The Impact of Parents Years-since-Migration on Children s Academic Achievement *

Transcription

1 The Impact of Parents Years-since-Migration on Children s Academic Achievement * Preliminary November 20, 2010 Helena Skyt Nielsen, School of Economics and Management, Aarhus University Beatrice Schindler Rangvid, Danish Institute of Governmental Research (AKF) Abstract In this paper, we analyse the disadvantages that the second generation immigrants inherit from their immigrant parents through their traditional marriage patterns. We exploit register data for eight cohorts of second generation immigrants to identify the impact of parents years since migration and marriage pattern on their children s school achievement. The identifying assumption is that conditional on observables, it is random whether the parents have spent a few more or less years in the country before they have a child. We find a substantial positive impact of parents years since migration on academic achievement. Key words: intergenerational mobility, years since migration, scholastic achievement, immigrant children, second generation. JEL codes: I21, J12, J62. * Contact information: Nielsen: hnielsen@econ.au.dk, School of Economics and Management, Bartholins Allé 10, DK Aarhus C, Denmark, Rangvid: bs@akf.dk, AKF, Købmagergade 22, 1150 København K. We are grateful for comments from Marianne Simonsen. We appreciate funding from the Danish Council for Independent Research (# ). The usual disclaimer applies.

2 1. Introduction In Western Europe, there is an increasing concern about the assimilation of the children of the large cohorts of guest-worker immigrants. Contrary to what one might expect, results from the international PISA, PIRLS and TIMMS studies show that in many Continental European countries second generation immigrants do not perform much better than their first generation peers (Schnepf, 2007; Rangvid, 2007). In the face of a rapidly growing population of second generation immigrant youth, this is a puzzle of major importance. In this paper, we focus on the disadvantages that the second generation immigrants inherit from their immigrant parents through their traditional marriage patterns. Although all second generation immigrant pupils have foreign-born parents, there is a considerable variation in immigrant parents years-since-migration and thus in the degree of integration. In particular, the widespread practice among immigrants in Denmark of marrying a marriage migrant from their country of origin 1 might slow down the integration process of the young immigrant generation. If one parent is a marriage migrant, the situation for the children is comparable with children of the previous generation: they grow up speaking the heritage language at home, and live in a traditional home country environment with one parent unaccustomed to life in a Western country. Previous research has not addressed this issue directly. However, the literature has approached the issue from two different angles. One branch of studies has focused on the effect of parents years since migration and language proficiency on education and employment of their children, and they detect a significant deteriorating effect on both (Åslund, Böhlmark & Skans, 2009; Van Ours & Veenman, 2006; Casey & Dustmann, 2008; Bleakley & Chin, 2008). Another branch of studies has focused on the impact of endogamous marriage on the education of the offspring, and they also find a negative effect (Van Ours & Veenman, 2010; Duncan & Trejo, 2009; Furtado, 2009). Our goal is to combine these two lines of thinking in order to understand the inherited disadvantages of second generation youth growing up in a context where endogamous marriage often implies marriage migration (Denmark: Celikaksoy, 2006; the Netherlands: Wal et al., 2008; Germany: González-Ferrer, 2006). We investigate the impact of each parent s years since migration on academic achievement. Formally, we estimate the local marginal impact of each parent s years since migration, while assuming that - conditional on observables -, it is random whether the parents have spent a few more or less years in the country before they have a child (see Behrman, Cheng &Todd, 2004). Thus, we indirectly infer the effect of marriage migration, which is the typical endogamous marriage choice among non-western immigrants in Denmark, and thus the main source of variation in years since migration. Although the research question is clearly relevant also for other Western countries, the data availability in Denmark gives us an advantage in this type of investigation. Therefore, our empirical analysis is based on Danish register data allowing us to combine information on all pupils in the 9 th grade cohorts of with information about their parents background characteristics in the year of immigration. 1 The expression marriage migration denotes the practice of immigrants already living in the destination country to get married to a person in their home country. 2

