Welfare and social protection: What is the link with secondary migration? Evidence from the 2014‐crisis hit Italian region of Lombardy

Correspondence Livia Elisa Ortensi, Department of Statistical Sciences “Paolo Fortunati”, Alma Mater Studiorum University of Bologna, Via delle Belle Arti, 41, 40126 Bologna, Italy. Email: livia.ortensi@unibo.it Abstract Evidence on the relationship between secondary international migration and welfare state (or formal protection) support is currently limited. Also, the experience of financial support from semiformal and informal social protection networks has seen limited inclusion in current reflections on secondary mobility patterns such as onward and return migration. Our study analyses the relationship between support from formal, informal and semiformal social protection and short-term secondary migration intentions. The study uses open-access data from the Regional Observatory for Integration and Multiethnicity of Lombardy (Italy) and adopts a competing-risk framework through multinomial logistic regression. Our data do not support the hypothesis of an ex-post “magnetic effect” of the Italian formal social protection on its beneficiaries: individuals on formal welfare are more prone to onward and return migration. However, the positive relationship observed between welfare entitlements and onward migration intentions cannot rule out any effect of welfare magnetism from more generous welfare systems. Monetary aid received from Italian friends is negatively related to return intention. At the same time, economic support from foreignborn friends is correlated to return migration. We interpret results according to social network theory. Economic support and social capital from bridging networks can act as an ex-post integration-driven magnet. Bonding social capital from ties with migrants in Italy cannot secure the migrants' stay in Italy. However, it can support return migration. Networks providing bonding transnational social capital, and expressed in the form of financial support from relatives living abroad, are instead positively correlated to both forms of secondary migration.

