The effect of education on income

Bachelor thesis in economics

Authors: Carl Thropp and Mathias Widerönn Supervisor: Johan Lindén

Spring of 2020

Abstract

This paper is about the effect of education on income. In the last two decades the real wages has increased a lot, and so has the amount of people with a higher education. This paper focus is to investigate the relationship between education and income. Other variables that might have an impact on the results will also be considered, such as experience in form of age, immigration, and employment. The reasons why these variables are included is because in one way or another these variables have a direct effect on the wage level. The foundation of this thesis regressions is based on the mincer equation, we will use aggregated data in all of Sweden’s 290 municipalities for the regressions.

The results from running these regressions is what we hoped to find, we can safely conclude that there is a positive and significant relationship between wages and education. On the other hand, we cannot safely say that there is a significant relationship with the other variables that where included such as immigration, experience, and employment. The optimal outcome from our regressions is to have a high school education consisting of 3 years and a college education of 3 years. This will result in the highest wage for the future.

Table of content

Introduction ... 1

Aim ... 2

Limitations ... 2

Previous Research ... 3

Immigration and wages ... 3

Returns to Education ... 3

Theory ... 5

The Schooling Model ... 5

Mathematical presentation of the Schooling Model ... 5

Graphical presentation of The Schooling Model ... 8

Potential Earning Streams ... 8

The Wage-Schooling Locus ... 9

Schooling as a signal ... 10

Mathematical expression of the model ... 10

Method... 12

Data ... 12

Results ... 15

High School 2 years ... 16

High School 3 years ... 16

College les

s

College 3 years or more ... 16

R𝑒𝑠𝑒𝑎𝑟𝑐ℎ𝑒𝑟 ... 16 Immigration... 16 Experience... 17 Experience2 _{... 17} Employment ... 17 Correlation Matrix ... 18

Variance inflation factor ... 18

Analysis ... 21

Conclusion ... 23

References ... 24

1

Introduction

This paper investigates the relationship between wages and education. The number of people with higher education has been increasing drastically the latter years. In 2000, there was 16% that had a higher education, which corresponds to people that have studied for three years or more after their years in high school. Today, this group of people with a higher education consists of 28% (Sweden Statistics, 2020). This increase is partly explained by the increase in studying possibilities as there are more universities with greater capacities that can handle a larger number of students.

As the number of people with higher education has been increasing, the proportion of people with lower education, that is people that only have a middle school education, has been decreasing. In 2000, there was 21% with this lower education compared to the 11% that we have in Sweden today (Sweden Statistics, 2020). Hence, it is more likely to meet a highly educated individual than an individual with a lower education.

The wages have also been increasing during the latest two decades. From the employee´s point of view, the real wage is more relevant than the nominal wage as the former reveals an individual´s purchasing power. Real wages are wages that is adjusted for the inflation. Meaning wages in terms of good and services that can be bought. Nominal wage is not adjusted to inflation, while real wage is. During 1970 to 1995, the increase in nominal wages was very high with an average increase of 8.1% per year. Even though, the increase in

nominal wages was high, it did not have a great impact on the real wage level since there was a substantial inflation of 7.5 %. In other words, there was a very small increase in the real wage of approximately .5% during this period (Ekonomifakta, 2020).

From 1995 and onwards, the trend has been different. The real wage level has been increasing by 2.1% per year in average whereas the nominal wage level has increased by 3.3% per year in average. The purchasing power of an individual has thus grown more rapidly during the latest two decades than between 1970 and 1995 (Ekonomifakta, 2020). Conclusively, the trends in wages and education have according to the statistics pointed in the same direction, why it would be interesting to see if the increase in real wages could be explained by the increase in the proportion of highly educated people.

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Aim

The main aim of this thesis is to empirically prove that there is a positive significant relationship between wages and education and to measure the strength of this relationship. Secondly, we would also like to see what impact the proportion of immigrants in a

municipality, the employment rate and experience in terms of age have on the wage level.

Limitations

The sample of observations is restricted to a municipality level due to time and resource limitations. Preferably, we would have liked to use individual data, but it has not been possible to access such data because of its unavailability. In the absence of individual data, we have used municipality data which have been categorized into age, gender and education intervals. We have chosen to measure the proportion of educated citizens in a municipality, not taking the proportional age level as well as the gender into consideration. Our sample is restricted to 290 observations, made in 2018, which is equivalent to the number of

municipalities in Sweden. Therefore, the thesis investigates the relationship between wages and education with aggregated data.

Regarding wages, we have not been able to find specific data on the wage level in the

municipalities. Consequently, the average earned income of a municipality has functioned as replacement. Most of the citizens´ income is assumed to consist of their wages, and is

therefore deemed to be an appropriate measure to use for our investigation.

We have not taken the wage level and education of other countries into consideration when conducting our analysis. The thesis merely focuses on Sweden and does not compare the situation in Sweden to other countries.

We do not compare the impact of different educations on the wage level such as the impact of the number of engineers versus the number of economists in a municipality. This limitation is set because of the difficulty in finding accurate data on a municipality level within the given timeframe for this work.

Some variables may have been more appropriate to include in the analysis, but have been left out due to its unavailability. For example, we have chosen to replace the unemployment rate with the employment rate since we found that it was difficult to manipulate the data that we found on the unemployment rate.

