the effect of school resources on educational attainment - SSRN

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Research 2005. Published by Blackwell Publishing, 9600 Garsington Road, Oxford OX4 2DQ, UK and 350 Main Street, Malden, MA 02148, USA Bulletin of Economic Research 57:2, 2005, 0307–3378

THE EFFECT OF SCHOOL RESOURCES ON EDUCATIONAL ATTAINMENT: EVIDENCE FROM DENMARK Eskil Heinesen* and Brian Krogh Graverseny *AKF, Institute of Local Government Studies, Denmark and yThe Danish National Institute of Social Research and The Graduate School for Integration, Production and Welfare

ABSTRACT

We investigate the effect of school inputs in primary and lower secondary schools on the probability of eventually passing upper secondary or vocational education. Danish administrative register data for a large number of young people and their parents are used. Educational outcome and controls for family background are measured at the individual level, whereas school expenditure and controls for municipal socioeconomic characteristics are measured at the municipal level. As unobserved characteristics may be correlated for pupils within the same municipality, we estimate linear probability and logit models with random municipal-specific effects in addition to standard OLS and logit models. With the full sample of pupils and the full set of controls, we find that expenditure per pupil has a statistically significant, but rather small, positive effect on educational attainment. Effects of teacher–pupil ratios are less significant. The expenditure effects are generally higher for pupils from disadvantaged backgrounds. Keywords: educational economics, generalized linear model, human capital, random effects, school expenditure, school quality JEL classification numbers: I21 Correspondence: Eskil Heinesen, AKF, Nyropsgade 37, DK-1602 Copenhagen V, Denmark. Email: [email protected]. The authors are grateful to Mike Utton, Steve Davies and Nigel Driffield for their comments on this article. We thank Martin Browning and anonymous referees for helpful comments and suggestions. Financial support from the Danish Social Science Research Council is gratefully acknowledged.

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BULLETIN OF ECONOMIC RESEARCH I. INTRODUCTION

Measures of school inputs are directly affected by government policy, and whether they matter for educational and labour-market outcomes of pupils is an issue of great public policy concern. At some level, school resources must matter. But, the issue is whether increasing resources, given the present level of inputs, would have significant positive effects on pupil outcomes. There exists an extensive literature on the effects of school resources (or school inputs) on student outcomes. Estimation of educational production functions is complicated, because there are many outputs from education and many inputs to the production process, and because it can be difficult to obtain good measures of both outputs and inputs. Apart from school resources, inputs related to family background and the local community are important. Measures of school inputs are typically expenditure per pupil, class size, teacher–student ratios and measures of teacher quality such as experience, wages or education. Measures of outputs are typically: (i) student performance on cognitive tests (while in school), (ii) educational attainment after school (most often measured by years of education) or (iii) labour-market outcomes (particularly earnings) later in life. For all three measures of output, there is controversy over whether school resources have significant effects on output. In his widely cited surveys, Hanushek (1996a, b, 1986) finds no systematic positive relation between school resources and student outcomes. However, other reviews of the literature conclude that there is a significant positive relationship (Krueger, 2003; Greenwald et al., 1996; Hedges and Greenwald, 1996; Hedges et al., 1994). Most studies covered by these reviews use test scores as the outcome measure. For labour-market outcomes (primarily earnings), Card and Krueger (1996a, b, 1992) find positive effects of school resources, whereas Betts (1996a, b, 1995) and Heckman et al. (1996) do not find significant effects, and Betts (2001) finds mixed results. On the basis of experimental data, Krueger (2003, 1999) finds positive effects of school resources on test scores. Using quasi-experimental designs, Angrist and Lavy (1999) find positive effects, though Hoxby (1999) finds clearly insignificant effects. Recent studies using British data find mixed results (Dustmann et al., 2003; Dearden et al., 2002; Feinstein and Symons, 1999). Using TIMSS data, Wo¨ssmann (2000) finds that international differences in pupil test scores (in mathematics and science) are caused not by differences in school resources, but are mainly due to differences in educational institutions, and Gundlach et al. (2001) find that in most OECD countries, the relative price of schooling has increased over 1970–94, while student performance has declined or remained approximately constant, implying falling productivity. In a French programme that allocates extra financial resources to schools in # Blackwell Publishing Ltd and the Board of Trustees of the Bulletin of Economic Research 2005.

