IMMIGRATION AND PEER EFFECTS: EVIDENCE FROM PRIMARY EDUCATION IN SPAIN

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1 IMMIGRATION AND PEER EFFECTS: EVIDENCE FROM PRIMARY EDUCATION IN SPAIN Florina Raluca Silaghi Master Thesis CEMFI No June 2011 CEMFI Casado del Alisal 5; Madrid Tel. (34) Fax (34) Internet: This paper is a revised version of the Master's Thesis presented in partial fulfillment of the Master in Economics and Finance at the Centro de Estudios Monetarios y Financieros (CEMFI). I am very grateful to my thesis advisor, Manuel Arellano, for his dedication, time and support, to Bryan Graham for helpful comments and valuable insights, to Brindusa Anghel for helping me in dealing with the data, and to FEDEA and the Consejería de Educación de la Comunidad de Madrid for letting me access the database. I also want to thank CEMFI's faculty for useful comments and suggestions, participants of the seminar of FEDEA, as well as my colleagues, especially Daniela Scida and Alonso Villacorta, for their unconditional support.

2 Master Thesis CEMFI No June 2011 IMMIGRATION AND PEER EFFECTS: EVIDENCE FROM PRIMARY EDUCATION IN SPAIN Abstract This study analyzes the effect of immigrant school composition on academic outcomes of Spanish sixth grade pupils from the region of Madrid, in the presence of social spillovers. OLS fixed effects analysis provides evidence of a negative and significant impact of the fraction of immigrants in schools on the academic achievement of native pupils. Also, quantile regression analysis shows that the results are driven by the lower part of the ability distribution. In addition, this paper attempts to measure the impact of reallocating the existing immigrant students across schools on academic achievements and on the inequality between native and immigrant pupils. Florina Raluca Silaghi Université de Rennes I raluflor@gmail.com

3 1 Introduction Western European Countries were faced with an increasing number of immigrants from less developed countries at the beginning of this century. This has lead to an increase in social tension in these countries, that has thus fostered a lot of research on the eects of immigration in the labor market. 2 on the eects of immigration in the educational system. 3 Nevertheless, there is little evidence There is however, a fairly large literature on peer eects in education, which tries to nd whether students contribute to the academic success of their peers. 4 In this paper, I want to combine elements from these two literatures and to study immigrants' peer eects in education. One of the most aected Western European countries by immigration in recent times is Spain, which over the last decade has received almost half of EU's total immigration ows. This is reected in the educational system that is characterized by substantial demographic changes, rapid immigration ows (the fast rising share of immigrant students reached 19% in 2009 in some communities) and increasing segregation of immigrant students in schools. The experience of other countries suggests that immigrant students tend to lag behind their native peers. This, in the presence of spillover eects in school, can aect the academic results of all the students. As human capital accumulation is an important determinant of economic success and therefore of inequality, the study of immigrants' peer eects in the Spanish educational system becomes particularly important nowadays. The aim of this paper is to contribute to the empirical literature on immigrants' peer eects in education, by taking advantage of a database arising from a standardized exam that Madrid's regional government has been conducting for 6th grade students (at the end of the primary school) over several years. My contribution is twofold. On the one hand, I estimate the average marginal eect of school immigrant composition on student achievement (reading and maths test scores) using OLS, panel 2 Two excellent papers in this area are Borjas (2003) and Cortes (2008). 3 Among the few exceptions I mention Gould, Lavy, and Paserman (2009) and Borjas (2004). While Gould, Lavy, and Paserman (2009) look at the eect of immigrant concentration on the longterm academic results of native students, Borjas (2004) examines whether immigrants crowd out natives from graduate programs. 4 Examples of such papers are Duo, Dupas, and Kremer (2008), Sacerdote (2001), Angrist and Lang (2004) and Hoxby (2000). The closest studies to my paper in terms of theme are the last two, that provide evidence on the eects of gender or/and racial composition on academic achievement. 3

4 data and quantile regression strategies. I nd that reading test scores of the native pupils are signicantly and negatively aected by the presence of immigrants, while immigrant pupils benet from the presence of immigrant peers in their school, for both reading and maths subjects. I verify the robustness of my results, through a series of robustness checks and nd that the results are quite robust. An estimator of the average marginal eect of school immigrant composition on student achievement does not correspond to an implementable policy. For example, it would not be possible to increase the percentage of immigrants across all schools, since an increase in one school requires a decrease in the percentage of immigrants in another school. In order to address this concern, I look at the eect of reallocating immigrant pupils across schools in the presence of social spillovers on academic outcomes and inequality (given a number of native and immigrant pupils). In doing this I follow the idea in a recent paper by Graham, Imbens, and Ridder (2009). Following their strategy, I compute two classes of estimators. First, I want to measure the average strength of social spillovers. Secondly, I am interested in nding the eect of a small increase in segregation on average outcomes of pupils and on the average outcome gap between native and immigrant pupils. This gives us an idea of whether there are welfare-increasing deviations from the status quo assignment of immigrant pupils to schools, and of whether this recent increase in segregation of these students is desirable or not. The results from estimating the average strength of social spillovers are compatible with the results in the rst part of the paper. Specically, I nd that an increase in the fraction of Spanish pupils positively aects the academic results of the pupils. Reallocation eects on outcomes are negligible, while a small increase in segregation leads to a small increase in inequality. As specied in the motivation of this paper, in spite of increasing research on peer eects in education and immigration eects in the labor market, there is little evidence in the literature about immigrant peer eects. However, the results that I obtain for the case of Spain are similar to the few available ndings corresponding to other countries. In particular, there is evidence in the related literature that immigrant students in Israel lower the academic results of low ability native students. Gould, Lavy, and Paserman (2009), although they nd that the percentage of immigrants in elementary schools has no eects on dropout rates, and barely a mild eect on matriculation rates, when they split the sample by parent's education and ethnic 4

