School Choice & Segregation

Transcription

1 School Choice & Segregation by Martin Söderström a and Roope Uusitalo b May 20, 2004 Preliminary draft Abstract This paper studies the effects of school choice on segregation. Segregation is measured along several dimensions; ability, socio-economic background, immigrant status and gender. We analyze the effects of a reform in the Stockholm municipality that changed the admission system of upper secondary schools. Before the year of 2000, students had priority to the school situated closest to where they lived, but from the fall of 2000 and onwards, admission is based on grades only. We show that the distribution of students over schools dramatically changed as a response to the introduction of school choice. A difference-in-difference analysis of segregation indices is used to capture the reform effect on segregation. As expected, the reform gave greater sorting by ability. However, the reform also increased sorting in other dimensions, such as socio-economic background and immigrant status. Keywords: School choice, Segregation. JEL classification: a Department of Economics, Uppsala University, Martin.Soderstrom@nek.uu.se. b Labour Institute for Economic Research, and IFAU, Roope.Uusitalo@labour.fi. IFAU School Choice & Segregation 1

2 Table of contents 1 Introduction The Swedish school system Regular compulsory school Upper secondary school The Stockholm admission reform Data and descriptive statistics Definition of variables Stockholm and schools Mobility Measuring segregation Sampling variation and random segregation Segregation indices Grade Point Average st generation immigrants st & 2 nd generation immigrants Parental education Parental income Gender Who chooses? Conclusions References IFAU School Choice & Segregation

3 1 Introduction The debate around school choice is centered on two key questions. The proponents of school choice argue that the competitive forces released by school choice increase efficiency. This increase in productivity benefits all students, also those not exercising choice themselves. As Caroline Hoxby puts it; School choice is a tide that lifts all boats. The opponents tend to be concerned about the effects on those left behind; arguing that choice merely increases segregation. According to a typical argument, the students will be increasingly sorted according to family background or ability. If peer groups are important to student outcomes, the students who get into better schools benefit, both because of higher school quality, and because they interact with better peers. On the other hand, the students left behind suffer not only because of lower school quality but also because of the decrease in the average peer quality. If the peer effects are linear in the average peer quality, and there are no efficiency gains from increased competition, the net effect of reallocating students across schools is zero. By now, the evidence on the efficiency effects from the school choice is accumulating mainly based on various voucher programs and charter schools operating in the United States. In contrast, peer effects and, therefore, the consequences of increased segregation have proven to be hard to estimate. (References.) The basic problem is that peer groups tend to be similar in their characteristics and face similar environment. Isolating the effect of peers from the effects of unobserved factors that affect the peer group in a same way is difficult in an absence of an experiment that would allocate individuals to peer groups randomly. In this paper we analyze the effect of a reform that changed the admission system of upper secondary schools in Stockholm in This reform drastically changed the allocation of students across schools within the city. We will focus on the effects of the reform on the segregation across schools, but note that this reform is an ideal large-scale natural experiment that can be used to identify the peer effects. However, we have currently no data on student outcomes, so analyzing the effects of the reform on student performance will have to wait until data on achievement in upper secondary schools will be available. Another issue that will be possible to evaluate in the future is the effect of the reform on college entry. Since finishing college brings high IFAU School Choice & Segregation 3

4 rewards, any changes that the reform causes on the college going behavior may well be the most important long-term outcome of the reform. In some sense school choice existed in Sweden already long before the 2000 admission reform. The students could apply to any school within the municipality and even across the municipality borders if the home municipality agreed to pay the costs. However, if the schools were oversubscribed the admission was based on the place of residence and those living closest to a school were given first preference. Therefore, the admission system prior to the recent reform resembled intra-district open-enrollment policies in the US. The admission system changed fundamentally in All residence based admission criteria were abolished and admissions became based on previous grades only. The intention was to reduce the effects of residential segregation and to open up the option of attend the most prestigious high schools in downtown Stockholm for all students, irrespective of where they lived. The reform where the admission is based on grades can be expected to lead to greater sorting by ability. However, as we will demonstrate below, the reform also increased sorting in all other observable dimensions. Perhaps a particularly worrying aspect is that the reform lead to greater concentration of immigrants and student from less advantaged backgrounds to some schools. As a first step in our analysis we calculate some mobility measures to study if the reform introduced a new distribution of students over schools, which is what we expect with the introduction of school choice. We then measure school segregation along four dimensions; ability, immigrant status, socioeconomic background and gender, for two pre-reform years and one postreform year. For each dimension we calculate three segregation indices, and we do this for Stockholm and for a comparison group. We use a difference-indifference approach to capture a potential reform effect. This analysis we do also for residential segregation to investigate whether residential patterns are the driving forces behind changes in school segregation. The concluding part of the analysis concerns school choice patterns, that is, which type of students that go to another school than they would have without the reform. In the next section, we will describe in some detail the admission system and the changes due to the reform. Section 3 describes the data. In section 4, we report measures examining the effects of the admission reform on student mobility patterns and after that, in section 5, discuss some measurement issues related to segregation. In section 6 we report the main results on the effects of 4 IFAU School Choice & Segregation

