemployment rate of 11.6% in the second quarter of 2023, the truth is that it continues to be a problematic market characterised by elevated long-term unemployment, high youth unemployment, strong segmentation, low regional and occupational mobility and wage inequality between men and women. To address the issue of gender pay inequality, in this paper, we combine the OB decomposition technique with the empirical framework of clustered contingency tables (CTs). We use labour-matching data from a large database of administrative records, the Continuous Sample of Working Lives (Muestra Continua de Vidas Laborales, MCVL) and structure them into a clustered CT that cross-classifies the information on gender and age of workers and occupation group and activity sector of job placements. The clustered CT allows us to represent the labour market in a segmented way. From this table, we can obtain a heatmap of the labour market that shows how workers, depending on their gender and age, tend to associate with different occupation groups and sectors of activity in the labour market. This heatmap allows us to identify idiosyncratic labour markets of men or women or both where pay inequalities can be very different. In our opinion, the problem of wage inequality cannot be approached as a problem of the labour market as a whole but has to be analysed in a segmented way, looking at each labour market segment. This segmented vision of labour matching in Spain will help to better design measures against the GWG.

There are several theoretical models that can offer support to our empirical analysis, such as the theories of labour market segmentation; the two-sided matching models (Gale and Shapley, 1962; Roth and Sotomayor, 1992), where the occupations and activities chosen by men and women would fundamentally depend on their respective preferences; or the models where companies have sufficient market power to allow themselves to discriminate against certain groups of workers. In this last line, we highlight Becker’s (1971) “discrimination of taste” model. Becker (1971) stated that an aversion felt by employers toward persons belonging to certain groups might constitute a source of discrimination and lead to lower wages for discriminated workers. He presented this hypothesis in formal terms by assuming that the gains these employers derive from employing workers include the profit of the firm and some taste parameters. However, such discrimination cannot persist under perfect competition, as employers with no preference will drive employers with discriminatory preferences out of the market by offering all workers equal wages. Hence, the presence of imperfect competition in the labour market is necessary to explain the existence and persistence of discrimination. In this sense, limitations on personal mobility permit firms to exercise monopsonistic power and to pay workers with identical productive abilities differently (Cahuc et al., 2014, Ch. 8). This low-mobility argument has been used to explain discrimination against women and certain ethnic minorities (see, for example, Gordon and Morton, 1974; Barth and Dale-Olsen, 2009). Our research hypothesis is that the mobility limitations of workers between occupation groups and/or sectors of activity in Spain may be giving companies market power in certain labour market segments and the opportunity to discriminate against workers according to their preferences.

There is literature that uses decomposition methods to analyse the GWG in Spain (and other countries). For instance, Hidalgo (2010) uses quantile regression to simulate counterfactual densities and decompose the Spanish wage inequality evolution (period 1980–2000) into changes due to coefficients, endowments and non-observable worker characteristics (following the methodologies of Machado and Mata, 2005; Autor et al., 2006, 2008). The data used are coming from the Household Budget Survey and the MCVL. According to this author, wage inequality follows a counter-cyclical trend from the mid-eighties onwards and changes in both, coefficients and endowments, play an important role in this evolution. Guner et al. (2014) observed a GWG in Spain of around 20% in 2010, a figure quite close to its value in 1994. The authors use data from the Spanish Labour Force Survey (Encuesta de Población Activa, EPA) from 1977 to 2013. Using two decomposition methods (OB and decomposition using quantile regression) and considering the problem of sample selection bias, they observe that the GWG is driven mainly by differences in returns to individual characteristics – women are more qualified than men in observable labour market characteristics but earn less. The same techniques are implemented by Dueñas and Moreno (2018), which analysed the GWG in the Spanish, French and German labour markets in 2015 using microdata from the EU Statistics on Income and Living Conditions (EU-SILC, 2016). The results obtained indicate that Spain is the country with the lowest wage gap and the biggest wage discrimination, Germany being the country with the biggest wage gap and the lowest wage discrimination and France in an intermediate position. Thus, in the case of Spain, practically the whole GWG is due to the unexplained part of the OB model (98.29%) – this percentage is lower in the cases of France (72.84%) and Germany (58.13%). For their part, Murillo-Huertas et al. (2017) examine regional differences in the GWG in Spain using matched employer–employee (EE) microdata: 2002, 2006 and 2010 waves of the Survey of Earnings Structure (Encuesta de Estructura Salarial, EES). Their findings suggest that Spain shows a significant regional heterogeneity in the size of the raw gap. Their OB decomposition analysis shows that although the bulk of the GWG in Spanish regions is due to differences in the endowments of productive characteristics between males and females, there is still a substantial part of the gender gap that remains unexplained.

