IN
DEGREE PROJECT TECHNOLOGY, FIRST CYCLE, 15 CREDITS
,
STOCKHOLM SWEDEN 2016
Student performance drivers
An analysis of the declining performance of
Swedish middle school students
MARKUS BELLMAN
GUSTAF BLIDHOLM
Student performance drivers
An analysis of the declining performance of Swedish
middle school students
M A R K U S B E L L M A N G U S T A F B L I D H O L M
Degree Project in Applied Mathematics and Industrial Economics (15 credits) Degree Progr. in Industrial Engineering and Management (300 credits)
Royal Institute of Technology year 2016 Supervisors at KTH: Fredrik Armerin, Jonatan Freilich
Examiner: Henrik Hult
TRITA-MAT-K 2016:03 ISRN-KTH/MAT/K--16/03--SE
Royal Institute of Technology
SCI School of Engineering Sciences
KTH SCI
SE-100 44 Stockholm, Sweden URL: www.kth.se/sci
Abstract
The PISA reports presented between 2000 and 2013 display a sus-tained decline in the mathematics proficiency of Swedish middle school students. The latest OECD reports suggest that the downward trend is still present, whereby the aim of this thesis is to investigate its under-lying causes. Can the decline be deduced from the poor performance of specific Swedish municipalities with significantly worse results than others? By analyzing the current situation in Swedish education from a national standpoint, the intention is to derive the main factors for good overall math performance in middle school within a municipality. Moreover, the thesis aims to identify areas of possible enhancement within the Swedish education system on a municipal as well as a na-tional level, by analyzing how political financial decisions and society as a whole factor into student performance. Finally, the impact of education on aspects of macroeconomics is analyzed. It is arbitrated that several factors controllable by the government have significant impact on the average math performance of students in a Swedish municipality. The results from the analysis indicate that governmen-tal expenditures are better spent on quality of teaching than on the quantity of teachers present.
Sammanfattning
PISA-rapporterna publicerade mellan 2000 och 2013 p˚avisar en tydlig ned˚atg˚aende trend i matematikresultat f¨or svenska h¨ogstadieelever. Nya OECD-rapporter tyder p˚a att trenden alltj¨amt kvarst˚ar. Denna uppsats ¨amnar unders¨oka vilka anledningar som ligger bakom den neg-ativa utvecklingen. Kan nedg˚angen h¨arledas ur skolresultat i specifika kommuner med s¨amre resultat ¨an andra? Den nuvarande situatio-nen i den svenska skolan analyseras ur ett nationellt perspektiv, d¨ar kommuner j¨amf¨ors med varandra. M˚alet ¨ar att unders¨oka vilka hu-vudfaktorer som leder till bra skolresultat i en kommun. Vidare ¨ar ett m˚al att identifiera hur det svenska skolsystemet kan f¨orb¨attras p˚a b˚ade kommunal och nationell niv˚a med hj¨alp av politiska finansier-ingsbeslut, samt att analysera vilka faktorer hos samh¨allet i stort som p˚averkar skolresulaten. Slutligen analyseras utbildningens p˚averkan p˚a aspekter inom nationalekonomi ur ett makroperspektiv. Slutsat-sen dras att flera p˚averkbara faktorer har signifikant inflytande p˚a elevers genomsnittliga matematikprestation i en kommun. Dessutom konstateras att statliga utgifter skulle g¨ora mer nytta om man valde att satsa p˚a l¨ararnas kvalitet ist¨allet f¨or att satsa p˚a ett ¨okat antal l¨arare.
Contents
1 Introduction 1 1.1 Background . . . 1 1.2 Purpose . . . 1 1.3 Problem formulation . . . 2 1.4 Earlier research . . . 2 2 Regression Theory 4 2.1 Definitions and Terminology . . . 42.2 Ordinary least squares . . . 5
2.3 Possible OLS model errors . . . 6
2.3.1 Heteroskedasticity . . . 6 2.3.2 Endogeneity . . . 7 2.3.3 Multicollinearity . . . 8 2.3.4 Anomalies . . . 8 2.4 Model construction . . . 9 2.4.1 Types of covariates . . . 9
2.4.2 Hypothesis testing and confidence intervals . . . 9
2.4.3 Goodness of fit, R2 . . . 10
2.4.4 AIC and BIC . . . 11
2.4.5 VIF . . . 11
2.4.6 P-P Plot and histogram of standardized residuals . . . 12
3 Method 13 3.1 Scope . . . 13
3.2 Collection of data . . . 13
3.2.1 Detection of outliers . . . 14
3.4 Basic model . . . 19
3.5 Table of parameters . . . 19
4 Results 21 4.1 Presentation of data and its properties . . . 21
4.2 Basic model . . . 22
4.3 Reduced model . . . 25
4.3.1 Reducing the basic model . . . 25
4.3.2 Results from the reduced model . . . 26
4.4 Final model . . . 28
4.4.1 Interaction terms . . . 28
4.4.2 Statistics for choice of model . . . 28
4.4.3 Results . . . 29
5 Analysis 31 5.1 Initial analysis of the final model . . . 31
5.1.1 Goodness of fit . . . 31
5.1.2 Consistency of results with earlier reports . . . 32
5.2 Causes of municipal disparities . . . 33
5.3 Potential adjustments on governmental level . . . 38
5.4 Long term effects on macroeconomics . . . 40
List of Figures
1 Histogram of std. residuals . . . 24 2 P-P Plot . . . 24 3 Residual plot . . . 24 4 Histogram of std. residuals . . . 27 5 P-P Plot . . . 27 6 Residual plot . . . 27 7 Histogram of std. residuals . . . 30 8 P-P Plot . . . 30 9 Residual plot . . . 30List of Tables
1 Table of parameters . . . 202 Basic model: Goodness of fit . . . 22
3 Basic model: ANOVA . . . 22
4 Basic model . . . 23
5 Statistics for reduction . . . 25
6 Reduced model: Goodness of fit . . . 26
7 Reduced model: ANOVA . . . 26
8 Reduced model . . . 26
9 Statistics for creation of final model . . . 28
10 Final model: Goodness of fit . . . 29
11 Final model: ANOVA . . . 29
1 INTRODUCTION
1
Introduction
1.1
Background
In Swedish politics today, education is one of the most discussed themes. Ar-guably student performance could be significantly influenced by the financing and economic decisions of political parties. The PISA reports presented be-tween 2000 and 2012 showed a continuous decline in the mathematics perfor-mance of Swedish middle school students [1]. Recent reports from the OECD suggests further decline since 2013 and the upcoming results from the 2015 PISA test are expected to confirm the indication [2]. Considering that Swe-den is one of the more economically developed countries in the world, the reports raise several questions. Is the quality of education in Sweden defi-cient or is there a general lack of knowledge and devotion among students? Quality of education and school results are two crucial factors for future de-velopment in a country [3]. Hence, it is of utter importance for Sweden to resolve the current situation.