EFFECT OF SCHOOL RESOURCES ON EDUCATIONAL ATTAINMENT

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disadvantaged zones, Benabou et al. (2003) find (using difference-indifferences and instrumental variables methods) that this allocation has no significant impact on student outcomes. A ‘paradox’ in the literature is that broad measures of inputs, such as expenditure per pupil, for which data are usually available only at a rather aggregate level (school district, local authority or state) are more often significant, whereas measures which can be more precisely related to an individual school or even a class, such as class size, teacher–pupil ratio, teacher salary or teacher education, are more often insignificant. One possible explanation is that the overall level of expenditure per pupil matters, and that the efficient allocation of expenditure on specific inputs depends on local conditions. For instance, in rural areas with small schools, it may be efficient to have small class sizes and reduce expenditure on other inputs, whereas the same need not be true for city areas with larger schools. Another explanation may be that class level measures of inputs are often associated with remedial training and the socioeconomic background of pupils. For instance, disadvantaged children are often assigned to smaller classes. Most studies on educational production functions have as output variable the test scores in school, and most studies of effects later in life focus on earnings. Analyses of the effects of school inputs in primary and lower secondary schools on later educational attainment are relatively scarce in the literature, even though effects on labour-market outcomes must largely be transmitted through educational attainment. In his survey of the rather limited American literature with later educational attainment as the outcome variable, Betts (1996a, pp. 181–2) concludes: ‘A much fuller analysis of the influence of school quality on educational attainment using existing microeconomic data sets should be a top priority in future research’. This is accordingly the focus of the present study. In particular, we investigate the effect of school inputs in primary and lower secondary schools on later educational attainment, focusing on one particularly important educational outcome: the probability of attaining an education (upper secondary or vocational) after lower secondary school. The considerable fraction of young people who do not get an education beyond compulsory school has been an issue of great public policy concern in many countries in recent years as a result of the falling demand for unskilled labour. An investigation of whether, and to what extent, increasing school resources might help reduce this fraction is therefore important. The basic methodological approach used in this study is to estimate educational production functions to test the significance of school resources, applying extensive controls for family background and socioeconomic conditions in the local community. The Danish data set which we use is particularly well suited to this kind of analysis, as we have # Blackwell Publishing Ltd and the Board of Trustees of the Bulletin of Economic Research 2005.

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BULLETIN OF ECONOMIC RESEARCH

information on each individual’s pathway through the educational system and also high-quality information on each individual’s family background, which is particularly important in studying educational attainment, in view of the overwhelming evidence of highly significant family background effects. The data set is based on data merged from several administrative registers using civil registration numbers. This is a panel data set for the period 1981–96, covering a 10 percent random sample of the cohorts born between 1965 and 1970 and their parents. These micro data are combined with data on school resources and socioeconomic conditions in the municipalities. The advantages of using administrative data are that it is feasible to establish data sets covering a large number of individuals and variables; that data are generally highly reliable (e.g., there is no recall bias); and that it is possible to get data for each individual over a long period of time without the severe attrition problems common in longitudinal data sets based on repeated surveys. Section II describes the Danish institutional setting. In Section III, we discuss methodological issues. Section IV describes the data set. Section V describes the calculation of school resources related to each individual. Estimation results are discussed in Section VI, and section VII sets out concluding remarks.

II.

THE DANISH INSTITUTIONAL SETTING

The present work looks at the effects on later educational attainment of school resources in public primary and lower secondary schools in Denmark. These schools are run by the 275 local authorities (municipalities) with on average about 18,500 inhabitants (ranging from 1

10,911 13,977 14,403 9,318 28,206 18,882 20,218

Females Males

19,478 19,884

0.182 0.135 0.009 0.166 0.045 0.148 0.050

(0.061)** (0.050)** (0.044) (0.063)** (0.036) (0.056)** (0.043)

0.110 (0.043)* 0.104 (0.045)*

Notes: Estimates for different groups of pupils defined in terms of parental background and gender. Robust standard errors (adjusted for clustering on school municipality at eighth grade) are reported in parentheses. Controls for personal characteristics, family background and socioeconomic conditions in the municipality (see controls A, B and C of Table 2) are included in all estimations, with the exception of controls rendered superfluous by the definition of the sample for each estimation. Details of controls are given in Table A1. *Significance at the 5% level. **Significance at the 1% level.