There is also literature for the Spanish economy on wage differentials between groups or collectives other than men and women but where the gender variable plays an important role as a control variable. For example, by adopting a regional perspective, García and Molina (2002) show that being a man reduces the wage gap between the different regions analysed (North, East, South or Centre of Spain) and Madrid. Such a discriminatory effect is higher in the North, East and South than in the Centre of Spain – on interregional wage differentials in Spain, see also Murillo-Huertas et al. (2020). In the field of labour insertion, we can highlight the paper of Arrazola et al. (2022). These authors show that there are gender differences in the labour insertion process of recent Spanish graduates. These differences are, in general, systematically negative for women and are especially important for the salaries received and the type of contract (part-time/full-time, temporary/permanent contract), although they also depend on the branch of knowledge of the studies – for example, in the engineering branch, the gender gap in the probability of having a relatively high salary (which is unfavourable to female graduates) is explained almost entirely by unobservable institutional or socioeconomic factors, i.e. by the unexplained part of the probability gap. Another wage gap analysed for the Spanish economy is the one that arises when comparing wages in the private sector and the public sector. For instance, this gap is analysed by Couceiro de León and Dolado (2023). These authors find that those unobserved female characteristics which increase the probability of working in the public sector have a favourable impact on wages, but this public wage premium is only observed for low-educated women. These findings are in part consistent with those of Hospido and Moral-Benito (2016) who find positive selection towards the public sector at the bottom of the wage distribution – in this field, see also the study of Antón and Muñoz de Bustillo (2015).

From the reviewed literature, at least three conclusions can be drawn: (1) It is evident that there is a wage gap unfavourable to women in the Spanish labour market and that a significant part of this gap is due to unobserved factors that affect either the constant of the Mincer wage equation or the return of their explanatory variables. (2) The use of the Spanish MCVL in GWG analysis is not common, and even though these data contain remuneration information at the individual level and a wide range of explanatory variables for that remuneration. (3) The reviewed literature clearly shows that the seminal methodological contributions of Oaxaca (1973) and Blinder (1973) have given way to a broad set of methodological advances that allow decomposition methods to adapt to different data structures and research questions – see the survey by Fortin et al. (2011). Among other improvements in the decomposition methodology, we can mention the following: incorporation of standard errors and confidence intervals into the estimates; contributions of simple covariates to the explained and unexplained components of the gap; treatment of dummy variables as explanatory variables; decomposition of discrete choice models; correction of sample selection bias (Heckman, 1979); decomposition of differences in mean outcome differentials (Smith and Welch, 1989; Juhn et al., 1991); combination of decomposition and matching techniques (Ñopo, 2008); gap decomposition along the wage distribution using quantile information (Machado and Mata, 2005; Melly, 2005; Firpo et al., 2018); and decomposition for panel data and mixed models (Smith and Welch, 1989; Kim, 2010; Kröger and Hartmann, 2021).

