The Same Fertility Ideals as in the Country of Origin? A Study of the Personal Ideal Family Size among Immigrant Women in Italy

: The role of the personal ideal family size for international migrants has rarely been studied in the current debate on fertility and migration in the European context. It is not known to which extent the reduction of fertility observed among immigrants who settle in a country where fertility is lower than in their country of origin is the result of a change in fertility norms among those immigrants. The study of migrants’ ideals family size has the potential to shed light on fertility norms without the interference of economic conditions and migration-related disruptive phenomena. Due to the complexity of its migration context, Italy is an interesting destination country for studying changes in migrants’ ideal family sizes. This paper uses data from the survey of the Italian National Institute of Statistics (ISTAT) on immigrant families conducted in 2011-12. We compare the personal ideal family size of women of reproductive age with the prevalent norm in their country of origin, applying a multinomial logistic regression analysis. Results show that the country of origin has an important role in the determination of immigrants’ ideal family sizes. Women from countries where large families are the ideal are more likely to show a lower personal ideal family size compared to their non-migrant co-nationals, while women from countries where two children are considered ideal mostly share the same norm. The occurrence of fertility preferences expressed in a non-numeric form (e.g. “Up to God”) changes between women with different countries of origin. This study con ﬁ rms that conformity with the ideal of the country of origin is more likely among women who migrated as adults. At the same time, the number of years spent in the destination country is not signi ﬁ cantly associated with a shift away from the norms prevalent in the country of origin. Finally, female empowerment and gender equity show their effects mainly on the reduction of non-numeric responses.


Introduction
The importance of norms has long been recognised in both sociology and demography (Bulatao et al. 1983).Many scholars assigned a key role to fertility norms in explaining essential processes such as the historical fertility transition and the process of fertility decline in developing countries (Liefbroer/Billari 2010).Among fertility norms, personal ideal family size is considered to be a good indicator of individual values and attitudes towards childbearing, though it has been established that it cannot be used to predict actual or fi nal fertility (Testa/Grilli 2006).Testa/Grilli (2006) emphasised the lack of scholarly refl ection on the personal ideal family size of native populations in Europe.This same conclusion can be drawn today regarding the study of the personal ideal family size of international migrants.
In the last decades, migration fl ows have determined the relocation of a considerable number of women who grew up and were socialised in a context where fertility ideals are remarkably different from those observed in their country of destination.Current theories about the migration-fertility nexus consider the role of fertility ideals as key, but due to the scarcity of specifi c data, research has so far mostly been based on migrants' actual behaviour.While some migrants move between areas that share similar ideals of relatively small families, others move from countries at different stages of the demographic transition.Thus they may have been socialised in contexts where large families are common and idealised (Fargues 2007).In the latter case, migrants may show fertility ideals and preferences similar to natives of the country of destination because they belong to select groups sharing ideals more similar to those in destination countries than in their origin country, a position known in the literature as the selection hypothesis (White et al. 1995).Alternatively, they may have different ideals upon arrival and then converge or adapt to the fertility norm of the country of settlement (Rindfuss 1976;Nauck 1987;Mayer/Riphahn 2000).Finally, they may instead preserve their ideals while showing fertility behaviour similar to destination-country natives due to transformations of their living conditions, including constraints and trade-offs typically related to migration -such as weak labour market attachment -which have an impact on both the timing and the number of births (Fargues 2007).However, the extent to which the reproductive behaviour observed among immigrants is consistent with fertility norms or instead differs as a consequence of fi nancial restrictions or other disruptive phenomena is unknown.The study of migrants' ideals has the potential to shed light on fertility norms without the interference of migration-related disruptive phenomena.
The few existing studies on the ideal family size of foreign-born citizens, which are mostly descriptive in their approach, show the presence of broad differences among ethnic or migrant communities, identifi ed as people who share the same foreign background.Individual factors such as religion, education, and the number of siblings emerge as signifi cant in shaping the ideal number of children in Great Britain, France, and Germany (Penn/Lambert 2002).
To fi ll this gap in the literature, we compare individual personal ideal family size among migrant women in Italy with the prevalent norms in the respective countries of origin as a proxy for the normative environment in which migrants were social-ised.We also focus on the role of gender equity and female empowerment among migrants, as several studies have underlined a direct relationship between these two dimensions and fertility in both developed and developing countries (Genereux 2007;Arpino et al. 2015;Blau 2015), which may also signifi cantly shape migrant fertility (Kulu et al. 2017).
Even though Italy has a less expansive history as a country of immigration than other European states do, six million of its residents -10 percent of the total population in 2017 -are foreign-born (Eurostat 2018).Due to the complexity of its migration context (King 2000), which is characterised by the presence of migrant communities from countries with different fertility behaviours, Italy emerges as an interesting country in the study of ideal family sizes of migrants.What furthermore makes Italy a compelling case is the persistence of the two-child family norm among native Italians, despite having de facto "lowest-low" fertility rates (Testa 2012).This paper aims to answer the following research questions: How many children would immigrant women in Italy like to have?Do their preferences differ from the norms in their origin country?And what is the impact of country of birth, migration-related characteristics, female empowerment, and gender equity?To address these questions, we analysed data on 7,307 immigrant women of reproductive age residing in Italy in 2011-12 from 101 countries 1 and compared their personal ideal family size with the national average ideal size in their origin country.