5 origins, nd that disadvantaged students are more likely to have been adversely affected by a higher concentration of immigrants among their peers. This is consistent with my ndings that low ability students are more strongly aected by the presence of immigrant peers. When we move from immigrant peer eects to the overall ndings on peer eects, for the same country, Lavy, Paserman, and Schlosser (2008) provide evidence of signicant and negative eects of the high fraction of low ability students (repeaters) on the outcomes of the other students. Repeater in their case does not necessarily mean a student who actually repeats a grade, but rather enters the rst grade one year after his/her normative entry date. Again, my results are compatible with their ndings. In the Spanish case we have seen that the immigrant students have on average lower ability than the natives. At the same time, I have found that the pupils that are older than 12 perform signicantly worse than the 12 years old pupils. Furthermore, the data shows that 34% of the immigrant pupils are older than 12, while only 10% of the Spanish pupils are aged 13 or more. Thus, a negative and signicant eect of the high fraction of immigrants on the outcomes of the native pupils, out of which 34% are, according to their denition, repeaters, is in accordance with their results. Finally, Lavy, Silva, and Weinhardt (2009) nd that a large fraction of bad peers at school as identied by the students in the bottom 5% of the ability distribution is detrimental to the other pupil's learning in secondary education in Great Britain. If we consider the immigrant students as low ability students, my results for Spain are compatible with their ndings. 5 The rest of the paper is organized as follows. In Section 2, I describe the data and the descriptive statistics. Section 3 presents the empirical strategy and the main results. A robustness analysis is provided in Section 4. Section 5 presents the quantile analysis. The outcome and inequality eects of an increase in segregation are reported in Section 6. Finally, Section 7 concludes. 5 Low ability students is dened here in the context of immigrant vs native students ( i.e. low vs high ability students). While it is true that on average immigrant students perform worse than the natives, their average results are not as low as the bottom 5% of the ability distribution. 5

6 2 Data The data used in this study comes from the Department of Education of the Regional Government of Madrid. It was obtained with the help of FEDEA, a research center from Madrid. The data contains the results of standardized exams administered to 6th grade students (at the end of primary school, typically aged 12) in the Region of Madrid. I have access to data for four cohorts from 2006 to This exam is called prueba CDI-prueba de Conocimientos y Destrezas Indispensables. It measures basic skills in mathematics, language and general knowledge, and it is compulsory for all primary schools (public, private and charter - private schools that receive public funding and that have to follow the same instructions as public schools). It consists of ve dierent tests: dictation, reading, general culture, and two mathematics tests. The grades for these subjects are on dierent scales from 0 to 5, 0 to 10 or 0 to 20. As measures of academic achievement I use an aggregation of test scores into two categories: reading and maths. 6 I normalize all grades such that they are on a scale from 0 to 10. In order to have the same scale, Unfortunately, for the rst three years I am only able to link the test scores with very few individual characteristics. These are: gender, immigrant status (whether Spanish or not), whether the student has special educational needs or any disability. These four variables are common for the four years. In 2009, a short questionnaire was passed to each student in which they were asked a few questions about themselves, their parents and their living environment. 7 Thus, for this last year I have the following additional individual variables: age of the student, country of birth, parents' education, parents' occupation, household composition and age at which the student started to go to school. Due to this structure of the data, I will focus my analysis on the rst three years pooled together, , and use the last cohort for robustness checks. 6 The rst category that I call reading is obtained by summing the points of dictation, reading and general culture tests, and then dividing the sum by two. The second category, maths, is the sum of points obtained in the two mathematics tests divided by two. Test scores of dictation, and the two mathematics tests are on a scale from Test scores for reading and general culture range from 0-5. Therefore my aggregations reading and maths are both from See questionnaire in Appendix A. 6

7 The rst additional individual variable for 2009 is age of the pupil. It takes values from 10 to 17 in the sample. One-year variation (11 or 12) is due to month of birth interacting with school enrollment rules. Further variation arising from the presence of older children is probably due to the fact that there are repeaters in the sample. At the same time, immigrant students can lose one year of school or more, when they move from their country of origin to Spain, if they are in course of completing one education year when migrating. Table 1: Descriptive statistics of individual variables cohorts Variable Mean Standard deviation 2006 cohort (50,509 students) Test scores (scale 0-10) Reading Maths Immigrant cohort (51,645 students) Test scores (scale 0-10) Reading Maths Immigrant cohort (53,072 students) Test scores (scale 0-10) Reading Maths Immigrant Regarding country of birth, the question that appears in the questionnaire has nine possible answers plus one other option. Out of these nine countries, ve are from Latin America. I aggregate these countries into one category. Therefore I dierentiate between the following categories: Spain, Romania, Morocco, China, Latin America and other. The latter category includes a variety of countries such as Ukraine, Poland, 7