3 To be specific, we study the impact of each parent s years since migration prior to birth of the child in question on pupil achievement as measured by subject-specific exam grades in the 9 th grade school exit exams. We find a significantly positive impact of years since migration, which is particularly prevalent for written Danish. Arriving to Denmark 10 years earlier approximately improves grades by one tenth of a standard deviation meaning that it would close 20% of the gap in grades between natives and descendants of immigrants. The effects persist for all subgroups and at most margins. The effect of mother s years since migration is slightly stronger than that of the father s in written Danish, while the effect of the father s years since migration is slightly stronger in math. Thus, we conclude that it matters for the school performance of second generation immigrant youth whether either their mother or father is a marriage migrant or not. The remainder of the paper is organized as follows: Section 2 describes previous research and how we contribute to this. Section 3 presents the dataset which is used for the study. Section 4 presents the empirical strategy, while section 5 contains the results of the empirical analyses. Section 6 concludes the paper. 2. Previous research The parents age-at-migration and years-since-migration are closely related to their marriage patterns, as marriage migrants by definition are late arrivals in the host country. 2 Therefore, two strains of literature are particularly important for our study, namely studies on the effects of immigrant parents age-at-arrival and years since migration as well as studies on the effect of marriage patterns on education of their children. The first strain of literature is rooted in the theory of transmission of human capital and language capital over generations. Looking first at the parent generation, these studies document that age-at-migration matters for immigrants own assimilation as measured by e.g. language proficiency, educational attainment and wages, because there exist certain critical ages where migration hampers language proficiency and educational progression. 3 As a consequence, the effect of parents age-at-migration may be transmitted to the children, and the transmission may work through several different channels. Both Bleakley & Chin (2008) and Casey & Dustmann (2008) show that the parents language skills translate into higher English proficiency and educational outcomes of their children. 4 Bleakley & Chin (2008) employ an instrumental variables technique where the instrument for parents language skills is the interaction between age-at-migration and non-english speaking country of origin. Casey & Dustmann (2008) employ a selection-on-observables strategy where they exploit rich background information such as parental education and permanent earnings, years since migration, country of origin dummies as well as survey information about contact of parents with residents in the host country. These papers focus very much on transmission on capital from each of the two single parents. They are silent about the potential deteriorating spillover effects on language exposure if one of the parents is a marriage migrant. Åslund, Böhlmark & Skans (2009) look at a sample of primarily Nordic immigrants, and exploit siblings fixed effects to identify the effect of mother s years since migration on e.g. education. They document that a 2 Research on marriage migration is part of the strand of literature on interethnic marriage (e.g. Van Ours & Veenman, 2010) vs. homogamous marriage. Yet, since marriages between non-western immigrants and ethnic Danes are rare in Denmark at least for the younger generation (Nielsen et al. 2009), this is no issue in the Danish debate. 3 E.g. Schaafsma & Sweetman (2001) for Canada; Bleakley & Chin (2004, 2010) and Chiswick & DebBurman (2004) for the US; and Van Ours & Veenman (2006) for the Netherlands. 4 In US research, a lack of English proficiency is often cited as the principle barrier for poor school performance among many firstand second generation children (Cosden et al., 1995; Alba et al., 2002). 3

4 10 years earlier arrival would increase length of education by 0.2 years, which should of course be seen in the light of the relatively advantaged sample of mainly Nordic immigrants. 5 Åslund, Böhlmark & Skans (2009) focus on the effect of the mother s years since migration, and thus neglect potential effects of diverse migration of the two parents. The second strain of relevant studies focuses on the impact of endogamous marriage on education. Van Ours & Veenman (2010) identify the impact of endogamous marriages among Moluccans in the Netherlands by exploiting the quasi-experimental geographical allocation policy. They find a positive effect on children s education if Moluccan fathers marry native females rather the resident Moluccan females. Duncan & Trejo (2009) investigate the effect of endogamous marriage among American-Mexicans on their children s outcomes. They find significantly worse outcomes in terms of high school dropout and language proficiency if the children are the product of endogamous marriages. If the children have one rather than two US-born Mexican parents, drop out declines by 2 percentage points (from a level about 4%) and language deficiency by 4 percentage points (from a level of about 10%). Furtado (2009) studies why endogamous marriage reduces education, and she finds that it is not only because intermarried families move out of the ethnic enclaves and because they better adapt to native culture, it is also explained by assortative matching on education in a market with large variation in education across ethnicity. These papers are informative about the impact of endogamous vs. exogamous marriage among residents of a given country, but they potentially understate the effect of endogamous marriage if it involves marriage migration. In a context where marriage migration is the predominant marriage pattern among certain groups of immigrants, we need to combine these two lines of thinking. The widespread practice among immigrants in Denmark of marrying a marriage migrant from their country of origin might slow down the integration process of the young immigrant generation. If one parent is a marriage migrant, the situation for the children is comparable with children of the previous generation: they grow up speaking the heritage language at home, and live in a traditional home country environment with one parent unaccustomed to life in a Western country. According to Celikaksoy (2006), the proportion of immigrants in Denmark who marry a marriage migrant from the source country is around 80% for immigrants from Turkey and Pakistan, who are the two largest groups of immigrants. 6 The practice of endogamous marriage (Duncan and Trejo, 2007) and the practice of importing a partner is related to low educational levels (Nielsen et al., 2009). Nielsen et al. (2009) investigate the effect of spouse choice of the children of immigrants in Denmark on educational attainment as measured by their dropout rate from education. They exploit a natural experiment of a policy change restricting marriage migration 7 to identify the causal effect of marriage on educational attainment. The main finding is that the causal effect of marriage on dropout for males is around 20 percentage points, whereas the effect for females is small and not significantly different from zero, indicating that the correlation between marriage and educational attainment for females is driven by unobservable variables such as norms, religion or traditions. 5 A similar point is made by Alba & Nee (2003). 6 Also in other countries, this pattern is prevalent among particular immigrant groups. For the Netherlands, Wal et al. (2008) find that around 60% of Turkish immigrants marry a marriage migrant, while for Germany, González-Ferrer (2006) find 34% and 50% for Turkish females and males, respectively, while most other immigrant groups marry co-nationals residing in the Netherlands. 7 The socalled 24-year-rule. 4