1.2
Purpose
The goal of this thesis is to derive the main factors for good overall perfor-mance of middle school students within a region. Moreover, an aim is to determine influential factors for mathematics performance within school pol-itics and societal attributes. This is to be used for identification of possible areas of enhancement in the Swedish education system on both national and municipal levels.
This thesis can in many ways be viewed from the perspective of industrial economics and management. Primarily, the topics of finance and macroeco-nomics will be focused on. The report investigates potential future conse-quences of decreasing student performance for the nation as a whole. The
purpose of the investigation in regards to industrial engineering is to provide an analysis on how the downward trend in results of Swedish students may affect future Swedish economy. The regression provides a groundwork for the performance drivers of students in the country, where a sub target is to identify how financing of education in Sweden can be improved.
1.3
Problem formulation
The intent is to investigate the following matters:
• What are the main drivers of student mathematics performance on a municipal level?
• Do local political decisions significantly affect student mathematics per-formance and contribute to municipal disparities?
• From a macro economical point of view, how can financing of education be improved on a governmental level and what are the potential future effects of the decreasing student performance?
1.4
Earlier research
Literature referred to in this analysis was mostly acquired from the OECD or the Swedish National Agency for Education. The OECD are responsible for PISA studies and their collected data is often used for international investi-gation. The Swedish National Agency for Education conducts the Swedish national tests and presents most of specific data on the Swedish education system. Since both institutions perform studies regarding education on dif-ferent levels, it could be interesting to compare their documented results. As mentioned, the objective of this study is to conduct an analysis on munic-ipal level, which gives an opportunity to compare results on three levels of
1.4 Earlier research 1 INTRODUCTION
education analysis. To specify, the municipal level results will be compared with international studies and individual student performance analysis. Studies from the OECD present the effects of socioeconomic factors on school performance, where they suggest that 50% of the variance in school re-sults can be deduced from student background such as parental educational level and income [4]. The Swedish National Agency for Education further strengthens this claim in a report regarding the impact on school performance of factors such as school politics and student background [5]. These are two central reports for this analysis. Furthermore, another OECD study (2015) suggests that the quality of teaching needs to be improved in Sweden. It suggests that previous investments made in the country’s education system have aimed to increase the quantity of teachers instead of the quality [2]. Regarding education’s return to macroeconomics, several studies have been presented throughout the past years. Sianesi and Van Reenen [6] present a merged analysis of numerous reports on education’s returns to society from the 20th century. Their main point is how school enrolment in a nation impact the GDP which is relevant for this analysis of student performance. Furthermore, Bassanini and Scarpetta [7] discusses the same theme in their report but with emphasis on average schooling years’ return to GDP. Ad-ditionally, a report written by Hanushek and Woessmann on behalf of the OECD provides an international comparison on education’s return to eco-nomic growth. Through a scenario analysis they present potential future effects of improved PISA results. For example, it is presented that a 25 point increase in PISA results would hypothetically lead to a 400% increase in GDP until 2090 [8].
In this paper, results of the regression analysis will be compared to above conclusions drawn in previous reports. To motivate choice of method; re-gression is often used in educational research. The OECD and the Swedish National Agency for Education use regression analysis frequently as a tool in their reports. Hence, the conclusion is drawn that the method is also relevant for use in this investigation.
2
Regression Theory
2.1
Definitions and Terminology
A general multiple variable regression model is specified as
yi =
k
X
j=0
xijβj+ εi i = 1, 2, ..., n (1)
or similarly, the regression model in matrix form
Y = Xβ + ε (2) where Y = y1 .. . yn , X = 1 x11 . . . x1k .. . ... . .. ... 1 xn1 . . . xnk , β = β0 .. . βk , ε = ε1 .. . εn
The terminology and symbols used are explained below.
• yi is a dependent variable, the variable to be explained by the model.
• xij are independent variables, or covariates. The dependent variable is
modeled as a function of the covariates.
• βj are the coefficients to be determined by which the dependent variable
depends on each of the covariates.
• εi is the error term, or residual. The error term is the difference in
actual value and the value predicted by the model. • n is the number of observations.
2.2 Ordinary least squares 2 REGRESSION THEORY
• k is the number of explanatory variables.
• x0 is set to 1 hence β0 can be regarded as the equation intercept; the
value of y when the remaining covariates are all 0.
2.2
Ordinary least squares
An ordinary least squares estimation minimizes the sum of the squared resid-uals. The estimated beta values are acquired from the from the equation
ˆ
Y = X ˆβ (3)
where ˆY = Y + e is the OLS estimate of Y and e is the estimator of the
residuals ε. The ˆβ that minimizes the squared residuals can be derived from
the normal equations
XTe = 0 (4)
to be calculated as
ˆ
β = (XTX)−1XTY (5)
Here ˆβ is denoted the ordinary least squares approximation of β which, as
described above, minimizes the sum of the squared error terms. This is the best choice of linear model for the data since it is known to be the best linear unbiased estimator. [9]
Assumptions for OLS estimation:
• The covariates do not in any way show perfect multicollinearity.
• The expected value of the residuals is 0, E(εi)= 0.
• The variance of the residuals is constant.
• The residuals are normally distributed and not correlated.
• Repeated sampling generates the same estimates, whereby covariates can be viewed as deterministic.
2.3
Possible OLS model errors
2.3.1 Heteroskedasticity
When the residuals in a regression have a constant variance, data is said to show homoskedasticity. Alternatively, if the variances of the residuals differ there is instead heteroskedasticity. Since it is assumed that the variance in er-ror terms is constant for ordinary least squares estimation, heteroskedasticity is to be avoided. There are some remedies for this.
Commonly, the residuals tend to scale with the size of the dependent variable, causing heteroskedasticity [10]. In a comparison between two municipalities, it may therefore be beneficial to use a per capita measurement of a statistic rather than statistics for an entire municipality. This takes into consideration the fact that one municipality might just have a greater population, and can remedy the problem of heteroskedasticity.
Another possible solution that can be applied to a heteroskedastic data set is logarithmization of the dependent variable. This can work since logarithmiz-ing the dependent variable transforms the nominal data into percentages that
2.3 Possible OLS model errors 2 REGRESSION THEORY
do not display the same spread of residuals. Finally, heteroskedasticity often occurs when there is a large difference among the sizes of the observations so this should be avoided.
Should it be necessary, a Breusch-Pagan test can be employed to identify and avoid heteroskedasticity. Also, the residuals can be plotted against the corresponding fitted values to check whether the necessary conditions for homoskedasticity are met. The residuals should then indicate a constant variance for all fitted values. Analyzing the plot of the residuals is commonly referred to as the Eyeball method.