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Lastly, we do not aim to investigate educational differences between municipalities. We restrict our focus to the respective municipality´s various education levels and its potential impact on the wage level. In other words, questions such as why some municipalities tend to have a larger number of educated citizens will not take part in our analysis.

Previous Research

Immigration and wages

Borjas (1995) is a professor in Economics at Harvard Kennedy School and is specialized in immigrational economics where he, amongst others, has studied how immigration effects and is related to the labour market. In one of his articles, “The internationalization of the U.S. labor market and the wage structure”, he discusses how the increased immigration and trade to the U.S has affected their wage structure. He begins to assert that an increased immigration and a larger and disproportionate difference in less skilled foreign workers and more skilled native workers may have increased the aggregate wage inequality. In addition, the increased supply of foreign workers may also have an impact on the earnings of similarly skilled native workers.

Altonji and Card (1991) assembled data from 1970 and 1980 Censuses on labour market outcomes of natives in 120 major cities in the U.S. They found that the average native wage in a city with 10% more immigrants than another city was only 0.2% lower. Another research by Topel and LaLonde (1991) on the same subject puts attention to the same relationship as they found that a doubling of the number of recent immigrants within a locale would reduce their relative earnings by approximately 3%.

Returns to Education

Gustavsson (2004) has investigated the change in the premium on education in Sweden. In his investigation, he has had access to individual data provided by Sweden Statistics and estimated Mincer equations to quantify returns to education. He concluded that the return on college education has increased from 1992 to 2001, whereas the return on high school

education has been constant during the same period. The return on a 3-year college education in relation to a 3-year high school education was in 1992 approximately 18%. At the end of 2001, it had increased to 25%.

His study does also show that the return on education has changed differently for men and women as well as for the public and private sector. The increase in returns has been the

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strongest amongst men in the private sector while the returns for women in the public sector has been relatively constant.

Mincer´s empirical analysis of schooling and earnings

Mincer (1974) performed an empirical analysis based on his Schooling Model, whose main points are described in the theoretical framework below. In his investigation, Mincer points out that there is a clear and positive relationship between schooling and earnings. The following graph, obtained from Mincer´s work Schooling, Experience, and Earnings (1974), presents the relationship that he found between years of schooling completed and annual earnings. The earnings profile in this graph is a function work experience.

The data used for constructing these curves was gathered from a U.S. Census in the year 1960. By Slope 3 and 4, which represents average earnings of workers with 10 years of experience, Mincer could show that workers with more experience had greater returns from additional years of schooling.

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Theory

The Schooling Model

Jacob Mincer was a famous labour economist known for constructing a linear model in his work Schooling, Experience and Earnings (1974) that explains how wage income is determined by the years of schooling and experience. The following part of this thesis

contains a structural presentation and explanation of this model which functions as a base for our investigation. The main idea with this presentation is to deepen the reasoning behind the relationship that this work focuses on. Therefore, the theoretical model that is introduced below is central in our regression equation that is introduced later in this thesis.

The presentation is divided into two parts. The first part explains the model mathematically whereas the second part builds on the labour economist George Borjas´s (2013) graphical descriptions of the model.

Mathematical presentation of the Schooling Model

𝑉𝑠= Present value of an individual's lifetime earnings at start of schooling.

𝑌𝑠= annual earnings of an individual with s years of schooling.

𝑛= length of working life plus length of schooling. = length of working life for persons without schooling. 𝑟= discount rate.

𝑡= 0, 1, 2, .. . , n time, in years

𝑑= difference in the amount of schooling, in years 𝑒=base of natural logarithms

𝑉𝑠 = 𝑌𝑆 ∑ ( 1 1 + 𝑟) 𝑡 𝑛 𝑡=𝑠+1

Mincer starts his theory by constructing an equation explaining how the present value of an individual´s lifetime earnings at the start of her schooling is a function of her annual earnings with s level of schooling multiplied by a discount factor. When the discounting process of her earnings is continuous, it becomes:

𝑉𝑠= 𝑌𝑠∫ 𝑒−𝑟𝑡𝑑𝑡 =

𝑌𝑠(𝑒−𝑟𝑠− 𝑒−𝑟𝑛)

𝑟

𝑛

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It then follows that an individual who engages in s-d years of schooling has a present value of lifetime earnings which is:

𝑉𝑠−𝑑=

𝑌𝑠−𝑑

𝑟 (𝑒

−𝑟(𝑠−𝑑)_{− 𝑒}−𝑟𝑛₎

The ratio of annual earnings after s years of schooling to earnings after s-d years of schooling, 𝒀𝒔

𝒀𝒔−𝒅, is in turn found by equating 𝑽𝒔 = 𝑽𝒔−𝒅, letting the ratio be denoted by 𝒌𝒔,𝒔−𝒅:

𝑘𝑠,𝑠−𝑑 = 𝑌𝑠 𝑌𝑠−𝑑= 𝑒−𝑟(𝑠−𝑑)−𝑒−𝑟𝑛 𝑒−𝑟𝑠_−𝑒−𝑟𝑛 = 𝑒𝑟(𝑛+𝑑−𝑠)−1 𝑒𝑟(𝑛−𝑠)₋₁ (1.1)

One can now readily see that the ratio 𝒌𝒔,𝒔−𝒅 is larger than unity, a positive function of r and a negative function of n. This implies that people with more schooling desires a higher annual pay, and the difference in earnings between two individuals is larger the higher the rate of return on schooling due to the difference in investment of d years of schooling. Moreover, a shorter span of working life entails a larger difference in earnings between the two

individuals since the one with more schooling must recoup its cost of schooling over a relatively shorter period.