5 The present project contributes to the literature as one of the first studies on the effect of parental marriage behaviour and years since migration on children s educational outcomes. In Figure 1, we describe the timing of the set-up. In the most common case, the father immigrates to Denmark first (e.g. as a guest-worker) and then he imports a partner for marriage afterwards, and then they have a child. This is the example illustrated in the figure. Figure 1: Timing of set-up Treatment measured Outcome measured Father immigrates Mother immigrates Child birth 9 th grade exit exam YSM f YSM m 3. Data description The data set contains information from administrative registers from Statistics Denmark on the full sample of pupils in the 9 th grade cohorts graduating in The sample constitutes about 480,000 pupils including about 10% pupils with immigrant origins. The share of second generation immigrants from non- Western countries more than doubles over the period (Figure 2), increasing from 3.0% to 5.8% of the total sample of pupils. 5

6 Figure 2: Number of second generation pupils in 9 th grade Note: the number for 2009 is preliminary due to current unavailability of 2009 register data on education variables (2009 includes only pupils in the grade-dataset, while numbers are pupils who in the beginning of the schoolyear are registered as 9 th grade pupils). This study focuses on second generation immigrant children and their parents. The reason why we focus on the second generation is that these children are more comparable to Danes than children born abroad, since they have had their entire education in Danish schools and have lived in Denmark all their lives. While it is understandable that the first generation underachieves compared to Danes (even after accounting for measurable socioeconomic differences), it is much less obvious why this should still be the case in the second generation. 3.1 Outcome variables The main outcomes considered are exam grades from the national school exit exams in Danish and math in 9 th grade. We use grades for for Danish and written math, while for oral math we use only grades for because this exam was abolished after There were structural breaks in the grading scale and in the exam subdomains which we accommodate in order to be able to use data for the entire period. Furthermore, whether pupils take the exam or not is analysed as an additional outcome, since taking the exit exam has not been compulsory before Our data show that, among pupils still enrolled in 9 th grade at the end of the school year, 5-6% of second generation pupils did not sit the exam in the years with the corresponding number for Danes being around 3%. Adding pupils who drop out during 9 th grade, these numbers increase to 9% for second generation pupils and 6% for Danes. Not taking the exam might impede the future education and /or labour market career of the adolescents. 6

7 Grades As a measure of pupils academic achievement, we use grades from the national school exit exams in 9 th grade. There have been some changes in recent years; changes in which subdomains of math are assessed by exit exams and introduction of a new grading scale. Danish. For the entire period of , grades are given in the following subdomains: oral Danish, written Danish and spelling (see Table 1). From 2007 onwards, reading is graded, too. To ensure a consistent common output measure for Danish over the period, we have chosen only to include the three grades that are given in every year in the composite measure: oral Danish, written Danish and spelling. We create two outcomes for Danish: written Danish and oral Danish, where the one-dimensional composite measure for written Danish is calculated as the simple mean of the pupils grades for written Danish and spelling. The outcome for oral Danish is the pupil s grade in the oral Danish exam. Math. Until 2006, grades are given for oral and written math (see Table 1). From 2007 onwards, the oral exam is dropped. Instead, two grades for written assignments are given in the subdomains of mathematical skills and problem solving. We consider two outcomes for math: written math and oral math, though oral math is limited to the period with an oral grade, namely from Table 1: Written and oral exams in Danish and math Written exams Oral exams Danish Math Written Danish Written Danish Written math Spelling Spelling Reading Oral Danish Oral Danish Oral math Mathematical skills Mathematical problem solving Note: Bold letters indicate grades that are included in the composite grade measure for Danish and math. Grading Scale. Before 2008, a 13-point numerical grading scale system was used. The possible grades were 00, 03, 5, 6, 7, 8, 9, 10, 11 and 13; where 6 is the lowest passing grade, and 8 represents average performance. From 2008 onwards, an internationally comparable seven-point scale was introduced. The possible grades are 12/A, 10/B, 7/C, 4/D, 02/E, 00/Fx, -02/F, and the average grade of 8.0 is supposed to equalize 6.0 on the new scale. It is not immediately possible to compare the grades across the structural break, although some translation of grades has taken place. Figure 3 shows average grades for descendants and natives for each of the sub-domains and for the composite measures for Danish (simple mean of written, oral and spelling grades) and math (simple mean of written and oral grades). Generally, exam results for the average descendants are lower than for the average native. 7