hypothesis" is somewhat mixed. Some studies reject this hypothesis; others, however, document the existence of a moderate welfare magnet effect for selected subpopulations of immigrants (see Barret & McCarthy, 2008;Brueckner, 2000;Jakubiak, 2017Jakubiak, , 2019, for detailed discussions of the state of the art over the years). Moreover, research suggests a distinction between the ex-ante (i.e., before migration) and ex-post (i.e., after migration) effect of social protection on mobility (Andersen & Migali, 2016). De Jong and de Valk (2020) have recently highlighted that the welfare state's relevance to migrants changes after migration and may play a more critical role in the secondary migration decision-making compared with the first migration.
Accordingly, after the migration, the destination context can be perceived-and should be analysed-as a new potential origin context.
Ex-post welfare magnetism becomes potentially relevant in the context of growing complexity of contemporary mobility patterns and increasing relevance of return and onward migration (Bonifazi & Paparusso, 2018;Castles et al., 2014;Jeffery & Murison, 2011;Monti, 2019). However, limited research exists on the relationship between these forms of secondary migration and social protection systems in migrants' first settlement countries.
Italy is a relevant case study in terms of ex-post social protection magnetism given its relatively recent experience as an immigration country (Colombo & Dalla Zuanna, 2019) and its familistic welfare regime (Esping- Andersen, 1999). As in other Mediterranean countries, the Italian welfare protection system relies strongly on families, with most support being provided in the form of income transfers (Esping- Andersen, 1999). Social expenditure is heavily concentrated on oldage pensions, a type of benefit that is minimally redistributive (Baldwin-Edwards, 2002) and absorbs nearly 60% of the total resources (Barrett et al., 2013). Italy allocates only a small share of its gross domestic product (GDP) to provision valuable and attractive to young migrant populations, such as social insurance support (e.g., cash transfers, food aid, housing subsidies, education fee waivers) or social assistance schemes (e.g., contributions-based unemployment or maternity benefits). It does not qualify, as a consequence, as an exante welfare magnet to international migrants. However, due to labour market openings to unskilled workers (Colombo & Dalla Zuanna, 2019), a sizable number of migrants have settled permanently in Italy, formed new families or applied for family reunification (Ambrosini, 2013). The concentration of migrants in low-paid and lowskilled jobs has resulted in an overrepresentation of foreign-born individuals among the population below the poverty line (ISTAT, 2020) and a growing number of migrants eligible for the (limited) Italian welfare benefits. The recent 2008 economic crisis increased the need for welfare support. High rates of unemployment led to a growing number of migrants qualifying for social protection. At the same time, many migrants opted for onward or return migration as a coping strategy to deal with financial difficulties (Dubow et al., 2019;Ortensi & Barbiano di Belgiojoso, 2018), a trend also observed in other Southern European countries (Mas Giralt, 2017;Prieto-Rosas et al., 2019;Ramos, 2018).
In this framework, forms of ex-post welfare magnetism towards beneficiaries of formal social protection may arise. Despite limited provision, are individuals on welfare more inclined to remain in Italy compared with other migrants? This issue is by no means trivial, given that recently some anti-immigration rhetoric has also been built on the competition with low-income native Italians over the limited social protection resources (e.g., social housing).
Formal social protection in Italy is heavily bound to eligibility (European Commission, 2018). Among eligible migrants, long-term stayers with children are overrepresented whereas some individuals in the most vulnerable categories are excluded (e.g., irregular migrants; Giulietti, 2014). The mismatch between eligible and vulnerable individuals in modern societies is a complex phenomenon that arises from the growing discrepancy between new social risks and welfare states designed after World War II to address risks primarily related to the male breadwinner's unemployment (Zimmermann, 2017). The mismatch between eligibility and vulnerability is even more relevant for migrants who may, as a coping strategy, rely on alternative-and less studied-forms of support.
The focus on the destination countries' national welfare systems as the predominant social protection provider to migrants has repeatedly missed the role of other forms of protection (Godin, 2020) provided from faith-based or nongovernmental organisations (NGOs) and informal social networks. The latter cannot be overlooked in a comprehensive reflection about the relationship between social protection and secondary migration being highly relevant to migrants and closely intertwined with formal welfare protection (Sabates-Wheeler & Waite, 2003;Serra-Mingot & Mazzucato, 2017).
Given this framework, we focus on ex-post social protection magnetism on foreign-born migrants 1 living in Lombardy (Italy). More in detail, we discuss the relationship between the experience of social protection support and short-term (i.e., in the 12 months following the interview) onward (international migration to a third country different from the country of birth) and return (to the country of birth) migration intentions. We consider social protection support received in the year before the survey from the welfare state (formal social protection), NGOs or similar organisations (semiformal social protection), and social networks of native and foreign-born friends and acquaintances (informal social protection). Although being aware that informal social protection provides much larger support than merely filling gaps in formal social protection schemes (Serra-Mingot & Mazzucato, 2019), we address informal social protection from a financial perspective. 2 Moreover, as suggested by theoretical considerations from Bilecen and Barglowski (2015) and Serra-Mingot and Mazzucato (2017), we consider the transnational dimension of migrants' informal support networks.
Our paper addresses the following research questions (RQs): RQ1) Formal welfare magnetism: deterrence against secondary movements-Are formal social protection recipients less likely to declare short-term onward or return migration intention than other migrants? RQ2) Informal and semiformal social protection network magnetism-(a) Are recipients of financial support from semiformal and informal social protection networks less likely to declare short-term onward or return migration intention than other migrants? (b) Are there differences according to the type of informal network (foreign, native and transnational providers) providing support?
To answer these RQs, we build on data collected by the Regional Observatory for Integration and Multiethnicity in the Northern Italian region of Lombardy (ORIM). Researchers repeatedly used ORIM surveys to provide ground-breaking evidence on migration when nationwide survey data were unavailable (e.g., Dustmann et al., 2017;Fasani, 2015). For our analysis, we use the 2014 survey that involved 4000 individuals with a migrant background and collected information on formal protection benefits and economic support from semiformal and informal networks.
The paper proceeds as follows: Section 2 presents previous studies that analysed the welfare magnetism effect on migrants' secondary migration movements; Section 3 expands the discussion to the role of financial support from semiformal and informal social protection networks, formulating some hypotheses when previous studies are not available. Section 4 provides evidence on the rising importance of secondary migration among migrants in Italy and Lombardy, and background information about the region. Section 5 describes the data and methods. Finally, we present the results in Section 6 and discuss them in Section 7. Additional details about ORIM survey data and control variables are provided in Appendix A.