5 the reform on segregation, and in section 7 we try to answer the question on school choice patterns and section 8 concludes. 2 The Swedish school system The educational system in Sweden has gone through a number of changes over the last 15 years. Between 1989 and 1990 the Swedish Parliament decided to decentralize the responsibility for the schools to the municipalities. Decentralization aimed at bringing higher quality in the education, greater flexibility in the organisation, and opening the school system up to local incentives to promote development. The public education system is designed and governed by the Swedish Parliament and the Government. The Ministry of Education sets guidelines on how education should be conducted in the Swedish schools and what should be accomplished. The municipalities are provided with an amount of money from the federal budget, and are then free to determine how much to give to the local school system. The Swedish public school system begins with non-compulsory pre-school, and continues with 9 years of compulsory schooling. A student can then apply for upper secondary school, which is not compulsory. About 90% of the student population complete 9 th grade, that is, they are eligible for upper secondary school. Of those, 98% continue to upper secondary schooling. With completed upper secondary schooling the student can apply for university or post-secondary education. 2.1 Regular compulsory school All children between the ages of 7 and 16 have to attend school. It is possible to begin school one year earlier, at the age of 6, if the parents wish to do so. Most schools are public and a child mostly attends the public school closest to home, but parents can choose other public schools or private schools. The private schools have to be approved by the National Agency for Education and they are financed with grants from the students home municipality. Private schools often have special focus, concerning pedagogical issues, language/ethnicity or religion, but the main group has general type education. IFAU School Choice & Segregation 5

6 Grades are given from the 8 th year, and at the end of year 9 final grades are given. Grades are set by the teacher, and include one of the following possible grades: Pass (G), Pass with Distinction (VG), Pass with Special Distinction (MVG). The system of grades was changed in 1995, and those leaving 9 th grade in 1998 were the first with this new system where teachers shall base their assessment according to stated achievement goals. Basic achievement of these goals corresponds to a grade of Pass. Awarding of the grades of Pass with Distinction and Pass with Special Distinction follows nationally approved assessment criteria. In principle these criteria are absolute not relative, but there is no guarantee that grading standards are equal across schools. In cases where a student fails to achieve a passing grade in a subject, no grade is given. The final certificate from 9 th grade is called meritvärde, Grade Point Average (GPA). It consists of the sum of the 16 best classes, where G earns a student 10 credits, VG 15 credits and MVG 20 credits, making the maximum value of GPA equal to 320. A student who has finished 9 th grade, and has passed in Math, Swedish and English is eligible for upper secondary schooling. The student chooses a program and will be guided to a school by the municipality, most often the school closest to where the student lives. 2.2 Upper secondary school All municipalities in Sweden are by law obliged to offer all students that have completed 9 th grade upper secondary schooling. A student has the right to begin upper secondary schooling up to the age of 20. After that age, there are opportunities in adult education. The upper secondary school consists of 17 national programs built on separate courses chosen by the student. All programs are 3 years and give eligibility to the university or post-secondary level. Most municipalities do not have all programs, and the student then has the right to attend such a program in another municipality, financed by the municipality where he or she resides. Private/independent schools above the compulsory school level can be one of two kinds: those that correspond to the municipal upper secondary schools, i.e., those that offer upper secondary programs and receive municipal grants or those that offer supplementary programs. Among the latter, there are schools with programs in fine arts and handicraft. In addition to the types of schools mentioned, there are also a number of international schools in Sweden, 6 IFAU School Choice & Segregation