8 Furthermore, grades at the oral exams are higher than at the written exam for both descendants and natives. There does not seem to be a systematic trend in the development of mean grades (e.g. a closing or widening of the gap between descendants and natives) over the period. In , grades are measured on the new grade-scale, which has a lower mean and a larger standard deviation. Both features are reflected in the 2008 and 2009 grades, which yield lower means in all three sub-domains and a larger spread in the mean grades for the three sub-domains (see Table 2). Figure 3: Average grades in Danish and math for each cohort of Descendents and Natives Danish: Descendants Danish: Natives Math: Descendants Math: Natives Concerning math grades, there is an additional transition on top of the introduction of the new grade scale. From 2007 onwards, the range of sub-domains which are graded is altered (oral math is dropped and written math is split into two sub-domains). Figure 3 and Table 2 suggest that average grades for the sub-domain mathematical skills are higher in 2007 than for written math in the years before. For the empirical analysis, we need to be able to compare grades across cohorts. Therefore, we standardize grades to mean zero and standard deviation within each cohort. 8

9 Table 2: Subject-specific grades by cohort for descendants Danish Written Mean SD #obs Spelling Mean SD #obs Mean: Written&spelling Mean SD #obs Oral Mean SD #obs Math Written Mean SD #obs Problem solving (written) Mean SD #obs Mathematical skills (written) Mean SD #obs Mean: Written exams Mean SD #obs Oral Mean SD #obs Taking the exam or not Until 2007, sitting the school exit exam has not been compulsory. As shown in Figure 4 (right hand side), the percentage of descendants not sitting the exam is about 5-6%, while the corresponding number for Danes since 2003 has been below 3%. After making the exam compulsory in 2007, there is a sharp drop in the rate for descendants to around 3% 8, while the already low rate for Danes drops only slightly from 2,5% to 2%. Counting also individuals who drop out of school during 9 th grade (see Figure 4, left hand side), and whom for that reason are not observed to take the exam, the 3% nonattendance for descendants increases to 9%. 8 A similarly remarkable drop is seen for immigrants, where the rate drops from almost 8% to 4-5%. 9

10 In the regressions, we define an outcome variable which equals one if the pupil has not taken at least one exam for a sub-domain of Danish and a sub-domain of math, and zero otherwise. We analyze this outcome both for the sample of individuals present in 9 th grade at the time of the exit exam, and for the sample of individuals who entered 9 th grade after the summer break. Figure 4: Proportion not sitting the exam. Natives, descendants and immigrants 3.2 Years since migration The variable of main interest in this study is time since arrival in Denmark. It is important to note that unlike other pieces of research in this area, we do not consider the time the child has spent in the host country, but the time his or her parents have spent here. The children in our sample are all born in Denmark. We investigate whether the degree of integration of the child s parents (approximated by the time the parents have lived in Denmark) spills over into children s educational attainment. As a backdrop for the presentation of the variable of interest, Figure 5 shows the distribution of immigration year for fathers and mothers in our sample of 2 nd generation pupils. The leftmost columns in the figures are accumulated number of fathers and mothers who immigrated before 1973 as we cannot distinguish immigration years before Note that there is also a spike in 1985/86 which is largest for men, while the influx of women is delayed due to family reunification or marriage migration related to the wave of immigrant men. 10