Actual fertility, family size preferences, and ideals
The analysis of fertility among migrants has so far been mostly based on data related to their actual behaviour, typically the number of children born after migration (e.g.Ortensi 2015), the transition to different parities (e.g.Andersson 2004;Milewski 2010;Mussino/Strozza 2012a, 2012b), or the contribution of migrants to the total number of births (Sobotka 2008).Differences between cultural norms in the countries of birth and destination have also been studied by looking at immigrants' ac- tual fertility (Algan et al. 2012).Cultural adaptation has been conceptualised as the convergence to the fertility norms of the destination country (Andersson 2004).
The selection hypothesis argues that many migrants' behaviour may indeed not change at all -rather, people who choose to migrate in the fi rst place are a self-selected group, whose fertility preferences are different -usually lower -than than the general average in their country of origin (Kulu 2005).The maintenance of country of origin fertility behaviors after migration has been interpreted in the logic of the socialisation hypothesis, which similarly builds on the premise that the fertility behaviour of migrants primarily refl ects the fertility preferences dominant in their childhood environment (Kulu 2005; Baykara-Krumme/Milewski 2017).Nevertheless, it is widely acknowledged that the timing and the number of births are not only shaped by norms and preferences, but also refl ect constraints and inequalities, such as precarious economic conditions, diffi culties in reconciling family life and demanding jobs, the unavailability of a suitable partner, poor health, infertility, or unplanned pregnancies (Martin 2004;Philipov/Bernardi 2011;Sedgh et al. 2014;Finer/Zolna 2016).In the case of migrants, the relation between norms, preferences, and actual fertility is even more complicated because -as with all life course events -fertility behaviours are sensitive to the act of migration (Holland/de Valk 2013).Consequently, the study of migrants' ideals, is crucial to explain the possible change in fertility norms without the interference of personal, fi nancial or health-related trade-offs and migration-related disruptive phenomena.
Differently from the analysis of actual and intended fertility, the study of concepts such as the "ideal family size", the "personal ideal family size", and the "desired/preferred family size" builds on evaluations made under "ideal conditions" (Philipov/Bernardi 2011), and it has been shown that societal norms concerning demographic behaviours are relevant, even in a society where the individualisation process is fairly advanced (Liefbroer/Billari 2010).Fertility ideals and desires have nevertheless been subject to criticism for being relatively "soft", abstract, and poorly defi ned concepts (Toulemon 2001;van de Kaa 2001;Quesnel-Vallée/Morgan 2003;Sobotka/Beaujouan 2014).However, family size desires are conceptually and empirically distinct from ideals: desires refl ect more "internal" factors, such as motivations, attitudes, and beliefs and have, therefore, been considered as a personal norm (Testa/Grilli 2006;Kuhnt et al. 2017).Desires are often uncertain and subject to change over the life course in response to new experiences and conditions (Thomson 2015).Personal ideals have instead been interpreted as refl ecting the normative context; they are shaped by the larger society after predominant societal pronatalist or antinatalist norms and, therefore, change more slowly than desires do (Trent 1980;Testa/Grilli 2006;Thomson 2015).
The analysis of migrants' personal ideal family size is not a trivial one: analyses of social distance between migrant groups and natives are at the core of academic and public discourses (Holland/de Valk 2013).While integration in some sectors such as the labour market and education can be relatively fast, changes in the private domain and the normative sphere, to which life course events are deeply related, are slower to occur and may require far more than a generation to be internalised (Gordon 1964;Lesthaeghe 2002).Ideals have the potential to provide insight into the balance between the persistence of norms from the country of origin and the processes of family change and socialisation after migration.
The few studies on fertility ideals carried out on ethnic groups or migrants in different destination countries suggest the existence of differences between different ethnic groups in both the preferred timing for family formation and the ideal family size (Penn/Lambert 2002;Holland/de Valk 2013).However, socialisation seems to play an important role.In the Netherlands, de Valk (2013) found intergenerational differences among all ethnic groups: usually children prefer smaller families than their parents did.Penn and Lambert (2002), who conducted a cross-national analysis of the ideal number of children among different ethnic groups and nationalities, found substantial differences between ethnic groups in Britain, Germany, and France.Indian and Pakistani respondents in Britain expressed signifi cantly larger ideal families than native Brits; at the same time Maghrebians in France also valued large families, but the difference to French natives was less evident.The study also found a preference for ideal families of two children among Turkish and former-Yugoslav migrants in Germany, and no signifi cant differences with German natives.These fi ndings suggest that ethnic group differences are essential to understanding fertility norms among migrants.