2.3.2 Endogeneity
Endogeneity occurs when one of the explanatory variables, a covariate, is correlated with the error term. In cases of endogeneity the ordinary least squares estimator is biased and inconsistent. Therefore the results of hy-pothesis testing on estimators are invalid. Some common causes of this are omitted variables, sample selection bias and erroneous measurement.
• Bias due to omitted variables occurs as a result of the over- or under-estimation of some factors when the model compensates for missing variables.
• Sample selection bias means that the data does not properly illustrate the characteristics of analyzed population hence the estimated β-values are incorrect.
• Systematic measurement error in independent variables becomes part of the error term in the regression equation resulting in endogeneity.
2.3.3 Multicollinearity
Multicollinearity is the issue of correlation between two or more covariates in a multiple variable regression, meaning there is an approximate linear dependence between them. Typically the remedy for multicollinearity is to increase the number of data points.
Furthermore, some covariates may need to be removed from the model. It is then of great importance to choose the appropriate covariate(s) to exclude. Methods for determining which variables are to be excluded are discussed later in this report.
The linear relationship between one or several covariates is more of an in-convenience than a specification error [9]. It causes the standard deviations of estimated β-values to become larger and thereby the point estimates of β-values are more imprecise. Consequently the research conclusions that can be drawn may be limited.
2.3.4 Anomalies
In a regression analysis, points in the data set that are significant outliers may cause inaccuracy in the approximated model. Therefore, the data set must be inspected to identify and possibly remove such points.
Before removal of data, its significance will be investigated. For example, an observation that is obviously incorrect will be removed whilst other suspected outliers might need further examination before removal. Here potential oper-ations include transformation of the variable in question such as calculating its square root or logarithmizating it. Any influential operations will be reported of when appropriate in the report.
2.4 Model construction 2 REGRESSION THEORY
2.4
Model construction
2.4.1 Types of covariates
• Dummy variables only take on values of 0 or 1. For example, a possible set of dummies could be acquired from a race variable, where only the dummy for a specific person’s race would be 1, and all others 0. • Quantitative covariates are variables that take on the observed value. • Interaction terms are indicators of synergy effects between variables.
An interaction variable with a significant impact indicates that there such an effect from two covariates being present simultaneously.
2.4.2 Hypothesis testing and confidence intervals
To test the statistical significance of one or more estimated β-values, an F-test can be applied. The null hypothesis that one or more of the β-coefficients are 0 is then tested against the alternative hypothesis that at least one of the coefficients is non-zero. The test variable for the F-test, namely the F-statistic, is calculated by F = ˆβ j− ˆβj0 SE( ˆβj) !2 (6) where ˆβ0
j is 0 in the case relevant to this report and SE( ˆβj) is the standard
error for ˆβj. The corresponding p-value is then
where Z ∈ F (1, n − k − 1) and the null hypothesis is rejected if p < α, and α is the selected significance level. A rejection of the null hypothesis provides significant evidence of non-zero test variable(s). An assumption for the F-test is that the residuals are normally distributed. [9]
A confidence interval for βj at level 1 − α is then
ˆ
βj±
p
Fα(1, n − k − 1)SE( ˆβj) (8)
To clarify the usage of F-tests in this paper, the case of testing one variable in an F-test can also be viewed as a student’s t-test. The relationship between
the F and t-statistics is in that case F = t2.
2.4.3 Goodness of fit, R2
The coefficient of determination R2 measures the goodness of fit and thereby
to what extent the data is explained by the model. It is defined as
R2 = SSreg
SStot
= 1 − SSres
SStot
(9)
where SSreg is the sum of squares due to regression, SStot the total sum
of squares and SSres the sum of squares of the residuals. Minimizing the
residuals gives the model a better goodness of fit. However, the goodness of fit always increases with the addition of more explanatory variables due to its
nature. The adjusted R2also takes the number of covariates in the model into
account. This allows for taking the model complexity into account with the
goodness of fit measurement. With a given R2, the adjusted R2 is calculated
by
¯
R2 = 1 − (n − 1)(1 − R
2)
2.4 Model construction 2 REGRESSION THEORY
2.4.4 AIC and BIC
Akaike Information Criterion and Bayesian Information Criterion provide ways to choose which variables are to be included in a model. They are measurements of the relative quality of different models for a defined data set. AIC = n ln(SSres) + 2k (11) BIC = ln(SSres k ) + ln(k) n + 1 k (12)
where n is the number of observations and k the number of explanatory variables. The goal is to minimize the above criteria. Unlike the coefficient of determination, AIC and BIC penalize the addition of more covariates in the model.
When comparing two models, the changes in AIC and BIC are calculated as
∆AIC = AIC∗− AIC (13)
∆BIC = BIC∗− BIC (14)
where the asterisks denote the variables attributed to a reduced model, and the unmarked variables represent the full model.
2.4.5 VIF
The variance inflation factor, commonly abbreviated VIF, quantifies the severity of collinearity of each covariate in ordinary least squares estima-tion. The calculated value is a measurement of how much the variance of the estimated β-coefficients has increased due to multicollinearity.
To calculate VIF for a covariate Xi, a regression is ran on Xi as a function
of all the remaining covariates. Then
V IF ( ˆβi) =
1
1 − R2
i
(15)
where R2i is the coefficient of determination calculated as showed in section
2.4.3. The collinearity is significant if 5 < V IF ( ˆβi) < 10 and should be
considered severe if V IF ( ˆβi) > 10. [11]
2.4.6 P-P Plot and histogram of standardized residuals
A P-P Plot and a histogram of standard residuals are commonly used to confirm or contradict the assumption of normally distributed residuals. The P-P Plot is used to investigate how well a theoretical distribution matches the distribution of an observed data set. It is not to be confused with the more widely used Q-Q Plot. However, both methods are used for the same purpose. While the Q-Q Plot compares the quantiles of two probability distri-butions the P-P Plot instead compares the cumulative distribution functions. The only difference when interpreting the plots is that a P-P Plot magnifies the deviations in the middle while a Q-Q Plot magnifies the deviations in the tails. [12]
To show normal distribution the histogram is ought to align with a Bell curve and the formation in the P-P Plot should be linear (x = y) to further establish the presumption.
3 METHOD
3
Method
Multiple variable regression models were used to critically analyze and de-scribe the reasons behind the trends in performance of Swedish middle school students. The regressions were performed using SPSS Statistics.