# Blackwell Publishing Ltd and the Board of Trustees of the Bulletin of Economic Research 2005.


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not here measure all potentially positive effects of increasing school resources. Thus, there may be positive effects on skills learned in school for pupils, for whom completion of an upper secondary or vocational education is not affected by the change in school resources; this may affect educational attainment beyond the secondary level as well as labour-market outcomes. Comparison of the present results with other published estimates is complicated by the fact that most other investigations of the effects on educational attainment after compulsory school use years of education as outcome, not the probability of obtaining a given level of education. Betts (1996a) gives a survey of US studies of the effect of school resources on educational attainment. His meta-analysis shows that a 1 percent increase in expenditure per pupil increases years of education by about 0.01 on average in studies that use state-level data, and by about 0.0015 in studies that use district-level data. As discussed in Section IV.2, the estimated quasi-elasticity of 0.1 in the present study suggests that an increase in expenditure per pupil of 1 percent leads to an increase of 0.1 percentage point in the fraction of pupils obtaining a vocational or upper secondary education. Since these are 3-year educations, the indicated increase in average years of education is 0.003. The total effect on years of education may be somewhat higher, as there may be a positive effect on educational choices above the upper secondary level as well. However, the estimate of 0.003 falls well within the range of typical US estimates in the Betts review. As we have discussed in Section III, Browning and Heinesen (2003) estimate effects of school resources using Danish data applying a regression discontinuity design. They estimate rather large effects, though these are not determined very precisely. The point estimates indicate that an increase by 1 percent in the number of teacher hours in normal classes per pupil in normal classes (the most narrowly defined school resource measure used in the present study) will increase the average number of years of education by 0.03, that is, ten times the expenditure effect estimated in the present study (and six times the effect with respect to teacher hours in normal classes per pupil in normal classes) and three times the high (state-level) US expenditure estimates as summarized in Betts (1996a). However, the estimates in Browning and Heinesen (2003) are only marginally significant. Methodological differences between the present study and Browning and Heinesen (2003), which may explain the rather differing results, are discussed in Section III. Though the overall effects of school resources estimated in this study may be small, our results indicate that school expenditure effects are considerably larger for pupils from disadvantaged backgrounds, in accordance with the results of other studies (Krueger and Whitmore, 2001; Angrist and Lavy, 1999). Thus, for pupils whose parents have high degrees of unemployment, our estimates indicate that the effects of # Blackwell Publishing Ltd and the Board of Trustees of the Bulletin of Economic Research 2005.

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raising school expenditure are about three times as high as for the average pupil. Targeting of increases in school expenditure towards pupils from disadvantaged backgrounds might have considerably larger beneficial effects than general increases in expenditure. Upon substituting expenditure per pupil by one of three different measures of the teacher–pupil ratio in the model, we find that these are all less significant, although all are significant at the 5 percent level for the full sample and the full set of controls. The point estimates of the quasi-elasticities with respect to teacher hours per pupil are very similar to the expenditure quasi-elasticities except for the most narrow teacher– pupil ratio, for which the quasi-elasticity is about 70 percent larger. The estimated effects of school resources prove to be sensitive to changes in the set of controls included in the estimations, as expected. The estimated effects are insignificant unless controls are included for both family background and socioeconomic conditions in the local community. Upon looking in detail at the sensitivity of the estimated school resource effects with respect to changes in the set of controls for family background, we find that, once we control for socioeconomic conditions in the local community, the point estimates of the school resource effects are not very sensitive to which group of family background controls is included in the model. However, the estimated school resource effects are generally somewhat smaller and less significant when only a small subset of family background controls is included. These results suggest that the estimates might be robust to the inclusion of additional relevant controls, which are not in the data set, and that the likely effect of including additional controls would be to increase the estimated school resource effects. It is not particularly surprising to find rather small effects of school resources for a country such as Denmark, with a very high level of school resources by international standards (OECD, 2003), as one may expect a concave relation between pupil outcomes and the amount of school resources per pupil. In addition, reducing inequalities in society is a high priority in Denmark, and this may make it difficult to observe a sizeable positive relation between school inputs and outputs even if a large causal effect exists. Even for the Danish system, however, the estimates suggest that school resource effects are considerably larger for pupils from disadvantaged backgrounds than for the average pupil. Equality considerations might therefore also be economically efficient.