11 Figure 5: Distribution of parents year of arrival The time the father and mother have spent in Denmark prior to birth of the child in question is a measure of the time the parents had to get accustomed to life in Denmark, learn the language, obtain host country education and labor market experience before the child was born and thus, before they started child-rearing. Notice that this variable does not have the same value for siblings: for younger siblings, parental time since arrival (as measured at child birth) is higher than for their older sisters and brothers. 9 This reflects the fact that the parents have had more time to integrate when raising their later born children. We consider both the father s and the mother s years-since-arrival, because they would most often not have arrived in Denmark as a couple. Part of the older immigrant population in Denmark has come to Denmark as children together with their parents. Since marriage migration of spouses is frequent, one parent would most often have been raised in Denmark, while the other comes to Denmark as an adult to marry the Danish resident. As mentioned above, a particular challenge for the analysis is that the immigration date has not been registered in Danish statistics before This means that about 10% of mothers and 20% of fathers in our sample has missing information on the key variable for calculating years since migration. Thus, while we do not know the exact year of arrival, we know that arrival was before In order to overcome this challenge, we design categories for years since migration such that the uppermost category includes all missing values. These categories are shown in Table 3. Virtually all fathers and mothers with missing year of arrival, have a value of YSM prior to birth of the child in question of 14 years or more. There are only 60 pupils (less than 0.5%) for whom this is not true. 10 They are deleted from the estimation sample. Figure 6 shows the distribution of time since migration for fathers and mothers at the time the child is born. Observations with valid information on father s and mother s year of arrival are summarized in the blue (parts of the) columns, while red indicates that information is missing and that observations in the red parts of the columns for e.g. 16 years mean 16 years or more since we only know that these parents have lived in Denmark since 1972 or longer. Many parents were recent arrivers to Denmark at the time of birth of their children, while very few parents have enjoyed a long residence in Denmark or even been growing up in Denmark. There are substantially 9 This is in contrast to the other measure, years since migration (at child s birth), where the value of the age-at-arrival measure is the same for all children in a family. 10 This happens due to occurrence of the infrequent combination of a 15-year old pupil taking the 9 th grade exam in 2002 (the normal age is 16 years) and a parent arriving before

12 more mothers than fathers who came to Denmark within max. five years before giving birth (10,000 compared to 7,000). And this is found for the total sample of all children in the sample no matter their birth order. The tendency is clearly much pronounced for first births. This feature in the data points at the fact that marriage migration is more frequent for women than for men (Nielsen et al. 2009). Figure 6: Histograms of fathers and mothers years since migration before childbirth In Table 3, frequencies for combinations of years since migration are shown. We operate with three categories: 0-4, 5-13, and 14 or more years since migration. The numbers in the table show that 54% of pupils have been born to recently arrived mothers and 34% to recently arrived fathers. 842 pupils (4%) are born to parents who both grew up in Denmark (time since arrival 14 years or more). As described in Figure 1, the most common family pattern is a situation where the father arrives before the mother. In our sample, 44% of the children grows up in such a family (the upper triangle of the table), while 37% grows up in a family where the parents arrived at roughly the same time (the diagonal). 11% of pupils have a father who arrived 14 years or more before the child was born, and a mother who was a recent arriver (presumably marriage migration), whereas only 6% of children have a family pattern of the opposite composition. Table 3: Distribution of the sample by years since migration of each parent YSM father YSM mother 0-4 years 5-13 years 14+ years All 0-4 years ,042 4,435 2,176 10, years ,534 2,573 2,104 6, years , ,928 All ,707 7,963 5,122 19,792 12

13 3.3 Control variables At the pupil level, we control for gender, country of origin, parents ages at arrival, parents education and older siblings born in the country of origin and in Denmark. Table 4 shows descriptive statistics for the control variables used in the regression. Of the second generation pupils in our sample, about 36% have origins in Turkey, about 13% in Lebanon and another 10% in Pakistan. Other, smaller, groups come from Yugoslavia, Morocco, Vietnam, Sri Lanka, Iran and Poland (between 3-5% each). The average age at arrival is 21.0 and 22.6 years for mothers and fathers, respectively, and although, information about education before arrival to Denmark is most often missing, it is striking that only 2.5% of the mothers and 3.5% of the fathers are observed to have acquired education beyond high school before arrival to Denmark. The average number of older siblings is 0.41 born before arrival to Denmark and 0.72 born after arrival to Denmark. 13

14 Table 4. Descriptive statistics Mother Father Parents' education from the country of origin Lower secondary school Vocational education High school Short cycle higher education Medicum cycle higher education Long cycle higher education Missing education Parents' age at arrival Age at arrival (if not missing) (SD Age at arrival) (6.340) (7.386) Missing age at arrival Older siblings Older siblings born in country of origin Older siblings born in DK Male Country of origin Turkey Lebanon Pakistan Ex-Yugoslavia Morocco Sri Lanka Vietnam Iran Poland Iraque Somalia Bosnia Thailand Number of observations , Empirical strategy We investigate the impact of each parent s years since migration (YSM) prior to birth of the child on the child s Grade. However, this effect cannot be estimated directly from a regression of Grade on YSM, since YSM reflects the parents marriage pattern (see Figure 1 above), and therefore, it is likely to be endogenous. One concern could be that the decision to marry a marriage migrant (rather than an immigrant already residing in Denmark or a native Dane) is associated with unobserved variables such as ability or norms that also co-vary with the child s educational achievement. Another concern could be that the timing of marriage to a marriage migrant or the timing of child birth is associated with inherited ability or norms. In the 14