What determines the ideal family size? Evidence from previous research
Previous research in the fertility domain, mainly building on evidence from Western countries' natives, has suggested a link between ideal family size and a set of potential explanatory variables.Age is one of them: attitudes and norms are more relevant at the beginning of the reproductive career, while perceived behavioural control plays a stronger role after the birth of the fi rst child (e.g.Testa/Grilli 2006;Mills et al. 2008;Billari et al. 2009).Age also has the potential to capture cohort effects and shape ideal family size according to respondents' own experiences of childbearing and parenthood (Weston et al. 2005;Kuhnt et al. 2017).Some studies have suggested that fertility ideals are adjusted in line with the size of the respondent's current number of children; for this reason, it is important to control for this item (Weston et al. 2005;Kuhnt et al. 2017).
Family size ideals are also likely infl uenced by the respondent's socioeconomic status.The infl uence of socioeconomic status here does not take hold through economic limitations that may affect childbearing, because ideals by defi nition are expressed regardless any current circumstance (Iacovou/Tavares 2011;Kuhnt et al. 2017).Rather, the role of socioeconomic deals with social norms of childbearing found within the social networks or categories which the respondents belong to and that are considered as their reference groups (Liefbroer/Billari 2010).
Partnership status does not seem to alter fertility ideals (Kuhnt et al. 2017).Ideals are consequently more stable than intentions or desires, because they are related to a social norm rather than to a shorter-term personal preference or contingencies (Thomson 2015).
The role of education also needs to be discussed when examining fertility ideals.While in developing countries, higher education is usually related to lower ideal fertility (Doepke/Tertilt 2018), in the European setting, a diverging trend has occasionally been observed.In some countries, a positive relationship between education and fertility has been observed after experiencing a period of low fertility related to educational expansion (OECD 2016).Education and human capital are often interpreted as a proxy for female empowerment, according to the idea that more educated women have more bargaining power in marriage (Mills et al. 2008;Doepke/ Tertilt 2018).Higher levels of education allow women to question traditional roles (McDonald 2006) and are often associated with a more equal division of household chores (e.g.Mencarini/Tanturri 2004).Scholars have repeatedly pointed out a signifi cant and complex link between unbalanced gender roles (in the form of unequal divisions of household labour) and fertility intentions and behaviour (Mills 2010;Tazi-Preve et al. 2004;Neyer et al. 2013).Consistently, gender equity, which captures perceptions of fairness rather than the strict equality of observed outcomes (Mc Donald 2013), may signifi cantly impact fertility ideals.
However, the results of the few studies that have considered the link between female empowerment and the ideal number of children in developing countries are mixed.A 2002 study based on Demographic and Health Survey (DHS) data in Eritrea found that women having the fi nal say in decisions regarding day-to-day household purchases was associated with a smaller ideal family size (Woldemicael 2009).At the same time, a more recent study based on data on Guinea, Mali, Namibia and Zambia found women's empowerment (measured as participation in household decision making, attitudes towards domestic violence, and attitudes toward refusing sex with one's husband) is not consistently associated with a desire for smaller families (Upadhyay/Karasek 2012).
Job participation is similarly related to gender roles: Homemaker mothers may be more likely to have traditional attitudes than employed mothers (Fan/Marini 2000;Zuo/Tang 2000;Bolzendahl/Myers 2004), but, more generally, gender equality and fertility have a U-shaped relationship (e.g.McDonald 2013; Upadhyay et al. 2014;Esping-Andersen/Billari 2015).Religion has also proven to be an important factor relating to fertility.In many contexts, women who describe religion as "very important" have higher fertility than others, especially those who declare they are unaffi liated with any religion (Frejka/Westoff 2008;Berghammer 2012;Peri-Rotem 2016).However, just as for education and female labour force participation, it has been argued that the fertility-religion nexus expresses a widespread association between religiosity and family behaviour, rather than specifi cally pronatalist views held in specifi c religions.In fact, it appears that factor at play is less religiosity per se, but rather certain more specifi c notions of family life often associated with religiosity, which include ideas about the importance of marriage and parenthood, the acceptability of non-marital sexual relations, and gender roles (Hayford/Morgan 2008).
Previous studies on migrants have found that ideal family sizes are different among different ethnic groups (Penn/Lambert 2002;de Valk 2013).However, for fi rst-generation migrants, age at arrival emerges as a crucial dimension.Sociali-sation studies assert that family (size) values formed in late childhood and early adolescence are retained throughout life (e.g.Westoff/Potvin 1967;Kulu 2005).According to this theory, people who migrated after having spent their childhood and early adolescence in their country of origin should preserve family ideals typical of the countries where they were socialised, even if after migration they may choose adaptive strategies to deal with the new context of settlement.By contrast, according to classical theories on immigrant assimilation (Gordon 1964), a long residence abroad implies a growing infl uence of the dominant family formation patterns in the destination country, which may also be internalised as family ideals (Holland/de Valk 2013).The relation between socialisation and adaptation at the individual level, therefore, may be associated to immigrants' duration of residence in the settlement country (Lieberson/Waters 1988;Alba/Nee 2003).
A factor potentially related to the effect of migration on ideal formation is language, which is a functional factor positively associated with aspects of social integration at the destination country (Ager/Strang 2008;Kearns/Whitley 2015).To be fl uent in the host country's language is a precondition for communication across cultural boundaries (Statham/Tillie 2016).However, studies on the effect on internalisation of norms are discordant.When analysing the association with fertility, Unger and Molina (1997) identifi ed language as an infl uential factor amongst Hispanic women in the United States: Those who spoke Spanish at home with their mother were far more likely to have a higher personal ideal number of children (particularly sons) than those who spoke English.By contrast, Penn and Lambert (2002) found no support for this "cultural" hypothesis in their study in Great Britain, France, and Germany.
A fi nal remark is needed about the occurrence of non-numerical responses.Women sometimes provide their ideal number of children in terms of words rather than numbers, for example, "it's up to God", "as many as possible", or simply "I don't know".The occurrence of this kind of answer has recently been declining in fertility surveys, suggesting that "numeracy about children" (Van de Walle 1992) is increasing across the developing world.A recent study based on DHS carried out in 32 countries in Asia, Latin America, and sub-Saharan Africa underlined that non-numerical responses are indicative of high fertility and pre-transitional contexts.Their occurrence declines with lower fertility rates.At the individual level, non-numerical responses are indirectly related to higher education and fertility-specifi c knowledge (Frye/Bachan 2017).Other studies suggest that women who provide non-numeric responses share traditional pronatalist cultural norms that imply preferences for "many" children rather than encouraging women to select a specifi c number as their ideal (Olaleye 1993).Other scholars have suggested that non-numeric responses are an indication of women's perceived lack of control over their fertility (Hayford/ Agadjanian 2011; Van de Walle 1992).