It is not surprising that an individual that has invested in some years of schooling requires a higher pay-off nor that if she is to work for a shorter time period has less time to recover her costs of schooling. However, it is not so obvious that 1.1 is a positive function of s.

Differentiating 𝒌𝒔,𝒔−𝒅 with respect to s (holding d constant):

𝑑𝑘 𝑑𝑠=

𝑟[𝑒𝑟(𝑛+𝑑−𝑠)_{− 𝑒}𝑟(𝑛−𝑠)_]

[𝑒𝑟(𝑛−𝑠)_{− 1]}2 > 0

That is, an increase in s leads to larger relative income differences where the ratio of two individuals is increasing the more schooling the individuals have. Mincer underlines that when n assumes a large number, a change in s and n is negligible on 𝒌𝒔,𝒔−𝒅, which allows one to treat 𝒌𝒔,𝒔−𝒅 as a constant:

𝑑𝑘

𝑑𝑠→ 0, 𝑤ℎ𝑒𝑛 𝑛 → ∞, 𝑑𝑘

𝑑𝑛→ 0, 𝑤ℎ𝑒𝑛 𝑛 → ∞

The constant 𝒌𝒔,𝒔−𝒅 is then true when spans of earning life, n, is assumed to be fixed. If one redefines n in this manner:

𝑉𝑠= 𝑌𝑠∫ 𝑒−𝑟𝑡𝑑𝑡 = 𝑌𝑠 𝑟 𝑒 −𝑟𝑠_{(1 − 𝑒}−𝑟𝑛₎ 𝑛+𝑠 𝑠

7 𝑉𝑠−𝑑= 𝑌𝑠−𝑑∫ 𝑒−𝑟𝑡𝑑𝑡 = 𝑌𝑠−𝑑 𝑟 𝑛+𝑠−𝑑 𝑠−𝑑 (1 − 𝑒−𝑟𝑛_)𝑒−𝑟(𝑠−𝑑)

Remembering that 𝑽𝒔= 𝑽𝒔−𝒅is synonymous to the ratio 𝒌𝒔,𝒔−𝒅 and equalizing 𝑉𝑠−𝑑 and 𝑉𝑠:

𝑘𝑠,𝑠−𝑑= 𝑌_𝑠 𝑌𝑠−𝑑= 𝑒−𝑟(𝑠−𝑑) 𝑒−𝑟𝑠 = 𝑒 𝑟𝑑 _(1.2)

Comparing 1.1 to 1.2, the latter does not depend on neither s nor n as the former does. In other words, Mincer asserts that the earnings ratio k is not affected by the individual´s level of schooling or the length of her working life when it is finite.

Finally, if one defines 𝒌𝒔,𝟎= 𝒀_𝒔

𝒀𝟎= 𝒌𝒔. Taking 1.2 into account gives 𝒌𝒔= 𝒆

𝒓𝒔_{. Mincer then} presents the logarithmic form of the formula:

𝑙𝑛 𝑌𝑠 = 𝑙𝑛 𝑌0+ 𝑟𝑠 (1.3)

By 1.3, Mincer finalizes his formula which presents his proposed theoretical relationship between the logarithmic form of annual earnings of an individual with s level of schooling as a function of the logarithmic form of an individual with no schooling plus the rate of return from schooling, r, multiplied by the level of schooling, s.

Conclusively, Mincer´s contribution is a theory of the impact of an individual´s level of schooling on the potential wage that the individual will earn. Mincer formulates this with a linear relationship between an individual´s logarithmic earnings and the time she has spent at school.

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Graphical presentation of The Schooling Model

Potential Earning Streams

Borjas, Potential Earnings Streams Faced by a High School

Graduate, Labor Economics 2013

The above graph builds on the theory (Becker 1964, referred to in Borjas, 2013) that was presented above, namely how an individual by his decision to study would earn a greater wage from studying compared to not studying, provided that the education gives a greater yield in the long run. In this case, it is required that the wage, 𝒘𝑪𝑶𝑳 ,the college graduate receives exceeds the wage,𝒘𝑯𝑺 ,that he would earn if she had not studied after high school. Referring to 1.1, this graph readily illustrates that the following must be satisfied for a high school student to decide to continue studying at college:

9 The Wage-Schooling Locus

Borjas, The Wage-Schooling Locus, Labor Economics 2013

Moving on to a graphical illustration of the relationship between years of schooling and the wage earned in terms of dollars, the Wage-Schooling Locus depicts what wage an employer is ready to offer an individual based on her level of schooling. The wage offered is dependent on the slope of the curve which in turn is determined by the supply of individuals that have an equal amount of schooling. According to the theory, the less people that have studied for 5 years, the more an employer would be willing to pay to obtain such an individual.