15 mentioned instances, the assumption that the error term of the educational attainment equation should be i.i.d. is violated. 4.1 Identifying assumptions Instead of focusing on the average impact of YSM on Grade, we explore the local effect of increasing years since migration 11 by assuming that the assignment into categories of years since migration is random conditional on observables. Thus, we assume that it is random whether an individual s partner arrives a few years earlier or later conditional on own arrival. This is consistent with a demanding long-distance search process preceding marriage to a marriage migrant and with complicated legal procedures with the purpose of dampening immigration to Denmark after For this assumption to hold, the conditioning set should include a rich set of pre-treatment variables thought to influence the marriage decision, timing of child birth after migration and grades. Below we discuss which variables are included in the conditioning set in order to satisfy this requirement. First of all, timing of child birth would of course be influenced by parents age at migration since that would indicate how close the individual was to partnership formation and child bearing ages at the time of migration. Secondly, the presence of older siblings would also influence the time from migration to child birth: presence of siblings born before migration would most likely reduce the time from migration to child birth if fertility was not already completed, while presence of siblings born after migration would most likely increase the time from migration to child birth. Thus, the presence of foreign born siblings increases the likelihood of being born to a lesser integrated parent, while the presence of native born siblings reduces this likelihood. Finally, country of origin is likely important as that would approximate systematic cultural differences in marriage patterns, timing of child birth and preferences and traditions for education. Furthermore, education of each parent at the time of migration is included as that would approximate inherent ability, which may affect grades as well as time to marriage and thus time to child birth. In addition, the previous literature indicates that education in itself is closely related both to the probability of intermarriage and marriage migration. Education most likely increases cultural adaptability, and furthermore, it may be traded off for norms or ethnicity in the marriage market (see Furtado, forthcoming; Celikaksoy et al., 2006). Our prior would be that low-ability individuals have children earlier after migration than others, and if that pattern is not accounted for by the conditioning set, it would give a negative bias on the effect of long duration of stay in Denmark on Grades. Similarly, we would expect that parents with a lack of tradition for education and a norm supporting endogamous marriage, such as for instance Turkish immigrants, would have children earlier after migration than others. 4.2 Parameter of main interest The parameter of main interest measures the average effect of increasing time since arrival at a given margin. If we denote the father s YSM by t, the average impact of increasing the father s time in the country is: 11 See Behrman, Cheng & Todd (2004) and Datta Gupta & Simonsen (2010). 15

16 (1) E [ Grade( t t) Grade( t) t, X ] +Δ. If we denote the mother s YSM by s, the average impact of increasing the mother s time in the country is: (2) E[ Grade( s s) Grade( s) s, X ] +Δ. Those are the average effects of increasing time since arrival from t to t + Δ t (s to s + Δ s ), conditional on spending t (s) years in the country before the child is born and conditional on X. The conditioning set, X, includes indicator variables for gender, country of origin, age of the parents at arrival, older siblings born in the country of origin and in Denmark as well as education of the parents at arrival. Whether or not X should include the other parent s YSM (t and s) is debatable. We know from Table 3 that the two variables are highly correlated, and the other parent s YSM may in fact be affected by the treatment variable if for instance the migration decision is joint. 12 No obvious answer can be given to this question, and therefore, we experiment with different combinations of each of the parent s treatment and control variables. The identifying assumption is that conditional on observables, it is random whether the parent spends t or t + Δt (s or s + Δs) years in the country before they decide to have a child. As long as the change Δ s ( Δ t ) is small, this seems to be a reasonable assumption. 13 Comparing parents who spend a similar number of years in the country before child birth bypasses the problem of large indirect effects stemming from unobserved variables influencing the more fundamental decision of whether to import a spouse or not (such as education and labour market attachment). It is generally not recommendable to condition on post-treatment variables such as education and labor market outcomes of the parents (see Rosenbaum 1984), and furthermore, we have reason to suspect that these variables are affected by the marriage decision and thus implicitly by YSM (see Nielsen et al., 2009). Our approach clearly implies that we can only address marginal effects stemming from local variations in the years since migration. 5. Results In this section we present the results from estimation of marginal effects of parents years since migration on the acquired grades at the school exit exams from 9 th grade. In the first subsection, we present the main results showing the effect on grades in written and oral Danish as well as written and oral math. In the second subsection, we investigate the effect of years since migration on dropout and on whether the student takes the exam or not. Then we investigate heterogeneity by focusing on particular subgroups, and finally, we perform a range of robustness checks. 5.1 The effect of years since migration on grades Before turning to the main results, we first ascertain that the conditioning set actually explains some of the variation in grades and years since migration. Therefore, in appendix Table A1 and A2, we present the full set of regression results including estimated parameters for the set of nine indicator variables measuring the different combinations of father s and mother s years since migration 14 as well as the conditioning variables. 12 See discussion by Rosenbaum (1984). 13 In practice, the variable of main interest is of course divided in a number of categories depending on the amount of data available, and whether these categories are narrow enough to satisfy the assumption is not immediately testable. 14 As also illustrated in Table 3. 16

