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The double penalty: How female migrants manage family responsibilities in the Spanish dual labour market

Objective: This study examines the convergence of employment behaviour and work-life balance of foreign-born women with those of native-born Spanish women between 2014 and 2018. Background: The changing role of women in the labour market is a central development of the past century. However, the study of female labour market participation has focused on native women, typically with a college education. Method: We use the Spanish Labour Force Survey and its 2018 ad hoc module on the reconciliation of work and family life to compare the working behaviours of native and migrant women. We use a matching algorithm to construct a sample of native workers with comparable human capital and living arrangement characteristics. Results: The segmentation of the Spanish labour market leads to the concentration of female immigrants in specific occupational niches with precarious employment conditions, regardless of the length of their stay in the country. The country’s employment and care regime forces female migrants to deal with their care responsibilities differently than their native counterparts: i.e., migrants are more likely than natives to interrupt their employment to fulfil household duties, and are less likely to engage in part-time work and to outsource care provision to family and professional caregivers. Conclusion: Female immigrants are doubly penalised as both immigrants and mothers.


Introduction
The reconciliation of work and family life is a core challenge in European welfare states. Over the last two decades, labour and family institutions have tried to accommodate women's new roles as professional workers by taking over their traditional caregiving role (Esping-Andersen 2009). Immigration has been regarded as a win-win strategy: households can outsource part of their domestic work burden to female migrants, which, in turn, improves both parties' economic opportunities, and eases the transition into a dual-earner model.
The Spanish experience illustrates the link between immigration and the increase in the number of professional women. During the last two decades, the employment outcomes of women in Spain have converged substantially with those of men (Guner & Sánchez-Marcos 2014). Farré et al. (2011) have shown that this success story was made possible by the large inflows of female migrants who filled the gap left by native women in care and cleaning tasks. However, the success of the increasing labour market participation of native-born women would be called into question if female migrants were not granted career and family opportunities comparable to those of female natives. This observation has led to more attention being paid to the linkages among economic integration, migration, and work-life balance (González-Ferrer & Cebolla 2013;Hobson et al. 2018;Sánchez-Domínguez & Fahlén 2018;Lawson et al. 2020). In this context, two questions arise: How do the employment trajectories of female migrants compare to those of their native counterparts? And, how do female migrants address the challenges of reconciling work and family life?
This paper examines the case of Spain to evaluate how female migrants' career and family opportunities differ from those of their native-born counterparts. We focus on the interplay between two key dimensions of gender equality: (1) labour market outcomes (employment and job quality) and (2) family responsibilities. We link these dimensions to two salient features of the Mediterranean welfare state that have been shown to be obstacles to gender equality (González et al. 2014): (1) the role played by families in the provision of care, and (2) the segmentation of the labour market. We explore whether these obstacles are more intense for female migrants, and whether they fade with the length of stay in the country (assimilation). We examine this gap as a function of the length of stay in order to better understand whether (and, if so, how) female migrants' economic situations improve over time.
We use data from the Spanish sample of the EU Labour Force Survey from 2014 to 2018 to compare the labour market outcomes of female immigrants as a function of their years of residence in the country to those of native workers with similar characteristics. We use a matching algorithm to pair each female migrant with her closest native-born counterpart based on her age, education, household composition, and geographical location. We then estimate the impact of the length of stay in the country on (a) the employment gap between female immigrants and female natives; (b) the gap in the quality of employment (focusing on atypical work arrangements and occupations); (c) the extent to which care responsibilities account for these gaps; and (d) the extent to which these gaps are attributable to the Spanish care regime.
We study the case of Spain during the 2014-2018 period for two main reasons. First, Spain has followed a trajectory similar to that of other Southern European welfare regimes, which are characterised by (1) unequal labour market opportunities between outsiders and insiders and (2) a heavy reliance on family ties in the provision of care. The second reason is that international migration is a relatively new phenomenon in Spain, as most of the foreign population first came to settle in the country two decades ago. Focusing on this period also allows us to study whether the end of the Great Recession created new opportunities for female migrants' occupations to converge with those of their native counterparts.
This paper highlights how the dual structure of the Spanish labour market and the Spanish care regime interact to doubly penalise female immigrants as both immigrants and mothers. As immigrants, the dual labour market improves female immigrants' access to employment (Rodríguez-Planas & Nollenberger 2016;Jiménez-García 2018), but it condemns them to the status of "outsiders" in the secondary sector. As mothers, female migrants find it harder than native female workers to access skilled and stable occupations (Aysa-Lastra & Cachón 2015). This results in increasing levels of inequality and poverty among those at the lower end of the occupational ladder. The Spanish care regime neglects the childcare needs of mothers of young children, and thus fails to support their careers.
In the next section, we present background information on Spanish migration and the country's care and employment regimes. We then discuss theoretical considerations regarding immigrant labour integration. In the third section, we describe our empirical strategy and data. We present our results in the fourth section. The final section concludes.