Working hypotheses
Based on the literature discussed above, the hypotheses tested in this study are the following: • H1: The personal ideal number of children is associated with the ideal number of children in the country of origin (H1a), even when we control for migratory and socio-economic factors (H1b).
• H2: Consequently, people arriving as adults are more likely to have a personal ideal number of children similar to that of their origin country, compared to those who migrated as children or young adults.
• H3: At the same time, a long and uninterrupted presence in Italy might be associated with a deviation from the prevalent norms of the country of origin.
• H4: Higher levels of female empowerment (education and labour market participation) and support for gender equity imply higher numeracy about children, and therefore a lower proportion of non-numeric responses.
In summary, this study analyses ideal family sizes of migrant women in Italy and how they differ from the prevalent norms in their countries of origin, thereby underlining the role of the country of origin, migratory characteristics, and gender roles in fertility ideals -three specifi c points that are currently under-researched in the fi eld of fertility and migration.

Measures of fertility intentions and attitudes
The norms observed in migrants' countries of origin has been defi ned as the mean ideal family size observed in national surveys available worldwide on this topic.This means that we must rely on different sources and slightly different wording of questions on the ideal family size in the country of origin.
The fi rst survey that included a question on ideal family size was carried out in 1936 (Blake 1966).Since then, hundreds of surveys around the world have collected information about family ideals in different countries and contexts (Sobotka/Beaujouan 2014).The 2011-12 Italian National Institute of Statistics' (ISTAT) survey "Social condition and integration of foreign citizens" formulated the question to measure personal ideal family size as follows: "How many children would you like to have in your life?" To account for the personal ideal family size norm in the immigrants' countries of origin, we assembled information from different surveys.Unfortunately, not all the surveys were run in the same year, so, in order to allow comparability with our survey and between countries, we rely on the most current version available.In these surveys, the questions did not always focus on the personal ideal family size -some focused on the general ideal family size (e.g."What do you think is the ideal number of children for a family?").To provide maximum comparability with the ISTAT survey, we collected the information on personal ideal family size when it was possible; otherwise, we used the information on general family size ideals (Table 1).
In a previous study, Testa (2012: 9) compared the relationship between responses to general and personal ideal family size using the 2011 Eurobarometer.She found a very close agreement between these two dimensions (see also Sobotka Beaujouan 2014).We rely on the original data set in the case of the Eurobarometer and the Demographic Health Survey (DHS), while for the countries that were not included in these two surveys, we collected the information from other sources.We report the original questions for comparison in Table 1.For each country survey we calculated the mean ideal family size applying individual survey weights, according to Sobotka and Beaujouan's (2014) approach.Data are always provided for women aged 15-49 except for countries covered by the World Values Survey, which is based on women aged 18-49.