3.1
Scope
This thesis encompasses a comparison between all 290 Swedish municipalities and their data for selected variables. The decision to include all municipal-ities in the analysis instead of counties for example was based on regression analysis theory to avoid multicollinearity. The scope is reasonable since mu-nicipal level is the most detailed state in which local governmental politics can still differ. Scoping out could mean looking at county level and scoping in could imply a comparison between specific schools. Neither of the mentioned scopes would add significance to the analysis, since analysis on county level could result in multicollinearity and an analysis on school level would have to include significantly more specific covariates. This would have less relevance for the problems addressed by this thesis. Private schools were excluded from the analysis as their general financing is not similarly connected to decisions and regulations on municipal or governmental level.
3.2
Collection of data
The quantitative data used in the regression analysis was mainly collected from the official web page of the Swedish National Agency for Education, their web page for data and statistics, SIRIS, and the website of the Cen-tral Bureau of Statistics. The collected data was recorded for school year 2014/2015 and reported in September 2015. Since data presented at these governmental websites are to be considered state papers there is no reason for
source criticism regarding the authenticity of data. This further establishes the premise that it is the selection of variables, rather than the retrieval of data itself, that will affect the quality of the analysis.
3.2.1 Detection of outliers
Outliers in this case could be municipalities with an insignificant amount of data. For example, a municipality with only one math teacher can obtain either 100 or 0 percent certified math teachers. That data was considered insignificant as the amount of data for the municipality was insufficient. Outliers in the collection of data were primarily detected within the area of expenditure allocation in the municipalities. Two municipalities were de-termined to be excluded from the data collection as their numbers were unreasonable in relation to remaining municipalities.
• Dorotea was excluded from the regression due to anomalies in the data set. The really small population in combination with unreasonable numbers led to the conclusion that the municipality was to be excluded. • Nykvarn was excluded from the regression due to anomalies in the data set. Nykvarn’s allocation of expenditures was remarkably different to all other municipalities. Nykvarn’s expenditures were all collected un-der the category other instead of showing the actual allocation between different categories.
3.3
Selection of variables
When deciding what variables to include in the regression model the potential issues presented in the theory section were considered. Choosing variables
3.3 Selection of variables 3 METHOD
has to be regarded as an essential part of regression analysis since it will determine the significance of the outcome of the model. Therefore, deter-mining a response variable as well as covariates required a thorough analysis of potential choices and their issues regarding for example collinearity. Earlier reports presented by administrative authorities were taken into consideration when choosing variables to include [5][13].
3.3.1 Response variable
National test results in mathematics
The chosen response variable in this regression analysis was the national test score for ninth grade students. This was the most prominent response variable available for judging student performance. The national tests are centrally created tests that intend to investigate whether students meet the expectations put up by the National Agency for Education.
Alternatives such as looking at students’ grades could be inconsistent since
requirements for grading could differ between schools. Examinations are
likewise probable to differ individually between teachers. Hence, one cannot be certain that final grades are a fair measure of mathematical knowledge.
3.3.2 Explanatory variables
There were several explanatory variables that could possibly enhance the re-gression model and the aim was to include the most significant ones while avoiding common regression errors such as multicollinearity. The basic model includes as many reasonable explanatory variables as possible, some of which are removed when reducing the model. Hence this section presents all the contemplated variables in the basic model while variables shown to be insuf-ficient will be ignored once the final model is determined.
The following variables were chosen for the basic model: Average yearly income in municipality
The Average yearly income in municipality was included to represent the financial status of the inhabitants of the municipality. The variable encom-passes the average salary of all individuals in the municipality and not only the salary of students’ parents. This variable is included to contribute with a quantitative index of the general socioeconomic status of the inhabitants in each municipality.
Students per teacher
A commonly discussed factor for school performance is the Students per teacher index. Having few teachers per student is said to affect student performance negatively and the issue of schools’ lack of personnel is often pronounced in media.
Left wing rule
Left wing rule is an indicator variable that states if a municipality is run by a left wing local government. This variable was employed as the benchmark variable for political ruling.
Right wing rule
Right wing rule is an indicator variable that states if a municipality is run by a right wing local government.
Mixed rule
Mixed rule is an indicator variable that states if a municipality is run by a mixed local government.
3.3 Selection of variables 3 METHOD
Political minority
Political minority is an indicator variable that states if a municipality is run by a local government in minority.
Education expenditures per student
Education expenditures per student is each municipality’s expenditures on education, per student. This mainly includes teacher salaries.
Property expenditures per student
Property expenditures per student is each municipality’s expenditures on properties, per student. Included is expenditures for buildings, janitors and cleaning personnel.
Food expenditures per student
Food expenditures per student is each municipality’s expenditures on food, per student.
Material expenditures per student
Material expenditures per student is each municipality’s expenditures on ma-terial, per student. This includes literature, computers, software, journals and other tools for education.
Health expenditures per student
Health expenditures per student is each municipality’s expenditures on health, per student.
Certified math teachers
The intention with this thesis is to investigate the reasons behind the decrease in performance specifically within the area of mathematics. Certified math teachers was included in the model to represent the teachers’ importance for student performance. One could think that certified teachers within the specific subject is a requirement, but according to data that is not the case on middle school level.
Teachers with educational college degree
A teacher’s knowledge within the specific subject is obviously important for educational purposes, but the knowledge is somewhat useless if a teacher lacks the ability to actually teach. Hence, Teachers with educational college degree was included in the model to add a factor of teachers’ capability to teach their subject.
Students with post-secondary educated parents
It is reasonable to believe that parents’ academical background generally affects the performance of their children. If there is a tradition of higher education in the family, presumably the student has grown up with expec-tations to pursue higher education as well. Post-secondary educated parents was added to the model to represent the proportion of students whose parents have obtained a degree from higher education.
Foreign students
Despite not necessarily true, one could argue that students with foreign back-ground can face additional challenges in Swedish school due to linguistic difficulties. A proportion variable, Foreign background, was included in the
3.4 Basic model 3 METHOD
model to investigate whether this has an effect on the performance in the national tests in mathematics.
3.4
Basic model
The variables described in the previous section were used in the basic regres-sion model.
TestScore = β1+ β2(AvgIncome) + β3(StudP erT each) + β4(P olRight) +
β5(P olM ix) + β6(M inority) + β7(CostEdu) + β8(CostP rop)
+ β9(CostF ood) + β10(CostM aterial) + β11(CostHealth) +
β12(CertT each) + β13(T eachEduDeg) + β14(EduP arents) +
β15(F oreign) + β16(P rivate) + β17(F emale)
(16)
3.5
Table of parameters
A summarizing table of all the variables in the basic model was constructed. Here, quantitative variables are presented with their unit.
Table 1: Table of parameters
Variables Variable type Unit/value
Response variable
National test mathematics score Quantitative Pts.