Background on the migration, care, and employment regimes in Spain: The playing field for female migrants
The Spanish case is relevant for various reasons. First, in a very short span of time, Spain has become one of the main European destination countries for international migrants. In the decades prior to 2000, Spain had been a source of migrants to both north-western Europe and Latin America. Beginning in 2000 ( Figure 1, Panel A), Spain became one of the main European destination countries for migrants. The 12-year-long economic expansion and the housing bubble that followed the formation of the Eurozone in 1998 were the main pull factors for immigrants to Spain. The unprecedented access to cheap credit increased the demand for foreign workers by both firms and households. On the one hand, the housing bubble increased the expansion of low productivity sectorsnotably real estate -and boosted the demand for cheap labour. On the other hand, the access to real estate ownership and the climate of increased economic prosperity created a sense of affluence among middle-class households that pushed them to outsource portions of their domestic work (González-Ferrer & Cebolla 2013). According to the 2007 wave of the National Immigrant Survey, immigration to Spain has mostly been motivated by economic reasons, and, to a lesser extent, by family reunification (Requena & Reher 2014) from non-European countries, mainly in Latin America, Eastern Europe, and Africa. The number of foreign-born inhabitants of Spain increased from four per cent at the beginning of the 21st century to 14 per cent in 2019. International migration reached its peak in 2012. As of 2019, the largest groups of migrants are from Morocco (13.0 per cent), Romania (8.7 per cent), Colombia (6.5 per cent), Ecuador (6.0 per cent), and Venezuela (4.8 per cent). Migrants to Spain now come from countries that are more culturally distant from the native population. Migratory flows from less wealthy regions to Spain have increased significantly since 2000. Currently, migrants are much more likely than natives to be employed in the lowest-skilled forms of work, such as care and cleaning jobs (Sánchez-Domínguez & Fahlén 2018).
From the onset of the migration boom, women have comprised a major component of migration flows, mainly from Latin American countries, and, more recently, from Eastern Europe (Figure 1,Panel B). Female immigrants have come to play an important role in specific Spanish labour market niches. In 2018, about 37 per cent of the working female immigrant population were employed in jobs related to care and cleaning. Recent research has shown that the employment conditions for migrant workers in care and cleaning jobs are characterised by precarity (low wages, poor working conditions, high labour instability) and informality (Hellgren 2015).
The second reason we chose to focus on the Spanish case is that it is considered a "familist" welfare regime due to the centrality of the institution of the family in the country's social structure and social protection mechanisms (Pérez-Díaz et al. 2010). This regime is built around the premise that the family is the central institution that provides care and social protection to dependent members. In recent decades, however, the pillars of this regime have been challenged by two developments. The first is the massive entry of women into the labour market. The second is the increased importance of care and cleaning jobs, and the growing shortage of care for children and the elderly (Estévez-Abe & Hobson 2015). The absence of public policies aimed at supporting work-life balance (Farré et al. 2011; has increased the demand for workers in the care and cleaning sectors, and has forced some households to rely on their extended families to provide care. International migrant care workers have helped bridge this care gap, and have reduced the pressure on politicians to expand public services (Banyuls & Recio 2015). This sector has become the main entry point into the labour market for female migrants. However, a female migrant with dependent members in her household is deprived of her family support network in her destination country, and her access to public or private care services is likely to be limited.
A final characteristic that makes the Spanish case interesting is the dual structure of its labour market, which perpetuates the country's social stratification. Since the 1990s, Spain has reported some of the highest unemployment rates among the OECD countries -e.g., in 2018, the rate was 15.3 per cent, second only to that of Greece. Job destruction during crises has mainly affected workers with fixed-term contracts (outsiders) (Bentolila et al. 2012), making unemployment one of the key drivers of inequality (Bonhomme & Hospido 2017). Spain was also one of the countries most affected by the 2008 financial crisis (OECD 2018), which coincided with the greatest influx of immigrants in the country's history. As Spain does not currently have a programme designed to promote the integration and inclusion of the foreign population, the employment assimilation of immigrants is seen as a key aspect of their integration and wellbeing.
These features motivated our choice to use Spain as an example of how Southern European countries have handled the care deficit caused by an ageing population and women's incorporation into the labour market. The absence of public support has forced households to address this care deficit privately, either within their extended family, or by outsourcing care. The migration boom during the first decade of the 21st century generated a supply of low-skilled workers who were willing to take on tasks that have traditionally been performed by native females, and the dual structure of the labour market facilitated their employment in the care and cleaning sectors. While these developments have helped female natives balance their work and family lives, the question of whether female migrants have been granted comparable career and family opportunities merits greater attention.

Theoretical background on migrant labour market integration
Prior studies have proposed multiple hypotheses to explain the factors that influence female migrants' success in the host labour market. The remainder of this section describes the three most important hypotheses in turn: (1) the structure of the host labour market, (2) the impact of family responsibilities and households' internal organisation, and (3) the mechanisms underlying economic assimilation.