The slope of the curve is upward sloping since an individual that has acquired a certain level of schooling is supposed to be more appealing for an employer to attract, which results in a higher wage paid to those that have a higher level of schooling. The slope of the curve does also reveal how much the individual would gain financially if she were to study one

additional year. In equation 1.3, the rate of return, r, is closely related to the slope as a higher return in the equation entails a higher proportional wage. Lastly, the curve is concave which implies that every additional year of schooling has a smaller impact on the wage received by the individual.

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Schooling as a signal

The base of this model (Spence 1974, referred to in Varian, 676) is that an educated worker is more efficient than a worker without an education. This will lead to a higher wage for the efficient worker. An alternative theory for this model is that an educated worker is not more efficient than one without. But instead sends a signal to the employer that the person with an education is more qualified and cut out for the job, which also leads to a higher wage. High productivity people have an incentive to signal employers that they are highly

productive. Employers have a strong incentive to interpret this kind of information to get a high performing person to their workplace. This is just what an education can do, send a signal to the employer that this person is a high performing individual. If employers are willing to pay more for a high performing individual than for a low performing individual and education is a signal that one is high performing, low performing persons will also get an education in order to get the higher wage.

The model states that it´s more costly for the low performing individual to go to school. So how can the employer know for sure that the person they are hiring is a high performing individual?

Let´s say that employers will require a certain amount of schooling. The higher cost for the lower performing individual will make them go to school for x amount of years. If the

employer sets a limit that it will pay higher wages for persons who have x+1 amount of years, they can make sure that the people they are hiring are in fact high performing individuals.

Mathematical expression of the model

𝑎2 - Ables worker marginal product

𝑎1 - unable workers marginal product 𝑎2−𝑎1

𝑐1

< 𝑒 ∗ <

𝑎2−𝑎1 𝑐2

𝑐1 - cost of unable worker 𝑐2 - cost of able worker.

𝑒 ∗ - the amount of education attained

This is a simplified model of the education market (Spence 1974, referred to in Varian, 677). There are two types of workers, able and unable. The able marginal product is a2 and the unable marginal product is a1, where a2 > a1. The cost of able workers education is c2 and

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the cost of an unable worker is c1, where c2 < c1. Meaning that the marginal cost of acquiring an education for the able worker is less than for the unable worker. The equilibrium of this model depends on education.

Let us say that all the able workers get an education equal to e* and the unable level of education is 0. Firms will pay wages according to education. The worker with e* will get a wage of a2 and the worker with 0 education will get a wage of a1. The firm is paying all the workers their marginal product. This means that the firms have no incentive to change and the unable worker who might have an incentive to change would in fact get no benefit of getting more education. Since the increase in wages would be a2-a1 and the cost for more education would be c1e*. a2-a1 < c1e* resulting in more costs than benefits to the unable worker.

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Method

The method that will be applied to investigate the relationship between the level of schooling and a municipality´s aggregated income level is a regression equation influenced by the Mincer equation and other relevant theories that are explained in the theoretical framework and the previous research chapters. As we have already pointed out in the limitations part, we will not obtain specific data on individual wage levels. The observations will instead consist of Sweden´s 290 municipalities where we will use the average earned income level in each municipality as the dependent variable. The earned income level is formulated in a

logarithmic form so that it corresponds to the Mincer equation.

As for the independent variables, we have decided to adapt those to a municipality level to make them correspond to the dependent variable. Regarding the independent variables that measure a municipality´s level of education, they will be expressed in proportions. The sum of these proportions is equal to 1. For example, when constructing a variable for college graduates that have studied for 3 years or more:

𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑜𝑙𝑙𝑒𝑔𝑒 𝑔𝑟𝑎𝑑𝑢𝑎𝑡𝑒 ≥ 3 𝑦𝑒𝑎𝑟𝑠 𝑜𝑓 𝑒𝑑𝑢𝑐𝑎𝑡𝑖𝑜𝑛 𝑖𝑛 𝑐𝑜𝑚𝑚𝑢𝑛𝑖𝑡𝑦 𝑥 𝑇𝑜𝑡𝑎𝑙 𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑖𝑛 𝑐𝑜𝑚𝑚𝑢𝑛𝑖𝑡𝑦 𝑥

Other proportional variables are computed in the same way.

The main data that we have used is presented in separate appendixes.

Data

The raw data is exclusively gathered from Statistics Sweden where we have downloaded several Excel-files from which we have manipulated data (described below) in order to run appropriate regressions. The regressions are all performed using Excel.

The regression equation that the investigation is based on is the following:

ln 𝑎𝑣𝑎𝑟𝑎𝑔𝑒 𝑖𝑛𝑐𝑜𝑚𝑒 = 𝛽0+ 𝛽1ℎ𝑖𝑔ℎ𝑠𝑐ℎ𝑜𝑜𝑙 > 3𝑦𝑒𝑎𝑟𝑠 + 𝛽2ℎ𝑖𝑔ℎ𝑠𝑐ℎ𝑜𝑜𝑙 < 3𝑦𝑒𝑎𝑟𝑠 + 𝛽3𝐶𝑜𝑙𝑙𝑒𝑔𝑒