In many of these methodological contributions underlies, in one way or another, the segmentation of the population (or the sample) analysed. Some studies approach segmentation exogenously (according to external classifications), for example, segmenting the sample by earning quantiles (Juhn et al., 1993), or analysing the GWG for different groups in the labour market (by race, region, period of time, public or private job, etc.) leading to an analysis of the gap between the gender gaps of the groups analysed (Smith and Welch, 1989; Juhn et al., 1991). On the other hand, other authors approach segmentation endogenously (i.e. using information from the sample/population to make the segmentation), for example, admitting that there are workers with different probabilities of accessing a job and, therefore, a salary (Heckman, 1979), or looking for groups of men and women which have comparable characteristics, giving rise to the OB analysis of the common support of the distributions of observable characteristics (Ñopo, 2008).

To our knowledge, none of the proposed segmentations control for the existence of labour segments where the propensity of young/older men/women to be matched to jobs may differ significantly. Our labour market segments are based not directly on spatial criteria (as, for example, in Manning and Petrongolo, 2017) but on how men and women of different age groups are matched with the different sectors of activity and occupation groups existing in the labour market. Combining CT and clustering methodologies, we can identify labour segments where men (or women) of certain ages show a high propensity to match/associate with certain sectors of activity and occupation groups – on this methodology see the works of Álvarez de Toledo et al. (2018), (2020). The fact that young/older men/women show different propensities to match up with certain activity sectors and occupation groups can be due to three reasons: (1) their respective preferences when looking for a job, (2) the preferences of companies when hiring them and (3) their search patterns and those of the companies that hire them (geographical search areas, search channels used, etc.).

Our statistical segmentation procedure is guided by an economic criterion: who matches with whom in the labour market. We want to relate the wage gap of each labour segment (or idiosyncratic market) with the propensity to match/associate men and women of different ages with the jobs offered in that segment. In principle, it would be expected that in those labour segments where the wage gap is more favourable to young (older) men, the propensity of young (older) women to match is lower and vice versa.

The rest of the paper is structured as follows: Section 2 presents our labour market segmentation methodology based on clustered CTs. Section 3 describes the labour-matching data used (MCVL). Section 4 offers the results of estimating a wage equation and decomposing the GWG adopting a segmented vision of the Spanish labour market. Finally, Section 5 shows the general conclusions of our work.

2. Labour market segmentation methodology

The use of CTs makes sense when there are categorical variables that provide relevant information about a phenomenon under study (Mosteller, 1968; Agresti, 2013). Each cell of the CT shows the frequency of a particular combination of categories of the different categorical variables that are cross-represented in it. From this starting table, correspondence (association) and clustering analyses can be carried out to obtain a new table containing the degree of association between the different categories of the categorical variables; we will call this table the heatmap.

The heatmap proposed in this study allows us to characterise the employment episodes of the MCVL by measuring the degree of association between the different categories of four categorical variables that have an important weight when it comes to segmenting the labour market; namely, gender and age group of the worker and occupation group and activity sector (industry) of the job. To obtain this heatmap, the first step is to cross-classify these four variables in a CT where the rows represent the combinations of the categories of the occupation and industry variables, and the columns represent the combinations of the categories of the gender and age group variables (see Table 1). Our economic hypothesis is that there are certain rows and columns of this CT which tend to be strongly associated (they tend to appear together in the CT) and this should be reflected in the heatmap; in other words, certain young/older men/women tend to match with job vacancies belonging to certain occupational groups and activity sectors. When we refer to strong association, we do not necessarily mean that a particular combination of categories of the four variables considered has a relatively high frequency in the CT, but that this frequency is higher than the one expected if the generation of category combinations were totally random.

By crossing 10 occupation groups and 10 activity sectors, 100 rows are generated in the CT and heatmap. By crossing 2 gender categories with 8 age groups, 16 columns are generated in the CT and heatmap. Therefore, these two tables have a total of 1,600 cells (16 rows × 100 columns). This high number of cells makes it difficult to identify association patterns in the heatmap of the labour market. To overcome this problem, we smooth the observed CT and apply a clustering procedure to its two sides; in this way, the analysis focuses on homogeneous groups of rows and columns rather than on individual rows and columns. The procedure to obtain the smoothed ordered (clustered) CT and the corresponding heatmap can be seen in Álvarez de Toledo et al. (2018, 2020). Here we summarise it in the following steps:

• 1. The observed CT is smoothed resulting in Table 1. Smoothing techniques in the CT framework provide solutions for estimating cell frequencies (and their probabilities) in the presence of “sparsity.” When in a CT the number of cells is too high and/or the finite sample is too small, some cells with positive occurrence probabilities can be zero or have a very small frequency – this phenomenon is known as a zero frequency problem or sparsity problem. In this scenario of sparse high-dimensional CTs, multivariate statistical analyses (as, for example, correspondence analyses, association factors or χ2 tests of independence) may lose the optimal properties that they show in larger samples.

