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Extracted abstract

Various studies suggest a positive effect of host country citizenship on the educational outcomes of immigrants' children. However, little is known about when and for whom citizenship matters and how much this is affected by potential endogeneity in the relationship between parental citizenship acquisition and their children's educational outcomes. Focusing on the Netherlands, this article exploits siblings' variation in their exposure to naturalization in order to net out the effect of time-constant parental characteristics. Results from a linear mixed model show that children who acquire Dutch citizenship have a substantial advantage in terms of academic performance over those who are still foreign citizens, especially if they naturalized in early childhood. A novel bounding estimator that gauges the sensitivity of the estimates to omitted variable bias confirms the robustness of these results. Moreover, the effects of citizenship are concentrated among students whose parents are at a disadvantage in the labour market and housing market, shedding light on hitherto under-explored effect heterogeneity.

Introduction

Immigrants' access to host country citizenship has received growing attention in the last decade. However, while there is converging evidence that naturalization contributes to immigrants' social, political and economic integration (e.g., Hainmueller, Hangartner and Pietrantuono, 2017; Peters et al., 2017; Gathmann and Keller, 2018) , little is still known about its potential consequences on their children's opportunities in host societies (Felfe, Rainer and Saurer, 2020; Colombo, Domaneschi and Marchetti, 2011) . This question is especially relevant in countries whose citizenship laws are based on ius sanguinis, whereby children have rights to the citizenship of their parents, not their country of birth (Honohan and Rougier, 2018, p. 350) . In such contexts, those born in the country to which their parents migrated-the so-called second generation-rely on their parents' ability and desire to naturalize if they are to acquire the citizenship of their country of birth and residence.

There is an emerging body of literature that examines the effect of acquiring host country citizenship on the educational achievement of second generation children, as a primary indicator of their life opportunities in host societies. These studies overall suggest that host country citizenship positively affects educational performance, both at the early and later stages of students' educational trajectories (Bean et al., 2011; Fibbi, Lerch and Wanner, 2007; Dronkers and Fleischmann, 2010; Kilpi-Jakonen, 2014; Cygan-Rehm, 2018; Felfe, Rainer and Saurer, 2020; Labussière, Levels and Vink, 2021 ). Yet, this positive effect may be due to self-selection for naturalization: parents acquiring host country citizenship have been shown to be positively selected for education, income, and country-specific skills (Peters, Vink and Schmeets, 2016; Jensen et al., 2019; Hainmueller et al., 2018) , which are also commonly associated with children's educational achievement (e.g., Schulz et al., 2017) . As some of these parental characteristics are typically not observable, standard estimates are likely to be upwardly biased due to common-cause confounding (Elwert and Winship, 2014) .

A few studies using the introduction of a conditional ius soli in Germany in 2000 as a natural experiment have provided causal evidence that children perform significantly better when they are granted German citizenship at birth (Felfe, Rainer and Saurer, 2020; Cygan-Rehm, 2018) . However, ius soli provisions are the exception rather than the rule in Europe (Honohan and Rougier, 2018) , and further research is needed to assess whether acquiring host country citizenship has a similar impact in ius sanguinis countries. In these countries, a significant proportion of second-generation children obtain citizenship only after birth through naturalization procedures, which raises the question of whether citizenship is equally important at older ages. Furthermore, previous studies tend to assume that citizenship has a uniform effect on children's outcomes, whereas children of immigrants form a heterogeneous group where the meaning and relevance of citizenship may vary considerably.

With this article, I aim to enhance our understanding of the effects of host country citizenship in ius sanguinis contexts. I conceptualize and assess not only whether citizenship matters for second-generation children, but also when and for whom. I examine how the effect of citizenship varies by the age of the child at the time of naturalization and the socioeconomic context of their family, shedding some light on the factors that condition the relevance of citizenship for second generation children. To address parental selection into naturalization, I use a family fixed-effects approach exploiting variation in siblings' exposure to host country citizenship. I estimate the effect of age at naturalization using the 'between-within' linear mixed model (Allison, 2009; Mundlak, 1978) , as coined by Sjölander et al. (2013) . The key advantage of this approach compared to standard fixed-effects models is that it explicitly models and adjusts for unobserved heterogeneity at the family level (Bell and Jones, 2015; Schunck and Perales, 2017) .

I investigate the impact of host country citizenship acquisition in the Netherlands. This is a country representative of the ius sanguinis citizenship tradition in Europe (Honohan and Rougier, 2018) , where children of immigrants can only acquire Dutch citizenship as minors through their parents' naturalization (Labussière and Vink, 2020) . The Dutch setting offers a unique research opportunity, thanks to the availability of detailed micro-data from administrative registers on children' educational achievement and their family context. The data include the entire population of second-generation students born between 1990 and 2010. Their educational performance can be traced back between 2008 and 2015 using their scores at a high-stakes standardized test at the end of primary school. This test is a core element of the multi-tiered and early stratified school system in the Netherlands (Crul, 2018) and offers a standardized measure of educational performance in early adolescence.