Labour market segmentation
The first set of obstacles in the labour market come from the outsider status of female migrants in a dual labour market. The theory of dual labour markets is one of the leading approaches to understanding horizontal inequalities among workers in Southern Europe (Polavieja 2003(Polavieja , 2005Güell & Petrongolo 2007;Bentolila et al. 2019 for a review). According to this theory, structural conditions endow insider and outsider workers who have similar productive characteristics (e.g., experience, education, geographical location) with different levels of bargaining power, and this asymmetry translates into different labour market statuses. In particular, outsiders are more likely to become unemployed, and are less protected by labour market institutions (Guell-Rotllan 2000).
This asymmetry results from a mixture of sectoral and institutional causes. Compared to in the primary sector, in the secondary sector, employment relations are more informal and short-term in nature, union presence and coverage by collective bargaining is lower, and labour legislation is harder to enforce. This is the case for care and cleaning jobs, and especially for domestic cleaning jobs, which have high levels of informality (Aysa-Lastra & Cachón-Rodríguez 2013).
Sector-specific conditions interact with institutional causes, and, in particular, with exceptions to the general employment regime. These exceptions take the form of atypical contracts that do not benefit from full institutional protection, such as fixed-term contracts (exempted from firing costs), involuntary part-time employment, and self-employment (exempted from labour legislation and social security contribution). These exceptions give employers a number of "escape clauses", and atypical contracts generate a continuum of grey areas between full employment protection and informality. The outsider status of migrants translates into insecure employment conditions, which has multiple ramifications. Guell-Rotllan (2000) argued that employers are motivated to rely on atypical contracts for two reasons. First, outsiders are cheaper to fire and can be used to buffer against adverse shocks. This is known as the buffer effect. As a result, outsiders are more likely to face frequent transitions between employment and unemployment. The second reason is that given their higher level of exposure to unemployment, outsiders are easier to discipline, which undermines their ability to call attention to violations of working time regulations or discrimination. This has been called the discipline effect (Polavieja 2003). Because welfare institutions, such as pensions or unemployment insurance, are often linked to an individual's employment status, frequent employment interruptions will result in inferior welfare protection.
We expect female migrants to be overrepresented among outsiders for three reasons. First, prior studies have found that they are at the intersection of the groups among whom fixed-term contracts are more prevalent: female workers, younger workers, and workers in jobs with low skill requirements (regardless of their human capital characteristics) (Polavieja 2005;Güell & Petrongolo 2007;Bentolila et al. 2019) Second, immigrants are likely than natives to have less bargaining power. On the one hand, individuals who decide to leave their home country for economic reasons tend to be more willing to accept poor employment conditions, or jobs that the native-born population perceive to be inferior (Zorlu & Hartog 2012;Bevelander & Irastorza 2014;Rodríguez-Planas & Nollenberger 2014). On the other hand, administrative rules and practices create a "discriminatory institutional framework" (for example, by restricting access to residence permits or making it difficult to validate foreign academic degrees). Moreover, by definition, informal employment due to irregular legal status is not protected by employment legislation.
The third reason why female migrants are overrepresented among outsiders, as posited by assimilation theory, is that immigrants may be sorted into secondary sector occupations because they lack country-specific skills (such as the ability to communicate in the host country language, and knowledge of local networks and social norms), which are necessary complements to their human capital, especially in skilled occupations (Chiswick et al. 2005). Another consequence of the discriminatory institutional framework is that it concentrates certain immigrant groups in ethnic niches (Schrover et al. 2007).
The following hypothesis captures all of the potential factors related to the labour market structure that should distinguish female migrants from their native counterparts with similar levels of education and experience: Hypothesis 1 (segmentation hypothesis): Compared to their female native counterparts with similar age, location, and educational characteristics, we expect female migrants to be more likely to be outsiders, and to therefore face worse employment conditions, including: -working in secondary sector jobs (caring and cleaning); -having atypical contracts (involuntary part-time, fixed-term contracts); and having a higher probability of dropping out of employment and of being unemployed.

Impact of family responsibilities and the internal organisation of households
The second hypothesis emphasises the key role of the immigrants' family situations (Powers & Seltzer 1998;Aysa-Lastra & Cachón-Rodríguez 2013). While the reconciliation of work and family life has been found to be a challenge for all female workers (de Quinto et al. 2020), female migrants are likely to face specific challenges. The fragility of female migrants' positions in the labour market are likely to reinforce the "child penalty". Previous studies have shown that having a child has a negative impact on labour force participation (Kleven et al. 2019;de Quinto et al. 2020) for both native and migrant women (Holland & de Valk 2014). However, native insiders benefit from longterm employment relationships, and their greater bargaining power and institutional protection can allow them to reach agreements with their employers for flexible schedules or part-time arrangements without interrupting their employment relationships. By contrast, immigrant outsiders are only able to absorb the burden of care by terminating their short-term employment relationships. We would therefore expect the more fragile employment situations of immigrants to translate into their use of different strategies (Lapuerta et al. 2011;Guner et al. 2014).
In addition, the households of migrant and native women may be organised differently. Households tend to adopt three types of strategies to allocate the burden of care responsibilities. First, the partners in a couple may bargain over their division of labour. Whether a household reaches a more or less symmetric outcome will typically depend on the partners' relative earning capacity and education. However, if a female migrant lives in a household in which her husband has a higher earning potential, we would expect to observe a more asymmetric division of labour.
Second, households may outsource care to professional care services. However, female migrant workers may have a limited ability to outsource private care/domestic services because they are not affordable for all families. For low-skilled female workers, the cost of such services is likely prohibitive.
Finally, households may outsource the burden of care to their extended family networks. This has been one of the key resources used by low-skilled female workers in Southern European countries. However, female migrants have very different networks of family support, since their extended family members typically remain in their country of origin. Thus, generally, only native females can rely on informal caregivers (Ryan 2011;Cobb-Clark & Moschion 2017).
Taking into account the household characteristics that are likely to influence female immigrants' labour market trajectories, we construct the following hypothesis: Hypothesis 2 (family responsibility hypothesis): We expect female immigrants to face specific obstacles in the reconciliation of labour and family life that differ from those of native women: -Female immigrants will tend to organise childcare within their household in the absence of extended family and informal networks. - The child penalty will thus be higher for immigrants, who will be more likely to leave the labour market to fulfil family responsibilities.