> 3𝑦𝑒𝑎𝑟𝑠 + 𝛽4𝐶𝑜𝑙𝑙𝑒𝑔𝑒 < 3𝑦𝑒𝑎𝑟𝑠 + 𝛽5𝑟𝑒𝑠𝑒𝑎𝑟𝑐ℎ𝑒𝑟 + 𝛽6𝑖𝑚𝑚𝑖𝑔𝑟𝑎𝑡𝑖𝑜𝑛 + 𝛽7𝑒𝑥𝑝𝑒𝑟𝑖𝑒𝑛𝑐𝑒

+ 𝛽8𝑒𝑥𝑝𝑒𝑟𝑖𝑒𝑛𝑐𝑒2+ 𝛽9𝑒𝑚𝑝𝑙𝑦𝑚𝑒𝑛𝑡

Regarding the educational variables, an important note is that an individual cannot be included in two educational variables at the same time. This means that you cannot be registered as a researcher and a high school student. In other words, you can only belong to one of these categories.

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ln 𝑎𝑣𝑎𝑟𝑎𝑔𝑒 𝑖𝑛𝑐𝑜𝑚𝑒 – The average income in a municipality. This variable is calculated by dividing a municipality´s total income by its population. This data is found on statistics Sweden by taking the average income of all people living in Sweden permanently, sorting by municipalities, all levels of education, men and women by the ages of 16-75 during 2018. ℎ𝑖𝑔ℎ𝑠𝑐ℎ𝑜𝑜𝑙 > 3𝑦𝑒𝑎𝑟𝑠 – The proportion of high school graduates in a community that have studied for 2 years or less. This variable is calculated by dividing a municipality´s number of abovementioned graduates by its population. This data is found on statistics Sweden. Sorting the data after municipalities, high school graduates that have studied for 2 years or less between the ages of 16-75, men and women, during 2018.

ℎ𝑖𝑔ℎ𝑠𝑐ℎ𝑜𝑜𝑙 < 3𝑦𝑒𝑎𝑟𝑠 – The proportion of high school graduates in a community that have studied for 3 years. This variable is calculated by dividing a municipality´s number of

abovementioned graduates by its population. This data is found on statistics Sweden. Sorting the data after municipalities, high school graduates that have studied for 3 years, 16-75 years of age, men and women during 2018.

𝐶𝑜𝑙𝑙𝑒𝑔𝑒 > 3𝑦𝑒𝑎𝑟𝑠 – The proportion of college graduates in a community that have studied for less than 3 years. This variable is calculated by dividing a municipality´s number of abovementioned graduates by its population. This data is found on statistics Sweden. Sorting the data after municipalities, college graduates that have studied for less than 3 years, 16-75 years of age, men and women during 2018.

𝐶𝑜𝑙𝑙𝑒𝑔𝑒 < 3𝑦𝑒𝑎𝑟𝑠- The proportion of college graduates in a community that have studied for 3 years or more. This variable is calculated by dividing a municipality´s number of abovementioned graduates by its population. This data is found on statistics Sweden. Sorting the data after municipalities, college graduates that have studied for 3 years or more, 16-75 years of age, men and women during 2018.

𝑟𝑒𝑠𝑒𝑎𝑟𝑐ℎ𝑒𝑟 – The proportion of researchers in a community. This variable is calculated by dividing a municipality´s number of researchers by its population. This data is found on statistics Sweden. Sorting the data after municipalities, number of researchers, 16-75 years of age, men and women, during 2018.

𝑖𝑚𝑚𝑖𝑔𝑟𝑎𝑡𝑖𝑜𝑛 – The proportion of people born in a foreign country in a community. This variable is calculated by dividing a municipality´s number of citizens born in a foreign

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country by its population. This data is found on statistics Sweden, sorting the data after municipalities, born abroad, 16-75 years of age, men and women, in the year 2018. 𝑒𝑥𝑝𝑒𝑟𝑖𝑒𝑛𝑐𝑒 – The average age of a municipality´s citizen. This variable is obtained by downloading this specific data from Sweden Statistics. Sorting the data after municipalities and sex, during the year 2018.

𝑒𝑥𝑝𝑒𝑟𝑖𝑒𝑛𝑐𝑒2_{- The quadratic form of abovementioned variable.}

𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 – The proportion of employed people in a municipality. This variable is

calculated by dividing a municipality´s employed population by its total population. This data is found on statistics Sweden, sorting by municipalities, level of employment, 16-75 years of age, men and women, during the year 2018.

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Results

We have done 9 different regressions in total, by adding one variable at the time. The last 3 regressions (7-9) will be presented this way in order to see what is happening to the

regression, and to make it easier for the reader to understand the impact of adding new variables to the regression equation.

Table 1

Estimates Regression 7 Regression 8 Regression 9

Constant 12,24992*** (83,51436) 13,52122*** (14,14766) 10,60503*** (10,84659)

High School 2 years

-0,37649 (-1,18096) -0,47551 (-1,45535) -0,28028 (-0,92371)

High School 3 years

1,09792** (3,118673) 1,09771** (3,122562) 0,69677* (2,110636)

College less than 3 years

-1,77763** (-3,27966) -1,79480*** (-3,31518) -1,15287* (-2,26487)

College 3 years or more

2,82293*** (8,909155) 2,75156*** (8,576828) 2,40055*** (7,977887) Researcher -3,40915* (-2,41684) -3,76267** (-2,62604) -1,46722 (-1,0747) Immigration -0,29380*** (-4,00873) -0,32386*** (-4,23259) 0,08978 (0,972333) Experience -0,00535* (-2,08812) -0,06250 (-1,46942) 0,03703 (0,885089) Experience2 0,00066 (1,346094) -0,00048 (-0,99364) Employment 0,85880*** (6,972805) R² 0,70162 0,70353 0,74740 R² adjusted 0,69421 0,69509 0,73928

Standard error of estimates 0,06167 0,06159 0,05695

F 94,7293*** 83,3533*** 92,0501***

P-value of F 2,7E-70 1,1E-69 2,4E-78

T-values for the respective parameters are presented within the parentheses. Stars (*) after an estimate indicates the level of significance according to a two-sided T-test.

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High School 2 years

From Regression 7 we can see that the proportion of the population that have studied in high school for 2 years or less have a negative coefficient (-0,37649). This means that this amount of schooling will affect the wage in a negative way (Earning less).

When adding the variable experience2 _{(regression 8), the coefficient changes value to}

-0,47551. Which means even greater negative effect.

Then in regression 9 when adding the level of employment, the coefficient drops to -0,28028.

High School 3 years

The coefficient for studying for 3 years in high school is positive (1,097925), meaning this amount of schooling has a positive effect on wages. There were no major changes when adding experience squared in regression 8.

When adding the level of employment, the coefficient for studying 3 years in high school changes to 0,0696768, it becomes less positive.

College less than 3 years

The proportion of college graduates in a community that have studied for less than 3 years in college have a negative coefficient. Again, meaning that this group earn less wages. It remains negative when adding both experience2 and employment.

College 3 years or more

College graduates that have studied for 3 years or more have the largest positive impact on the wages. A coefficient equal to 2,822929. The addition of experience2 and employment changes the coefficient first to 2,751561 and then to 2,40055 making it less positive, but still in fact positive.

R𝑒𝑠𝑒𝑎𝑟𝑐ℎ𝑒𝑟

The coefficient for researcher is strongly negative in this regression with a value -3,440915. Meaning a strong negative impact on wages. The adding of experience2 makes the coefficient more negative -3,76267, then when adding employment, the numbers drop to -1,46722.

Immigration

The proportion of people in a community born in another country has a negative coefficient (-0,2938) and again this means a discouraging impact on earnings. The coefficient does not

17

change that much in regression 8(-0,32386), but in regression 9 the coefficient completely changes from negative to positive (0,089778).

Experience

The average age in a community that we have as a variable for experience is also negative in this regression. With a value of -0,00535 meaning a week negative impact on income. Adding the experience2 does not make the coefficient change too drastically (-0,0625), but when adding employment, the whole variable changes from negative to positive (0,037034).

Experience2

In regression 8 we have added the variable experience squared. When adding the squared average age, the result does not correspond to the theory since experienceis negative and experience2 is positive.

Employment

An interesting consequence of adding the proportion of employed people in a municipality is that experienceand experience2now correspond to the theory that experience should result in a higher wage. Immigrationdid also change its sign as a result of the added variable. The low t-scores of these three variables suggest that they do not have a significant impact on the average wage level in a municipality.

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Correlation Matrix

Table 2

A correlation value which exceeds 0.8 does generally indicate that there is presence of multicollinearity in the regression. To note is that there are 6 values in the matrix that lie above 0.8 where the correlation between experience and its quadratic form is at the top with a correlation value of 0.999. The second highest correlation value of -0.889 is between College 3 years and more and high school for 2 years.

Correlation Matrix High School 2 years High School 3 years College less than 3 years College 3 years or more Rese- archer Immi- gration Exper- ience Exper- ience2 Empl- oyment High School 2 years 1,000 0,543 -0,841 -0,889 -0,732 -0,264 0,780 0,776 0,088 High School 3 years 0,543 1,000 -0,461 -0,600 -0,621 -0,369 0,316 0,305 0,308 College less than

3 years -0,841 -0,461 1,000 0,892 0,680 0,138 -0,653 -0,646 -0,036 College 3 years and more -0,889 -0,600 0,892 1,000 0,835 0,114 -0,610 -0,600 0,009 Researcher -0,732 -0,621 0,680 0,835 1,000 0,149 -0,515 -0,503 -0,101 Immigration -0,264 -0,369 0,138 0,114 0,149 1,000 -0,415 -0,407 -0,678 Experience 0,780 0,316 -0,653 -0,610 -0,515 -0,415 1,000 0,999 0,191 Experience2 _{0,776 0,305 -0,646 -0,600 -0,503 -0,407 0,999 1,000 0,192} Employment 0,088 0,308 -0,036 0,009 -0,101 -0,678 0,191 0,192 1,000

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Variance inflation factors

The Variance Inflation Factor are values that represents the existence of multicollinearity. Multicollinearity exists when the independent variables in the regression equation are

interrelated. In other words, the movement in one independent variable affects the movement in another independent variable. This is a problem which can affect the validity of a

regression since it may overstate an independent variable´s impact on the dependent variable. Variances, and consequently, standard errors of independent variables that are correlated will increase, which in turn results in decreased t-values. Another problem that multicollinearity entails is that the R-squared, that measures the overall fit of the regression equation, will be unaffected. Therefore, the existence of multicollinearity makes the R-squared represent a false fit, since a high value of the R-squared will be contradicted by low t-values.

(Studenmund, 2014).

There are remedies that may ease the consequences of multicollinearity. One may erase a variable from the equation if the variable in question measures the same thing as another, or if it is theoretically unreasonable to include. Another solution is to increase the sample size since a larger sample leads to more accurate estimates. Finally, one can do nothing.

Multicollinearity may not always make t-scores drop to an insignificant level or to make them differ from one´s expectations, why multicollinearity may not mean anything. (Studenmund, 2014).

The following results are the variance inflation factors that we have calculated by running regressions between our explanatory variables. The resultant R-squared values are then used in the formula below, which is the computation of the Variance Inflation Factor. Larger values of the R-squared result in larger variance inflation factors since the R-squared

measures how well the movement of the dependent variable is explained by the independent variables. A value above 5 does usually indicate that there is multicollinearity involved in the regression.

𝑉𝐼𝐹 = 1

20 Variance inflation factor (VIF)

High School 2 years 9,157

High School 3 years 14,901

College less than 3 years 6,145

College 3 years or more

2,257 Researcher 4,203 Immigration 2,905 Experience 1078,206 Experience2 1057,299 Employment 2,309

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Analysis

In regression 9, in which all variables are included, we can see that studying at high school for only 2 years have a significant negative impact on the aggregated earned income of a municipality. In other words, a relatively large proportion of people with less than 2 years high school education seems to result in a lower aggregated income, that is a 28% lower earned income in average. A plausible explanation could be that people who quit high school earlier, or have lesser years in school, generally end up working with a lower-paying job. Firms that are hiring these “drop-offs” require a small amount of schooling which, according to the theory, should result in a lower wage.

On the contrary, a large proportion of college graduates that have studied for less than 3 years have a positive impact on earned income which is plus 40% in average. This is also what we predicted before running the regression, since theory suggests that more education leads to a higher wage. Consequently, a municipality with a large proportion of citizens that have graduated high school is also likely to have a relatively high aggregated income amongst its population.

Likewise, this relationship is even more valid for those who have 3 years or longer college education.A municipality with a large proportion of college graduates, that have studied for at least 3 years, is according to theory also likely to have a relatively high aggregated income. The positive coefficient of approximately 2.4, which means plus 240% earned income in average, and its significant t-value of 7.98 suggest that this certainly is the case.

A result which we did not expect beforehand is the negative impact of a researcher education as this variable has a coefficient of approximately -1.47, which is 147% lower income in average. To notice though, is that the t-value is rather insignificant suggesting that there cannot be any clear conclusions drawn from this result. The fact that the proportion of researchers in the municipalities is low as they range from 0.03% to 4.36% may explain the somewhat illogical result. If the result had been in conjunction with theory, the years that are required to be qualified as a researcher should entail a relatively higher wage. Another reasonable explanation is that Umeå, Uppsala and Lund are amongst the municipalities that have the biggest proportion of researchers. These municipalities are so called “university municipalities” which implies that a large share of their populations consist of students. Since students do not earn any greater wages as they are occupied by their studies, these

22

municipalities with the highest earning population, we found Täby and Lidingö, which both are upper-class municipalities where the population have finished their studies. These two municipalities are also found amongst the ones that have the largest share of college graduates that have studied for 3 years or more.

Multicollinearity is likely to affect the results of immigration and employment as these variables have a correlation of approximately -0.68. Another sign which makes you suspect that there really is multicollinearity is the drastic change of the immigration variable when including the employment rate. In other words, when the proportion of foreign born in a municipality increases, the proportion of employed citizens decreases. The multicollinearity does probably explain why immigration corresponds to prior research suggesting a negative correlation when employmentis omitted, but not when employment is included.

The results of experience and experience2 are a bit tricky. In regression 8, they do not have their expected signs whereas, with the inclusion of employment, they do. This change may also be the multicollinearity coming into play. Interestingly, discarding immigration and replacing it with employment,make the variables assume the expected signs. However, even though the experience variables do assume the expected signs under some circumstances, they appear with an overall low significance. It may be that our measurement of experience with a municipality´s average age is not appropriate. Having access to an individual data set may result in more theoretically correct and significant coefficients.

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Conclusion

The results that we have gotten from our regression equation do fulfil the main purpose of this thesis which was to prove that there is a positive and significant relationship between wages and education. The results indicate that municipalities with larger proportions of college educated citizens tend to have a 240% larger aggregated earned income in average. We feel therefore safe to assert that there is a positive and significant relationship between education and the wage that a worker earns.

When it comes to our second purpose, which was to see what impact the proportion of immigrants in a municipality, the employment rate, and the experience have on the wage level, we have not completely fulfilled this aim. We can conclude that there is a positive and significant relationship between a municipality´s employment rate and its aggregated earned income in average. We cannot convincingly conclude that a high proportion of foreign-born citizens has a negative and significant impact on a municipality´s aggregated earned income in average. Neither can we conclude that a municipality´s average and its aggregated earned income in average have a positive and significant relationship.

If you complete a high school education of 3 years you will earn in average 70% more than one without an high school education, and if you attend collage for 3 years or more this will result in average 240% more aggregated income compared to a person without a degree.

24

References

Altonji G. Joseph & Card David. 1991. The Effects of Immigration on the Labor Market Outcomes of Less-skilled Natives. Abowd John & Freeman Richard (ed.). Immigration, Trade and the Labor Market. Cambridge: National Bureau of Economic Research, 201-234.

Borjas, George. 1995. The Internationalization of the U.S. Labor Market and the Wage Structure. Economic Policy Review 1(1):3-8.

https://www.newyorkfed.org/medialibrary/media/research/epr/95v01n1/9501borj.html

Borjas, George. 2013. Labor Economics. 6. ed. New York: McGraw-Hill Education. Ekonomifakta. 2020. Löneutveckling och Inflation.

https://www.ekonomifakta.se/Fakta/Arbetsmarknad/Loner/Loneutveckling-och-inflation/

(Retrieved 2020-04-30).

Gustavsson, Magnus. 2004. Changes in Educational Wage Premiums in Sweden: 1992-2001. Diss., Uppsala University.

https://www.econstor.eu/bitstream/10419/82777/1/wp2004-010.pdf

LaLonde J. Robert & Topel H. Robert. 1991. Labor Market Adjustments to Increased Immigration. Abowd John & Freeman Richard (ed.). Immigration, Trade and the Labor Market. Cambridge: National Bureau of Economic Research, 167-199.

https://www.nber.org/chapters/c11772.pdf

Mincer, Jacob. 1974. Schooling, Experience, and Earnings. Cambridge: National Bureau of Economic Research.

Studenmund, A.H. 2014. Using Econometrics: A Practical Guide. Edinburgh: Pearson Education Limited.

Sweden Statistics. 2020. Utbildning, Jobb och Pengar. https://www.scb.se/hitta-statistik/sverige-i-siffror/utbildning-jobb-och-pengar/ (Retrieved 2020-04-30).

Varian, H. R 2002. Intermediate microeconomics (6th _{edition) W.W. Norton & Company,}

N.Y.

Data found on statistics Sweden

Experience

https://www.statistikdatabasen.scb.se/pxweb/sv/ssd/START__BE__BE0101__BE0101B/BefolkningM

edelAlder/?fbclid=IwAR0V3hSZvYCQNzAaJ5JJma-QZMv2uIR4jg6uIF_MEQXuCuPHhgCm3iULadc(Retrieved 2020-04-30).

25 https://www.statistikdatabasen.scb.se/pxweb/sv/ssd/START__BE__BE0101__BE0101E/InrUtrFodda RegAlKon/(Retrieved 2020-04-30). Introduction https://scb.se/hitta-statistik/sverige-i-siffror/utbildning-jobb-och-pengar/utbildningsnivan-i-sverige/(Retrieved 2020-04-23). https://www.ekonomifakta.se/Fakta/Arbetsmarknad/Loner/Loneutveckling-och-inflation/?fbclid=IwAR25u3AWY9ep5UnAFQMIRQA2COadgXR2vTpQTQTUbAUCDo8E473GBKuq-8o (Retrieved 2020-04-23). (https://www.scb.se/hitta-statistik/sverige-i-siffror/manniskorna-i-sverige/invandring-till-sverige/) https://www.unicef.org/somalia/education(Retrieved 2020-04-23). Level of education https://www.statistikdatabasen.scb.se/pxweb/sv/ssd/START__UF__UF0506/UtbBefRegionR/ (Retrieved 2020-04-30). Level of employment https://www.statistikdatabasen.scb.se/pxweb/sv/ssd/START__AM__AM0207__AM0207H/BefSyssAl dKonK/ (Retrieved 2020-04-30).

Population in the municipalities

https://www.statistikdatabasen.scb.se/pxweb/sv/ssd/START__BE__BE0101__BE0101A/BefolkningN y/ (Retrieved 2020-04-30).

Total income

https://www.statistikdatabasen.scb.se/pxweb/sv/ssd/START__HE__HE0110__HE0110A/SamForvInk 1c/(Retrieved 2020-04-30).

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Appendix

Testing for Heteroskedasticity

Estimate _{Reg 1 Reg 2 Reg 3 Reg 4 Reg 5 Reg 6} Constant _{12,65933 12,56769 12,25790 11,81426 11,83888 12,03635} High School 2 years -2,41081 -2,57691 -1,77729 -0,43473 -0,43553 -0,75682 High School 3 years 0,67058 0,68319 1,91515 1,75072 1,28696 College less than 3 years 1,95466 -1,49326 -1,75003 -1,56412 College 3 years or more 2,67780 3,04088 2,67919 Researcher _{-3,18799 -3,00956} Immigration _-0,23850 R² _{0,52150 0,52743 0,55135 0,67861 0,68412 0,69701} R² adjusted _{0,51984 0,52413 0,54664 0,67410 0,67856 0,69058} Standard error of estimates 0,07728 0,07694 0,0751 0,06367 0,06323 0,06204 F _{313,88 160,157 117,155 150,441 123,015 108,503} P-value of F _{5,2E-48 1,9E-47 1,7E-49 5,5E-69 6,3E-69 2,1E-70}