17 Table A1 shows results where the conditioning set is gradually extended for written Danish, while Table A2 shows results for the full model for all four sub-domains of grades: written Danish, oral Danish, written math and oral math. We note that the explanatory power is high for all groups of variables: gender and country of origin, age of the parents at arrival, education of the parents at arrival and presence of older siblings. 15 In Table 5, we present the parameters of main interest, namely, the effect of a change in years since migration from one category to the subsequent category conditional on holding the partner s years since migration fixed. These are what we earlier denoted local marginal effects, and they are computed directly from the numbers in Table A2. For instance, if we take the top two coefficient estimates in the first column of Table A2, we find that the effect of the father being a long-term resident (14+) rather than having stayed 5-13 years is an increase of in grades in written Danish, conditional on the mother having arrived within 0-4 years. 16 A local marginal effect of corresponds to one tenth of a standard deviation due to the standardization which is necessary to cope with the structural break in the grading scale. The left hand side (LHS) of Table 5 shows the marginal effect of the mother s years since migration conditional on the father s years since migration, while the right hand side (RHS) shows the opposite. The general picture from the LHS of the table is that, no matter how long the father has been in Denmark, it most often improves the child s grades if the mother has been in Denmark for 14+ years rather than just 5-13 years. The general picture from the RHS of the table is that, if the mother has been in Denmark for 14+ years, there is a tendency that the father s YSM is less important. Thus, it seems that the mother s YSM is more important than the father s YSM. The coefficients at the LHS are generally larger and ranges from 8.0 to 17.2 percentage points, while the coefficients at the RHS ranges from 4.4 to 12.1 percentage points. Looking at the results for grades in Danish, both parents years since migration have significantly positive effects on grades. In particular, the mother s years since migration is significant at all margins for written Danish, while only four out of six parameters are significant at a 10%-level when it comes to the father s years since migration and when it comes to oral Danish. If the mother is a long-term resident, the effect of the father s years since migration is insignificant. This is most likely partly a small sample problem stemming from the fact that it is much more common that long-term resident fathers have married a marriage migrant mother than vice versa (see Table 3). Looking at the results for grades in math, the father s years since migration is more often significantly different from zero than the mother s years since migration. For written math, the mother s years since migration matters only at the margin from 5-13 years to 14+ years, while the father s YSM matters at all but one margin. For oral math, the mother s years since migration is never significantly different from zero. 15 The exact parameter estimates are not commented on because these variable account for selection, and thus the coefficients reflect the combined effect on years since migration and grades. 16 In table A3, we base the computations on separate regressions for each specific cell rather than basing it on the large regressions presented in Table A2. In the particular example mentioned in the text, we would then run the regression for fathers with YSM equal to 5-13 and 14+ combined with mothers having YSM equal to 0-4 years, and we get a local marginal effect of rather than

18 Table 5. Local marginal effects of YSM on grades YSM, father YSM, mother Written Danish YSM, 5-13 vs YSM, 5-13 vs mother 14+ vs father 14+ vs Oral Danish YSM, 5-13 vs YSM, 5-13 vs mother 14+ vs father 14+ vs Written math YSM, 5-13 vs YSM, 5-13 vs mother 14+ vs father 14+ vs Oral math YSM, 5-13 vs YSM, 5-13 vs mother 14+ vs father 14+ vs Note: Bold letters indicate significance at a 5%-level while italics indicate significance at a 10%-level. Conditioning set: gender, country of origin, parents education at arrival in Denmark, prevalence of older siblings. 5.2 The effect of years since migration on dropout and no exam In the previous subsection, we focused on individuals who actually took part in the exit exam after 9 th grade. However, as mentioned earlier around 9% are not present at this exam; around 6% dropout, while around 3% stay in school but choose not to sit the exam (see Figure 4). In this subsection, we investigate whether YSM influences whether an individual drops out or does not take the exam. Table 6 shows that neither the mother s nor the father s years since migration are generally important for the dropout decision, while both parent s YSM are important for the decision to sit the exam. Moving up one category in YSM can explain up 1-2 percentage points attendance in the exam at many margins. 18