Economic and work-life balance assimilation
A natural question is whether the obstacles that female migrants face are temporary, or whether their outcomes converge with those of natives the longer they stay. Do female migrants become insiders? And do their family responsibilities become more similar to those of native workers? Assimilation into the labour market is closely related to an individual's insideroutsider status. The original justification for atypical contracts was to serve as a stepping stone for outsiders that would enable them to acquire experience and skills, and to become insiders in the medium term (Bentolila et al. 2019). Similarly, immigrants may improve their situations the longer they stay in the host country, in parallel with their social and economic integration. For female migrants, taking on temporary and lowskilled jobs could be a stepping stone while they acquire human capital in the receiving country (Rodríguez-Planas & Nollenberger 2016), or while they wait to acquire the legal right to work. Through these mechanisms, female migrants are more likely to become insiders (in the primary sector, with a more stable employment position) the longer they stay in the country.
However, the stepping stone hypothesis is not the only possible medium-term outcome for initial outsiders (Güell & Petrongolo 2007). Given the short-term nature of their employment relationships and their role as buffers, it seems likely that employers will be less prone to invest in outsiders and to promote them to more stable positions. Similarly, secondary sector job ladders may be characterised by less upward mobility, given the types of demands and the organisation of the work (for example, the care and cleaning sectors), or because they require employers to invest heavily in human capital. Finally, gender and ethnic stigmatisation may trap female migrants into a limited number of jobs, some of which have no channels for upward mobility given the types of demands and the organisation of the work (such as the care and cleaning sectors), or because they require a heavy investment in human capital. As a result, female migrants are likely to remain trapped in their outsider status.
Do migrant women's family responsibilities become more like those of native women the longer they stay? Assimilation in terms of family responsibilities may or may not occur for three reasons. First, the impact of the family responsibilities of female migrants may decrease with their length of stay because children need less intensive care as they grow older.
Second, if female migrants are more likely to have care responsibilities due to their more fragile position in the labour market, becoming an insider could enable them to close the gap with native women. If female migrants' labour market positions become more solid over time, their bargaining power -both in the labour market and within the household -may increase, allowing them to converge with natives in terms of their family responsibilities. However, if female migrants remain stuck in their outsider status, they may also stay trapped in their traditional gender roles.
Finally, migrant households may become more similar to native households due to their exposure to a similar sociocultural and institutional environment. The preferences and cultural norms that organise households are likely to be at least partially a product of the environment. As exposure to that environment increases the longer they stay in the host country, migrant households may adopt the cultural norms and preferences of native households. Alternatively, migrant households may preserve the cultural norms and preferences of their country of origin.
Hypothesis 3 (assimilation hypothesis): We expect to find that as the length of stay in the host country increases, the outcomes of female immigrants become more similar to, but do not completely converge with, those of native-born workers with similar characteristics due to the obstacles they face in the dual labour market and in their family arrangements.
In sum, previous studies have suggested that the assumptions discussed above depend on the immigrants' individual characteristics as well as on the economic and institutional contexts. It is, therefore, more appropriate to talk about complementary hypotheses rather than about mutually exclusive hypotheses. Immigrants' individual and family characteristics, such as their gender, educational level, family status, and family networks in the destination country, should be taken into account when seeking to explain their levels of labour market integration and labour market success.

Empirical strategy
Our hypotheses predict that the employment outcomes and strategies female migrants use to reconcile work and family differ from those of their native counterparts. Our empirical strategy seeks to answer two questions: (a) Do female migrants systematically differ from natives with similar characteristics in terms of the outcomes outlined in the segmentation and family responsibility hypotheses? (b) Does this gap shrink or even disappear with the length of stay (assimilation hypothesis)?

Data
For our analysis, use data from the Spanish sample of the EU Labour Force Survey (LFS) for the years 2014 to 2018 1 . The LFS interviews households quarterly, asking them about their labour market status and working conditions. We pooled all of the survey waves from the end of the recession (2014)  The annual version of the LFS provides detailed information about each respondent's current job and household and individual characteristics, which allows us to evaluate the convergence of immigrants' labour market outcomes as a function of the length of their stay. We also rely on data from the 2018 ad hoc module of the LFS (henceforth referred to as AHM18) on the reconciliation of work and family life to explore the specific strategies immigrants use to balance their personal and professional responsibilities.