REFERENCES

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Gundlach, E., Wo¨ssmann, L. and Gmelin, J. (2001). ‘The decline of schooling productivity in OECD countries,’ Economic Journal, 111, pp. C135–47. Hanushek, E. A. (1986). ‘The economics of schooling: production and efficiency in public schools,’ Journal of Economic Literature, 24, pp. 1141–77. Hanushek, E. A. (1996a). ‘School resources and student performance’, in Burtless, G. (ed.), Does Money Matter? The Effect of School Resources on Student Achievement and Adult Success, Washington, DC: Brookings Institution Press. Hanushek, E. A. (1996b). ‘Measuring investment in education,’ Journal of Economic Perspectives, 10(4), pp. 9–30. Heckman, J., Layne-Farrar, A. and Todd, P. (1996). ‘Does measured school quality really matter? An examination of the earnings-quality relationship’, in Burtless, G. (ed.), Does Money Matter? The Effect of School Resources on Student Achievement and Adult Success, Washington, DC: Brookings Institution Press. Hedges, L. V. and Greenwald, R. (1996). ‘Have times changed? The relation between school resources and student performance’, in Burtless, G. (ed.), Does Money Matter? The Effect of School Resources on Student Achievement and Adult Success, Washington, DC: Brookings Institution Press. Hedges, L. V., Laine, R. D. and Greenwald, R. (1994). ‘Does money matter? A meta-analysis of studies of the effects of differential school inputs on student outcomes’, Educational Researcher, 23(3), pp. 5–14. Heinesen, E. (2004). ‘Determinants of local public school expenditure: a dynamic panel data model’, Regional Science and Urban Economics, 34, pp. 429–53. Hoxby, C. (1999). ‘The effects of class size on student achievement: New evidence from population variation’, Working paper, Harvard University and National Bureau of Economic Research. Krueger, A. B. (1999). ‘Experimental estimates of educational production functions’, Quarterly Journal of Economics, 114, pp. 497–532. Krueger, A. B. (2003). ‘Economic considerations and class size’, Economic Journal, 113, pp. F34–63. Krueger, A. B. and Whitmore, D. M. (2001). ‘The effect of attending a small class in the early grades on college-test taking and middle school test results: Evidence from project STAR’, Economic Journal, 111(January), pp. 1–28. Moulton, B. R. (1990). ‘An illustration of a pitfall in estimating the effects of aggregate variables on micro units’, Review of Economics and Statistics, 72(2), pp. 334–8. OECD. (2003). ‘Education at a Glance’, OECD Report, Paris. Todd, P. E. and Wolpin, K. I. (2003). ‘On the specification and estimation of the production function for cognitive achievement’, Economic Journal, 113, pp. F3–33. Wo¨ssmann, L. (2000). ‘Schooling resources, educational institutions, and student performance: The international evidence’, Working paper no. 983, Kiel Institute of World Economics.



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APPENDIX

Descriptive Statistics Descriptive statistics are summarized in the first column of Table A1. All family background variables are recorded at the time the child was 15 years old. The degree of unemployment (i.e., the fraction of the year a person is unemployed) is defined only for people in the work force. For persons not in the work force, the degree of unemployment is set to zero. In view of the lack of reliable income data for self-employed persons, income from employment is set to zero for the self-employed and a dummy for being self-employed is included in the estimations. An alternative specification would be to set the income of self-employed equal to the average income in their municipality, which would make better sense if the income of the self-employed varies with average income in the municipalities. We have tried this alternative specification, but it does not alter any results with respect to the effect of school resources. The percentages of self-employed among fathers and mothers are 19.3 and 11.7, respectively. Income, wealth (defined as taxable wealth) and school expenditure are measured at 1996 prices using a wage index. Correlation coefficients between municipal-level variables, both the controls and the four school resource variables, are summarized in Table A2.