19 Table 6. Local marginal effects of YSM on drop out/no exam YSM, father YSM, mother Drop out or no exam YSM, 5-13 vs YSM, 5-13 vs mother 14+ vs father 14+ vs No exam YSM, mother 5-13 vs YSM, 5-13 vs vs vs father Note: Bold letters indicate significance at a 5%-level while italics indicate significance at a 10%-level. Conditioning set: gender, country of origin, parents education at arrival in Denmark, prevalence of older siblings. 5.3 Heterogeneity Now we investigate whether the local marginal effect of parents years since migration is heterogeneous across subgroups. In table 7, we present the effects on grades in written Danish for four sub-groups: boys, girls, descendants of Turks and descendants of Pakistanis. Due to the smaller samples, not all parameters are significant. We find that parents years since migration tend to be important for all subgroups. The result that we saw in Table 5 that the mother s YSM is more important than the father s YSM to also prevails for the subgroups, although it seems to be particularly driven by the subsample of boys and Pakistanis. 19

20 Table 7. Local marginal effects of YSM on grades in written Danish By subgroup Boys YSM, mother YSM, father YSM, mother vs YSM, 5-13 vs vs father 14+ vs Girls YSM, mother 5-13 vs YSM, 5-13 vs vs father 14+ vs Turkey YSM, mother 5-13 vs YSM, 5-13 vs vs father 14+ vs Pakistan YSM, mother 5-13 vs YSM, 5-13 vs vs father 14+ vs Note: Bold letters indicate significance at a 5%-level while italics indicate significance at a 10%-level. Conditioning set: country of origin, parents education at arrival in Denmark, prevalence of older siblings. 5.4 Robustness A number of robustness checks are performed in order to understand how sensitive the main results are to small changes in the specifications. As discussed in section 4, one may argue that parent s YSM are highly correlated, and therefore, the other parent s YSM may in fact be affected by the treatment variable if for instance the migration decision is taken jointly. Therefore, in Table 8, we present the results without conditioning on the other partner s years since migration. The effects show the same patterns as the main results in Table 5. There have been two important structural breaks in the data material during the observation period: the subdomains of the tests have changed (2006/07) and the grading scale has changed (2007/08). In Table 9, we investigate whether our main results are driven by these structural breaks by analyzing local marginal effects for different observation periods. The standard errors of course increase as the sample size declines, but the point estimates are fairly robust. 20

21 Table 8. Local marginal effects of YSM on grades in written Danish No conditioning on partners YSM Written Danish YSM, 5-13 vs YSM, 5-13 vs mother 14+ vs father 14+ vs Oral Danish YSM, 5-13 vs YSM, 5-13 vs mother 14+ vs father 14+ vs Written math YSM, 5-13 vs YSM, 5-13 vs mother 14+ vs father 14+ vs Oral math YSM, 5-13 vs YSM, 5-13 vs mother 14+ vs father 14+ vs Note: Bold letters indicate significance at a 5%-level while italics indicate significance at a 10%-level. Conditioning set: gender, country of origin, parents education at arrival in Denmark, prevalence of older siblings. 21

22 Table 9. Local marginal effects of YSM on grades in written Danish Different sample periods YSM, father YSM, mother YSM, 5-13 vs YSM, 5-13 vs mother 14+ vs father 14+ vs YSM, 5-13 vs YSM, 5-13 vs mother 14+ vs father 14+ vs YSM, 5-13 vs YSM, 5-13 vs mother 14+ vs father 14+ vs YSM, 5-13 vs YSM, 5-13 vs mother 14+ vs father 14+ vs YSM, 5-13 vs YSM, 5-13 vs mother 14+ vs father 14+ vs Note: Bold letters indicate significance at a 5%-level while italics indicate significance at a 10%-level. Conditioning set: gender, country of origin, parents education at arrival in Denmark, prevalence of older siblings. 6. Conclusion We analyse the disadvantages that the second generation immigrants inherit from their immigrant parents through their traditional marriage patterns. We employ register data for eight cohorts of second generation immigrants to identify the the impact of each parent s years since migration prior to birth of the child in question on pupil achievement as measured by subject-specific exam grades in the 9 th grade school exit exams. The identifying assumption is that conditional on observables, it is random whether the parents have spent a few more or less years in the country before they have a child. We find a significantly negative impact of years since migration, which is particularly prevalent for written Danish. The magnitude of the effect means that arriving to Denmark 10 years earlier approximately improves grades by one tenth of a standard deviation meaning that it would close 20% of the gap in grades between natives and descendants of immigrants. The effects persist for all subgroups and at most margins. The effect of mother s years since migration is slightly stronger than that of the father s in written Danish, 22

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