Dependent variables
We examine five dependent variables: occupational status, nature of the employment (temporary vs. permanent), care incidence on employment outcomes, and care strategies.
Occupational status. We use the respondent's occupational status at the time of the survey to assess the segmentation hypothesis. To explore this dimension, we combine the author's (Sánchez-Domínguez & Fahlén 2018) classification of the International Standard Classification of Occupations (ISCO-08 codes) with the activity status of non-employed. Partitioning occupational status in this way allows us to examine migrant women's integration into the labour market, as well as their sorting into the primary and secondary sectors.
1. Professionals/clerks are high-skilled occupations such as legislators, senior officials, managers, professionals, technicians, associate professionals, and clerks (ISCO codes 010-422). This category constitutes the core of the primary sector. 2. Service jobs are all other semi-and low-skilled service occupations not considered care/cleaning, such as protective services workers and shop and market sales workers. Service jobs can be considered an intermediate category between the primary and secondary sectors. 3. Care/cleaning jobs are a subset of service jobs that are closely linked to the outsourcing of domestic work, which has allowed native women to enter the labour market (Farré et al. 2011). Native women regard these tasks as undesirable due to their low status and poor working conditions, which are often related to the shadow economy. Such jobs constitute the core of the secondary sector for female work. We classify individuals in care and cleaning jobs as less-skilled, institutionbased personal care workers (including home-based personal care workers, childcare workers, and other personal care and related workers), domestic helpers, cleaners, and laundry workers (ISCO08 codes 510,516,530-532,325,910:912). 4. Elementary jobs are other low-skilled occupations not considered care/cleaning jobs, such as agricultural and fishery workers, craft and related trades workers, plant and machine operators and assemblers, and sales and services elementary occupations (ISCO08 codes 600-909,920-933, 950-962). 5. Unemployed refers to all women who are currently not working but are looking for a job. 6. Inactive refers to all women who are not working and are not currently looking to become employed. Temporary vs. permanent jobs. A core distinction between insiders and outsiders is their level of job security. Following prior studies (Polavieja 2003;Bentolila et al. 2019), we compare the percentage of female immigrants and native employees (i.e., excluding nonemployed and self-employed workers) with fixed-term contracts.
Care incidence. Following Hypothesis 2 (family responsibility hypothesis), we want to investigate whether native and migrant workers are affected differently by the burden of care: Are they more likely to work part-time, or to opt out of the labour market? To investigate this question, we divide all women aged 16 to 64 into five categories according to their employment status and the reasons why they are in this status 2 : 1. Full-time workers are all female workers who have regular full-time jobs. This status represents an individual's complete integration into the labour market. 2. Part-time workers due to care reasons are all workers who have a part-time schedule, as defined by the LFS, and who attribute that status to looking after children or incapacitated adults, or to having other family responsibilities. 3. Part-time workers due to other reasons are all part-time workers who attribute their status to other reasons (including own illness or disability, inability to find a fulltime job). 4. Individuals who are not working due to care reasons are women who are inactive or unemployed, and who either left their last job or are not looking for a job due to care responsibilities. 5. Individuals who are not working due to other reasons are all non-employed women who do not fit into the previous categories. This variable allows us to measure the incidence of care responsibilities based on women's self-assessments of their labour market situations. We expect to find that female immigrants are more likely than native women to drop out of employment for care reasons. We also expect to observe that native women, who tend to have more stable employment conditions than migrant women, are more likely to be able to manage their care responsibilities without interrupting their employment trajectories.
Care strategies. To test Hypothesis 2 (family responsibility hypothesis), we seek to understand how women manage their care responsibilities. The AHM18 asks respondents with childcare responsibilities whether they use professional childcare services, and, if not, why not. We combine these items in order to divide respondents into six categories. Our first category (a) includes those who do not have care responsibilities. Among those who do, we build category (b) by selecting those who fully outsource care responsibilities. Finally, we divide those who have family responsibilities and do not outsource them fully into (1) those who attribute this decision to the cost or the unavailability of services; (2) those who manage care within the extended family or informal networks; (3) those who manage care within the household; and, finally (4) those who regard children as being able to take care of themselves. Hypothesis 2 implies that in the Spanish care regime, female natives will be more likely to outsource childcare or to manage care within their extended family network. In addition, we expect to find that female migrants consider childcare to be too costly, or that they regard children as able to take care of themselves.

Independent variables
According to our hypotheses, the dependent variables for native and immigrant female workers should differ. Analytically, we can distinguish between three components in these gaps: (a) the part that can be attributed to differences in observable characteristics (common to both migrants and natives), (b) the part that can be attributed to immigrantspecific characteristics, and (c) the part that results from the interaction of the two. Therefore, we divide our explanatory variables into the following groups: respondents reported looking after children or incapacitated adults or having other family responsibilities, we also classified them as "Not working due to care reasons". We classified all other non-employed persons as "Not working due to other reasons".
Common characteristics of all women: human capital and living arrangements. With respect to human capital, the market value of the stock of skills of immigrants and natives is likely to differ. Following the classic Mincer (1958) specification, we approximate the stock of human capital according to education (codified as lower, medium, and higher in the LFS) and experience (approximated by five-year age groups). We also expect employment outcomes to vary naturally due to the demand for human capital in the local labour market, since immigrants tend to make specific residential choices (Albert and Monras 2017). We take those choices into account, including three urban densities: cities (densely populated area), towns and suburbs (intermediate density area), and rural area (thinly populated area); and 19 regional dummies (NUTS 2).
Immigrants and natives are also likely to differ in their living arrangements. Hypothesis 2 predicts that living arrangements are likely to have a large impact on the burden of care responsibilities. Therefore, we seek to take into account the specific household characteristics of female natives and migrants. First, we divide households into four categories: "Couple no children" (living with a partner, but no children), "Couple with children" (two-adult household with one or more children under age 15), "Single, no children" (no children and no partner in the household), and "Single parent" (at least one child under age 15, and no partner in household). Second, for women who live with a partner, we are interested in controlling for the partner's level of education (low, medium, or high), since the value of his human capital will affect how the couple's joint decisions are made.
Immigrant-specific characteristics. A final set of explanatory variables is specific to immigrants. Years of residence in Spain is the key variable we use to assess whether female migrants' outcomes converge with those of female natives (Hypothesis 3). Years of residence is grouped into five categories: less than two years, 3-5 years, 6-8 years, 9-15 years, and more than 16 years living in the country.

Methodology
For each of our dependent variables, our goal is to examine the gap between female migrants and native workers with similar common characteristics (human capital and living arrangements). To test our assimilation hypothesis, we need to examine how the gap changes as a function of the length of stay (a variable that is only present for immigrants). We do so in two steps. First, we use a matching algorithm to pair each female immigrant worker in our sample with a native with similar characteristics. Second, we compare the means of the native and immigrant samples as a function of the immigrant's length of stay.
For each female migrant, the algorithm finds its "most similar counterpart" among the natives in the sample (see Stuart 2010 for a review of matching estimators). It evaluates similarity based on the human capital covariates (age, education, degree of urbanisation, and region) as well as those related to the living arrangements (household type and partner's education). We constrain the algorithm to match migrants and natives exactly on education (three categories) and household type (four categories). We consider these to be the core variables to assess human capital and living arrangements. For the remaining variables (age, urbanisation, region, and education of the partner), the similarity is evaluated using the propensity score function, conditional on the covariates estimated with a logistic function.
The choice of matching to construct a comparison sample has multiple advantages (see Heckman et al. 1998;Ho et al. 2007). Unlike parametric alternatives (such as logistic regression) that can be used to control for observable characteristics, comparing balanced sample proportions does not assume that control covariates affect outcomes additively (Ho et al. 2007). It excludes the influence of native observations that are not similar enough to immigrant observations in all dimensions. This helps reduce the imbalance not only in individual controls, but also in their interactions. 3 In addition, comparing means in matched samples allows us to analyse how the gap changes when the sample is split based on immigrant characteristics. This comparison is easier to interpret than multiple interaction effects in a parametric model, and is particularly convenient when some characteristics are only present for immigrants (like the length of stay).

Description of the sample before and after matching
Our motivation for using a matching algorithm is that the female native and the migrant samples are likely to have different household and human capital characteristics, and this asymmetric composition is likely to drive part of the gap in outcomes. Therefore, we start by describing the composition of the migrant and the native female samples, and how the matching algorithm corrects the imbalance in their covariates.
The living arrangements of female migrants and female natives differ considerably (Table 1). Female migrants are more likely to have children (in either a nuclear or a singleparent family), and are less likely to live alone. With regard to human capital, 37.8 per cent of natives, compared to 27.0 per cent of migrants, have completed higher education before matching. Similarly, the partners of female migrants are, on average, less educated than the partners of native-born women (21.0 per cent vs. 16.8 per cent have higher education, and 12.5 per cent vs. 19.2 per cent have mid-level education before matching). However, our algorithm adjusts the imbalance on these covariates almost exactly to match the migrant sample proportions (Table 1). Table 1 also shows how matching adjusts the imbalance in other covariates. Female migrants are, on average, younger than natives: the proportion of females over age 55 is twice as large for natives as for migrants, while the opposite pattern is observed for the 25-35 age group. Both proportions are almost exactly the same after matching. Before matching, migrant women are much more likely (54.5 vs. 50.3) to live in urban areas, which is consistent with the concentration of suitable jobs in cities.

Determinants of labour market convergence among migrants and native women in a segmented labour market
This section evaluates how the length of stay in the country affects the occupational status gap between migrants and natives, and the incidence of temporary jobs among migrants. Figure 2 displays the proportions of immigrants and natives in each occupational status 4 . The most salient gap is in activity rates: close to 40 per cent of female migrants are inactive (Figure 2.6) within the first two years of their stay in Spain, compared to 25-30 per cent of natives with similar characteristics. This gap persists for the first decade of residence in the country, but migrants' activity rates eventually converge with those of natives (which supports the assimilation hypothesis). 4 Figure A1  However, the convergence in activity rates is not mirrored by the convergence in other employment outcomes. As predicted by the segmentation hypothesis, once they enter the labour market, female migrants have substantially worse employment opportunities. First, the share of female workers who are employed in care and cleaning jobs (Figure 2.3) increases to up to 20 per cent for immigrant women, while the share for comparable native women remains stable at around 10 per cent. Female migrants are disproportionately concentrated in the secondary sector. In comparison, the gap between migrants and natives in the primary sector (professional and clerical (Figure 2.1) and service jobs (Figure 2.2) looks very different. In the service sector (Figure 2.2) the gap is not reduced until after the migrants have been in the host country for at least a decade, and it stays unchanged even after migrants have spent 15 years in the professional and clerks sector. This finding indicates that secondary sector care and cleaning jobs are the central avenues of employment for migrant workers, while their opportunities to transition into the primary sector are limited. 5 The gap in unemployment rates (Figure 2.5) also illustrates the inferior employment opportunities open to migrant workers. Figure 2.5 shows that the unemployment rate for migrant workers is stable at nearly 20 per cent (versus 15 per cent for comparable natives). Figure 3 displays the percentages of female immigrants and native employees (i.e., excluding non-employed and self-employed workers) with fixed-term contracts by years of residence in Spain. The Figure 3 illustrates that when female migrants are employed, they are disproportionately likely to be outsiders in the Spanish dual labour market (in line with the segmentation hypothesis). The share of migrant workers with temporary contracts is 5 Figure A2 (Appendix) shows the convergence in occupational status by education and the length of the stay. 46-52 per cent (versus 30-35 per cent for comparable natives) for the first five years of their stay. The gap between migrants and natives with similar household and human capital characteristics is reduced, but persists at five per cent. The information displayed in Figures 2 and 3 broadly confirms our segmentation hypothesis: i.e., the dual structure of the labour market imposes specific obstacles on migrant women that differ from those of their native counterparts. Migrants have worse employment opportunities than natives, and when they do enter the labour market, they are mainly concentrated in the secondary sector, and are often employed with unstable temporary contracts. While some assimilation in activity rates and in the incidence of fixed-term contracts is observed, female migrants never manage to enter the primary sector at the same rates as their native counterparts. As a result, female migrants are more likely to remain outsiders, and to be economically inactive.