I find that second-generation students who acquired Dutch citizenship in early childhood outperform their peers of foreign nationality by about 0.1 standard deviations on the standardized test. This advantage decreases from the age of 7 and then becomes negligible when students naturalize at the end of primary school. Based on the between-within model, I do not find probative evidence that these results are significantly biased by the omission of confounding factors at the family level. My results are also robust to use of a new bounding approach developed by Oster (2019) . Overall, this study provides further evidence that citizenship has an independent effect on educational performance, net of parents' self-selection for naturalization (Felfe, Rainer and Saurer, 2020; Cygan-Rehm, 2018) . However, the effects are concentrated among children whose parents are at a disadvantage in the labour market and housing market, which sheds light on hitherto under-explored effect heterogeneity.

Theoretical background

Citizenship and educational achievement

While the benefits of host country citizenship for firstgeneration immigrants have received ample attention in previous literature (for an overview, see Peters and Vink, 2016) , we still know little about whether and how host country citizenship affects their children's life opportunities in destination countries. This lack of attention is puzzling considering that citizenship is the only status guaranteeing full formal membership and legal protection in one's country of residence. Becoming a citizen bestows a number of rights and benefits, such as the right to vote in national elections, join the armed forces, and run for various high-ranking positions in the law and public sectors. It also comes with a host country passport, which allows for considerable international mobility and facilitates access to occupations requiring transnational mobility. Previous work suggests that these citizenship privileges, both formal and practical, matter for young people of migrant background (Frauenfelder, 2007; Colombo, Domaneschi and Marchetti, 2011) .

Although the right to school access and resources is generally independent of children's legal status, there is evidence that host country citizenship also influences educational outcomes (e.g., Felfe, Rainer and Saurer, 2020; Kilpi-Jakonen, 2014; Bean et al., 2011; Patler, 2017) and the way students navigate and interact with educational institutions (Cebulko, 2014; Labussière, Levels and Vink, 2021) . Children of immigrants who get access to host country citizenship, either by birth or by naturalization, are found to perform better in terms of cognitive skills and grades than those who remain foreign citizens (Felfe, Rainer and Saurer, 2020; Avitabile, Clots-Figueras and Masella, 2014) . They are also more likely to follow an academic (vs. vocational) orientation (Felfe, Rainer and Saurer, 2020; Kilpi-Jakonen, 2014; Fibbi, Lerch and Wanner, 2007; Cygan-Rehm, 2018) , stay longer in education (Bean et al., 2011) , and are at lower risk of dropout (Patler, 2017; Labussière, Levels and Vink, 2021) .

An important mechanism to explain this 'citizenship advantage' (Patler, 2017) is found in the human capital theory: because citizenship is associated with better employment opportunities, it is expected to increase the long-term rate of return on parental investments in children's human capital (Felfe, Rainer and Saurer, 2020; Cygan-Rehm, 2018) . Parents are thus incentivized to make early investments in their children's education, for instance by enrolling them in non-compulsory pre-school (Felfe, Rainer and Saurer, 2020; Avitabile, Clots-Figueras and Masella, 2014) . Other authors argue more broadly that citizenship increases immigrant families' orientation towards the host society (Kilpi-Jakonen, 2014) or that the lack thereof contributes to processes of delayed assimilation (Bean et al., 2011) . Access to host country citizenship may also have a direct effect on children's motivation and ability to succeed in school by increasing their sense of security and belonging, particularly in adolescence and young adulthood (Cebulko, 2018; Colombo, Domaneschi and Marchetti, 2011) .

In ius sanguinis citizenship regimes where the acquisition of citizenship by children depends on the naturalization of their parents, a mechanism less often considered is that children may benefit from their parents' improved position in the host country. There is indeed ample evidence that naturalized immigrants experience a 'citizenship premium' in the labour market (Gathmann and Keller, 2018; Steinhardt, 2012; Peters et al., 2017) and that naturalization can act as a 'catalyst' for social and political integration (Hainmueller, Hangartner and Pietrantuono, 2017) . These parental resources, both material and nonmaterial, are expected to help parents assist their children's educational careers effectively. Moreover, parents may acquire or further develop relevant skills during the naturalization process itself, or through experiences with privileges afforded to citizens only (Peters et al., 2017; Patler, Gleeson and Schonlau, 2020, p. 16 ).

Acquiring host country citizenship: a selective process

An alternative explanation for the positive effects of citizenship on education may be selection. Naturalization procedures typically carry a broad range of financial and non-financial costs that immigrants may not be able or willing to incur. Among the hurdles to overcome, naturalization candidates have to meet increasingly strict language and integration requirements (Goodman, 2010; van Oers, 2013) , which predominantly impact candidates with a low education level (Jensen et al., 2019) . Relatively high application fees have also been shown to constitute a substantial financial barrier for low-income households (Hainmueller et al., 2018) . Moreover, the bureaucratic nature of the naturalization process often requires candidates to navigate complex institutions, which favours immigrants who are familiar with the host country language and context.

At the same time, these financial and socio-cultural resources involved in naturalization propensity are likely to be associated with children's educational outcomes. There is indeed well-established evidence that parents' education, occupation, and resources are important factors for educational success, including among children of immigrants (van De Werfhorst and Van Tubergen, 2007) . What is more, parents seeking host country citizenship despite its substantial cost may have higher aspirations for their children and be more oriented towards the host society regardless of whether or not they naturalize. The relationship between citizenship and education may therefore be driven by a process of social selection, due to a number of parental characteristics influencing both naturalization propensity and children's educational outcomes.

The relevance of timing and effect heterogeneity

While a number of studies do consider the issue of selection bias (Kilpi-Jakonen, 2014; Patler, 2017) , only a few are able to control for unobserved heterogeneity due to data limitations. An exception lies in a series of studies in Germany, where the introduction of a conditional right to German citizenship at birth in 2000 provides a unique natural experiment for assessing the impact of birthright citizenship (Felfe, Rainer and Saurer, 2020; Cygan-Rehm, 2018; Avitabile, Clots-Figueras and Masella, 2014) . Overall, these approaches provide further evidence for an independent effect of citizenship on education. Yet, by design such studies only consider a potential effect of host country citizenship at birth, whereas, certainly in Europe, a substantial share of second-generation children only acquire citizenship after birth through standard naturalization procedures (Labussière and Vink, 2020) . It is therefore necessary to analyse whether citizenship has a similar effect on education beyond the specific German context, paying more attention to when children become citizens.

The relevance of the timing of citizenship for second-generation children has hitherto received scant attention, both conceptually and empirically. By contrast, a number of studies show that the timing of naturalization matters for their parents' outcomes: the earlier immigrants are eligible to apply for citizenship, the more relevant citizenship is for their socioeconomic integration (e.g., Gathmann and Keller, 2018; Peters et al., 2017; Hainmueller, Hangartner and Pietrantuono, 2017) . Early acquisition of host country citizenship may also be important for children, as it would limit legal uncertainty and possible feelings of exclusion in adolescence (Colombo, Domaneschi and Marchetti, 2011; Patler, 2017) . Moreover, in ius sanguinis contexts, parents' accelerated integration trajectory could have positive spillover effects on the resources they can make available to their children. Immigrant parents who acquire citizenship early in the settlement process may be better informed and equipped to assist their children when they enter the school system. Conversely, obtaining host country citizenship may be less relevant once the school career is well underway, especially in education systems where important decisions for students' educational opportunities take place at an early stage. I therefore hypothesize that the earlier second-generation students acquire Dutch citizenship, the greater their advantage over their non-Dutch counterparts in terms of educational achievement.

In addition to timing, another still under-explored aspect pertains to effect heterogeneity. Few studies analyse whether the effect of citizenship is modulated by the characteristics of students and their families (Dronkers and Fleischmann, 2010; Cygan-Rehm, 2018 ). Yet, there is consistent evidence that citizenship matters more for some immigrants than for others. Previous studies point to higher returns on naturalization among immigrants from less developed countries and/or marginalized groups in the host country (Hainmueller, Hangartner and Pietrantuono, 2017; Vink, Prokic-Breuer and Dronkers, 2013; Peters, Vink and Schmeets, 2016) . This suggests that the catalyst effect of naturalization is most effective for immigrants who otherwise lack the resources to achieve a stable socio-economic position in the host society (Hainmueller, Hangartner and Pietrantuono, 2017) . In ius sanguinis contexts, such interaction effects between naturalization and immigrants' characteristics are likely to be reflected at the level of their children. Furthermore, second-generation children may value host country citizenship differently depending on their social background: while remaining a foreign citizen may be of little importance for those who have a privileged position, it may be an additional obstacle for those living in socially and economically marginalized families. As a result, I expect naturalization to act as a compensatory mechanism: the lower the socioeconomic status of students who acquire Dutch citizenship, the greater the effect of acquiring host country citizenship on school performance.

Context: becoming a citizen of the Netherlands

Following the principle of ius sanguinis, individuals born in the Netherlands to immigrants inherit the citizenship of their parents. Children of immigrants can thus receive Dutch citizenship at birth by descent if at least one parent was naturalized before their birth. Otherwise, they can be included in the naturalization procedure of (one of) their parents as long as they are minors. The acquisition of Dutch citizenship by children before the age of majority is therefore legally linked to the naturalization of their parents.

To be naturalized, immigrant parents must meet a number of requirements. First, they must have a residence permit for an undefined period of time and have resided legally in the Netherlands for an uninterrupted period of 5 years. Second, they must renounce their existing nationality, although numerous exceptions exist (Vink and de Groot, 2010, p. 721) . Third, they must demonstrate that they 'have a reasonable knowledge of the Dutch language and are accepted into Dutch society ' (van Oers, 2013, p. 43 ). In the 1990s and early 2000s, when most parents of the studied population naturalized, compliance with the language and integration requirement was assessed in a brief interview with a local official. Naturalization candidates also have to pay for naturalization fees, which amounted to €316 for a couple in 2001.

In this study, most families acquired Dutch citizenship under relatively accessible conditions, before the restrictive turn in Dutch citizenship policy (van Oers, 2013) . The social selectivity of the naturalized population is thus expected to be moderate, although the nonfinancial costs of undertaking the procedure should not be underestimated: conducting a procedure in a foreign language requires time and knowledge of the institutions, and parents may have had to renounce their existing citizenship.

Research strategy

Between-within linear mixed model Some of the characteristics associated with both the naturalization propensity of immigrant parents and the educational outcomes of their children are generally unobservable, such as their country-specific skills and orientation to the host society. In this article, I exploit variation in siblings' exposure to naturalization to net out the effect of stable parental characteristics. The approach is to compare the outcomes of siblings who obtained Dutch citizenship at different ages, assuming that this is indicative of how the younger siblings would have fared in education if, like their elders, they had become citizens at a younger age. The use of siblings as counterfactuals has been employed in other contexts to account for unobserved heterogeneity at the family level (Nielsen and Rangvid, 2012; Böhlmark, 2008; Sigle-Rushton et al., 2014) . This approach seems particularly relevant for assessing the strength of parental self-selection for naturalization because the key characteristics involved in parental desire and ability to naturalize are expected to be fairly stable over time and thus shared by siblings.

Unlike previous studies, I analyse the withinfamily effect of age at naturalization using the socalled 'hybrid' or 'correlated random-effects' model (Mundlak, 1978; Allison, 2009) , increasingly known as the 'between-within' model (Sjölander et al., 2013) . Contrary to standard fixed-effects modelling, the between-within approach explicitly models heterogeneity bias and does not control out family-invariant covariates (Bell and Jones, 2015) .

Let subscript i denote the individual level and j denote the family level. I define the following betweenwithin model:

y ij = 𝛽 BW 0 + 𝛽 BW 1 (x ij -x j ) + 𝛽 BW 2 c j + 𝛽 BW 3 x j + (𝛿 j + 𝜖 ij ) (1)

where y ij is the educational outcome of child i in family j, x ij a (series of) covariate(s) measured at the individual level, and c j a (series of) covariate(s) measured at the family level. In the between-within model, the individual-level variables x ij are decomposed into a between-cluster (x j = n -1 i ∑ n i t=1 x ij ) and a within-cluster (x ij -x j ) component (Allison, 2009; Schunck, 2013, 66) , so that the within-cluster (𝛽 BW 1 ) and between-cluster (𝛽 BW 3 ) effects are clearly separated. This decomposition allows the unobserved heterogeneity at the family level to be explicitly modelled as a linear function of the mean values of x ij (see Supplementary Materials, section 3 for details).

The estimator

β BW 1

is identical to the fixed-effects estimator: it is robust to unobserved heterogeneity at the family level. By contrast, β informs us about the extent to which individuallevel coefficients are biased when unobserved heterogeneity is not modelled (Schunck and Perales 2017, 96) . More specifically, testing if 𝛽 BW 1 = 𝛽 BW 3 provides a regression-based alternative to the Hausman test: if one cannot reject the hypothesis that the within-and between-cluster effects are equal, there is no evidence against the exogeneity assumption of the randomeffects (RE) estimation (Snijders and Berkhof, 2008, p. 145) and (1) collapses to a standard RE model:

y ij = 𝛽 RE 0 + 𝛽 RE 1 x ij + 𝛽 RE 2 c j + (𝜇 j + 𝜖 ij ) (2)

The between-within model thus indicates the extent to which the relationship between y ij and x ij is driven by unobserved heterogeneity at the cluster level. However, an important limitation of this approach is that it does not control for time-varying unobserved characteristics at the family level. Changes in the family may entail systematic differences in achievement between siblings without being consequences of the naturalization process. For example, parents' host country specific skills such as language proficiency may increase with years since migration, while the family's socioeconomic resources can change according to parents' employment status. Three factors help mitigate this limitation. First, as explained below, the chosen observation window limits the maximum age gap between siblings: 72.5% of siblings in the sample have an age gap of 4 years or less (see Supplementary Figure S1 ). This increases the chance that siblings grew up in roughly the same family environment. Second, the model includes a number of time-varying parental characteristics to account for changes in the family between dates of measurement of sibling educational outcomes. Third, as a robustness check, I use a novel bounding technique developed by Oster (2019) to gauge the sensitivity of the findings to both constant and time-varying unobserved characteristics.

By design, the within-family approach allows analysis of the effect of the timing of naturalization. To investigate effect heterogeneity-that is, whether the effect of naturalization varies across students-I add interaction terms between naturalization and common family socio-economic characteristics that may condition the relevance of Dutch citizenship for second-generation children.

Bounding analysis

As a robustness check, I assess the sensitivity of the results to unobserved heterogeneity using a bounding method formalized by Oster (2019) , which relies on different assumptions than the between-within model. This method consists of assessing selectivity bias based on the amount of selection on the observed characteristics in the model. It is adequate when researchers are able to include a relatively broad set of relevant regression controls, which are informative about the relationship between the regressor and unobservable confounding factors (Altonji, Elder and Taber, 2005, p. 171) . In this study, and as described below, data are available on various parental, family, and household characteristics that are known to matter both for parents' naturalization propensity and their children's educational achievement.

Oster developed a formal bounding argument linking selection bias to coefficient and R 2 stability. A consistent estimator for the bias-adjusted treatment effect 𝛽 ⋆ can be approximated with:

𝛽 ⋆ ≈ β -𝛿 [ β -β ] R max - R R - Ṙ (3)

where ( β , R) and ( β , Ṙ) are the coefficients for naturalization and the (non-adjusted) R-squared resulting from the controlled and uncontrolled regression, respectively. 𝛿 is the selection ratio, which can be interpreted as 'the degree of selection on unobservables relative to observables that would be necessary to explain away the result' (Oster, 2019, p. 195) . Another key input is R max , the R 2 resulting from the hypothetical regression where one would control for the full set of unobservables. Following Oster's recommendation, I set R max = 1.3 R in the main specification (see Supplementary Materials, section 5 for details and alternative R max values). Estimating 𝛽 ⋆ with different values of 𝛿 indicates the extent to which the conclusions drawn from the controlled regression remain valid when considering different degrees of selection on unobservables.

I perform the analysis using Stata 16.0. I use the commands xthybrid to estimate the between-within model (Schunck and Perales, 2017) and psacalc to perform the bounding approach (Oster, 2019) .

Data and operationalization

Register data and study population I use Dutch administrative registers, supplied by Statistics Netherlands, which offer longitudinal micro-level data covering the entire legally resident population of the Netherlands (Bakker, van Rooijen and van Toor, 2014) . For this research, I follow the cohorts of second-generation children who were first enrolled in secondary education between 2008 and 2015. This observation window includes siblings with a birth interval of approximately 7 years at the most (including possible grade-repetition and grade-skipping in primary school). This covers the typical birth spacing patterns in the Netherlands while ensuring sufficient comparability between siblings.

I define second-generation children as those born in the Netherlands to two foreign-born parents, who themselves are born to at least one foreign-born parent. Children of mixed descent are excluded from the scope of the analysis because, having one native parent, they ought to obtain Dutch citizenship at birth by descent. Children born in the Netherlands from second-generation parents-the third generation-are not included either, since they acquire automatic birthright citizenship according to the so-called double ius soli principle. For related reasons, I also exclude children from specific origin groups: children originating from the Caribbean territories of the Kingdom of the Netherlands, who are Dutch citizens; and children whose parents come from the former Dutch colonies and thereby had privileged access to Dutch territory and citizenship (van Meeteren et al., 2013, pp. 115-116) . I further restrict the study population to children who were not in institutional care (N = 150,0.1 %) or enrolled in practical education (Praktijkonderwijs, N = 6,806,5.3 %), as the latter targets students with low IQ and learning gaps. The final study population consists of 122,356 students.

For all of these students, I have identifiers of their parents or legal guardians, which I use to identify family units. Note that these family units do not necessarily identify the adult(s) with whom children are actually living. Since minor children can only naturalize together with (one of) their legal guardians, it is relevant to focus on legal ties only. I identify families based on mother's identifier alone because there is a slightly higher number of children who are not associated with any father in the Dutch registers. This leads to cluster the study population into 85,607 families. As a robustness check, I replicate the analysis using an alternative definition of family based on both mother's and father's personal identifiers (see Supplementary Materials, section 6).

Educational outcome

As a measure of educational performance, I use the scores of a high-stakes aptitude test taken at the end of primary school, which corresponds with a key turning point in the Dutch education system. In the Netherlands, students follow primary education for 7 years from the age of 5, after which they are allocated to a specific track for all subjects in secondary education. There are three main tracks: pre-university (VWO), general (HAVO), and vocational (VMBO). Although this stratified and early-tracking system comes with a certain degree of flexibility, students are not equally likely to move between tracks due to the complexity of its educational arrangements (Crul, 2018; Forster and van de Werfhorst, 2019; Labussière, Levels and Vink, 2021) . The initial track placement is therefore a crucial stage in students' subsequent educational careers. Students' track allocation is mainly based on their score at a standardized test, which they take in the final year of primary school, around age 12. I use students' test score as my outcome, for two main reasons. First, although these standardized tests are primarily designed to measure students' cognitive abilities, they also reflect different levels of parental commitment and investment (Inspectie van het Onderwijs, 2016). Parents who are not familiar with the Dutch education system may not perceive the test as a high-stakes event or may lack the resources to effectively assist their children. Second, these test scores provide an objective measure of students' educational performance, which is not directly influenced by teachers.

One important limitation lies in the fact that test scores are only available for students whose schools registered with the main test provider, Cito, representing about 77% of the population. In the absence of external information on the profiles of the schools registered with a different provider, I assess schools' selectivity based on their students' sociodemographic characteristics (see Supplementary Materials, section 1). As differences are relatively limited, I only conduct the analysis on the sample of students with a valid test score. This leads to a final sample of 95,015 students, clustered into 69,909 families.

The Cito score is developed by the Central Institute of Test Development and includes multiple choice questions on Dutch, mathematics, and information processing. To make the Cito test scores comparable over the observation period, I standardize students' scores by year to have a mean zero and unit variance (Sigle-Rushton et al., 2014; Nielsen and Rangvid, 2012) .

Measurements

My main variable of interest is age at naturalization, which is identified based on yearly observations of respondents' nationality(ies). I use a categorical variable to capture potential complex timing patterns in the relationship between citizenship and education. While I expect the effect of naturalization to decrease as children grow older, this relationship may not be linear due to possible breakpoints at children's development stages. I distinguish seven categories: those who are Dutch citizens from birth (age 0); those who naturalize at ages 1-2, 3-4, 5-6, 7-10, 11-13; and those who are still foreign citizens at age 14. Note that the results are robust to using different age groupings (including age dummies) and an alternative upper censoring bound at age 10 (see Supplementary Materials, sections 1 and 6).

When estimating within-family effects, it is important to control for sources of systematic differences in outcomes across siblings (Sigle-Rushton et al., 2014) . I therefore control for gender, as girls are usually found to outperform boys in education, including among second-generation students (Fleischmann and Kristen, 2014) . I also include a dummy capturing whether the respondent is first-born, since there is evidence that it confers an advantage in education (see, e.g., Kantarevic and Mechoulan, 2006) . Finally, I add the date of birth to account for broader societal changes that may systematically differentiate older and younger siblings in terms of test scores, in ways that are not due to their different family experience (Sigle-Rushton et al., 2014, p. 166) .

I add a number of parental and household characteristics that are expected to influence both parents' naturalization propensity and their children's educational achievement. To control for parental socioeconomic background, I use two complementary variables: parents' main source of income, which indicates whether the parents are in employment (including selfemployment), are social benefit or pension recipients, or lack any registered source of income; and a dummy capturing whether at least one parent is registered as a homeowner. Access to homeownership reflects a variety of resources among immigrant families, from their ability to secure a mortgage to their understanding of the complex process of buying real estate in the Netherlands. To approximate the financial resources available to children, I include household standardized disposable income. I also control for parental education level, albeit imperfectly. Such information tends to be missing and/or unreliable for first generation parents, and is difficult to impute without indication of parents' exact occupation. I take the highest education level obtained among parents, and code the missing values as a separate category (see Supplementary Materials, section 1, for more details). I distinguish between low (primary education), middle (completed some secondary education), and high (bachelor or higher) levels of education.

Two household characteristics are included to proxy the parental time and financial resources available to children: the number of children registered in the household and the type of household, either two or single parent. In the absence of reliable information on parents' migration motive and date of arrival, I add mother's country of birth to capture systematic differences in immigration and integration patterns across origin groups. 1 Parental and household characteristics are measured at the time of the test, so that to take into account potential changes in the family situation between the two Cito dates. Note that there is an exception for parental level of education, which is time constant due to data limitations. Supplementary Table S2 gives the detailed coding of the variables. Note that for the descriptive statistics and regression models, the sample (cluster) size decreases to N = 94,727(69,894) following the exclusion of a few individuals with punctual missing values on some of the socio-demographic variables (N = 288,0.3 %).

Analyses

Descriptive statistics

Table 1 shows the distribution of age at naturalization groups in the sample, while Supplementary Table S3 displays descriptive statistics for the covariates. Two-thirds of respondents were Dutch citizens at birth (age 0) and thus acquired Dutch citizenship by descent through the prior naturalization of their parents. Among those who were foreign citizens at birth, 38% were naturalized by the age of 4. Naturalization propensity then steadily decreases with age: only 6.4% of students naturalized between 11 and 13. Importantly, most of those (80%) who had not acquired Dutch citizenship at age 14 were still foreign citizens at the end of the observation period, in their late teens or early twenties (see Supplementary Table S4 ).

The family fixed-effects approach followed in this article requires sufficient variation in age at naturalization within the families (Gilman and Loucks, 2014) . In the sample, 14,393 (15.2%) students did naturalize at a different age from their siblings, with a difference of 3 years on average. In most cases (91.5%), siblings were no more than 5 years apart at the time of naturalization (see Supplementary Figure S2 ). This means that the within-family effect of more than 5 years of delay in citizenship acquisition falls largely outside the support of the data. This should be considered when interpreting the within-cluster effects below.

Within-and between-family effects of citizenship

I perform the analysis using the full set of covariates described in Section Data and operationalization. As I hypothesize that students who naturalize before the Cito test have an advantage over their non-Dutch counterpartsin terms of test scores, I use those who are still foreign citizens when entering secondary education ('≥14') as the reference group.

The results for the effects of age at naturalization are presented in Table 2 . Column 1 reports the results from the standard random-effects model (𝛽 RE 1 ), for comparison purposes. Those who acquire Dutch citizenship before the age of 6 have a substantial advantage over those who are still foreign citizens at age 14: their test scores are between 0.09 and 0.1 standard deviations higher. The coefficient decreases to 0.6 for those who naturalize at ages 7-10, while those who naturalize just before or after the Cito test between the ages of 11 and 13 do no have a significant advantage over those who are still foreign citizens at age 14. 2 Column 2 shows how these coefficients evolve when I separate the within-cluster (𝛽 WB 1 ) and the betweencluster effects (𝛽 WB

3 ) in the between-within model. The within-cluster effects, based on siblings' comparison, are slightly higher than the random effects. However, the precision of the estimation for the within-cluster effects has substantially decreased. This is particularly true for the coefficient associated with those who are Dutch from birth (age 0): despite a meaningful effect size (𝛽 WB 1 = 0.105), the coefficient is imprecisely estimated (P = 0.125). As mentioned below, relatively few siblings are more than 5 years apart when they naturalize (see Supplementary Figure S2 ), which complicates the estimation of long delays in citizenship acquisition between siblings. By contrast, the between-cluster effects are fairly comparable to the random-effects, both in terms of effect size and statistical significance.

Although there are differences between the withinand between-cluster effects, the estimated coefficients are of the same order of magnitude. Column 3 of Table 2 , which gives the p-values from the formal test of the null hypothesis 𝛽 WB 1 = 𝛽 WB 3 for each age group coefficient, indicates that we cannot reject the hypothesis that the two sets of coefficients are equal. In other words, changes in age at naturalization exert a similar effect on Cito test scores within a given family as they do across families. This is evidence in favour of using a standard random-effects model, since the data do not support the rejection of the exogeneity assumption.

Based on the between-within model, I conclude that the observed relationship between age at naturalization and educational achievement is not exclusively driven by unobserved selectivity at the family level. Acquiring Dutch citizenship is associated with a substantial and significant advantage in terms of test scores, especially when it is acquired in early childhood. This advantage decreases from the age of 7, and is no longer sizeable when students are in their transition to secondary education. Such findings provide mixed results in favour of the timing hypothesis: while there is evidence that the effect of citizenship varies with age, the relevance of citizenship only decreases towards the end of childhood. a I include all the covariates described in Section Data and operationalization: gender, birth order, date of birth, household type, mother's and father's SES, homeownership status, household income, highest educational level among parents and mother's country of birth. For full between-within model, see Supplementary Table S5 .

To investigate the effects of the other covariates in more detail, I refer to the more parsimonious random-effects model. The full results, displayed in Table 3 , compare the effects of age at naturalization with other important predictors of educational achievement. The effect magnitude of acquiring Dutch citizenship before the age of 7-versus after age 14-is comparable to that of having at least one parent being a homeowner (𝛽 = 0.11), or to live in a single-parent household (𝛽 = -0.10). The benefit of naturalizing in early childhood is slightly below that of having at least one parent with a secondary education qualification, versus none (𝛽 = 0.15). Yet, it is well below the effect of having at least one parent with a higher education diploma (𝛽 = 0.46), which is one of the strongest associations in the model. Unlike parental education, there is only a limited effect of parental income or socio-economic status (SES). Overall, these results are consistent with earlier work on the Dutch case showing that education level is a stronger predictor of educational achievement than occupational status (Tieben, de Graaf and de Graaf, 2010; Büchner and Velden, 2013) .

Finally, I assess whether the effects of age at naturalization are conditioned by parental socioeconomic resources. To do so, I test interactions between age at naturalization and a number of covariates, which operationalize parents' socio-economic position: their level of education, SES, homeownership status and level of income. I find notable interactions only with parental level of education and homeownership status, which are the strongest socioeconomic predictors of school performance in the main model (see For ease of interpretation, I focus on the effect of Dutch citizenship regardless of timing when presenting the results. I estimate interaction effects with a naturalization dummy capturing whether the respondent has acquired Dutch citizenship before the age of 14 (see Supplementary Tables S7-S9 for the full results and Supplementary Tables S8-S10 for the interactions with age at naturalization).

Figure 1 displays predicted average scores at the standardized test according to students' citizenship status and their parents' education level (Figure 1a ) and homeownership status (Figure 1b ). In line with my expectations, there is a negative interaction between citizenship and parents' highest level of education, especially at the higher end. Children whose parents only completed primary or secondary education benefit from naturalization in a comparable way, with an increase of about 0.12 standard deviations in their school performance. By contrast, those with at least one highly educated parent do not have any significant advantage when they naturalize before the age of 14. Figure 1a also suggests that citizenship is not a panacea: although naturalized students whose parents have a secondary qualification have above-average test scores, they are clearly outperformed by students with highly educated parents-regardless of the latter's citizenship status.

In a similar fashion, those with at least one parent who is a homeowner derive substantially less benefit from naturalization in terms of test scores, compared to those whose parents are renters. Figure 1b shows that naturalization before the age of 14 closes the gap to the average for those whose parents are renters, while it only marginally increases the predicted test scores of those whose parents are homeowners. Altogether, these findings provide valuable evidence that naturalization primarily matters for children of immigrants whose parents are at a disadvantage in the labour market and housing market. Note: P-values are in parentheses (standard errors are bootstrapped using 1,000 replications). I set R max = 1.3 R = 0.13 as recommended by Oster (2019) . The controlled regression includes all the covariates described in Section Data and operationalization. The uncontrolled regression includes gender, birth order, and date of birth, which are considered to be unrelated to the selection process.

Bounding analysis

The between-within model suggests that the relationship between citizenship and education is not substantially driven by unobserved heterogeneity at the family level. However, this model does not control for parental unobservables that may vary over time, such as parents' language proficiency or knowledge of Dutch society. Although siblings in the sample are relatively close in age, I cannot rule out the possibility that the effects of age at naturalization are confounded by changes in the family environment.

To further assess the sensitivity of the results to unobserved heterogeneity, I use the novel bounding approach developed by Oster (2019) . As it has not yet been developed for non-binary categorical treatment variables, I use a dummy variable capturing whether the respondent has acquired Dutch citizenship before the age of 14. I analyse the effect of Dutch citizenship on test scores with the same set of covariates as in the main specification, using OLS, randomeffects, and between-within models (see Supplementary Table S11 ). Considering the limited differences between the random-effects estimates and OLS estimates, I use the simpler OLS model to perform the bounding analysis.

The upper panel of Table 4 shows that the advantage of those who acquire Dutch citizenship before the age of 14 decreases from 0.16 to 0.10 standard deviations when observed parental characteristics are controlled for. The lower panel gives the bounded estimator 𝛽 ⋆ for different values of the selection ratio 𝛿. Even when the selection on unobservables is as important as the selection on observables (𝛿 = 1), children who naturalize before 14 outperform those who are still foreign citizens at that age by 0.07 standard deviations. This advantage decreases to 0.04 standard deviations when the selection on unobservables is twice as important as the selection on observables (𝛿 = 2) and is no longer sizeable nor significant when 𝛿 ≥ 3. Even if some of the covariates are imperfect proxies for parents' socioeconomic position, such a high selection ratio seems unlikely considering the wide range of relevant control variables included. The bounding analysis brings thus further evidence that the results are likely to have a causal interpretation.

Discussion

This article studied the relationship between host country citizenship acquisition and the educational achievement of the children of immigrants in the Netherlands. My aim was to assess the extent to which the observed relationship is driven by immigrant parents' self-selection for naturalization. Beyond the question of whether host country citizenship matters, I also analysed if the effect of citizenship varies with children's age and with the other socioeconomic resources available to them.

Using Dutch administrative micro-level data, I analysed the effect of age at naturalization on the scores obtained at a high-stakes standardized test at the end of primary school. My results show that secondgeneration students who acquired Dutch citizenship in early childhood outperform their peers of foreign nationality by about 0.1 standard deviations on this test. I used a family fixed-effects approach to assess whether this relationship is confounded by unobserved heterogeneity at the family level. The comparison of the between-and within-family effects indicates that the results are not significantly biased by the omission of stable parental characteristics. I used an alternative approach developed by Oster (2019) to assess potential biases due to residual time-varying unobserved heterogeneity. The bounding estimator indicates that selection on unobservables would have to be three times more important as the selection on observables to explain the positive effect of naturalization. As a result, while the covariates considered in this study do not exhaust the range of relevant predictors of educational achievement, I find evidence that the main confounders are included in the model. This study makes an important step forward in approaching a causal effect of citizenship on education in ius sanguinis contexts, where children of immigrants inherit citizenship from their parents. Consistent with prior work, it suggests that being a citizen of one's country of birth and residence significantly improves the educational outcomes of second-generation children (e.g., Fibbi, Lerch and Wanner, 2007; Kilpi-Jakonen, 2014; Felfe, Rainer and Saurer, 2020) . This article complements earlier studies that examined the effects of acquiring host country citizenship at birth under the ius soli principle (Felfe, Rainer and Saurer, 2020; Cygan-Rehm, 2018) , extending the focus to children who become citizens at birth or after birth through the naturalization of their parents. The findings suggest that the timing of naturalization matters: the later students acquire Dutch citizenship, the weaker their advantage over their peers of foreign nationality in terms of test scores. This is especially true when students approach adolescence, after age 7. This result is consistent with previous evidence in the literature that the sooner immigrants get host country citizenship, the more it improves their economic and social integration (Gathmann and Keller, 2018; Hainmueller, Hangartner and Pietrantuono, 2017; Peters et al., 2017) . The benefits of early acquisition of citizenship among immigrants may have spillover effects on their children's academic development. By contrast, children who only acquire citizenship in late childhood may have experienced stress and negative emotions due to legal uncertainty, with detrimental impact on their well-being and school performance (Patler and Pirtle, 2018; Patler, 2017) . The acquisition of Dutch citizenship at the end of primary school may also come too late for parents to effectively support their children in their transition to secondary school. An alternative explanation for the decreasing effect of citizenship is that the benefits of naturalization gradually develop over time. As those who naturalize at older ages have less time to reap the benefits of Dutch citizenship before the test, their advantage in education may be underestimated. Unfortunately, the data do not measure children's outcomes in late adolescence to identify possible catch-up effects. This article therefore focuses on identifying the short-term effects of naturalization, leaving open the question of how the effects of citizenship unfold over the long-term in the lives of children of immigrants. Despite this limitation, this article makes an important contribution in showing that, in the Dutch context, those who naturalize at the end of childhood enter secondary education at a disadvantage, with lower test scores limiting their tracking options. Further exploration of the temporal dynamics of citizenship acquisition for children and youth is a promising avenue for future research, as the meaning and value they attach to their legal status may change over time and according to their stage of life (Gonzales, 2011) .

This article also shows that naturalization does not have a uniform impact on educational achievement: its effects are concentrated among children whose parents have at most a secondary education qualification and do not have access to homeownership. Students who benefit from citizenship are therefore likely to be those whose parents face structural barriers in the Netherlands due to lack of (recognized) educational qualifications and/or inability to obtain a mortgage. This is consistent with the literature on firstgeneration immigrants (e.g., Hainmueller, Hangartner and Pietrantuono, 2017; Peters, Vink and Schmeets, 2016) , which shows that naturalization mainly matters for the socioeconomic integration of the most marginalized groups. Dutch citizenship appears to act as a compensatory mechanism, favouring the academic performance of children whose parents are most dependent on naturalization to achieve a stable socioeconomic position. To further investigate such intergenerational dynamics however, more detailed measures of parental resources are needed. I do not have precise information on parents' actual occupation, which would be a more accurate proxy for their social status. Likewise, the variable capturing parents' education level lacks precision. Thus, it would be important for future work to disentangle further these different dimensions of socioeconomic resources, as well as their interplay with naturalization.

In addition, future research could model family resources as both confounders and mediators. This requires measuring family characteristics before and after naturalization, which current data do not allow. I measured household and parental characteristics at the time of the test to ensure better comparability of siblings' outcomes, but this may create over-adjustment bias if some of those characteristics are influenced by naturalization. The measured effects may therefore be direct-and not total-effects. With more precise longitudinal data, future research could specifically explore how parental characteristics mediate the relationship between citizenship and education. This would provide a more complex understanding of the effects of citizenship, beyond the 'selection vs. causation' dichotomy.

This study provides further evidence that difficulties and delays in acquiring the citizenship of one's country of birth and residence have detrimental impacts on well-being and educational opportunities (Colombo, Domaneschi and Marchetti, 2011; Frauenfelder, 2007) . Citizenship is certainly not a panacea compared with other predictors of educational achievement, such as parental education or social status. Nevertheless, this study shows that it has the potential to mitigate some of the obstacles children of immigrants may face in education.

Notes

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