• 2. From the smoothed and unclustered CT (Table 1), two auxiliary tables are generated that, respectively, collect the observed and expected probabilities of having an employment episode in each cell – note that these two probabilities are calculated on the already smoothed CT. The observed probability in each cell i,j comes from the quotient ni,j/n, while the expected one is obtained as the product of the row marginal probability ni+/n and the column marginal probability n+j/n corresponding to each cell i,j.

• 3. The quotient of both auxiliary tables allows for obtaining a table of association factors (aij) between rows and columns [1]: aij=nijnni+n·n+jn=nnijni+·n+j. Factor values higher than one would mean that the association between the corresponding row and column of the table is greater than in a random assignment scenario and vice versa. As an example, Figure 1 represents an association table with an arbitrary order of six rows and six columns. For better visualisation, we have coloured the cells according to the values of the association factor, the higher the factor, the darker the cell.

• 4. The CT is clustered on the row side and on the column side. The hierarchical (average linkage) clustering methodology is based on a similarity measure between the elements that are clustered (row categories or column categories). We measure the similarity between each pair of rows of the CT (iA and iB) as the overlapping or percentage of coincidence of their respective row profiles niAjniA+ and niBjniB+ with each of the different column categories j: simiA−iB=∑jmin(niAjniA+,niBjniB+). This measure of similarity moves by definition between 0 and 1 and can be calculated in an analogous way on the column side; i.e. two column categories of the CT are more similar, the more they resemble the way they are matched with the row categories.

• 5. The clustering process on both sides of the CT gives rise to separate row and column dendrograms. The dendrogram graphically shows how the row (or column) categories are joined sequentially to give rise to homogeneous groups or clusters of categories. By definition, the base of each dendrogram (the one with the rows and the one with the columns) places the respective clustered categories by proximity. So, these respective bases can be used to order the rows and columns of the association table giving rise to a clustered association table or heatmap (or “gravity” map) that makes it possible to get a panoramic view of how certain groups/clusters of rows tend to be associated with certain groups/clusters of columns and vice versa. Figure 2 shows the association table from Figure 1 after it has been sorted using the information of the clustering process. As can be seen, this figure shows the existence of row clusters and column clusters. For example, rows i₁, i₆ and i₄ form a row cluster because they are similar in the way they are associated with the columns of the table, and columns j₁ and j₂ form a column cluster because they resemble the way they are associated with the table rows.

Our segmentation scheme is not incompatible with the existence of occupational/sectoral mobility in the labour market; in fact, the existence of certain mobility between nearby occupations and/or activities may be favouring the formation of the clusters that we observe in the heatmap (for example, the mobility of older men between the agriculture and construction sectors in certain regions of Spain). It is also true that if disruptive changes in mobility patterns were observed, the heatmap would change its shape, but this type of change occurs slowly because it requires the retraining of workers. In any case, there is evidence of low occupational and sectoral mobility in Spain, which gives our heatmap stability in the short term – see, for example, Anghel et al. (2020) and Fernández-Cerezo and Montero (2021) at sectoral level and Caparrós-Ruiz (2016) and Bisello et al. (2022) at occupational level.

It can happen that a cluster of rows tends to be associated with a cluster of columns and vice versa. This case is called a bicluster (or labour market segment) and can be explored for idiosyncratic features – three possible biclusters have been marked with red borders in Figure 2. For example, we could look inside a particular bicluster to analyse its structure by gender and age of the worker, region of the workplace, activity sector and occupation group of the job placement, worker earnings, etc. In this study, we will focus on analysing the wage gap by gender.