Determinants of the interplay between female labour market outcomes and work-life balance
We have seen that the dual structure of the Spanish employment regime relegates female migrants to the status of outsiders in the secondary sector. In this section, we analyse the incidence of care responsibilities based on all of the women's self-assessments of their employment status. The variable "care incidence" (Figure 4) divides the population into five categories based on how their employment status is affected by their care responsibilities. It compares female migrants to their native counterparts with identical burdens of care (measured by household composition) and human capital characteristics. Figure 4 shows the asymmetry in the responses of migrants and native workers. Within the first two years of arriving in the country (Figure 4.4), almost 20 per cent of migrant women are out of work due to care responsibilities, compared to five per cent of natives. Like the activity rates, these shares converge in the long run, but only after 16 years of stay. We attribute this finding in part to the effects of (1) assimilation, given that the employment situations of female immigrants tend to improve the longer they stay in Spain, in parallel with their levels of social and economic integration. However, this pattern can also be seen as (2) as a by-product of the lower burden of care as children become older, which occurs in parallel with immigrants' length of stay.
Natives are half as likely as immigrants to interrupt their careers to care for children or dependent adults (Figure 4.4), and are instead more likely to engage in part-time work (Figure 4.2) to accommodate their care burdens, which is consistent with the family responsibility hypothesis. Interestingly, although immigrants are more likely overall to have a part-time job than natives after their sixth year of stay (Figure 4.2), they do so for other reasons (Figure 4.5) (the other two possibilities are illness or disability, or the inability to find a full-time job). We interpret this finding as suggesting that natives are more likely to engage in part-time work due to their insider status (ability to bargain a time reduction to manage their care responsibilities, instead of quitting their job), while for immigrants, being in part-time work seems to be a sign of their outsider status. The effect of care responsibilities is contingent on living arrangements. To further explore the interactions between care incidence and living arrangements found in Figure  4.4, Figure 5 compares the share of non-working women who are not working for care and other reasons as a function of living arrangements. Our goal in this figure is to shed light on the relative effects of the burden of care (measured by the presence of children) and the division of household labour within the household (measured by the presence of a partner).   Figure 5 shows that the gap between natives and migrants observed in Figure 4.4. is disproportionately driven by households in which both a partner and children are present. As expected, the gap in non-employment due to care responsibilities is non-existent when we compare native couples without children to their migrant counterparts (top Figure 5.1). While there is a 15 per cent gap in employment between natives and migrants in the first five years of their stay, this gap is driven by other reasons (Figure 5.1,bottom). The opposite is the case for couples with children (Figure 5.2). On average, in the first five years of their stay, 60 per cent of migrant women living with a partner and children are non-employed (compared to 25 per cent among natives); of these, two-thirds (40 per cent) are in that status due to care responsibilities (only 15 per cent among natives) (top Figure  5.2). Finally, the gap in employment is also significant for migrant single mothers, especially in the first years of residence in the country (Figure 5.3). In summary, Figures 4 and 5 show (a) that native workers enjoy better working conditions, which allow them to reconcile their work and family life, while (b) female migrants are forced to opt out and withdraw from the labour market to fulfil their care responsibilities; and (c) that withdrawal is even more likely for migrants who are supported by their partner, and can therefore afford a more traditional division of labour.
In Hypothesis 2 (family responsibility hypothesis), we also suggested that, in the absence of extended family and informal networks, female migrants tend to organise childcare within their household. Table 2 displays the difference in our "Care strategies" variable (section 4.1.1). As expected, female migrants are less likely to receive support from informal and family networks. Moreover, they are less likely to outsource childcare responsibilities to professional services, and are more likely to report that these services too costly or unavailable. We interpret the findings shown in Table 2 as evidence that female migrants are constrained in their ability to organise the provision of care within the household (and thus retreat from the labour market), or reduce the amount of care provided to let their children take care of themselves.