Data and methods
This paper uses data from the ISTAT survey "Social condition and integration of foreign citizens".The survey was conducted in 2011-12 with families that have at least one member with foreign citizenship.Families were randomly sampled from the civil registry.The fi nal sample survey is made up of 12,000 households in 800 municipalities of different demographic sizes.For this study, only foreign-born women were selected from the original sample.Our fi nal sample consists of 7,307 foreignborn women aged 15 to 49.They come from 101 countries for which information on the individual family size is available.About 37 percent of the foreign-born women in the sample were childless, 27 percent had 1 child, 26 percent had 2 children, and the remaining 10 percent had 3 or more children.
We study the personal ideal family size by comparing the individual ideal number in Italy with the norm in the country of origin, by different origin groups.We plot and map personal ideal family size in Italy and in the countries of birth of migrant women.
Through a set of multinomial logistic regression analyses, we investigate the factors that infl uence the (dis)agreement between the personal ideal family norm and the norm in the origin country.(Dis)agreement is categorised into 5 groups: the same personal ideal number of children as in the country of origin (-0.5 < x ≤ 0.5); a lower personal ideal number of children than in the country of origin (x ≤ -0.5); a larger personal ideal number of children than in the country of origin (x > 0.5); "as many as I may have" (as this category is generally translated as "Up to God", we will also use this phrase); and "I don't know".The reference category is the one in which the personal ideal family size matches the country of origin norm.To show the substantive and practical signifi cance of the fi ndings, we present population marginal means (e.g.Searle et al. 1980;Williams 2012) while holding the covariates fi xed at the population means for the main independent variables.Additional results are in Table A3 in the Appendix.
Our study focuses on the (dis)agreement between the personal ideal number of children and the mean value observed in the country of origin.In analysing our data, we control for demographic and socioeconomic factors.To test hypotheses H1a, H1b, H2 and H3, in addition to country of birth, 2 we examine the age at migra-tion and distinguish if the women arrived before age 16, between 16 and 20, or after age 20; time since migration (up to 5 years in Italy, between 6 and 10, more than 10 years); and the stability of their presence (stable/uninterrupted vs. unstable/discontinuous).To test hypothesis H4 we examine labour market participation, education, and gender equity 3 (no support for gender equity vs. support for gender equity).Additionally, we control for the frequency of religious-service attendance (sometimes, never, often) and Italian profi ciency (good vs. bad) (see Appendix Table A1 for details).
Because one of the aims of our study is to evaluate the importance of the country of birth for the difference between the personal ideal number of children in Italy versus the origin norm, we compare the estimation power of the models using Akaike's information criterion (AIC) and the Bayesian information criterion (BIC).These two tests allow for comparing non-nested models if the results come from the same data (results are in Table A2 in the Appendix).

How many children would immigrant women in Italy like to have?
Figure 1 illustrates the mean number of children that immigrant women in Italy would like to have, by country of origin.Among the migrants residing in Italy, the majority of groups would like to have 2 children.The mean ideal personal number of children for women from Ireland, Israel, The Gambia, Pakistan, Bolivia, Guinea, Senegal, and Burkina Faso is 3, and for women from the Democratic Republic of Congo and Mali, it is more than 4. The average for most of the women from Eastern Europe (Latvia, Belarus, Estonia, Ukraine, Czech Republic, Poland, Bulgaria, Georgia, Romania, Croatia, Lithuania, Slovenia), Southern Europe (Greece, Portugal), Africa (South Africa, Madagascar, Angola, Ethiopia), the Middle East and Asia (Iraq, Iran, Vietnam, Japan, Thailand, Indonesia, Kazakhstan), Western Europe (Austria, Switzerland, Belgium, Denmark), and the Americas (Honduras, Venezuela, Brazil, Mexico) is less than 2 children.The data for Italian natives -1.95 according to the 2011 Eurobarometer survey -is also included in Figure 1.

Do their preferences differ from the norms in their origin country?
For each country of origin, or area (in the case of small communities in the sample), Table 2 shows the percentage of women who express same, lower or larger personal ideal numbers of children than their country of origin average, and the incidence 3 We measure equity by agreement ("completely agree") with the statement that men should help with domestic work.We tested different indicators; the survey contains seven questions related to gender norms.We ran separate models for each indicator and while the direction of the coeffi cients was the same for each indicator, the signifi cance level and the contribution in the model was signifi cantly higher for the selected indicator.
of non-numerical answers.32.8 percent of the women in the sample have the same ideal number of children as the norms in their country of origin, while 33.5 percent have a lower ideal.Women who have a larger ideal number of children than their non-migrant peers make up only 11.9 percent of the sample.Non-numerical responses indicating an undefi ned desired number of children (7.5 percent of the sample) are most common among women from Nigeria, Senegal and Sri Lanka.At the same time, women who are undecided (14.3 percent of the sample) are most common among those born in Macedonia, Nigeria and Bulgaria.
Figure 2 shows the association between the prevalent norm among emigrants and non-migrants by origin country.We plot the mean personal ideal number of children in Italy for the main migrant groups (i.e.those with more than 50 women in the sample) alongside the mean calculated among women aged 15-49 in the respective origin countries.
The points near the 45° line represent the migrant groups living in Italy that have a preference close to the norms in their origin country.The greater the distance between the points and the line, the higher the difference in the expressed ideal family size between the immigrant group in Italy and their counterparts in the origin country.Few immigrant groups seem to share the same exact preference as that of their country of origin; namely, Romania, Bulgaria, and Ukraine have a desired number of children below 2 in both groups and Bosnia Herzegovina 2.5.Most of the groups living in Italy report a lower personal ideal family size than the one in their origin country, with the largest distances observed for women from Nigeria, Senegal, Pakistan, and Ghana, where the mean ideal family size at the national level is above 4  Source: Own calculations based on ISTAT survey "Social condition and integration of foreign citizens" 2011-12 and nationals surveys (most recent year available).Frequencies are ordered by having the same preferences.
children.Interestingly, women from China and Bangladesh have on average an ideal number of children slightly higher than that in their countries of birth.