Explanatory variables
Average yearly income in municipality Quantitative kSEK
Students per teacher Quantitative Nr
Right wing rule Dummy 0 or 1
Mixed rule Dummy 0 or 1
Political minority Dummy 0 or 1
Education expenditures per student Quantitative kSEK
Property expenditures per student Quantitative kSEK
Food expenditures per student Quantitative kSEK
Material expenditures per student Quantitative kSEK
Health expenditures per student Quantitative kSEK
Certified math teachers Proportion %
Teachers with educational college deg. Proportion %
Post-secondary educated parents Proportion %
Foreign students Proportion %
Students in private schools Proportion %
4 RESULTS
4
Results
4.1
Presentation of data and its properties
A number of graphs were compiled to justify the presumption of normally distributed residuals. The included graphs are the following:
• Histogram displaying the distribution of standardized residuals • P-P Plot of the cumulative distribution for standardized residuals • Scatter plot of standardized residuals vs. standardized predicted value
To show normal distribution, the histogram is ought to align with a Bell curve and the formation in the P-P Plot should be linear to further establish the presumption.
The scatter plot was conducted for visual inspection, a method commonly referred to as the eyeball method. The plot provides a simple way of identi-fying patterns in the data. A systematic pattern in the scatter plot is a sign of heteroskedasticity.
The Variance Inflation Factor (VIF) was acquired to identify potential issues regarding multicollinearity. As presented in the theory section a VIF that exceeds a value of ten implies severe multicollinearity whereas a VIF below five indicates little or no multicollinearity. A VIF value between five and ten indicates that multicollinearity is present and should be further investigated. All of the graphs and data mentioned above will be presented for each of the models to continuously confirm or contradict the central presumptions of OLS estimation.
4.2
Basic model
The 16 covariates were entered into the basic regression model. The acquired results are listed in table format below.
Table 2: Basic model: Goodness of fit
R R2 Adjusted R2 Std. Error of Estimate
0,644 0,415 0,380 1,098
The goodness of fit R2 for the basic model was 0,415 indicating that it
ex-plains roughly 41,5% of the average mathematics national test result for a
municipality. The adjusted R2 was 0,380 and the standard error of the
esti-mate was 1,09785.
Table 3: Basic model: ANOVA
Sum of Squares df Mean Square F p-val
Regression 231,273 16 14,455 11,993 0,000
Residual 326,630 271 1,205
Total 557,903 287
The ANOVA table shows statistical significance of the model with a p-value
4.2 Basic model 4 RESULTS
Table 4: Basic model
Unstd. Coeff. Std. Coeff. t p-val 95,0 % Conf. Int. β Std. Error β Lower Upper VIF (Constant) 10,175 0,129 78,874 0,000 9,921 10,429
Average yearly income in municipality 0,012 0,004 0,312 3,521 0,001 0,005 0,019 3,624 Students per teacher 0,103 0,081 0,086 1,269 0,206 -0,057 0,264 2,103
Right wing rule 0,244 0,175 0,081 1,398 0,163 -0,100 0,588 1,555 Mixed rule 0,069 0,172 0,023 0,400 0,690 -0,269 0,406 1,595 Political minority -0,095 0,149 -0,032 -0,640 0,523 -0,389 0,198 1,158
Education expenditures per student 0,034 0,014 0,139 2,401 0,017 0,006 0,061 1,543 Property expenditures per student 0,028 0,018 0,076 1,545 0,124 -0,008 0,064 1,126 Food expenditures per student 0,016 0,054 0,016 0,290 0,772 -0,091 0,122 1,419 Material expenditures per student 0,054 0,043 0,060 1,249 0,213 -0,031 0,140 1,082 Health expenditures per student 0,150 0,066 0,114 2,265 0,024 0,020 0,280 1,170
Certified math teachers 0,032 0,009 0,202 3,535 0,000 0,014 0,050 1,515 Teachers with educational college deg. 0,005 0,017 0,017 0,276 0,783 -0,028 0,038 1,671 Post-secondary educated parents 0,040 0,011 0,311 3,678 0,000 0,019 0,062 3,299 Foreign students 0,012 0,009 0,072 1,311 0,191 -0,006 0,031 1,411 Students in private schools -0,011 0,007 -0,088 -1,522 0,129 -0,026 0,003 1,540 Female students 0,026 0,041 0,030 0,628 0,531 -0,055 0,107 1,047
The 16 variable basic model results were used to create three graphs, whose purposes are introduced at the beginning of the results section.
Figure 1: Histogram of std. residuals Figure 2: P-P Plot
Figure 3: Residual plot
The graphs indicate that none of the relevant conditions for the normal distri-bution of errors have been violated. In addition, conditions for homoskedas-ticity are met.
4.3 Reduced model 4 RESULTS
4.3
Reduced model
Next, the removal of non-significant variables was considered in an attempt to reduce the complexity of the model.
4.3.1 Reducing the basic model
To identify and exclude non-significant variables AIC and BIC were calcu-lated. Also, t-tests were performed. An individual decision was made on whether to remove a variable after each step in the removal process. The
values considered were primarily the changes in AIC, BIC and adjusted R2
when one variable was removed. Below the reduced variables are presented together with relevant test statistics.
Table 5: Statistics for reduction
Covariate removed Covariates SS Res AIC ∆AIC BIC ∆BIC Adj. R2 ∆Adj. R2
(Basic) 16 326,630 1699,182 - 0,460 - 0,380 -Uni deg 15 326,722 1697,263 -1,919 0,441 -0,019 0,382 0,002 Food exp 14 326,842 1695,369 -1,894 0,421 -0,019 0,384 0,002 Mixed rule 13 327,047 1693,549 -1,819 0,402 -0,019 0,386 0,002 Female students 12 327,483 1691,933 -1,616 0,384 -0,018 0,387 0,001 minority 11 328,111 1690,485 -1,448 0,366 -0,018 0,388 0,001 foreign 10 329,812 1689,974 -0,511 0,352 -0,014 0,387 -0,001 Mats exp 9 331,935 1689,822 -0,152 0,339 -0,013 0,386 -0,001 Private schools 8 334,008 1689,615 -0,207 0,325 -0,013 0,384 -0,002 Property exp (Final model) 7 336,141 1689,448 -0,167 0,312 -0,013 0,382 -0,002
Furthermore the removal of additional statistically less significant variables
was attempted. However, further reduction would either cause negative
changes in at least two of the monitored criteria, or the removal of a variable with vital importance to the investigation.
4.3.2 Results from the reduced model
Table 6: Reduced model: Goodness of fit
R R2 Adjusted R2 Std. Error of Estimate
0,630 0,397 0,382 1,095
As can be seen, the above table shows a slightly lower goodness of fit
com-pared to that of the basic model. However, the adjusted R2 has increased
slightly due to the reduced number of covariates included in the regression.
Table 7: Reduced model: ANOVA
Sum of Squares df Mean Square F p-val
Regression 221,763 7 31,680 26,389 0,000
Residual 336,141 280 1,201
Total 557,903 287
Table 8: Reduced model
Unstd. Coeff. Std. Coeff. t p-val 95,0 % Conf. Int.