Estimation Results The last two columns of Table A1 summarize the full estimation result for model 4 of Table 2 (in Section VI) with expenditure per pupil used as school resource measure. The symbols * and ** indicate significance at the 5 and 1 percent levels, respectively. At the bottom of the table are the log-likelihood value, pseudo R2, the mean of the dependent variable and the number of observations. It can be seen that most family background controls are highly significant and have the expected signs. Thus, growing up in a broken family or having many siblings have negative effects on educational attainment, whereas parents’ education level, income and wealth in general have positive effects on a child’s educational attainment. There are negative effects on child educational attainment if parents have a high degree of unemployment, receive social assistance or are not in the labour market. The point estimates for the categories ‘immigrant’ and ‘second generation immigrant’ are negative, but insignificant (which may be because only a very small share of the six cohorts analysed belongs to these groups). Relative to the youngest cohort, the estimated effects of the five older cohorts are positive, but # Blackwell Publishing Ltd and the Board of Trustees of the Bulletin of Economic Research 2005.

B

A

1 Number of siblings aged 0–17 1 Has younger siblings 1 Lives with single mother 1 Lives with mother and stepfather 1 Lives with single father 1 Lives with father and stepmother 1 Does not live with father or mother 1 (Father and mother live together)

(child not with parents) 1–4 Mother not in the register 1–4 Father not in the register 1 Teenage mother (at time of birth) 1 Teenage father (at time of birth)

Born in 1965 Born in 1966 Born in 1967 Born in 1968 Born in 1969 Female Immigrant Second generation immigrant

Variable

0.868 0.500 0.320 0.241 0.125 0.109 0.132 0.063 0.094 0.276 0.338 0.191

0.009 0.083 0.132 0.038

0.387 0.392 0.379 0.362 0.357 0.500 0.088 0.024

SD

0.793 0.502 0.116 0.062 0.016 0.012 0.018 0.004

0.184 0.189 0.173 0.156 0.150 0.495 0.008 0.001

Mean

0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

Minimum

1 1 1 1

12 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1

Maximum

0.021 0.034 0.068 0.074 0.138 0.146 0.134 0.163 0.148 0.083 0.034 0.059

0.003 0.399** 0.150** 0.150**

0.052 0.048 0.046 0.046 0.045 0.024 0.128 0.405

Robust SE

0.091** 0.230** 0.423** 0.494** 0.546** 0.612** 1.005** 0.037

0.029 0.068 0.161** 0.008 0.032 0.012 0.234 0.134

Coefficient

TABLE A1 Descriptive statistics for the explanatory variables (39,362 observations) and results from the logistic regression for the probability of having passed upper secondary school or a vocational education at the age of 25

138 BULLETIN OF ECONOMIC RESEARCH


2 Mother upper secondary school 2 Mother vocational education 2 Mother short further education 2 Mother long further education 2 Mother higher education 2 Mother’s education unknown 2 Father upper secondary school 2 Father vocational education 2 Father short further education 2 Father long further education 2 Father higher education 2 Father’s education unknown 3 Mother self-employed 3 Mother student 3 Mother receives social assistance 3 Mother not in the labour market 3 Father self-employed 3 Father student 3 Father receives social assistance 3 Father not in the labour market 3 Mother’s gross income from employment (in DKK 10,000) 3 Father’s gross income from employment (in DKK 10,000) 3 (Mother’s income)

(does not live with mother) 3 (Father’s income)

(does not live with father) 3 Mother’s degree of unemployment 3 Father’s degree of unemployment

0.091 0.461 0.242 0.207 0.096 0.317 0.099 0.486 0.195 0.248 0.196 0.298 0.322 0.067 0.110 0.349 0.394 0.034 0.072 0.201 9.857 18.166 2.974 8.381 18.495 15.647