| WELFARE MAGNETISM AND SECONDARY MIGRATION
The "welfare magnet hypothesis" postulates that individuals make migration choices based on formal social protection available in the destination area to insure themselves against unemployment and financial difficulties. 3 Immigrants are expected cluster in countries and regions within countries where welfare provision is most generous and accessible (Borjas, 1999). Therefore, an open and generous welfare system could boost immigration and, at the same time, disproportionately attract migrants with limited expected income.
Welfare magnetism may also affect secondary migration by deterring the mobility of individuals who, without social protection, might be more inclined to return to their country of origin or migrate onward. 4 Moreover, the relevance of welfare to migrants is expected to change over the life course (e.g., after childbirth or regularisation) and could factor differently into the first and secondary migration decision making (De Jong & de Valk, 2020). While the link between openness and generosity of welfare states and first migration has been repeatedly investigated, research on the relationship with secondary international migration is scarce and mostly based on observed migration rather than intentions. Reagan and Olsen (2000), using US longitudinal data on residential histories and focusing on generation 1.5 immigrants (i.e., individuals who immigrate to a new country before or during their early teens), found that welfare programme participation negatively impacted on the immigrants' likelihood of returning. Giulietti, in his 2014 review of evidence on the welfare magnet hypothesis, observed that "there is virtually no evidence on the interactions between return migration and welfare dependency," and he acknowledged that this relationship "represents a potential avenue for future research" (Giulietti, 2014, p. 9).

| Welfare magnetism and return migration
Most evidence in the European context analyses patterns of EU citizens. Bratsberg et al.'s (2014) study on individual longitudinal data of post-EU accession Eastern European labour migrants to Norway found that the 2008 financial crisis increased return migration. However, the majority of labour migrants remained in Norway claiming unemployment benefits. Andersen and Migali (2016) focused on the link between unemployment benefits and return migration. Their analysis of EU28 migrants living in former EU15 member states, Norway and Switzerland, concluded that the stay or return migration decision is more sensitive to welfare generosity than the first migration decision. Accordingly, relatively "low" 5 unemployment benefits in the country of settlement do not curb return migration, and most migrants return home if they become unemployed. "Sufficiently high benefit levels" result in return migration only for migrants with low migration costs, whereas others tend to stay. More recently, Dubow et al. (2019) studied EU migrants settled in Germany, Italy, Spain, Sweden and the United Kingdom, combining in-depth focus groups, interviews and survey data within the H2020 Reminder project framework. Their research confirmed previous evidence that higher quality social security and public services in the origin country is an essential determinant of return movements for migrants from Sweden and Germany. This finding is consistent with De Jong and de Valk's (2020) claim that the welfare system of the country of origin is also crucial in shaping migrants' return decisions.