8 Bulgaria, Mexico, etc. Table 2: Descriptive statistics of individual variables 2009 cohort Variable Mean Standard deviation Test scores (scale 0-10) Reading Maths Individual characteristics Immigrant Romania Morocco China Latin America Other Start school Before Between 3 and At At 7 or more Father education Univ Higher secondary Vocational training Lower secondary Didn't nish compulsory Father occupation Business, ministry, city hall Professional Household composition Single parent Only child Single parent and only child Observations 56,960 In the case of the education and the occupation of the parents, pupils provide information about both the mother and the father. The education variable is grouped into ve categories: university education, higher secondary education, vocational 8

9 training, lower secondary education and no compulsory education. With respect to the occupation of the parents, I aggregate the possible answers from the questionnaire into three categories: professional occupations (such as lawyers, psychologist, doctor), business and administrative occupations (entrepreneur, civil servant) and low-skilled jobs (cleaning lady, reman, waiter and so on). Pupils also provide information about the persons they live with. They can select various answers: mother, father, one sister/brother, more than one sister/brother, other family members or other situations. Based on their answers I dene my household composition variables as follows: I construct a dummy variable for pupils living with a single parent and another dummy variable for pupils who are the only-child. Finally, the last individual variable is the age at which pupils started going to school or kindergarden. I distinguish between four categories: before 3, between 3-5, at 6, and at 7 or more. Additionally, for public schools, I have a second category of control variables. These are variables at school level such as: teacher/pupil ratio, average age of the teachers, share of pupils that qualify for a free meal and school size. However, there is a number of few variables at school level, that are available for all schools and these are: enrollment in the 6th grade, share of immigrant pupils in the sixth grade, share of pupils with special educational needs and geographical location of the school in the region of Madrid (North, South, East, West or Capital), as well as district/municipality data. As I do not have access to most of the school level variables for private and charter schools, and I prefer not to drop these from my sample (as they represent 40% of the sample), I will add school xed eects in my analysis, and I will have included in this way the contribution of any school variable that does not change with time such as location and type of school. Unfortunately, I do not have data at class level, only at school level. That is why whenever I refer to fraction of immigrants, I mean fraction of immigrants in the sixth grade across all the school (that can have one or several classes), and not only in a class. The same happens with enrollment, that is enrollment in the sixth grade. To mitigate this problem I also present results for a subsample of small schools, for which one may expect school-level outcomes to approximately coincide with classlevel outcomes. Not surprisingly, I nd sharper results for this subsample. My data set for the cohorts contains a total of 155,226 students in 9

10 1,237 schools, out of which 735 are public. The data set for the last cohort 2009 is composed of 56,960 students in 1,227 schools, out of which 735 are public. The descriptive statistics are presented in Table 1 and Table 2. 8 The most important thing that we can notice in these tables is that fraction of immigrants increases over time from 0.13 in 2006 to 0.19 in Estimating the eect of school immigrant composition on student achievement: main results I begin by presenting the empirical strategy that I use, and the results obtained from each estimation. In order to estimate the average marginal eect of school immigrant composition on student achievement, I start with basic OLS regressions of test scores on fraction of immigrants, the main regressor of interest, and other individual variables. This gives us an idea of the basic correlations in the data, although the causal implications could be misleading, as the estimator could be biased. This is due to the endogeneity of fraction of immigrants in this regression, as I can only control for few individual and school characteristics. My main regressor, fraction of immigrants is possibly correlated with other unobservables that I cannot control for, that determine the academic results of the pupils. Therefore, as a way of controlling for the endogeneity of fraction of immigrants, I perform panel data analysis, including school xed eects. Pooling data on the rst three years together, that share the same individual variables, I add school dummies to the previous regressions. The eect of fraction of immigrants is still identied after including school dummies, thanks to its variability over time and school. 9 The rst natural thing to do when interested in analyzing the eect of immigrant composition on student achievement is to start with OLS regressions of test scores on fraction of immigrants, controlling for individual and school characteristics. As the rst three years share the same individual characteristics, I pool them together and introduce time dummies. The specication is the following: 8 See Anghel and Cabrales (2009) for complementary descriptive statistics. 9 To allow for a more exible form of school-eect endogeneity, in the next section I consider both additive school dummies and school dummies interacted with a time trend. 10

11 Y ijt = α + βd ijt + γf rimig jt + δ 1 X 1ijt + δ 2 X 2jt + σ 1 Dummy07 + σ 2 Dummy08 + ɛ ijt, where Y ijt represents the test score of student i that belongs to school j in period t, d ijt represents a dummy for immigrant status equal to one if student i from school j in period t is immigrant, and zero otherwise, F rimig jt represents the fraction of immigrant pupils in the sixth grade in school j and period t, X 1ijt represents a vector of individual characteristics, X 2jt represents a vector of school variables, and Dummy07, Dummy08 are two time dummies for the years 2007 and 2008 respectively. The results of this estimation are reported in Table 3, columns (1) and (4). 10 We can see that for both reading and maths, the fraction of immigrants negatively and signicantly aects the academic results of their peers, with slightly higher eects for reading. At the same time, we notice that immigrant pupils perform worse than natives. This is also the case for pupils with disability or educational needs. Regarding the gender of the pupils, girls do better in reading, while boys do better in maths. This is similar to other ndings in the gender literature, in particular to the evidence presented by Guiso, Monte, Sapienza, and Zingales (2008). The only school characteristic that I include in this specication, is a dummy for public schools. Related to this, conrming results from previous research (Anghel and Cabrales (2009)), I nd that pupils in public schools perform on average worse than pupils from concerted or private schools. Nevertheless, one has several reasons to think that this specication is aected by the endogeneity of fraction of immigrants. One of the characteristics of the Spanish educational system is that selection of students on admission in public and charter schools are mainly based on residential criteria. Thus, the dierent distribution of native and immigrant pupils across schools should be mostly due to dierences in housing locations. However, there are some extra rules that aect the distribution 10 In all estimations for the full sample I include only schools that appear in each of the three years from 2006 to Thus, and taking into account few missing values for reading and maths test scores, I have a nal sample of 150,429 observations for reading and 150,442 observations for maths. 11

12 of pupils across schools. For instance, pupils that attended pre-school education in a certain school, are given preferential access to the primary education level in the same school. This also happens for pupils that have brothers or sisters in a school. Adding to this that pre-school education used to be paid in charter schools, one would expect to have a higher fraction of immigrants in public schools that are situated in economically poor, immigrant populated neighborhoods, from the margins of Madrid or from villages outside Madrid, where housing is cheaper. Thus, fraction of immigrants is correlated with socio-economic status, parental background and school characteristics. As I cannot control for these variables in my analysis, I expect my main regressor to be endogenous in the previous regression. Table 3: Baseline regressions cohorts Reading Maths (1) (2) (3) (4) (5) (6) Immigrant *** *** *** *** *** *** (0.0235) (0.0230) (0.0413) (0.0237) (0.0232) (0.0416) Fraction of Immigrants *** * *** *** (0.1156) (0.1870) (0.1936) (0.1226) (0.1825) (0.1886) Immigrant*Fr_imig *** *** (0.1205) (0.1231) Public school *** dropped dropped *** dropped dropped (0.0460) (0.0523) Female *** *** *** *** *** *** ( ) (0.0120) (0.0119) (0.0163) (0.0121) (0.0121) Spec educ needs *** *** *** *** *** *** ( ) ( ) (0.0295) ( ) (0.0323) (0.0323) Disability *** *** *** *** *** *** (0.0524) (0.0475) (0.0475) (0.0551) (0.0515) (0.0515) Constant *** *** *** *** *** *** (0.0352) (0.0203) (0.0203) (0.0397) (0.0252) (0.0252) School dummies NO YES YES NO YES YES Time dummies YES YES YES YES YES YES No Obs R squared Robust standard errors clustered at school level in parentheses. * signicant at 10%, ** signicant at 5%, *** signicant at 1%. The highly negative and signicant coecient of fraction of immigrants that I have 12

13 previously found, might be capturing other unobserved characteristics of the schools or of the students that I cannot control for. Therefore, as a way of controlling for the endogeneity of fraction of immigrants, the next step is to add school dummies to this specication. Including school xed eects controls for the endogenous sorting of students across schools based on socioeconomic background. I report the results in column (2) and (5) of Table 3. First of all, we notice that the dummy for public school has been dropped. As schools do not change type over time, the type of school will be xed in time, so this variable is absorbed by the school dummies. However, our main regressor of interest, fraction of immigrants, is not aected by this problem, as we have seen in the data section, that there is a lot of variation over time in the fraction of immigrants (with an ascendant trend from 0.13 in 2006 to 0.19 in 2009). Secondly, we observe that the coecients of all individual variables have remained unchanged after the introduction of the school dummies. Finally, we can see that our main estimators have gone down in absolute value and have lost signicance. Compared to columns (1) and (4), the coecient of fraction of immigrants in the case of reading decreases to and is only signicant at the 10 percent level, while in maths, the coecient is very close to zero and nonsignicant. Hopefully, by adding these school dummies I have eliminated a great part of the endogeneity of fraction of immigrants. In order to further explore the data, I add to the last specication an interaction term between immigrant status and fraction of immigrants. This is actually my preferred specication, that I will take from now on as my baseline regression. The specication is as follows: Y ijt = α+βd ijt +γf rimig jt +θd ijt F rimig jt +δx ijt +η j +σ 1 Dummy07+σ 2 Dummy08+ɛ ijt, where η j represents a school xed eect. The coecients of interest are in this case γ and θ. The results of this regression are available in columns (3) and (6) of Table 3. In the case of reading test scores, the fraction of immigrants negatively and signicantly aects the test scores of the native students, although quantitatively this eect is quite small. For instance, moving from a school with no immigrants, to a school with 50% immigrants would decrease the test scores of native students by 0.24, on a scale from 0 to 10. On the other hand, 13

14 in the case of maths test scores, the coecient of fraction of immigrants increases a little bit in absolute value, but it is still non-signicant. Thus maths results of native students are not aected by the presence of immigrants in schools. However, the new interaction term added appears to have a positive and signicant eect on both test scores. Combining both coecients γ and θ, we see that immigrant pupils benet from the presence of other immigrant peers in school.note that even if we accept the causal validity of these results, they have no implications for the eect of reallocations of a given stock of immigrants. This question is addressed in Section 6 below. The results presented so far are based on data from years pooled together, and they include data for all schools, irrespective of type or size. However, there is a lot of heterogeneity in the distribution of enrollment in the sixth grade. That is, we have schools where the number of pupils in the six grade is very small of the order of 10-15, this happens especially in schools that are located in small villages in the Region of Madrid. At the same time, we have very large schools, where the number of pupils in the sixth grade reaches 175. From now on, as I am only interested in the number of pupils in the sixth grade, I will abstract from the presence of other pupils from other grades in school, and I will refer to the number of pupils in sixth grade as school size, for simplication. Unfortunately, the data that I have is data only at the school level, and not at class level. This can be a problem, as size measured at school level is a noisy measure of size at class level (with the extent of measurement error increasing with school size), and it is well known that measurement error decreases the size of the coecients. 11 Therefore, I would like to provide separate estimates for small, medium and large schools, as I expect fraction of immigrants to more closely proxy peer eects in small schools. Given the distribution of school sizes in my data sample, I choose 2 thresholds for school size, that are 25 and 50. Thus, small schools will be schools with less than 25 pupils in the 6th grade (closer to an average class size), medium schools are 11 The fraction of immigrants in the schools with more than one class in the 6th grade is measured with error. This is due to the lack of data at class level, which is the one that matters most for peer eects. Thus, instead of having the fraction of immigrants computed separately for each class in the 6th grade, my variable is an average of the fraction of immigrants across all the classes in the 6th grade belonging to a certain school. This implies assuming that all the 6th grade classes in a school have the same fraction of immigrants. This is where the measurement error arises from. 14

15 schools with a number of pupils in the sixth grade between 25 and 50, and nally large schools are schools with more than 50 pupils in the 6th grade. 12 Table 4: School size thresholds cohorts Reading Maths (1) (2) (3) (4) Immigrant *** *** *** *** (0.0229) (0.0416) (0.0231) (0.0419) Fr_ Imig*size< ** *** *** (0.2357) (0.2523) (0.2611) (0.2760) Fr_ Imig*25<size< * *** (0.2034) (0.2123) (0.2074) (0.2143) Fr_ Imig*size> (0.3300) (0.3353) (0.3590) (0.3710) Imig*Fr_imig*size< *** *** (0.1441) (0.1577) Imig*Fr_imig*25<size< *** * (0.1402) (0.1384) Imig*Fr_imig*size> (0.1885) (0.2139) Enrollment *** *** ** ** (0.0028) (0.0028) (0.0059) (0.0059) Female *** *** *** *** ( ) (0.0119) (0.0121) (0.0121) Spec educ needs *** *** *** *** ( ) ( ) ( ) (0.0322) Disability *** *** *** *** (0.0473) (0.0473) (0.0514) (0.0514) Constant *** *** *** *** (0.0904) (0.0913) (0.1801) (0.1805) School dummies YES YES YES YES Time dummies YES YES YES YES No Obs R squared Robust standard errors clustered at school level in parentheses. * signicant at 10%, ** signicant at 5%, *** signicant at 1%. In order to obtain estimates for each school size, I make some transformations 12 For more details on the school size thresholds see Appendix B. 15

16 to my preferred baseline specication. I construct rst three dummies for the three school sizes, and then I interact the two regressors of interest, fraction of immigrants and the interaction between fraction of immigrants and immigrant status, with these three dummies. So we will have the impact of fraction of immigrants in small schools, medium and large, and the same for the eect of the interaction between fraction of immigrants and immigrant status. The results of this desegregation are available in Table 4. Indeed, as expected, when we increase school size, the coecients go down both in absolute value and signicance. This happens for both subjects, and also for both regressors (columns (1), (3) for fraction of immigrants, columns (2), (4) for the interaction). The coecient of fraction of immigrants in the case of reading test scores decreases in absolute value from for schools with less than 25 pupils in the sixth grade, to almost zero for schools with more than 50 pupils in the sixth grade. Contrary to the previous results that showed that maths test scores of natives are not aected by the presence of immigrants,the fraction of immigrants has now a negative and signicant eect on maths test scores of natives. The eect is slightly smaller than for reading test scores. At the same time, the results dier forthe group of immigrant students as well. Before, they beneted from the presence of immigrant peers, now we can see that our β and γ almost cancel out for both subjects. So there is no eect of fraction of immigrants on test scores of immigrant students in small schools. For large schools with more than 50 pupils in the sixth grade, none of the coecients is signicant, for none of the subjects. This is an indication that fraction of immigrants more closely proxies a peer eect in small schools. All in all, we have found a negative and signicant eect of fraction of immigrants on native test scores for both subjects, with no impact on immigrants test scores in small schools, and no eects in large schools. 4 Robustness analysis In what follows, I would like to check the robustness of my results to dierent specications. The aim of this analysis is to nd out whether the results are sensitive to the introduction of new controls, or to alternative specications. Therefore I will 16

17 perform ve robustness checks. 4.1 Public versus non-public schools To begin with, I want to see whether there is any dierence between public and non-public schools. This concern is motivatedby two distinct reasons. On the one hand, there is evidence of increasing segregation of immigrants across public and private schools. Table 5: Public vs non-public eects Reading Maths (1) (2) Immigrant* Public *** *** (0.0493) (0.0497) Immigrant* Private *** *** (0.0697) (0.0722) Immigrant*Fr_imig*Public *** *** (0.1403) (0.1410) Immigrant*Fr_imig*Private *** ** (0.2250) (0.2622) Fraction of Immigrants *** ( ) (0.1887) Female *** *** ( ) (.0121) Spec educ needs *** *** ( ) (.0324 ) Disability *** *** ( ) (.0516) Constant *** *** (0.0407) (0.0407) School dummies YES YES Time dummies YES YES No Obs R squared Robust standard errors clustered at school level in parentheses. * signicant at 10%, ** signicant at 5%, *** signicant at 1%. 17

18 According to data from the Spanish Ministry of Education, the proportion of native students in public schools has decreased substantially over the last decade in pre-primary education and slightly in primary and secondary education. For instance, the fraction of Spanish students in pre-school education in public schools has decreased from 67.6% in 1999 to 62.5% in 2008, while the fraction of foreigners has increased from 76.4% to 83% during the same period of time. 13 On the other hand, both this paper (Table 3 columns (1) and (4)) and previous research (Anghel and Cabrales (2009)) have found that pupils from public schools perform signicantly worse than pupils from private and charter schools. Hence, there are reasons to expect that immigrants might have a dierent impact in public than in non-public schools. Table 6: Year by year regressions - reading Reading (1) (2) (3) (4) Immigrant *** *** *** *** (0.0594) (0.0673) (0.0586) (0.0520) Immigrant*Fr_imig * *** *** *** (0.1890) (0.1997) (0.1552) (0.1502) Female *** *** *** *** ( ) (0.0206) (0.0189) (0.0191) Spec educ needs *** *** *** *** ( ) (0.0499) (0.0411) (0.0442) Disability *** *** *** *** ( ) (0.0736) (0.0573) (0.0743) Constant *** *** *** *** (0.0096) (0.0093) (0.0134) (0.0094) School dummies YES YES YES YES Time dummies NO NO NO NO No Obs R squared Robust standard errors clustered at school level in parentheses. * signicant at 10%, ** signicant at 5%, *** signicant at 1%. 13 For more details, see Zinovyeva, Felgueroso, and Vázquez (2008). 18

19 Therefore, in order to check whether there is any dierence between public and non-public schools, I interact immigrant status and the interaction between fraction of immigrants and immigrant status, with two dummies, one dummy for public schools, and another one for non-public schools, that includes private and concerted schools. I report the results of this robustness check in Table 5. Contrary to what I expected, I nd that there are no signicant dierences between public and non-public schools with respect to the eects of being an immigrant, and to the impact of the presence of immigrant students in schools on academic achievement of their peers. 4.2 Year by year results Table 7: Year by year regressions - maths Maths (1) (2) (3) (4) Immigrant *** *** *** *** (0.0661) (0.0658) (0.0585) (0.0529) Immigrant*Fr_imig *** *** *** (0.2133) (0.1942) (0.1649) (0.1483) Female *** *** *** *** ( ) (0.0199) (0.0196) (0.0201) Spec educ needs *** *** *** *** ( ) (0.0499) (0.0456) (0.0457) Disability *** *** *** *** ( ) (0.0801) (0.0553) (0.0734) Constant *** *** *** *** (0.0108) (0.0090) (0.0140) (0.0098) School dummies YES YES YES YES Time dummies NO NO NO NO No Obs R squared Robust standard errors clustered at school level in parentheses. * signicant at 10%, ** signicant at 5%, *** signicant at 1%. The second robustness check is to verify how stable the results are over time. The baseline results obtained so far are based on pooling the rst three years together. In 19

20 this robustness check, I run the same regressions as in Table 3 columns (3) and (6), for each year from 2006 to That is I regress the test scores of the students on the immigrant status, on the interaction between fraction of immigrants and immigrant status, and on the other three individual variables available for all years. At the same time I control for school xed eects. As I have separate regressions for each year, and the variation in the fraction of immigrants is at school level and not at individual level, this variable will be absorbed by the school xed eects. Fortunately, I can still have as a regressor the interaction between fraction of immigrants and immigrant status, as here I have variation at individual level. The results from this robustness check are presented in Table 6 for the reading test scores, and Table 7 for the maths test scores. We can see that, with the exception of year 2006, the results are quite stable over time. Being an immigrant decreases your reading test scores by 0.9 in 2009, and 1.2 in 2007, and your maths test scores by an amount between 0.71 in 2008 and 0.84 in Taking into account that grades are on a scale from 0 to 10, the dierences between years are quite small. The same happens for the interaction between fraction of immigrants and immigrant status, the results are very similar over time, with the exception of Add extra variables for 2009 In the next robustness check, I want to take advantage of the extra individual variables that I have available for the last year, 2009, and to include them in the baseline specication. Most ndings in the literature on economics of education attribute an important role to parental background, that includes parents' education and occupation, among the factors that aect the academic achievement of the students. I am interested in nding whether, after controlling for parental background and other individual variables, my estimates are still signicant. Again, as this estimation will contain data from only one year, and I control for school xed eects, the eect of fraction of immigrants will be absorbed by the school xed eects. Nevertheless, I can still include the second main regressor, the interaction between fraction of immigrants and immigrant status. The results from this estimation are reported in Table 8. 20

21 Table 8: Extra variables cohort 2009 cohort Reading Maths (3) (4) Immigrant*Fr_imig *** *** (0.1806) (0.1828) Student from Romania (0.0992) (0.1017) Morocco *** (0.1497) (0.1821) China *** *** (0.1950) (0.2173) Latin America *** *** (0.0697) (0.0723) Other Country *** *** (0.0702) (0.0780) Female *** *** (0.0212) (0.0233) Spec educ needs *** *** ( ) (0.0604) Disability *** *** (0.0958) (0.0922) Age Aged *** *** (0.1435) (0.1752) Older than *** *** (0.0363) (0.0395) Start school Between *** *** (0.0219) (0.0253) At *** *** (0.0748) (0.0797) At 7 or more *** *** (0.1092) (0.1175) 21

22 Table 8 (cont.): Extra variables cohort Education father University *** *** (0.0513) (0.0558) Higher secondary *** *** (0.0515) (0.0537) Lower secondary *** *** (0.0552) (0.0572) Vocational training *** *** (0.0492) (0.0528) Education mother University *** *** (0.0569) (0.0597) Higher secondary *** *** (0.0563) (0.0591) Lower secondary *** *** (0.0605) (0.0635) Vocational training *** *** (0.0524) (0.0545) Occupation father Professional *** *** (0.0275) (0.0320) Business *** *** (0.0280) (0.0316) Occupation mother Professional *** *** (0.0332) (0.0396) Business *** *** (0.0320) (0.0367) Household composition Single parent *** *** (0.0404) (0.0449) Only child *** *** (0.0260) (0.0298) Single parent and only child * (0.0606) (0.0671) Constant *** *** ( ) ( ) No Obs R-squared Robust standard errors clustered at school level in parentheses. * signicant at 10%, ** signicant at 5%, *** signicant at 1%. 22 Both regressions include school xed eects.

23 First of all, we can see that the interaction between fraction of immigrants and immigrant status still has a positive and signicant eect, and is similar in size with the result obtained when I do not control for these extra variables. Thus, the results from the baseline specication are robust to the introduction of these controls. Secondly, as I have now the country of origin of the pupils, I can include some dummy variables for country of origin, instead of using one single dummy for immigrant status (whether Spanish or not). Given the distribution of country of origin in my sample, I divide the students in ve categories, as explained in the data section: students from Romania, Morocco, China, Latin America (here I aggregate students from Ecuador, Columbia, etc) and other countries. Regarding the results obtained, we can see thatthe students from Romania are not signicantly dierent from the Spanish students, neither for reading, nor for maths test scores. The Moroccan students appear to perform worse in reading than the Spanish, but are not signicantly dierent in maths, while Chinese students perform worse in reading, although a lot better in maths. A student from China has on average a grade with 1.34 points higher than a Spanish student. The Latin American students do worse than the Spanish in both reading and maths. This is quite surprising, as Latin Americans have Spanish as their native language and perform worse in reading than for example Romanians. One has to be careful in interpreting these results, as the nationality of the student could be capturing the eects of some unobserved characteristics that we cannot control for. For example, I do not control for the eort of a student, nor for the number of years that a student has been living in Spain. 14 Regarding the age of the pupils, these pupils are at the end of their primary education (6th grade), and they are typically aged 12. However, the age varies from 10 to 17 in the sample, as explained in the data section. Given this age distribution I am interested in nding out how younger pupils perform compared to a typical 12-years-old. Specically I want to see how pupils aged 11 do compared to pupils aged 12, as there is evidence in the literature that month of birth has an eect on 14 Fortunately, a question about the number of hours that a pupil studies per day has been introduced in 2010, and future studies could take advantage of this new variable that can be a proxy for the eort of a student. Regarding the number of years that a student has been living in Spain,Anghel and Cabrales (2009) control for this variable, and they still nd very similar results to the ones presented here. 23

24 school and economic outcomes. 15 For this, I added an individual dummy for pupils aged 11. At the same time, I also want to see how older students perform, that is why I introduce another dummy for older than 12 aged pupils. The data shows that 34% of the immigrant students are older than 12, while only 10% of the Spanish students are aged 13 or more. This dierence can be due to dierent normative entry dates in the rst grade in the countries of origin of the immigrants, or can be caused by migration during a school year of the pupil, making the pupil lose one year of school. We can see in Table 9, that both categories of students, aged 11 and older than 12 perform worse than the typical 12-years-old student, for both subjects, and the eects are stronger for the latter. An older than 12 pupil has 1.2 points less in reading compared to a 12 years old pupil. Next, we can look at the age at which pupils started going to school (or attend pre-school institutions such as kindergarden). For this, I introduce three dummies for pupils that started school between 3-5, pupils that started at 6, and pupils that started school at 7 or more. The excluded category is the category of pupils that started school before 3. What I nd is that pupils with pre-school attendance perform better. As the years of pre-school education decrease, the academic achievement of the pupils decreases as well. With respect to the parental background, I control for parents' education and occupation. In the case of education, I include dummies for four categories: parents with university degree, higher secondary education, lower secondary education and vocational training. The excluded categories is parents who did not nish compulsory education. I nd that the pupils whose parents have a better education perform better in both subjects, with higher eects for maths results. Specically, the pupils who have parents with a university degree obtain 0.4 more points in maths test scores than the pupils whose parents did not nish compulsory education. The eects are similar for father education and mother education. In the case of parental occupation, I introduce two dummies for professional occupation and for business occupation. 16 omit low skilled jobs such as cleaning, working in constructions. Again the results 15 See Angrist and Krueger (1991). 16 The dummy of professional occupation is equal to one when the answer to question 8 in the questionnaire is c) and zero otherwise. The dummy for business and administrative occupation is equal to one when the answer to question 8 in the questionnaire is b) and zero otherwise. I 24

25 show that the occupation of the parents has a signicant impact on the results of their children, the pupils whose parents have a professional or business occupation perform better than the pupils whose parents have a low skilled job, with greater eects for the latter. More concrete, the pupils whose fathers have a business occupation obtain 0.4 more points in maths test scores than the pupils whose fathers have a low skilled occupation. The eects of the occupation of the father are a lot stronger than those of the mother. Table 9: Average fraction of immigrants Reading Maths (1) (2) (3) (4) Immigrant *** *** *** *** (0.0233) (0.0595) (0.0235) (0.0614) Fraction of Immigrants ** (0.1925) (0.2010) (0.1940) (0.2026) Immigrant*Fr_imig *** *** (0.1316) (0.1378) Average fr_imig ** ** (0.7287) (0.7336) (0.8665) (0.8767) Immigrant*Ave_fr_imig * (0.2678) (0.3054) Female *** *** *** *** (0.0121) (0.0122) (0.0123) (0.0124) Spec educ needs *** *** *** *** ( ) (0.0305) (0.0333) (0.0335) Disability *** *** *** *** (0.0495) (0.0497) (0.0536) (0.0538) Constant *** *** *** *** (0.1132) (0.1136) (0.1330) ( ) School dummies YES YES YES YES Time dummies YES YES YES YES No Obs R squared Robust standard errors clustered at school level in parentheses. * signicant at 10%, ** signicant at 5%, *** signicant at 1%. Finally, we can look at the eect of household composition on pupils' outcomes. For this purpose, I use the dummies for pupils who live with a single parent, and for 25

26 pupils whoare a single child. Moreover, I add an interaction term between these two. I nd that the pupils who live with a single parent perform worse than the pupils who live with both parents, and the pupils who are the only child perform worse than the pupils who live with brothers and sisters. The interaction term between the two is not signicant. 4.4 Add average fraction of immigrants in the neighborhood Another check that I am interested in doing is adding a new control in my baseline specication, and that is the average fraction of immigrants in the neighborhood of the school. As the fraction of immigrants has an ascendant trend throughout time, I will have variation in my new control over time, so the impact of this variable will not be absorbed by the school xed eects. Neighborhood is dened as municipality for schools outside the capital, so from villages or small cities in the region of Madrid. In the case of Madrid city, neighborhood is dened as district, and this is a variable that appears in the database. Thus, I have pupils from21 dierent districts from the city of Madrid. However, there are some schools that are unique in their neighborhood, as in the case of small villages that have only one school. Consequently, I drop the pupils belonging to these schools from the estimation. The sample size decreases by around 6,000 observations out of approximately 150,000 that I had in the baseline regressions. I present the results in Table 9. Looking at the right panel of the table, we can see that the maths results are robust to the introduction of this new control, and the average fraction of immigrants in the neighborhood has no signicant impact on maths test scores. However, in the case of the reading test scores, we notice that the fraction of immigrants has a smaller eect and at the same time is less signicant. Nevertheless, the interaction between immigrant status and fraction of immigrants is still positive and highly signicant, the coecients slightly increase from 0.56 to 0.64 in the case of reading, and from 0.36 to 0.44 in the case of maths. Overall, I can say that the results are robust to the introduction of this new control. 4.5 Add a heterogeneous school trend A potential problem with the results from Table 3 is that there might exist sorting and matching of students across schools. For example, if native students were moving 26