0.008 0.306 0.062 0.045 0.009 0.113 0.010 0.382 0.040 0.066 0.040 0.099 0.117 0.005 0.012 0.142 0.192 0.001 0.005 0.042 11.447 19.764 0.425 2.188 6.027 4.692

0.000 0.000

0.000

0.000

0.000

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.000

100.000 100.000

226.100

53.314

657.900

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 115.549

0.002 0.001 0.001

0.006** 0.008**

0.006

0.002

0.168 0.029 0.059 0.080 0.198 0.048 0.143 0.033 0.075 0.073 0.087 0.056 0.060 0.191 0.109 0.048 0.059 0.321 0.123 0.048 0.002

0.000

0.002

0.009**

0.461** 0.432** 0.422** 0.585** 0.822** 0.233** 0.539** 0.315** 0.448** 0.600** 0.612** 0.149** 0.021 0.078 0.655** 0.275** 0.310** 0.093 0.335** 0.275** 0.004


139


C

Proportion of bilingual children (%) Rate of unemployment in the school municipality (%) Proportion with a vocational education (%) Proportion with a further or higher education (%)

3 (Mother’s degree of unemployment) (not with mother) 3 (Father’s degree of unemployment) (not with father) 4 Mother’s taxable wealth (in DKK 100,000) 4 Father’s taxable wealth (in DKK 100,000) 4 (Mother’s taxable wealth) (not with mother) 4 (Father’s taxable wealth)

(not with father) 4 Lives in rented dwelling 4 Lives in not categorized dwelling 4 Type of dwelling unknown 4 Number of rooms per person 4 Number of rooms per person unknown 4 Lives in socially deprived area

Variable

0.425 0.134 0.102 0.469 0.081 0.191

0.237 0.018 0.011 1.191 0.007 0.038

4.607

5.799

0.093

12.403

0.384

0.011

4.596

11.436

3.038

29.788

2.358

0.377

1.762 2.651

8.726

1.242

1.149 9.010

5.297

SD

0.438

Mean

Table A1 Continued

1097.610 18.108 1097.610

235.911 22.616 113.577

3.409

17.665

0.000 1.969

34.890

46.472

11.830 18.556

1 1 1 7.500 1 1

190.685

33.395

0 0 0 0.000 0 0

100.000

100.000

Maximum

0.000

0.000

Minimum

0.005

0.005

0.007 0.003

0.021 0.008

0.035 0.077 0.155 0.041 0.218 0.056

0.361** 0.145 0.423** 0.340** 0.561** 0.158** 0.050* 0.016

0.008

0.033

0.004

0.007

0.002

0.003

Robust SE

0.006

0.020

0.007

0.032**

0.008**

0.004

Coefficient



Expenditure per pupil in the municipality (in DKK 1,000) Teacher wage hours per pupil in the municipality (per week) Teacher lessons per pupil in the municipality (per week) Teacher lessons in normal classes per pupil in normal classes Regression diagnostics Pseudo-likelihood Pseudo R2 Mean of dependent variable Number of observations 0.115 0.066

1.473

13.072

5.831

1.750

13.542

7.277

0.182

8.644

5.024

2.152

8.634

7.358

4.867

15.363 16.187

73.871 16.487

29.966

5.427

11.271

1.295

1.441

1.696

21.802

0

0

0

0

45.378 0

2.850

1.850

2.153

2.906

46.702

70.000

91.000

55.000

58.000

157.027 77.000

30.890

0.003 0.002 0.001 0.001

0.005* 0.003 0.002 0.003**

–

–

–

21,306.715 0.089 0.718 39,362

–

–

–

0.006

0.002 0.002

0.006* 0.005*

0.017**

0.008

0.011

Notes: Model 4 of Table 2 with expenditure per pupil as school resource measure and the full set of controls. Robust standard errors are adjusted for clustering on school municipality at eighth grade. The reference category for cohort dummies is ‘born in 1970’, for family structure it is ‘lives with both parents’, for parents’ educational level it is ‘compulsory school’, for labour-market status it is ‘wage earner’, for type of dwelling it is ‘lives in owner-occupied dwelling’ and for urbanization variables it is ‘proportion living in towns with more than 5,000 inhabitants’.

D

Proportion of pupils from single-parent families Income per capita (at 1996 prices) Proportion living in rural areas (%) Proportion living in towns with 200–800 inhabitants (%) Proportion living in towns with 800–1,500 inhabitants (%) Proportion living in towns with 1,500–3,000 inhabitants (%) Proportion living in towns with 3,000–5,000 inhabitants (%)


141


1.00 0.14 0.14 0.37 0.50 0.38 0.26 0.16 0.10 0.03 0.11 0.12 0.18

1.00 0.37

0.46

0.09 0.60 0.25 0.23 0.12 0.13 0.08 0.33 0.24 0.25 0.12

1.00 0.11 0.06

0.18

0.80 0.40 0.49 0.41 0.30 0.24 0.18 0.67 0.46 0.40 0.26

0.34 0.73 0.50 0.42 0.26 0.16 0.12 0.36 0.27 0.19 0.05

1.00 1.00 0.55 0.73 0.61 0.44 0.36 0.23 0.73 0.55 0.45 0.25 1.00 0.69 1.00 0.58 0.74 1.00 0.38 0.53 0.29 1.00 0.28 0.34 0.22 0.11 1.00 0.23 0.23 0.17 0.02 0.11 0.64 0.42 0.36 0.24 0.23 0.53 0.33 0.28 0.22 0.22 0.46 0.22 0.20 0.17 0.17 0.23 0.08 0.03 0.07 0.01

1.00 0.20 0.17 0.12 0.04

1.00 0.79 0.72 0.63

1.00 0.95 0.69

1.00 0.76

Note: The variables are: The percentage of bilingual children from non-western countries; the unemployment rate; the percentage with a vocational education and the percentage with a further or higher education; the percentage of children from single-parent families; average income; the percentage living in rural areas, and the percentages living in towns with 200–800 inhabitants, 800–1500 inhabitants, 1500–3000 inhabitants and 3000–5000 inhabitants, respectively; school expenditure per pupil; teacher wage hours per pupil; teacher lessons per pupil; and teacher lessons in normal classes per pupil in normal classes.

Bilingual Unemployment Vocational education Further education Single Income Urbrural urb28 urb815 urb1530 urb3050 Expenditure Wage hours Lessons Lessons in normal classes

Vocational Further Wage Bilingual Unemployment education education Single Income Urbrural urb28 urb815 urb1530 urb3050 Expenditure hours Lessons

TABLE A2 Correlation coefficients for school resource variables and controls at municipal level




143

only one is significant. The estimated cohort effects may be caused by several underlying factors: changes over time in how common it is to take a year or two out of the education system after compulsory school, the effect of changes in the overall unemployment rate on incentives to stay in school and the difficulty in getting apprenticeships for persons entering vocational educations. Controls measured at the municipal level are in general less significant than controls for individual family background, although the proportion of bilingual children, income per capita and urbanization variables are all significant at the 5 percent level. A high proportion of bilingual pupils has a negative effect on educational attainment (given school expenditure and the other controls), which may reflect a negative peer group effect or the fact that it is more costly to teach bilingual pupils. If a high proportion of the population lives in rural areas or small towns (relative to the reference category of the proportion living in towns with more than 5,000 inhabitants) then the likelihood of obtaining a secondary education is smaller. One possible explanation is that schools are more costly in less densely populated areas, as schools and average class sizes are generally smaller, implying lower school quality given expenditure per pupil. Another explanation is that it is more costly in travel time for students in less densely populated areas to attend a secondary education. The coefficient of per capita income is negative, which is surprising since one would expect high average income to indicate positive peer group effects. There are several possible explanations for this result. First, if relative income of parents is important (in addition to absolute income), one may expect a negative effect of per capita income in the municipality, given individual parental income. Second, average municipal income may be positively correlated with income inequality, and this may have a negative effect on educational attainment through peer group effects and a non-homogenous teaching environment. Unfortunately, we have no measure of inequality of income at municipal level in the data set; hence, we have not been able to test this hypothesis. Finally, per capita income is positively correlated with urbanization (Table A2), which has a positive effect on educational attainment, hence the urbanization variables may encapsulate some positive non-linear effects of income per capita.