Conclusion
In this paper, we investigated the obstacles that female migrants face in the Spanish labour market. While the labour market status of women in Spain has improved substantially in recent decades, in this paper, we argued that Spain's employment, migration, and care regimes likely impose a specific penalty on female immigrants. We tested this hypothesis by comparing the labour market participation patterns of female migrants between 2014 and 2018 to those of natives with comparable human capital and living arrangement characteristics. First, we found that female immigrants face distinctively worse employment opportunities than their native counterparts. We argued that this gap is closely linked to their status as outsiders, which often condemns them to taking temporary jobs, to working in care and cleaning occupations, and to having higher levels of unemployment. As a result, even skilled female migrants are frequently relegated to taking jobs that most natives would reject. In the Spanish dual labour market (Guell-Rotllan 2000;Polavieja 2003), this sorting results in job instability and worse employment conditions for migrant women.
Second, we explored the connection between having worse employment opportunities and the challenge of balancing work and family life. We hypothesised that the fragility of the position of female migrants in the labour market would interact with their care responsibilities. Indeed, we found that native and immigrant women differ in their worklife balance strategies: native women are more likely than migrant women to have stable careers and to work part-time in response to their care responsibilities, while female immigrants are disproportionately more likely their native counterparts to respond to their care responsibilities by interrupting their working lives.
However, we also found that the higher care penalty (measured by whether children are in the household at the time of the survey) faced by immigrants in the Spanish labour market is not driven exclusively by their worse opportunities in the labour market. Instead, we showed that this penalty is likely linked to the specific characteristics of the Spanish care regime. The absence of public, widely accessible childcare services pushes all of the burden of care provision onto households and extended family networks. In contrast to their native counterparts, female migrants are unable to outsource childcare either to professional caregivers (who are costly or unavailable) or to extended family networks (who remain in the country of origin). Therefore, the Spanish care regime pushes them out of the labour market altogether.
The Spanish care and employment regimes therefore interact to impose a double penalty on female migrants. Migrant women face substantial obstacles to finding stable jobs due to the dual structure of the labour market. At the same time, the Spanish care regime provides almost no support to help them balance their work and family life. As a result, female migrants are trapped on both the labour market and the domestic fronts in careers that resemble those of low-skilled native women of the previous generation: i.e., they tend to have frequent career interruptions, low levels of employment stability, and a more traditional division of labour arrangements.
We argued that the double penalty faced by female migrants has consequences beyond their labour market status. This finding opens at least three promising avenues for further research. First, outsiders face disadvantages not only in the labour market, but in access to public services linked to career trajectories, and specifically to the pension system. The penalties faced by female migrants during their working lives are, therefore, likely to apply to their lives in retirement as well. Second, if the constraints generated by caregiving result in female migrants being more likely to leave their children to take care of themselves, this can have long-term effects, as recent research has found that childhood conditions are strongly correlated with disadvantages at later ages (Cunha & Heckman 2007). Thus, lower investments in their children by first-generation immigrants could result in the transmission of disadvantages to second-generation immigrants. Third, it is well-known that worse employment opportunities for women are strongly related to gender inequality in other dimensions, such as intra-household inequality or intimate partner violence (González & Rodríguez-Planas 2018;Rice & Vall Costelló 2018).
Overall, this paper underlines the importance of institutions that seek to ensure gender equality among all segments of population. The Spanish case illustrates how the outsourcing of the burden of care has allowed a large portion of native women to escape traditional labour and family roles. However, our findings suggest that the status of female migrants is unlikely to fully converge with that of native-born women as long as two key institutions remain in place: the Spanish "familist" care regime and its dual labour market.
A central limitation of our study is the difficulty of capturing the effects of institutions in a single country study. As both familist care regimes and dual labour markets are prevalent in southern Europe, our analysis suggests that migrant women will face similar obstacles in countries with similar care and labour market institutions; e.g., in Italy. Further research is therefore needed in a comparative perspective to fully understand the effects of country-specific characteristics on migrant women.
A premise of this paper was the observed labour market segmentation of migrant workers. In this appendix, we illustrate some additional results. Figure A1 shows the evolution of occupational sorting over time. The plot was elaborated by combining waves of the LFS. It shows that the occupational sorting that we analyse in the paper has persisted for the last decade and a half. While approximately half of native-born women are employed as professionals, the share of migrants employed in that sector is below 25 per cent.  Figure A2 shows how occupational outcomes vary by level of education. In our assimilation hypothesis, we stated that we expect the convergence of immigrants with natives with similar characteristics to be imperfect. We argued that this could be due to the complementarity of country-specific skills with human capital. However, we also suggested that the segmentation of the labour market would trap workers in low valueadded occupations. The figure illustrates this mechanism. While the share of less educated women female migrants who are professional/clerks is comparable to that of natives for (close to zero), highly educated migrants are half as likely as comparable natives to be employed in that sector. In contrast, these latter groups are disproportionately likely to be unemployed or inactive, consistent with their overqualification for low-skilled jobs. As highly-skilled immigrants find their way into the Spanish labour market, they seem to do so mainly in the quasi-secondary service sector (at a higher rate than native women). Interestingly, we show that the overrepresentation among immigrant women of a factor of two in the care and the cleaning sector is real even when compared to that of low-skilled native women. Overall, the immigrant penalty increases with education.