β Std. Error β Lower Upper VIF
(Constant) 10,182 ,079 128,599 0,000 10,026 10,338
Average yearly income in municipality 0,011 0,003 0,269 3,231 0,001 0,004 0,017 3,217
Students per teacher 0,081 0,077 0,067 1,049 0,295 -0,071 0,232 1,890
Right wing rule 0,196 0,148 0,065 1,325 0,186 -0,095 0,488 1,123
Education expenditures per student 0,035 0,014 0,144 2,535 0,012 0,008 0,062 1,505 Health expenditures per student 0,145 0,063 0,110 2,297 0,022 0,021 0,270 1,076
Certified math teachers 0,030 0,008 0,189 3,917 0,000 0,015 0,045 1,084
4.3 Reduced model 4 RESULTS
Figure 4: Histogram of std. residuals Figure 5: P-P Plot
Figure 6: Residual plot
Again, the graphs indicate that none of the relevant conditions for the normal distribution of errors have been violated. Also conditions for homoskedastic-ity are met.
4.4
Final model
4.4.1 Interaction terms
To further improve the model, adding interaction terms was considered. An
exploratory approach was used to search for potential additions. It was
found that some variables showed this multiplicative factor of impact on the response variable. Those were then added to the model, as seen in the tables below.
4.4.2 Statistics for choice of model
Table 9: Statistics for creation of final model
Covariate removed Covariates SS Res AIC Delta AIC BIC Delta BIC Adj R2 Delta Adj R2 (Basic) 16 326,630 1699,182 - 0,460 - 0,380 -(Reduced) 7 336,141 1689,448 -9,734 0,312 -0,148 0,382 0,002 (Final with int. var.) 10 318,349 1679,786 -9,662 0,316 0,004 0,409 0,027
Regarding choice of model, it was decided that the model including three interaction effects was to be used. The choice was made by inspection of the above table. Here, we see a significant decrease in AIC when compared to the
remaining models, and a high value for adjusted R2. Finally, the Bayesian
Information Criterion increases by a small amount. This however is relatively small percentage increase in comparison with the other variables’ respective change in desired direction.
4.4 Final model 4 RESULTS
4.4.3 Results
Table 10: Final model: Goodness of fit
R R2 Adjusted R2 Std. Error of Estimate
0,655 0,429 0,409 1,07204
Table 11: Final model: ANOVA
Sum of Squares df Mean Square F p-val
Regression 239,555 10 23,955 20,844 0,000
Residual 318,349 277 1,149
Total 557,903 287
Table 12: Final model
Unstd. Coeff. Std. Coeff. t p-val 95,0 % Conf. Int.
β Std. Error β Lower Upper VIF
(Constant) 10,041 0,086 117,357 0,000 9,872 10,209
Students per teacher 0,136 0,077 0,113 1,772 0,077 -0,015 0,287 1,958
Average yearly income in municipality 0,009 0,004 0,215 2,425 0,016 0,002 0,015 3,814
Right wing rule 0,212 0,145 0,071 1,465 0,144 -0,073 0,498 1,125
Education expenditures per student 0,035 0,014 0,143 2,484 0,014 0,007 0,062 1,615 Health expenditures per student 0,138 0,062 0,105 2,231 0,026 0,016 0,260 1,079
Certified math teachers 0,032 0,008 0,205 4,091 0,000 0,017 0,048 1,218
Post-secondary educated parents 0,039 0,010 0,298 3,798 0,000 0,019 0,059 2,984 Education Expend. * Students/teacher -0,021 0,008 -0,136 -2,747 0,006 -0,036 -0,006 1,187 Educ. parents * Cert. Math Teachers 0,001 0,001 0,093 1,862 0,064 0,000 0,003 1,209 Educ. parents * Students in priv. school 0,001 0,000 0,118 2,245 0,026 0,000 0,002 1,351
Figure 7: Histogram of std. residuals Figure 8: P-P Plot
Figure 9: Residual plot
The graphs for the final model also show that none of the relevant conditions for the normal distribution of errors have been violated and that conditions for homoskedasticity are met.
5 ANALYSIS
5
Analysis
5.1
Initial analysis of the final model
The underlying factors and their significance were analyzed through exami-nation and interpretation of the final model and the results presented in the previous section. The reduction of the model determined that Students per teacher, Average yearly income, Right wing rule, Education expenditures per student, Health expenditure per student, Certified math teachers and Post-secondary educated parents, have a positive effect on ninth graders’ national test scores in mathematics.
5.1.1 Goodness of fit
The reduced model showed a relatively low coefficient of determination of 0,4. This is reasonable since the lower coefficient of determination partially comes from the inevitable exclusion of unquantifiable yet relevant variables. Additionally, some variables cannot be included due to the unavailability of relevant statistical data.
One example of an important factor without official data presented is middle school truancy rate. Presumably, the truancy rate is a relevant measurement of students’ motivation to study and learn. This could potentially have sig-nificant impact on school performance. Likewise, the definitive teacher salary numbers based on municipality were unattainable. The variable education expenditures per student includes the amount money spent on teaching (per student), but it does not serve as an index of quality as would have been the preference. For this purpose, an average teacher wage variable could be relevant.
It is important to realize that school performance is not limited to external factors only. In fact, the conditions under which students perform well in
school are extremely individual, in particular within the subject of mathe-matics. While impossible to quantify, variables such as general smartness or logical thinking would probably leave a significant remark if they were to be included in the regression. It is reasonable to assume that these are partially correlated with parents’ level of education; a variable included in the model. There are several other variables that are difficult to quantify, for exam-ple the students’ willingness to study and the students’ ability to motivate and assist each other. These align with classroom environment which is an-other presumably significant unquantifiable factor. The exclusion of variables with explanatory power will naturally decrease the explanatory power of the model.
The variables included in the final reduced model are the most significant fac-tors for average ninth grade national test scores in mathematics. However, variables without statistically significant effect are also to be considered for analysis purposes as the exclusion of a variable could be just as interesting as the inclusion of another. This is especially true for frequently discussed factors that are determined to have no statistically significant effect in con-tradiction to general belief.
5.1.2 Consistency of results with earlier reports
The results gathered show many similarities when compared to those of pre-vious investigations on the topic of educational performance and its returns to society. Initial thoughts were centered around that the acquired results further support research on the impact of socioeconomic factors as well as teaching factors.
Socioeconomic factors
As was discussed above, the analysis demonstrates that socioeconomic fac-tors such as Average yearly income and Post-secondary educated parents have
5.2 Causes of municipal disparities 5 ANALYSIS
positive impact on mathematics performance. These findings coincide with those of the National Agency for Education in Sweden, in studies on individ-ual student level [5].