| Welfare magnetism and onward migration
Social provision and openness to migrants vary significantly from country to country, even among developed countries where welfare programmes are well established (Giulietti, 2014). Therefore, better social protection or easier access may act as attraction factors for would-be onward migrants located in first immigration countries characterised by limited welfare provision such as Southern European countries. Migrants who have already borne the "fixed cost" of leaving their home country may be more likely than natives to relocate to states where they may receive more and better benefits or qualify as beneficiaries while currently excluded. Existing studies suggested that generosity, and especially openness, of the welfare states factor into the decision-making of migrants at the extreme end of the social ladder, potentially attracting both the most vulnerable and the most privileged. Research has recurrently underlined the relevance of welfare state generosity to asylum seekers and refugees (Long & Sabates-Wheeler, 2017). Brekke and Brochmann (2014) found that Eritrean asylum seekers in Italy aspired to migrate onwards to Norway or Sweden because of more generous reception and welfare standards. Dubow et al. (2019), in the previously mentioned study, found that more favourable welfare entitlements were the main reason for the intra-EU onward movement of refugees mainly from Greece to Germany. At the same time, welfare generosity also attracted highly skilled migrants whose international work opportunities provide them with the possibility to choose carefully between different potential destination countries (Dubow et al., 2019).
In the European context, the right to free movement granted by naturalisation, EU citizenship and denizenship/long-term migrant status (Zhang, 2014)   A relevant form of assistance is the semiformal social protection, usually provided by faith-based organisations, NGOs and private institutions to meet specific needs, vulnerabilities and risks. Examples of services more commonly provided include occasional monetary aid, food parcels, clothes, blankets, medicine, free medical care, legal and social advice (Serra-Mingot & Mazzucato, 2017).
Although receiving financial support from semiformal entities, such as private institutions or NGOs, is not an expression of belonging to networks, we can make different considerations for financial support from social networks (or informal social protection). Informal social protection is a vital form of support to migrants provided by family, community or social networks based on collective norms and belonging. It includes a complexity of factors such as financial support, care relations, exchange of information, interpersonal and transnational ties involving family, kinship, friendship and community as actors providing social support (Bilecen & Sienkiewicz, 2015;Serra-Mingot & Mazzucato, 2017). As well-established, social networks provide access to different resources depending on the network type (for detailed discussions of the state of the art, see Bankston, 2014). The family and community are closed networks with dense ties and deep trust based on solidarity, usually defined as "bonding social capital"; an ambivalent cohesive mechanism providing help to co-ethnics but sometimes preventing access to the host country resources (Bankston, 2014;Lancee, 2012). Monetary aid received from foreignborn friends and acquaintances is a strong expression of bonding social capital. 6 Networks established with natives are instead considered "bridging social capital" because they grant access to new and valuable social capital that extends beyond the community, thus connecting migrants with natives (e.g., Bankston, 2014;McLellan, 2009). Financial support from Italian friends and acquaintances is a strong expression of access to bridging social capital and ties to the country of immigration.

| Financial support from semiformal and informal social protection and secondary migration. An underresearched link
There is scant evidence on the relationship between financial support from semiformal and informal social protection and secondary migration. Few recent studies focus on the role of occasional financial help from the transnational family network and friends in curbing economic hardship driving return migration. This form of support usually aims to assist migrants at the beginning of their stay or address unexpected financial needs reflecting reciprocal provision and the actors' interdependence (Palash & Baby-Collin, 2019;Singh & Gatina, 2015).
The relationship between secondary migration and financial support from informal social protection networks is particularly interesting due to their bridging and bonding nature. The bridging social capital, like formal and semiformal social protection, is highly location specific and minimally transferrable; it is expected to act (mostly) as a magnet by deterring emigration due to its positive impact on integration. The transnational structure of networks providing bonding social capital entails a more complex relationship with secondary mobility. Transnational networks may potentially offer support in the country of origin, destination and in third countries where members are settled, and also before, during and after migration (Godin, 2020). Our study focuses on Lombardy (NUTS 32 code ITC4). This region, especially the area of Milan, is one of the wealthiest in Europe (Eurostat, 2020b). It is the most densely populated area and hosts about a quarter of Italy's foreign-born population. Within the framework of substantial territorial differences and fragmentation of the Italian welfare provision (Barrett et al., 2013), Lombardy has one of the most comprehensive and generous welfare provision compared to other Italian regions (Carradore, 2014). These elements, and the availability of updated and detailed survey data on welfare provisioncurrently unavailable at the national level-make Lombardy a relevant case study. ORIM surveys provide the possibility to analyse a 10-year set of cross-sectional data on self-declared short-term emigration intentions, distinguishing between the intention of onward migration and return to the country of birth. Short-term secondary migration intentions among foreign-born migrants reached the highest level in 2014 (17.1%) and reduced in the following years ( Figure 2). Our analysis is based on the 2014 data, therefore referring to the moment when secondary migration intentions among first-generation migrants peaked in Lombardy due to the crisis. We discuss the implications of this period's effects in the concluding section.
The global economic crisis played an essential role in shaping national and regional emigration trends. In Italy, GDP fell dramatically between 2008 and 2013, and the economy subsequently struggled to recover fully (Colombo & Dalla Zuanna, 2019). In Northern Italy, the  Table 1 describes the variables used in the model. Following the literature previously discussed, we considered support from formal, semiformal and informal social protection. The dependent variable, expressing self-reported mobility intentions for the 12 months following the survey, has three categories:

| Variables
"Intention to remain in Italy" (reference category), "Intention to return to the country of origin" and "Intention to migrate onward to a third country." 8 The assumption that the respondent's intention to leave Italy in the 12 months following the survey is a reliable proxy of reemigration is crucial in order to analyse the relationship with onward and return migration. There is broad agreement about the value of intentions to study re-emigration, 9 although they may overestimate the scale of mobility (Boeri et al., 2002). Carling and Pettersen (2014) argued against scepticism in using future relocation intentions, emphasising that these are a necessary-but not sufficient-criterion for action, implying that actual movers will be among the people who intend to return or to re-emigrate.
Moreover, the use of a short, well-defined, fixed term to define the timing of mobility reduces the discrepancy between intention and behaviour, helping us to identify real future emigrants and freeing intentions from other normative dimensions such as the sense of belonging or the myth of return (Carling, 2015).

| Methods
We used multinomial stepwise logistic regression (Long & Freese, 2014) to model migration intention 10 (see Appendix A to see partial models and covariates) due to our dependent variable having three categories and the need, unanimously recognised by scholars, to analyse onward and return migration data in a competing-risk framework (Barbiano di Belgiojoso & Ortensi, 2013;DaVanzo, 1976;Toma & Castagnone, 2015).
To implement the competing-risk framework, we tested the independence of the irrelevant alternatives assumption that allows us to check that the introduction of another alternative does not change the preferred option. 11 For example, if "Stay" is preferred to "Onward" in the choice between "Stay" and "Onward," introducing the alternative "Return" must not make "Onward" preferable to F I G U R E 2 Short-term secondary migration intentions among the first-generation migrant population (percentages). Lombardy (Italy) 2010-2019 "Stay." We verified all the alternatives. The test results indicated that we could not reject the equality of the coefficients across the models; therefore, we could use a multinomial logistic regression.
To better substantiate and describe the results, we also estimated the probability of short-term onward and return migration intention according to the types of support received.
T A B L E 3 Formal, semiformal and informal social protection received in the 12 months before the survey (percentages) by foreignborn migrants in Lombardy (Italy), 2014 6 | RESULTS

| Sample description
As shown by Table 2, overall, women account for 47.7% of our sample. 12 If we restrict the analysis to individuals who received at least one form of support, however, we observe a proportion of women as high as 63%. The family composition impacts the likelihood of receiving any form of support and the type of support received: 81.1% of respondents on formal welfare live in families with children.
We observe a similar composition among individuals who received provision from multiple sources in the 12 months before the survey (75.4% are in families with children). Unsurprisingly, the family members' job status is relevant: unemployed and precariously employed are more represented among those who received social protection from one or multiple sources.
There is considerable variability in short-term migration intentions according to patterns of social protection provision received in the 12 months before the survey. Among migrants who received only informal provision or received multiple forms of support, short-term onward migration intention is twice as high as for the overall subsample, and three times as high compared with those who did not receive any welfare benefits.

| Descriptive findings
As shown in Table 3, nearly one migrant in three received at least one form of social provision in the 12 months before the survey. Formal social protection is the most frequent (19.4%) followed respectively by informal (13.2%) and semiformal social protection (9.1%). A total of 11.6% of the migrants received only formal social provision, 6.0% only F I G U R E 3 Predicted probability of return migration intention: differences compared to the reference profile "no social provision received in the last 12 months" informal and a negligible proportion received only semiformal provision (1.8%). In some cases (6.5%), migrants benefited from two types of social provision. A considerably smaller group received all forms of provision (3.1%).
This overall picture masks significant differences among countries or areas of origin in terms of both percentages of beneficiaries and type of welfare received (

| Multivariate analysis
Model results 13 (Table 5)  also holds when support through bridging networks is combined with help from networks providing bonding social capital that is, instead, per se positively related to return migration (e.g., formal social protection and relatives who live abroad). Indeed, we observe that migrants who received money from relatives who live abroad (TBO) and foreign-born friends or acquaintances (BO) are significantly more likely to declare return migration intention than migrants who were not supported by any source of social protection.
Moving on to onward migration intentions, we observe that individuals who received at least one form of support are more likely to declare onward migration intention (Figure 4).
Migrants who have received formal social protection are always more likely to intend to migrate onward than migrants who have not received any form of support. Indeed, we do not observe any form of welfare magnetism among receivers of formal social protection in the form of secondary migration deterrence. Moreover, we also observe an interaction between support sources: if a migrant receives support from many different sources, the probability of onward migration intention is higher. Networks providing bridging social capital are the only source whose support is correlated to a deterrent effect on return migration that can be interpreted as magnetism. We do not observe a similar relationship with bridging social capital when short-term onward migration intentions are analysed.

| DISCUSSION AND CONCLUSION
In the last few decades, scholars have dedicated much effort to testing the ex-ante formal welfare magnetism hypothesis in different European countries. The relationship between ex-post welfare magnetism and secondary migration is, conversely, currently underresearched. Even less evidence exists on the relationship between semiformal and informal social protection and secondary migration. The focus on semiformal and informal social protection is crucial. These sources of support are essential to vulnerable individuals not eligible for formal social protection.
We based our analysis on cross-sectional data collected in 2014 in Lombardy (Italy), a region characterised by high-level social provision within the heavily pension-oriented Italian social protection system framework.
Our study provides descriptive evidence of differentiated patterns of access to formal, semiformal and informal social protection across groups. These patterns might reflect differences in expectations in terms of public welfare support (Albertini & Semprebon, 2018), the strength of informal ethnic networks and compositional differences in terms of the incidence of poverty, presence of children, proportion of single low-income families and undocumented migrants across groups.
We analyse the relationship between the experience of social protection support and short-term secondary migration intentions.
First, we observe that secondary migration intentions are higher among migrants on formal welfare compared with other migrants (RQ1). Our data, therefore, do not support the hypothesis of an expost "magnetic effect" of the Italian formal social protection on its beneficiaries. At the same time, the positive relationship observed between welfare entitlements and onward migration intentions cannot rule out any effect of welfare magnetism from other, more generous welfare systems, especially for EU citizens, naturalised Italians and long-term migrants whose status enables legal mobility and work in another EU country. Migrants on welfare in Italy might expect to qualify as welfare recipients in other countries, too. Therefore, they could be more interested in relocation than other migrants, as The relationship with return migration intention is also interesting: migrants on welfare are more likely to declare return migration intention. Even the relatively generous support provided by Lombardy's formal social protection system is not enough to deter migrants from returning to their countries of origin.
The analysis of the relationship between short-term secondary migration intentions and semiformal and informal social protection underlines the different role of these forms of support (RQ2a). We do not observe any significant relationship between support from semiformal social protection and secondary migration. In analysing informal social protection, the network's bridging or bonding nature providing support is crucial (RQ2b). The theory of bridging and bonding human capital (Lancee, 2012)  Despite these promising findings, our paper has limitations that we hope will be overcome by future studies. First and foremost, our data are representative only of the Italian region of Lombardy. On the positive side, Lombardy is one of Italy's wealthiest areas, offering migrants some of the most developed welfare provision in the country. Therefore, it is particularly suitable to study the nexus between secondary international migration and social protection. On the negative side, results cannot be representative of Italy. Especially in southern areas, where weaker formal welfare provision is available, different relationships might exist between informal and formal social protection and mobility. Second, as already noted, there is no information about the destination of would-be onward migrants in order to assess potential welfare magnetism between Italy and the other countries. Third, as we adopted a competing-risk framework (DaVanzo, 1976), we did not explicitly consider the role of the welfare state in the country of origin, which could foster migrants' intention of returning home. Recent evidence has pointed out the relevance of the welfare state in the countries of origin in shaping return migration (De Jong & de Valk, 2020), a relationship that needs to be studied further in the Italian context. However, in our analysis, most migrants originate from less developed countries, whose welfare is usually even less generous than that of Italy.
Another critical limitation regards missing detailed information about the structure and location of migrants' transnational networks and the amount of aid received from each source. The latter set of information would be crucial in order to discuss how magnetism from formal welfare relates to magnetism from bridging social networks, and if these effects can be compared. We are also lacking information on the reasons driving the first migration to Italy. Better data at the national level focusing on migrants' social protection experience during their life course is needed to advance the theoretical reflection on the link with secondary migration.
Finally, our data are impacted by localised effects relating to the economic crisis, as they refer to the year when short-term secondary migration intentions peaked in Lombardy. Migrants in Lombardy (and in general in the centre-north of Italy) were particularly badly hit by the crisis due to their concentration in factories, small business and building and manufacturing industries (Zanfrini, 2014). Our data refer to a year when job opportunities in Italy were particularly scarce.
What was initially a limitation might become a point of strength, as the crisis driven by the COVID-19 pandemic is expected to lead to a probably worse situation when compared to 2014. Formal welfare states, semiformal and informal networks are already under intense pressure from rising unemployment, poverty and increasing inequality.
Our findings may contribute to future debates on migrants by rejecting the Italian formal welfare magnetism hypothesis during economic crises.
To conclude, in a context of recurring economic crises, complex migration trajectories and increased legal mobility across Europe (EU citizens, naturalised and denizens/long-term migrants), new data are needed to understand the interactions between forms of social protection and secondary mobility.

CONFLICT OF INTEREST
The authors declare that they have no conflicts of interest.

DATA AVAILABILITY STATEMENT
The data that support the findings of this study are openly available through the Lombardy Open Data site at https://www.dati.lombardia.

ORCID
Livia Elisa Ortensi https://orcid.org/0000-0003-1163-8440 Elisa Barbiano di Belgiojoso https://orcid.org/0000-0001-5782-ENDNOTES 1 Internal migration is not addressed in this paper. Consistently, we use the term "migrant" to refer to a foreign-born individual who migrated internationally and is currently living in Italy. We also use the terms "foreign-born" and "migrant" as synonyms. The same goes for the terms "migration" and "international migration." How to cite this article: Ortensi LE, Barbiano di Belgiojoso E. The information about the number of centres attended and the frequency of visits can be used to correct the sample, giving each interviewee a different weight according to how likely they were to be found by interviewers. The Centre Sampling Technique provides "the same representativeness as a hypothetical simple random sample stratified with respect to the distribution of the profiles of attendance at the centres" (Baio et al., 2011, p. 454). onward migration intention is both a strategy to cope with unemployment and instability, or to seek possibilities to improve the family's financial situation elsewhere. Previous internal mobility along the Italian peninsula fosters the goal of returning home, while the effect is not significant for onward migration.
As for the demographic characteristics of the migrants, due to the higher-monetary and nonmonetary-costs of family migration (Finney & Simpson, 2008;Silvestre & Reher, 2014), the presence of the family (children and/or partner) when emigrating considerably reduces the intention to leave Italy. Furthermore, onward migrants are more likely to be men, as found by the vast majority of studies on onward migrations (e.g., Haandrikman & Hassanen, 2014;Monti, 2019;Nekby, 2006;Ortensi & Barbiano di Belgiojoso, 2018;Schroll, 2009;Toma & Castagnone, 2015). As the length of stay in Italy increases, the likelihood of a second migration decreases: along with their permanence in Italy, migrants acquire capital specific to the location and, as the time passes, the cost of a new emigration becomes higher (DaVanzo, 1976;Rashid, 2009 Only for couples. *p < 0.05. **p < 0.01. ***p < 0.001.