7 intended primarily for the children of foreign nationals whose stay in Sweden is temporary. In the school-year 1998/99 there were private upper secondary schools in 35 of the 288 Swedish municipalities, with a total of students. In the Stockholm municipality, there were 13 private schools where 6,5% of the student population attended. The number of private schools is continually increasing. (Nyare siffror) 2.3 The Stockholm admission reform As stated above, the design of the local educational system rests in the hands of the municipality. In Stockholm, the political right carried through a reform concerning upper secondary schooling in the fall of Up to 1999 a student had priority to the upper secondary school that was situated closest to home, the so called närhetsprincipen. A student only applied for a program, with grades deciding admission. Given acceptance, a student could express wishes about which school to go to, but the ones living close to a specific school had priority. From the fall of 2000 and onwards, the students apply for both program (including specialization) and school, grades ranking the students, the so called betygsprincipen. If a student is not accepted to his/her first choice, the second is considered and so forth. As was the case prior to the reform, students from other municipalities can compete on the same conditions, if the program is not an option in that municipality. To specially designed programs, the students from outside compete given that the home-municipality are willing to pay. The reform did not change the way students from other municipalities compete for schools in the Stockholm municipality. Gothenburg and Malmö, the second and third largest cities in Sweden, have also reformed the admission procedure to upper secondary school. In Gothenburg, the private schools use a strict grade procedure, while the public schools use a hybrid form of lottery and grades. Malmö has also abandoned närhetsprincipen, and in those cases where the program is available at different schools, the applicants are allocated to schools according to the grades. IFAU School Choice & Segregation 7

8 3 Data and descriptive statistics The data comes from the database at IFAU, Uppsala, consisting of all the students in the educational system. We define the student population as those who graduated from the 9 th grade in a school situated in the Stockholm County in the spring of 1998, 1999 or We then follow these students, creating three cohorts of 1 st year students in the upper secondary school. Data from years later than 2000 are not available, and prior to 1998 the grade system was different, so including older cohorts would not be directly comparable along the ability dimension. For these three cohorts we have information about the students gender, upper secondary school attended, parish of residence, grades when leaving comprehensive school (GPA and grades separately for math, Swedish and English), country of birth, immigrant status, parental income, parental education and parents immigrant status. A family in this data is defined as those living in the same household as the student. 3.1 Definition of variables Table 1 displays some descriptive statistics of the variables we use. Since we will use a difference-in-difference analysis we show the figures separately for the two groups. The Stockholm County is divided into Stockholm (the municipality, the treatment group) and Comparison (the rest of the county, the comparison group). Grades, measured as GPA, can take the values 0 (worst) to 320 (best). 1 st generation immigrant is defined as if the student is born outside Sweden and the variable 1 st & 2 nd generation immigrant is defined as if the student is born outside Sweden or has at least one parent born outside Sweden. Parental education is a dummy-variable which takes the value one if the student has at least one parent with a university degree. Parental income is the sum of the two parents income. This means that parental income captures the effect of having parents that are working or not working, and also the effect of living with one or two parents. School refers to upper secondary schools, public as well as private. 8 IFAU School Choice & Segregation

9 Table 1. Descriptive Statistics, mean and standard errors Stockholm Comparison Stockholm Comparison Stockholm Comparison GPA (60.050) (58.632) (71.709) (60.888) (76.101) (70.771) Female (0.500) (0.500) (0.500) (0.500) (0.500) (0.500) Age (0.223) (0.214) (0.250) (0.222) (0.267) (0.227) 1 st generation immigrant (0.345) (0.304) (0.366) (0.320) (0.355) (0.317) 1 st & 2 nd generation immigrant (0.471) (0.459) (0.476) (0.464) (0.474) (0.464) Parental income (351996) (300084) (330551) (330767) (445714) (365014) Parental education (0.499) (0.498) (0.499) (0.497) (0.499) (0.498) Going to school in Stockholm (0.353) (0.299) (0.362) (0.331) (0.378) (0.331) Going to school in Comparison (0.299) (0.350) (0.316) (0.377) (0.324) (0.385) Parishes Schools N Stockholm and schools Stockholm is the largest municipality in Sweden with a total of inhabitants. It is the heart of Stockholm County (26 municipalities) with about 1,5 million inhabitants. The metropolitan area is dynamic and homogenous. People commute to work over the entire region and the economic and social interactions are considerable. IFAU School Choice & Segregation 9

10 The Stockholm municipality is divided into 28 geographical parishes, the smallest unit for residence in the normal Swedish dataset. The size of the parishes varies substantially, where the smaller ones are located in the central part of the city. On average a parish has about 200 students, and the smaller inner city parishes can be regarded as wealthier and more educated. Concerning the upper secondary schools, the public schools are spread out quite evenly over the municipality while the private schools are more concentrated in the central part. 4 Mobility As an indication of what happened after the reform, we begin with studying student mobility. We suspect that the mobility and distribution of students over schools has changed as a result of the introduction of school choice with new opportunities for students opening up. In Table 2 we display some measures capturing the mobility pattern in the Stockholm municipality, and we observe increased mobility. The average commuting distance (kilometres) is a rough measure of mobility across geographical regions. We can locate all schools and residence of students to a certain parish. Based on the map coordinates of the mid point of each parish, we can calculate the commuting distance. In Table 2 it is clear that the distance increases, particularly between 1999 and The second row of Table 2 calculates the share of students going to school in another parish than where they live. The figures are pretty high, driven by the fact that some parishes are without an upper secondary school, making the share of students in that parish equal to one. Nonetheless, a sharp increase is observed for the reform year. To be able to capture those students who travel a larger distance to school, we create a measure displayed in the third row that calculates the share of students going to a school outside an area where they live, where the area is defined by the home parish and all adjoining parishes. As with the former measures, it indicates a large increase of mobility between 1999 and Finally we calculate two other indices that aim to measure the variation in the school choices among the students who live in the same parish. The first is the market share of the three largest schools and second the Herfindahl- 10 IFAU School Choice & Segregation