Further the Agency for Education has clearly stated that one of its goals is to reduce socioeconomic factors’ impact on school results. However, results presented in this report further strengthen the idea that these factors still have significant impact on student performance. While the above is an un-derstandable goal, one could argue whether or not it is reasonable to achieve. Factors outside the scope of this report such as levels of social equality and segregation would need to be considered to execute appropriate analysis with such broad perspective.
Teaching factors
As has also been recently reported, there seems to be a strong connection between the quality of teaching and the performance of students. Recent governmental action has been taken. For example, the government recently announced that a yearly amount of SEK 3 billion will be invested in currently
employed teachers [14]. It has been strictly said that in no way should
this investment further decrease the average number of Students per teacher. Instead the goal is to increase the attractiveness of the teaching profession by only reaching out to people currently in the business. This is in line with results of this report, and intuitively it should increase teaching quality. Further comparison of results in this report is found in upcoming sections, where teaching quality is a central point of analysis.
5.2
Causes of municipal disparities
One interesting way to view the results of the final regression is to specifi-cally look at what actions can be taken on a local political level to improve
student performance. The relevant coefficients that were entered into the ini-tial regression equation are expenditures per student, percentage of teachers with an educational degree and certification, as well as number of students per teacher. The remaining variables cannot directly be influenced by authori-ties, yet they possess explanatory power regarding student performance. For example, political reforms cannot increase the percentage of post-secondary educated parents in a municipality in a short term perspective.
Right wing rule
Although not statistically significant, the results showed a disparity in school performance between municipalities with different political ruling. While Left wing rule was employed as a benchmark variable the Right wing rule-dummy showed positive effect on school results. However, it is imperative to distinguish the difference between statistical significance and substantial ex-planation. Political majority within a municipality can generally be derived from the socioeconomic status of the inhabitants as the political parties nat-urally attract voters who benefit from their specific politics. Presumably, the left wing attracts voters from a lower social class as their political program is beneficial for low-paid professions, while the right wing generally attracts voters from a higher social class.
Instinctively, this rises questions about effect and cause. Regardless of whether or not the right wing rule variable presents a positive effect on national test scores, it is reasonable to question the order of cause and effect. The right wing rule dummy can be seen as an effect of other variables presented in this analysis such as Students with post-secondary educated parents and Average yearly income in municipality which show statistically significant positive ef-fect on student performance. Following the previous argumentation regarding general political tendencies, a municipality with high average salaries and a large proportion of post-secondary educated parents is more likely to be
un-5.2 Causes of municipal disparities 5 ANALYSIS
der right wing rule. The Right wing rule variable showed results of statistical insignificance, presumably due to above mentioned uncertainty.
Expenditures per student
The significance of numbers for expenditures per student were limited for three of the five included variables. However, health and education expendi-tures were statistically significant in the final model; increased values of both variables contributed positively to student performance.
Intuitively, increasing the amount of money spent on any aspect of educa-tion would improve the results of students for different reasons. The acquired regression results support this for the two above variables at a statistical sig-nificance level of 95%. For the other three variables there is no statistical significance. Nevertheless does this prove the opposite; that student perfor-mance is negatively affected by increased expenditures in property, materials or food.
For a municipality, it can then be argued that financing budget decisions should prioritize education and health. With the significance of the results, it has been shown that funds spent on these will improve the performance of students. A further study of for example a set minimal level for food, property and material expenditures could be of interest. This could help de-termine how much in the budget for these could be compromised for increased financing of education and health of students.
Teacher certification and educational level
Furthermore, the impact of teacher certification and educational degrees of teachers was considered. It was concluded that primarily, the data provided statistical evidence of positive impact on test score for the percentage of certi-fied math teachers in a municipality. The variable Teachers with educational
college degree was statistically insignificant, and was therefore removed from the model.
The above relationship between national test score and the percentage of certified math teachers in a municipality establishes the conclusion that the educational level of teachers should be a priority for local politicians. For example, one action to take could be to ensure that all new teachers being employed are certified, including reserve teachers. This is directly related to the education expenditures per student discussed in the subsection above, since hiring certified teachers almost surely will be more expensive than hiring non-certified teachers.
In modern day Swedish politics, the attractiveness of teaching as a profession is often discussed. In addition to the fact that the teaching environment is poor, many argue that salaries of teachers are too low. This is considered to lead to a shortage of certified teachers. The required amount of certified teachers that are currently demanded is therefore not reached and schools may be forced into employing non-certified teachers instead. Additionally, there are no significant career opportunities within the profession in Sweden. This contradicts the situation in well performing countries, where higher salaries as well as good career opportunities have been prioritized [15]. Fur-thermore, OECD surveys from 2013 point out that only about half of the Swedish teachers would choose to become teachers again while the proportion for teachers in Finland is almost 90% [16].
Interaction effects
Through an exploratory study of potential interaction effects between in-cluded variables, it was found that three interaction variables showed statis-tical significance.
First, there was an interaction between education expenditures and the num-ber of students per teacher. This indicates that high numnum-bers of students
5.2 Causes of municipal disparities 5 ANALYSIS
per teacher with a simultaneous presence of high expenditures on education indicate a better average test score for students in a municipality. Further discussion on this topic is enclosed in upcoming sections of this report. Secondly the regression indicated that there was a significant interaction effect between parents’ level of education and the percentage of certified math teachers. The conclusion drawn from this is that the combined presence of high numbers in these otherwise very influential variables further enhances average national test score.
The final significant interaction effect included in the final model was one be-tween parents’ level of education and percentage of students in private school. Data used in the analysis was only obtained for public schools. With that in mind, the cause of the interaction effect could be that the combination of higher percentage of post-secondary educated parents and percentage of stu-dents in private school simply suggests a more well-functioning municipality. Of the above interaction effects, the first two can be directly influenced in
some way by the government. They further establish the importance of
expenditures on education and the percentage of certified teachers.
Number of students per teacher
It was lastly looked into whether there was significant evidence of improved student performance with less students per teacher. Surprisingly the opposite was almost statistically significant. Results told that at a 90% significance level, it can be concluded that there is a positive correlation between perfor-mance of students and the number of students per teacher. This indicates that the addition of more students per teacher generates a higher test score. There could be several explanations to this unanticipated result. First, mu-nicipalities with educational issues and low test scores could see the addition of more teachers to their schools as a primary solution to their problems.
Intuitively this seems like a probable cause. As a result, municipalities who have taken these actions will indicate exactly what the study results in this report have shown; namely the relationship that less students per teacher in a municipality means that students in that municipality score worse on national tests.
In addition, the results can be explained by existing reports. According to the OECD, Sweden has prioritized smaller classes over better teachers. Reports suggest countries with better general school performance choose to allocate resources differently, to favor the quality of teachers rather than the quantity [17].