And what is the impact of country of birth, migration-related characteristics, female empowerment, and gender equity?
Because we aim to identify the control variables with high predictive values in explaining differences with the norm in the origin country, we fi rst run AIC and BIC tests.These two statistical tests follow a similar approach that allows us to see the predictive power of different covariates when the models are not nested.BIC is more susceptible to the degree of freedom, which is why the results are not always identical.Results are presented in Table A2 (in the Appendix) and show that the information with the largest predictive value is the parity; however, despite the large degree of freedom, the second-most important variables are the country of birth and gender equity.
For graphical reasons, we present the adjusted predictions at the means obtained from the multinomial logistic regression analyses of having the same, a low- er, or larger personal ideal number of children compared to the country of origin norm, or "Up to God" (UtG), or "I do not know" (IDK), by country of birth (Fig. 3), by age at arrival (Fig. 4), by duration of stay (Fig. 5), education (Fig. 6), labour market participation (Fig. 7) and by gender equity (Fig. 8).For each fi gure, the controls that were set to the population means are specifi ed in the notes.The details about relative risk ratios obtained from the model for the independent variables are presented in Table A3 and A4 (in the Appendix).
Figure 3 shows the adjusted predictions of (dis)agreement between the personal ideal family size and the prevailing norm in the origin country.On the left side of the graph, we have the nationalities for which we observed larger proportions of women who have the same or larger ideal numbers of children norms than those prevalent in their origin country.These are all women from countries with ideal fertility norms of around 2 children.Women from Peru, Brazil, Germany, France, Bangladesh, and China are among the group showing non-negligible shares (between 21 and 30 percent) of women with an ideal number of children higher than their non-migrant co-nationals.Women from India, Bulgaria, Poland, Russia, Ukraine, Romania, other EU15, and other developed countries (ODC) for the most part share the same personal ideal family size of their country of birth (two children).Similar results were shown in the descriptive statistics (see Table 2).
Conversely, shares of women with a personal ideal number of children lower than their non-migrant co-nationals are found among natives of Ghana, Senegal, Nigeria, Tunisia, Morocco, other African countries (residual category), Albania, Moldova, Kosovo, Macedonia, Ecuador, Sri Lanka, the Philippines, and other Asian countries (residual category).
Those who are unsure about their ideal number of children are mostly women from the Philippines, Nigeria, other African countries (residual category), Macedonia (FYROM), EU15 and ODC citizens, other European countries (residual category), the Dominican Republic, and Ecuador.Finally, larger shares of women who do not quantify an ideal number of children by leaving it to "fate" or "God" (between 10 and 14 percent) are found among women born in Nigeria, Morocco, Senegal, other Latin American countries (residual category), Sri Lanka, and India.We therefore observe a signifi cant effect of the country of origin even after controlling for other covariates (H1a and H1b).
While agreement is more likely among women that move from a country characterised by the same average ideal fertility of Italy (two children), a deviation from the national norm towards a lower ideal number of children than the country of origin is more likely among women socialised in countries where large families are the norm.However, a non-negligible proportion of women who have a larger ideal than their country of origin (and also higher than the Italian norm) exists among women from countries characterised by the two-child norm.
In our second hypothesis, we assume that arriving as an adult might strengthen the preference for a personal ideal number similar to the origin country, compared to migrating as a child or young adult (H2).Figure 4 shows that, according to the adjusted predictions at the means obtained from the multinomial logistic regression analyses, the largeest share of women with a personal ideal family size matching the country of origin is estimated to be among those who migrated at an older age (41 percent).This proportion decreases among those who came as a young adult (37 percent) and even more among those who arrived as children (28 percent).Among the latter group, the share with an ideal number of children lower than the Notes: We control for parity, marital status, age at the interview, age at interview squared, age at arrival, duration of stay, circular migration, education, gender equity, church attendance, labour market participation, and Italian profi ciency.The controls are set to the population margins in destination countries, adjusted predictions at the means (APMs).
Source: Own calculation based on ISTAT survey "Social condition and integration of foreign citizens" 2011-12.
norm in the country of origin or who were unsure increases considerably.The effect of the time spent in the country of origin on the match of personal ideals with fertility ideals of the country of origin is, therefore, signifi cant.Although the effect of age at migration is signifi cant, almost no differences in the adjusted predictions at the means exist among groups with different durations of stay in Italy (H3).Therefore, once other variables are controlled for, no sign of divergence from the origin norm due to the time spent in Italy emerges from the analysis.The proportions of women who have the same preferences as their birth-country peers were 37 percent for women who arrived less than 6 years ago, 38 percent for women who migrated between 6 and 10 years ago, and 40 percent for those who have spent more than 10 years in Italy (Fig. 5).