11 index 1. Both are calculated by parish and then averaged over parishes using the number of students in the parish as weights. Both these indices indicate that the variation in school choices among the students who live in the same parish has increased. The increase is rather large. In 1998 some 57 percent of the students attended the three most popular schools in each parish. By 2000, the market share of the three most popular schools has declined by 13 percentage points to 44 percent. It is slightly puzzling that this increased variation in school choices occurred already before the 2000 admission reform. For reasons unknown to us, the reform started to bite already a year before it happened? Table 2. Different mobility measures Average commuting distance (km) Share of students going to school in another parish than where they live Share of students going to school in another area than where they live Market share of three most common schools in parish (3.779) (0.417) (0.499) (3.834) (0.410) (0.500) (3.805) (0.365) (0.495) Herfindahl index Measuring segregation The methods for measuring segregation have a long history in sociology and in demography. Various segregation indices have been designed since the 1950 s. 1 The Herfindahl-index is defined as the sum of the squared market shares. IFAU School Choice & Segregation 11

12 Typical early applications were concerned with dichotomous racial categorizations, most often between white and minority populations. The most common measure of segregation is the dissimilarity index, often called the Duncan index according to Duncan and Duncan (1955). The dissimilarity index is defined as D = 1 2 J s= 1 A s A Bs B, where J is the number of categories (eg. schools), A is the number of individuals belonging to group A (eg. race) and B the number of individuals belonging to group B. A s and B s are the corresponding numbers of individuals belonging to these groups in category s. The index measures the sum of the absolute differences in the fraction of the group in each category. If groups are evenly divided across categories, so that the fraction of the group in each school equals its share in the population, the index is zero indicating that there is no segregation. The index reaches its maximum value of one when there is total segregation, so that the student body in each school consists of only a single group. Another common interpretation of the dissimilarity index is that it expresses the proportion of members of one of the two groups that would have to move in order to achieve an equal distribution of both groups in all categories. A major weakness of the dissimilarity index is that it can measure only segregation among dichotomous groupings. Because segregation indices were mainly used to measure segregation between the black and white populations, there was not much need to develop measures that could accommodate more than two groups. More recent developments in the racial patterns, as well as, applications of segregation measures to other problems have created a need to develop measures that can be applied to multiple groups. One particularly useful index is Theil s entropy index of segregation (Theil 1972). It is defined by first calculating diversity in the population using a measure of entropy E E = n r= 1 1 Qr ln, Q r 12 IFAU School Choice & Segregation

13 where Q r is the proportion of population made up of group r. E reaches its maximum value of ln(n) when each group is represented equally in the population and a minimum value of 0 when only one group is present. To calculate Theil s entropy index of segregation H, one first calculates the diversity E of each school and the diversity of the area as a whole. H is then defined as J t s ( E E ) s = 1 i H = T, E where T is total enrollment and t s enrollment at school s. H can be interpreted as the weighted average difference between the diversity of the area and the diversity in each school. H ranges between 0 when there is no segregation and each school is as diverse as the whole area, and one when there is complete segregation. A useful characteristic of the Theil index is that it can be decomposed to between and within components. For example, one can decompose segregation to part due to differences across geographical areas and to segregation across schools within these geographical areas. While dissimilarity index measures segregation between dichotomous groups, the Theil index can handle multiple groups. However, neither index makes use of the ranking of the groups. For measuring segregation in income levels it would clearly be useful to treat income as continuous or at least ordinal rather that nominal measure. (???) A simple segregation index, that accounts for the cardinal measures, and is also probably most intuitive for economists, is the ratio of between school variance to total variance (R 2 ). Essentially this measures the fraction of the total variance that is due to variation across schools. One can define R 2 as R 2 s= 1 = N J i= 1 n s N ( yˆ y) ( y y) i s 2 2 / N R 2 reaches the maximum value of 1 when all units within groups are equal, so that across group variance equals total variance, and it is zero when there is no variation across groups i.e. the means of each group are equal. An easy way of IFAU School Choice & Segregation 13

14 calculating R 2 is to regress individual outcomes on the full set of school dummies and calculate R 2 from this regression. 5.1 Sampling variation and random segregation There are two important issues that have to be accounted for when interpreting the segregation indices. First, like all sample statistics also the segregation indices are influenced by sampling variability. This is particularly important when analyzing the changes in segregation. We would certainly like to evaluate whether the observed changes are statistically significant or whether they could occur by chance. Still, most studies of segregation provide no information on the sampling variability of the estimates. This is slightly odd given that often the whole purpose of condensing information to a single segregation index is to be able to compare the levels of segregation in different places or changes over time. Second, even if the population were randomly allocated to the different categories, the allocation would not be completely even. The usual segregation indices measure the extent that the allocation deviates from evenness, instead of measuring the deviation from random allocation. Simulation results by Carrington and Troske (1997) indicate that the most common indices of segregation indicate substantial segregation even when the population is randomly allocated across groups. The deviation from evenness is particularly strong when the categories are small or when the minority share is small. In a simple example, Carrington and Troske note that if a large population of men and women are randomly allocated into categories of two, 50% of categories would consist of one man and one woman, while the other 50% would consist of only men or only women. All segregation indices would report substantial gender segregation in this case. Furthermore, the dependence of segregation indices on the size distribution of the categories causes problems when comparing the segregation indices calculated over categories of varying size. Both of these problems are important for analyzing the change in the segregation after the admission reform in Stockholm. Calculating standard errors or confidence bands for the indices is, of course, necessary if we wish to claim that segregation changed due to the reform. We would also like to compare the extent of segregation across the schools to the residential segregation. Both schools and our geographical units are rather small (In 2000, the average cohort size in Stockholm schools was 135, and the average parish 14 IFAU School Choice & Segregation

15 had 212 students). Also the size distribution of schools and parishes is different implying that the segregation indices measuring segregation across schools would get different values than indices measuring segregation across parishes even if the student population were randomly allocated both across schools and across geographical units. Even more importantly, the number of schools has increased over time, and this increase could change the values of the segregation indices even if no changes in segregation occurred. In this paper we follow the suggestion of Carrington and Troske (1997) and adjust the segregation indices to measure the deviation from randomness, instead of measuring the deviation from evenness. We, therefore, first calculate the expected values of all our segregation indices according to the random allocation, given the school size distribution each year. Since analytical expressions for finite samples and varying category sizes are hard to calculate, we do this by simulation. We reallocate randomly the students to schools keeping the size distribution of schools fixed. We draw 500 random replications from the reshuffled data and take the mean of these random draws as the expected value of the segregation index. In our sample the expected values of the segregation indices under random allocation appear to be only moderate in size. For example, the expected dissimilarity index on segregation of income groups across schools in 1998 is 0.066, and the same index on segregation between natives and immigrants in 1998 is The increase in the number of schools and the corresponding decrease in the average school size do not appear to have a major effect. The expected values of segregation indices change only slightly when the number of schools increases. A partial reason for this is that new schools are rather small and their weight on the expected segregation indices rather small. We then calculate the adjusted segregation indices by subtracting the expected segregation index from the observed segregation index. For example, the adjusted segregation index in the case of the dissimilarity index is then ˆ D D * D = if D>D*, (1 D*) where D* is the expected segregation index under random allocation. As the original dissimilarity index, also the adjusted index ranges from 0 to 1 with 0 IFAU School Choice & Segregation 15

16 indicating that segregation equals expected segregation under random allocation, and 1 that there is complete segregation. 2 Finally, to evaluate the extent of sampling variation in the adjusted segregation indices, we calculated the bootstrap standard errors for all the segregation measures. We drew with replacement 500 replications of size N from the original sample and calculated the segregation indices for each draw. The standard deviation of these draws provided us with the standard error for each segregation index. Since we adjust each segregation index, we also need to adjust the estimates for the standard error by dividing the bootstrap estimate with (1-D*). 6 Segregation indices We have measured segregation along six dimensions: Grade Point Average, 1 st generation immigrants, 1 st & 2 nd generation immigrants, parental education, parental income and gender. For each dimension we have measured residential and school segregation with the R 2 -index, the Duncan index and the Theil index. In each case we calculated these measures separately for the Stockholm municipality and the comparison group. We argue that the rest of the Stockholm County can act as comparison group, and we use this in a difference-in-difference analysis. Furthermore, since our indices are adjusted with a random distribution a la Carrington & Troske, we are free from dependence of the size and number of units, and can directly compare residential and school segregation. 6.1 Grade Point Average In the descriptive statistics we observed that the variation in GPA increased over time. Since we do not want this to influence our results, we have chosen to use percentile ranked GPA in our calculations. The GPA has many potential outcomes, the Duncan index can handle only two, and therefore we compare 2 In principle, it is also possible that there is excess unevenness if the observed segregation is smaller than expected segregation under random allocation. In this case D < D*, and the adjusted segregation index would get negative values. 16 IFAU School Choice & Segregation

17 the highest achieving quartile to the rest. The Theil index uses the four quartiles as different groups. The results for GPA are presented in Table 3. It seems that nothing happens over time concerning segregation between parishes, neither for Stockholm nor the comparison group. The R 2 -index indicates that about 5% of the variation in GPA can be explained by where a student lives. The segregation between schools increases over the years, more in Stockholm than in the comparison group. More sorting along GPA is what we expect as a reform outcome, but we did not expect this large increase in the year prior to the reform or in the comparison group. The level of diversity in 2000, as measured with the Theil index, is 11.1% lower between schools in the comparison region than in the total comparison region area. In 1998 the corresponding figure was 8.2%. The diff-in-diff result shows large shifts in the between school variation, an indication of a reform effect on top of a potential time trend. For example, between 1999 and 2000 the Duncan index increased 15 percentage points more in Stockholm than in the comparison group, which is significant at the 1% level. It is safe to say, that the sorting on GPA has dramatically increased between schools and that we can not observe any corresponding trends in the residential segregation. IFAU School Choice & Segregation 17

18 Table 3. Segregation index for GPA. Segregation between schools (compared to randomness) Segregation between parishes (compared to randomness) R 2 Stockholm Comparison (0.007) (0.007) (0.007) Duncan Stockholm (0.014) Comparison (0.012) (0.012) (0.012) (0.014) (0.012) Theil Stockholm Comparison (0.004) (0.004) (0.002) (0.002) (0.002) Difference-in-difference; Stockholm vs comparison Between schools Between parishes 1998/ / / /2000 R *** (0.017) 0.123*** (0.017) Duncan *** (0.026) (0.024) Theil 0.041*** 0.073*** (0.009) Significance level: *** = 1%, ** = 5% and * = 10% (0.025) * (0.024) IFAU School Choice & Segregation

19 6.2 1 st generation immigrants As been stated before, one of the purposes of this reform was to reduce the connection between residential segregation and segregation in schools. Studying the figures in Table 4 it seems that the segregation between schools increases somewhat over the years in Stockholm. According to the Duncan index 20.0% of the immigrants or the natives have to be moved to another school to achieve a distribution that correspond to a random allocation in 2000, the corresponding figure in 1999 was 17.5%. In the comparison group there is no such change, but we find no significant effect in the diff-in-diff analysis. For the residential segregation we can observe an increase in segregation between 1998 and 1999 and thereafter a decrease to 2000 in both groups, and we find no significant estimates in the diff-in-diff analysis st & 2 nd generation immigrants When including 2 nd generation immigrants in the definition of immigrant status the results become sharper. In Table 5 we note that the segregation between schools does not change much between 1998 and 1999, but for the reform year we observe an increase in the Stockholm municipality and a decrease in the comparison group. The Theil index increases from 4.0% to 5.2% in Stockholm, and it decreases from 6.3% to 5.3% in the comparison region, yielding significant diff-in-diff estimates at the 5% level. There are indications of a reform effect for all indices. For example, the segregation between schools measured with the R 2 -index is 2.8 percentage points higher in Stockholm than for the comparison group, significant at the 5% level, for the reform year. The point estimates of the segregation between parishes hint at an increase, but no significant patterns can be found. Along both dimensions of immigrant status it is worth pointing out that the level of residential segregation is about twice as large as the school segregation. IFAU School Choice & Segregation 19

20 Table 4. Segregation index for 1 st generation immigrants. Segregation between schools Segregation between parishes (compared to randomness) (compared to randomness) R 2 Stockholm (0.007) (0.007) Comparison (0.004) (0.004) (0.004) (0.004) Duncan Stockholm (0.019) Comparison (0.014) (0.018) (0.017) (0.014) (0.018) (0.015) (0.017) (0.014) (0.018) (0.014) Theil Stockholm (0.007) Comparison (0.007) Difference-in-difference; Stockholm vs comparison Between schools Between parishes 1998/ / / /2000 R Duncan (0.033) Theil (0.012) (0.031) (0.012) Significance level: *** = 1%, ** = 5% and * = 10% (0.032) (0.014) (0.032) IFAU School Choice & Segregation

21 Table 5. Segregation index for 1 st & 2 nd generation immigrants. Segregation between schools Segregation between parishes (compared to randomness) (compared to randomness) R 2 Stockholm (0.007) (0.009) (0.009) (0.009) Comparison (0.007) Duncan Stockholm Comparison (0.014) Theil Stockholm Comparison (0.004) (0.004) Difference-in-difference; Stockholm vs comparison Between schools Between parishes 1998/ / / /2000 R (0.012) Duncan (0.024) Theil ** (0.012) 0.041* (0.023) 0.022** Significance level: *** = 1%, ** = 5% and * = 10% (0.016) (0.024) (0.016) (0.023) IFAU School Choice & Segregation 21

22 6.4 Parental education For parental education the segregation between schools increases from year to year in Stockholm, with a large shift from 1999 to 2000, as can be noted in Table 6. For example, the R 2 -index increases from 11.6% in 1999 to 13.8% in In the comparison group no pattern is obvious. There is no clear picture of trends in residential segregation, although a slight decrease can be seen in the entire county from 1999 to When comparing levels it can be noted that schools are more segregated than parishes. The Theil index for schools in Stockholm in 2000 is 10.7%, and the corresponding value for residential segregation is 6.1%. The difference-in-difference analysis supports the view of a reform effect, with a significant 2 percentage point increase between 1999 and Parental income As with GPA we have chosen to percentile rank parental income. The Duncan index compares the top quartile to the rest, and the Theil index uses the quartiles as different groups. In Table 7 there seems to be a decrease in residential segregation between 1999 and Concerning segregation between schools there is a sharp increase in Stockholm and not such an obvious pattern in the other municipalities. According to all indices, the school segregation and residential segregation were at the same level in After the reform the school segregation sharply increased while residential segregation decreased. In Stockholm in the year of 2000 the Duncan index was 23.4% for schools and 16.6% for parishes, a significant difference. The difference-in-difference analysis supports the view of a reform effect with significant estimates for 1999/ IFAU School Choice & Segregation

23 Table 6. Segregation index for parental education. Segregation between schools Segregation between parishes (compared to randomness) (compared to randomness) R 2 Stockholm (0.007) (0.007) Comparison Duncan Stockholm Comparison (0.012) (0.012) (0.009) (0.012) (0.009) Theil Stockholm (0.007) Comparison (0.007) (0.004) (0.004) Difference-in-difference; Stockholm vs comparison Between schools Between parishes 1998/ / / /2000 R (0.014) Duncan (0.022) Theil ** (0.014) (0.022) 0.024** Significance level: *** = 1%, ** = 5% and * = 10% (0.023) (0.022) IFAU School Choice & Segregation 23

24 Table 7. Segregation index for parental income. Segregation between schools Segregation between parishes (compared to randomness) (compared to randomness) R 2 Stockholm (0.007) (0.007) Comparison Duncan Stockholm Comparison (0.014) (0.015) (0.014) (0.015) (0.014) Theil Stockholm Comparison (0.002) (0.002) Difference-in-difference; Stockholm vs comparison Between schools Between parishes 1998/ / / /2000 R Duncan 0.041* (0.025) Theil 0.010* 0.029** (0.014) 0.057** (0.025) 0.011* Significance level: *** = 1%, ** = 5% and * = 10% (0.014) 0.049* (0.026) (0.025) IFAU School Choice & Segregation

25 6.6 Gender For segregation between schools we can identify an increase between 1999 and In the difference-in-difference analysis we can see that the fall in segregation in Stockholm between 1998 and 1999 together with an increase in the rest of the County gives significant estimates. In terms of trying to explore a reform effect, not much can be said. Table 8. Segregation index for gender. Segregation between schools (compared to randomness) Segregation between parishes (compared to randomness) R 2 Stockholm (0.434) Comparison (0.004) (0.004) (0.179) (0.206) (0.002) Duncan Stockholm (0.012) Comparison (0.009) (0.009) (0.104) (0.115) Theil Stockholm Comparison (0.004) (0.004) (0.004) (0.002) (0.184) (0.002) (0.214) (0.417) (0.002) Difference-in-difference; Stockholm vs comparison Between schools Between parishes 1998/ / / /2000 R * Duncan (0.021) Theil * (0.022) (0.009) Significance level: *** = 1%, ** = 5% and * = 10% (0.273) (0.156) (0.282) (0.481) (0.116) (0.469) IFAU School Choice & Segregation 25