5.3
Potential adjustments on governmental level
Teacher certification
This study was partly conducted to investigate how aspects of current gov-ernmental school politics impact student performance in national test scores. Conclusions on this topic can be drawn in similar areas as discussed above under the impact of local political decisions. In a broader perspective, it has been shown that expenditures of municipalities on education and health of students positively impact average test scores. The combination of this with the fact that the percentage of certified teachers also has a positive impact on test score shows that a primary target for the government should be to ensure the availability of certified teachers. Logically there should exist a re-lationship between expenditures on education and the percentage of certified teachers.
Teacher shortage and profession attractiveness
The Swedish Teachers Union declares that currently in Sweden the teaching profession is becoming less attractive by the day. It predicts a shortage of 65
5.3 Potential adjustments on governmental level 5 ANALYSIS
000 teachers by 2025 and therefore admonishes action to be taken to enhance the attractiveness of educational professions. The acquired results in the final regression model boost the significance of these predictions. [18]
Likewise the Teachers Union further suggests that with the correct national and local political decisions, the teacher shortage could be ceased. Together with improving the attractiveness of teaching, consideration of current teach-ers is to be the solution. More specifically the union asserts the importance of increased teacher salaries. This is based on research indicating that six of ten teachers consider leaving the profession, with low salary and heavy workload as their main reasons. [19]
Other available statistics tell that only 53% of lower secondary school teachers would stick to their chosen occupation if given the chance to reconsider [16]. According to Statistics Sweden (SCB), 38 000 teachers have already with-drawn from their jobs and one of four students opt out from the teaching business due to low future wages [19]. An OECD report states that between 2000 and 2010 salaries of Swedish teachers increased on average by 8%, while those of teachers in other OECD countries increased by a substantially higher value of 22% [20].
In the same OECD report, it was concluded that only 6.8% of Swedish sec-ondary school teachers were younger than 30 years old while 41.2% of teach-ers were aged 50 or above. It is claimed that the education system could be negatively influenced in several ways from the disproportionate age distri-bution. For example, the report suggests possible teacher shortage as many approach retirement. The need for new teachers grows but since expected low salaries limit the pool of available talent, questions are raised regarding quality of new teachers. The same report further discusses budgetary aspects of the issue. In general, salary increases with teaching experience and with experienced teachers leaving the system, there should be budgetary space for resource reallocation favoring younger teachers and the profession as a whole. The conclusions drawn in the article are consistent with those drawn
in this report, namely that making the teaching profession more attractive is likely a good solution to the current situation. [20]
In today’s society, the demand for higher educated employees is higher than ever. There is a growing need for anyone seeking career success to possess
some sort of post-secondary education. Reversely, there is also a higher
than ever psychological threshold for a given person to consider themselves successful. By investing in teacher quality and certification, the teaching profession could regain some of its past appreciation to once again become a profession associated with higher status.
5.4
Long term effects on macroeconomics
The results presented in this report suggest that there is a significant cor-relation between the average national test scores and several influenceable variables. A common point generally agreed upon regarding education is its positive effects on economic growth for a country. For that reason, im-proving a malfunctioning education system should be of high interest to the government in a long term perspective.
It is reasonable to believe that the response variable in this analysis, namely the national test score, is correlated with Swedish scores on the PISA test. They are similar tests and both measure the mathematical proficiency of stu-dents. Therefore the acquired results are appropriate to consider when de-cided how to deal with the current situation of continuous decline in Swedish student performance. Countries where students perform similarly to those in Sweden on the international PISA test, for example Greece and Turkey, have much lower gross domestic products per capita [21]. Students in countries that are economically similar to Sweden such as Germany, the Netherlands and Finland display a higher level of knowledge [21]. Regarding Finland, cal-culations published by the OECD show that if students in Sweden acquired
5.4 Long term effects on macroeconomics 5 ANALYSIS
the same level of knowledge as those in Finland it could lead to a yearly increase in gross domestic product (GDP) of SEK 135 billion [22].
An article by Van Reenen and Sianesi from 2003 presents a merged result of several relevant studies from the 20th century regarding education’s impact on GDP growth. It is suggested that a 1% increase in middle school enrolment would lead to a two percentage point increase in the per capita GDP growth rate [23]. An increase in middle school enrolment is obviously not equivalent
to an increase in education quality. Nevertheless, it provides an idea of
education’s importance for growth. In the article it is stated that school enrolment has a greater effect on countries suffering from poverty [23]. Since Sweden is an economically developed country with mandatory middle school enrolment, it is reasonable to believe that educational quality in Sweden could be a similar factor to school enrolment in poorer countries.
The quality of education on middle school level potentially has an impact on students’ willingness to obtain higher education. Primary and middle school education compose the groundwork in which students are prepared for fur-ther education. An article by Bassanini and Scarpetta based on neoclassical economic theory suggests that a one year increase in average schooling is ex-pected to increase GDP per capita by approximately 6%. In the analysis an average of ten years of schooling is employed as a benchmark. [24] Increased quality of education in Swedish primary and middle school can potentially increase the average years of schooling as a result of more students obtaining post-secondary education.
In conclusion, the current decrease in student performance can be portrayed as a threat to future economic growth in Sweden. The reports presented above display positive effects of improved education on GDP growth. Con-trarily it is reasonable to believe that a deteriorating education system could result in a recession instead.
6
Conclusion
There is significant variation in the average performance of students in dif-ferent Swedish municipalities. What are the main drivers for an increased average national test score in a municipality? This report concludes that so-cioeconomic factors that cannot be directly influenced by political decisions such as higher average income and higher parental level of education have positive impact on student performance.
Conjointly there exists several factors that actually can be changed through governmental action. These are for example financing decisions regarding what areas of education to invest in and promotion of the teaching pro-fession, particularly through higher wages and greater career opportunities. According to the OECD, the latter has been of low priority in Sweden in comparison to countries displaying better student performance[15].
It seems investments in Swedish education have been aimed at increasing the quantity of teachers. The study concludes that as expected, money spent on education generally has a positive impact on student performance. However, there is also a strong connection between test score and the percentage of certified teachers in a municipality. Based on this it is evidently better to spend money on the quality of teaching than the amount of teachers. This matches what is often concluded in recent literature. Other investigations of the issue draw similar conclusions, independent of whether the analysis is international or on an individual level. This manifests the significance of results provided in this report.
Furthermore the potential long term effects of the negative trend were looked into. The general conclusion drawn from studying reports on this matter was that the gross domestic product as well as its growth rate are influenced by the educational level of the population. Hence, it is determined that improv-ing the education system should be of great interest to the Swedish govern-ment to ensure future economic growth and the well-being of the country as a whole.
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