Fig. 4:
Predicted probabilities of having same, lower, or larger personal ideal number of children compared to the country of origin norm, or nonnumeric responses, by age at arrival Notes: We control for parity, marital status, age at the interview, age at interview squared, country of birth, duration of stay, circular migration, education, gender ideology, church attendance, labour market participation, and Italian profi ciency.The controls are set to the population margins in destination countries (APMs).
Source: Own calculation based on ISTAT survey "Social condition and integration of foreign citizens" 2011-12.Finally, we hypothesised an effect of variables related to female empowerment (education and labour market participation) and gender equity on holding fertility preferences typical of the country of origin (H4).The main effect we observe is mostly a reduction of non-numeric responses.In particular, among women with high secondary school and post-secondary education, the proportion of "I don't know" decreases signifi cantly compared to other women.
Labour market participation shows a similar effect of education: the share of non-numeric responses is higher among women not in the labour force.These women are also less likely to express a lower ideal than the country of origin.
The effect of variables related to empowerment (education and job participation) is similar to that observed regarding gender equity.Strong differences emerge in Notes: We control for parity, marital status, age at the interview, age at interview squared, age at arrival, country of birth, circular migration, education, gender ideology, church attendance, labour market participation, and Italian profi ciency.The controls are set to the population margins in destination countries (APMs).
Source: Own calculation based on ISTAT survey "Social condition and integration of foreign citizens" 2011-12.
the proportions of adjusted predictions at the means by support for gender equity (Fig. 8).The effect of support for gender equity is most evident regarding a reduction of the share of women who are unsure about their ideal family size, or who leave fertility to fate or God, thereby indicating a preference for having as many children as possible.Data show that women who support gender equity also have a clearer idea of their fertility ideals, showing that they have internalised the idea that fertility can be legitimately controlled and personal ideals matter (5 percent vs. 13 percent UtG and 13 percent vs. 20 percent IDK, respectively, for women with equal gender equity vs. no equity).
Our main interest is to compare migrants' ideal number of children with the typical ideal number of children of people remaining in the country of origin -by   Notes: We control for parity, marital status, age at the interview, age at interview squared, country of birth, duration of stay, age at arrival, circular migration, gender ideology, church attendance, education, and Italian profi ciency.The controls are set to the population margins in destination countries (APMs).
Source: Own calculation based on ISTAT survey "Social condition and integration of foreign citizens" 2011-12.