26 Let us summarize. We have, as expected, identified a large increase in sorting on GPA over schools, but we also observe an increase in the between school segregation along dimensions such as immigrant status, parental education and parental income, that can not be seen in the comparison group or be explained by a change in residential patterns. 7 Who chooses? In the previous section we have demonstrated that segregation indeed increased after the admission reform in all the observable dimensions, in particular, the reform lead to increased sorting by ability. The increase in segregation was not due to an increase in residential segregation, nor did it occur outside Stockholm city. Hence, the increase was almost certainly due to the admission reform; the only puzzling feature being that segregation increased slightly already before the reform. An increase in segregation implies that some students must have made different school choices after the admission reform than what they would have done without the reform. Our finding that mobility has increased so that the place of residence has less impact on the school choices after the reform is consistent with this. Trivially, the finding that residential area became less important for school choices implies that some other factors have become more important. Pretty obviously this other factor is ability, as indicated already by noting that the increase in sorting according to the previous grades increased the most. In order to understand what really happened after the reform, we would like to know who these students are, that made different choices under the new admission system. It would also be interesting to know who chose a different school because new options opened up and who were forced to choose differently because they were no longer admitted to their first best choice. The question on who were affected by the reform is not easy to answer. In the data, we observe school choices by all individuals under either grade or residential based admission rules, but never both. Since allocation of students to schools were not deterministic even under residence based system, there is no easy way of determining which school a given student would have been allocated if the admission system was different from the one that was in force when the students made their school choices. 26 IFAU School Choice & Segregation

27 Even if we cannot place a student with certainty to any given school under an alternative admission system, we can do this with some probability. To be more precise, we can estimate predicted probabilities that a student i attends school s under the pre-reform and post-reform admission rules. A change in these predicted probabilities can then be interpreted as the effect of the change in the admission system on the school choice. There are several possibilities for estimating the predicted probabilities. In practice, however, the large number of potential choices limits the options. For example, in a multinomial logit-model the number of parameters equals the number of options times the number of explanatory variables. With just the dummy variables indicating the parish of residence, and a couple of additional variables describing student characteristics the estimation problem quickly becomes unfeasible. We chose to model the choice probabilities in a non-parametric fashion making as few assumptions as possible. We divided the data into groups by parents income, average grades from the comprehensive school and the parish of residence. Dividing income and grades into two groups and using all 28 parish codes splits the data into 112 groups with, on average, 46 students in each group in We then calculated the fraction of students going to each secondary school in each of these groups and treated these fractions as predicted probabilities. Changes in the predicted probabilities in these groups from year to year can be used as an estimate of the changes in school choices due to the reform. Figure 1 illustrates the results of these calculations for the four largest groups. 4 To make the comparison more informative, we have also ranked the schools according to the average GPA of the students in It turned out that it was necessary to merge some of the smallest parishes because some groups would otherwise have zero observations. In our current version we have only merged Domkyrkoförsamling (01)with Hedvig Eleanora (05), ending up with 108 groups, but some additional aggregation may be useful in future. 4 In the following calculations we limit the attention to schools that existed both in 1998 and Between these years 5 schools with total of 292 students in 1998 closed and 14 new schools with total of 383 students in 2000 were founded. Compared to the total number of students 4755, the effect of closing some schools and opening some new schools is of minor importance. IFAU School Choice & Segregation 27

28 Västerled, high inc, high gr, 1998 Hägersten, high inc, high gr, Density Skärholmen, low inc, low gr, 1998 Spånga, low inc, low gr, School ranking in 1998, 1 = lowest GPA Graphs by group(forsamli incgr betgr) Västerled, high inc, high gr, 2000 Hägersten, high inc, high gr, 2000 Density Skärholmen, low inc, low gr, 2000 Spånga, low inc, low gr, School ranking in 1998, 1 = lowest GPA Graphs by group(forsamli incgr betgr) Figure 1. School attendance patterns of the four largest groups. 28 IFAU School Choice & Segregation

29 Some interesting observations can be made directly from these graphs. For example, the students with high grades and high income parents living in Västerled in the top left corner are heavily concentrated in one senior secondary school. That is Blackebergs gymnasium, a school which is one of the best, where the students still attend after the reform. There is a large shift (10%) from St Jacobi, a school in the lower part of the distribution, to Bromma gymnasium. A significant fraction of the students end up in one of the very best schools, that is, in Östra Real, Norra Real or Södra Latin, after the reform. A similar pattern occurs also with the students with high grades and high income parents living in Hägersten. Before the reform some 35% attend to Brännkyrka Gymnasium, but after the reform the fraction had decreases to about 20% and the share going to Frans Schartau increases with about the same amount. Comparing the location on the school quality distribution, both of these groups gain, on average, from the reform. Similar comparisons can be made for the other two large groups plotted in the bottom part of the Figure 1. For example, in Spånga the student share in Thorhildsplans gymnasium decreases with more than 10% and there is a large increase in the share going to St Jacobi. In both Spånga and Skärholmen the average school quality decreases after the reform at the same time as the choices get more dispersed. To sum up, there are results showing that as choice is introduced.. 8 Conclusions To be written IFAU School Choice & Segregation 29