The GWG can be analysed by following the OB decomposition. This statistical method is used to analyse the differences in mean outcomes between two groups. As can be seen in Eq. (1), the OB decomposition of the wage differential helps researchers to understand the extent to which differences in observed characteristics (“endowments” or explained factors) and differences in the returns of those characteristics (“coefficients” or unexplained factors, including discrimination) contribute to the overall GWG. For example, we can measure whether men earn more than women because they have more experience in the labour market or because the same level of experience is more highly valued in the case of men. For its part, the “interaction” component shows a simultaneous effect of differences in endowments and coefficients, and it usually presents a small or negligible effect on the explained differential.

Note that the Mincer equation, estimated, respectively, for men and women, provides the respective coefficients {β0m,β0f,βkm,βkf} that are used in the OB decomposition of GWG. A novel aspect of our analysis is that the effect of the association factor (aij) can be considered in the wage equations and thus in the OB decomposition. As previously mentioned, the association factor is calculated in this study on a CT where rows (i) represent worker segments defined by the age group and gender of the employee, and columns (j) represent job segments defined by the occupation group and activity sector of the job position. Under this definition of segmentation, the estimated OB coefficient for aij lets us know who benefits most from showing a higher association (or dependence) with jobs belonging to certain occupations and activities, young or older men or women. Additionally, the formation of labour biclusters (darker areas of the heatmap) allows a segmented analysis of the wage differential. Indeed, we can analyse the GWG in those segments of the labour market where women or men (or both) tend to go (given their preferences in the labour-matching process). This segmentation analysis allows us to know both the relative situation of women in different segments of the labour market and whether their preferences in labour matching are related to going to those labour segments where the wage gap is less unfavourable for them.

3. Data description

The MCVL is a set of individual microdata extracted from the Spanish Social Security records. The Social Security information is completed with tax information from the State Agency for Tax Administration (Agencia Estatal de Administración Tributaria, AEAT) and with information from the Continuous Register provided by the Statistics National Institute (Instituto Nacional de Estadística, INE). This database offers annual information on more than a million people who appear each year in the Social Security records as recipients of income from work, subsidies or pensions. To make the sample, 4% of the population registered in Social Security in a certain year are selected through a simple random sampling system; therefore, the MCVL is representative only of the population that is related to Social Security in the reference year – note that our analysis is cross-sectional, for the year 2021.

The MCVL is compatible with our research because it allows obtaining and estimating, cross-sectionally (for the year 2021), the wage (Mincer) equation that explains the individual’s wage through a series of variables that describe attributes of the worker, the firm and the job position that he/she occupies. In the year 2021, the MCVL contains 649,893 workers, 247,822 employers (private companies or public administrations) and 1,265,406 employment episodes (labour contracts) – we only consider the employment episodes for which the information of all the variables that are going to be used in the econometric analysis is known. These episodes correspond to workers who already had a job at the beginning of the year or who found one during the year.

The wage information comes from the tax module of the MCVL, which allows us to obtain the annual income from work (whether in cash or in-kind) for each combination employee–employer (hereinafter EE) observed. Figure 3 shows the density function by gender of the annual income of the EE relationships. As can be observed, women show a higher density in intermediate wages, while men do so at higher wages. The average wage of women is €13,450 (sd = €14,214, median = €9,076), while that of men is €15,404.03 (sd = €15,551, median = €11,499). There is, therefore, an average wage gap favourable to men in the Spanish economy.

The (continuous or categorical) variables that will be used in the estimation of the wage equation and in the OB decomposition of the GWG are listed in Table A1, in the Annex. For its part, Table A2 (also located in the Annex) shows the employment distribution of those variables in Table A1 that produce the CT used to segment the job matching process; namely, the gender and age group of the worker and the occupation group and activity sector of the job position – descriptions of the rest of variables in Table A1 are available as supplementary material.

As shown in Table A2, the most frequent categories of each variable are the male gender (52.48%); the younger and intermediate age groups; the occupation groups of officers and specialists, unqualified workers and administrative assistants; and the services in the private sector, especially trade, hotels and restaurants, transport and communications and other services [2].

4. Results and discussion

5. Conclusions

In this study, we have tried to show that the process of labour matching and the possible existence of gender wage discrimination in the Spanish labour market are phenomena that cannot be studied by treating the whole population/sample (employment episodes) homogeneously. On the contrary, it is necessary to segment the employment to find idiosyncratic labour markets that can be analysed from a gender perspective. Using matched EE data for the year 2021 in Spain (we use the MCVL provided by the Spanish Social Security), we take four variables that are key to segmenting the labour matching process: the gender and age group of the worker and the occupation group and activity sector of the job placement. By applying CT and hierarchical clustering techniques, we create a heatmap (clustered association table) of employment episodes in the year 2021 that allows us to identify employment biclusters (idiosyncratic labour markets) where workers of one gender (men or women) show a higher degree of association than workers of the other gender with certain sectors of activity and occupation groups and vice versa; the analysis is further refined by discriminating workers by different age groups.

Our study provides an in-depth analysis of workers' remuneration in the Spanish economy. We estimate a wage equation for the full sample and for men and women separately and perform the OB decomposition to try to explain the existing wage differential in favour of men. The OB estimation shows a wage differential of 13 logarithmic points in favour of men, most of it due to the different returns that both genders obtain from their respective matching-related attributes – this result is in line with the literature on Spain in this field. Additionally, we analyse the GWG in different idiosyncratic markets which are defined by different clusters of occupation groups and activity sectors where certain clusters of men and/or women (of different age groups) tend to seek employment and get a job. These crossings of clusters with high internal association (denoted as biclusters) are extracted from the mentioned employment heatmap. The application of the OB model to these idiosyncratic markets based on “who matches with whom” constitutes a novel aspect within the literature on gender wage discrimination.

Our gender labour segmentation analysis shows that the labour market to which women attend is visibly different from that of men. For instance, while women tend to be associated with service activities (especially, public services, such as health or education), men are mainly associated with extractive, manufacturing and construction industries and with private services. Furthermore, it is observed that women are associated more intensely than men with the highest occupation groups (those with the highest qualification). This segmented scenario implies that the phenomenon of gender wage discrimination cannot be analysed with a global and homogeneous vision of the labour market and addressed with general policies. Effectively, the different idiosyncratic markets extracted from our employment heatmap show different wage gaps, as well as different weights of the observed (endowments) and unobserved (coefficients) heterogeneity. The overall analysis of these labour market segments produces two interesting conclusions. On the one hand, women tend to be placed in those labour biclusters where the wage differentials with men are smaller. For women, not only is the wage level important, but also the situation of wage inequality with respect to male workers. On the other hand, in those biclusters where wage differences are more important, these differences are mainly due to the characteristics of men and women, and not so much to the different return of these characteristics, although this last component is not negligible. In fact, when we use data from the entire labour market, which would imply using information from the entire heatmap (and not just from the idiosyncratic biclusters), the unexplained component of the OB decomposition explains most of the wage gap.

Our combination of methodologies (clustered contingency tables and wage gap decomposition) is versatile and flexible (it can be applied to other economies or worker groups: migrants/natives, public/private employees, university graduates/other educational levels, etc.) and provides a better understanding of the underlying segmentation in the labour matching process and the effect of this segmentation in the gender wage issue. A more comprehensive knowledge of the underlying structure of the labour market helps in the efficient design of labour policies from a gender perspective; for instance, it would be necessary to act in those idiosyncratic labour markets where men continue to earn more than women fundamentally for reasons that are not justified by their respective characteristics. Our methodology allows us to identify these markets. The quantile analysis of the wage differential by labour segments, the consideration of the regional dimension in the heatmap and the application of our methodological tools to specific groups in the labour market are other possible lines of extension of our research.