Conclusion and discussion
The study of the personal ideal family size of immigrants has a promising and so far underdeveloped potential to disclose the relationship between migration and fertility.In this study, we compared the personal ideal family size of migrant women in Italy to the prevailing norm of stayers in their respective countries of origin and analyse determinants of agreement and disagreement between these norms.Despite fi lling an unexplored gap in the current literature related to the migration-fertility nexus, our study has a limitation that should be taken into consideration when reading our results.The lack of information about personal fertility ideals before migration prevents us from explicitly testing two fundamental hypotheses Notes: We control for parity, marital status, age at interview, age at interview squared, age at arrival, duration of stay, circular migration, education, country of birth, church attendance, labour market participation, and Italian profi ciency.The controls are set to the population margins in destination countries (APMs).
Source: Own calculation based on ISTAT survey "Social condition and integration of foreign citizens" 2011-12.
about migrant fertility -namely, the selection and the adaptation hypotheses.While analysing (dis)agreement with the country of origin norm, we cannot infer whether migrants shared that norm before migration.When analysing women who show a different ideal compared to their country of origin average, it is unknown whether they held such ideals even before migration (i.e.self-selection; the selection hypothesis) or if living in Italy changed their ideals (adaptation hypothesis).We cannot even a priori exclude, despite the hypothesis being highly unlikely, that a minority of women might have "reactivated" their "ethnicity" and adopted the country ideal due to phenomena of reactive ethnicity (Diehl/Schnell 2006), despite having a different fertility ideal before migration.
Bearing this limitation in mind, our paper shows that among migrants residing in Italy, the majority would like to have two children.One woman out of three in the sample shares the norm of their country of origin, and another one in three has a lower ideal than the country of origin average.Women who have a higher ideal number of children than their non-migrant peers represent only 11 percent of the sample.The agreement between personal ideal family size at the moment of the survey and the average country norm is associated with women's specifi c country of origin background (H1a), even when we control for socio-economic and demographic factors (H1b).Our results confi rm that the country of birth has a large predictive value in explaining the occurrence of agreement with the country of origin norm and the possible direction of shift in the ideal family size.Agreement with the national fertility ideal is typical of women from countries where two children are the fertility norm.A deviation towards a lower ideal number of children than in the country of origin is more likely among women who grew up in countries where large families are idealised.However, women with larger ideal families than those in the country of origin are also observed.The country of origin background also has an overall effect on the prevalence of non-numeric responses.The share of women unsure or expressing a preference for a maximum number of children, leaving its determination to fate or God, varies signifi cantly by country of origin.Relations and social networks between members of the same origin community in the destination country might build and reinforce fertility norms shared within a community, explaining the role of country of origin.
Even more interestingly, our results show that the correspondence between the personal ideal and the ideal of the country of origin is mostly related to socialisation in the country of origin: arriving as an adult is related to the overall agreement with the country of origin ideal (H2).Few differences exist between women who migrated at 21 and over and between age 16 and 20.This fi nding suggests that, in the likely event that women whose ideals match their average country norm had that same ideal even before migration, ideals are imprinted during the early years of a woman's life and retained during adulthood according to the socialisation hypothesis.Moreover, the 1.5 generation has a higher share of "I don't know" answers.Despite model's controls, this might still be affected by a younger age at the interview among these women, since fertility ideals of adolescents and young adults tend to be more uncertain compared to those of older women (Berrington/Pattaro 2014;Kraus/Castro-Martín 2017).
Another crucial result underlined by our study is that time since migration has no signifi cant impact on the match between personal ideals and the average family ideals of the country of origin, rejecting the hypothesis that a longer time spent in the country of migration might cause a shift away from the ideals imprinted during childhood and adolescence (H3).In other words, we cannot say whether women whose ideal stated in the survey does not match their country average formed that ideal before migration (selection) or changed it because of migration.However, we can say that if migration drove the change, the effect is not time-dependent.This result is entirely in line with the literature affi rming that personal ideal family size is more of an assimilated social norm than a personal preference, and for this reason does not change over time (Thomson 2015).
Our study further confi rms the association between support for gender equity and empowerment and fertility ideals.The effect observed is most evident in the occurrence of non-numeric responses (family size is "up to God" or "I don't know").Higher support for gender equity, education, and participation in the job market results in a lower proportion of non-numeric responses.Support for gender equity and empowerment is related to a reduction in uncertainty, implying that more empowered women who support gender equity are also more likely to consider fertility as a sphere in which they can have an opinion and express ideals.
Finally, our results raise the question of whether a possible replication of this study in a more gender-equal country (e.g.those in Northern Europe), compared to the rather traditional Italy, would result in an even stronger effect of gender beliefs on fertility ideals.

Fig. 1 :
Fig. 1:Personal ideal family size of immigrants to Italy by country of origin

Fig. 2 :
Fig. 2:Personal ideal family size in Italy compared to the country of origin norm for groups with at least 50 women sampled

Fig. 3 :
Fig. 3:Predicted probabilities of having the same, lower, or larger personal ideal number of children compared to the country of origin norm, or non-numeric responses, by country of origin

Fig. 5 :
Fig. 5:Predicted probabilities of having the same, lower, or larger personal ideal number of children compared to the country of origin norm, or non-numeric responses, by duration of stay

Fig. 6 :
Fig. 6:Predicted probabilities of having the same, lower, or larger personal ideal number of children compared to the country of origin norm, or non-numeric responses, by education

Fig. 7 :
Fig. 7:Predicted probabilities of having the same, lower, or larger personal ideal number of children compared to the country of origin norm, or non-numeric responses, by labour market participation

Fig. 8 :
Fig. 8:Predicted probabilities of having the same, lower, or larger personal ideal number of children compared to the country of origin norm, or non-numeric responses, by support for gender equity / Notes: We control for parity, marital status, age at the interview, age at interview squared, country of birth, duration of stay, age at arrival, circular migration, gender ideology, church attendance, labour market participation, and Italian profi ciency.The controls are set to the population margins in destination countries (APMs).
Relative risk ratios (RRR) of personal ideal number of children compared to origin country.The reference category is "equal".In the model we control for age at arrival, duration of stay, gender beliefs, and country of birth Note: Obs: Observations; ll(null): log likelihood for the null model; ll(model): log likelihood for the full model; df: degree of freedom; AIC: Akaike's information criterion; BIC: Bayesian information criterion.Source: Own calculation based on ISTAT survey "Social condition and integration of foreign citizens" 2011-12Tab.A3: