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The Capital Share of Income and

Economic Growth

Bachelor thesis, academic year 2015-2016 Faculty of Economics and Business

Universiteit van Amsterdam Daan Kik, 6145477

Supervisor: Gabriele Ciminelli Amsterdam, February 2016

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This document is written by Student Daan Kik who declares to take full responsibility for the contents of this document.

I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it.

The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.

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Abstract

This study investigates whether an increase in the capital share of income has an effect on the real growth(%) of the GDP per capita, in eight countries. The work of Piketty is discussed in order to provide background information on the rising capital share of income. A theoretical analysis is made through which channels the capital share of income may have an influence on the economic growth. These channels are that a higher capital share of income could lead to less investment in education (Human capital accumulation theory), a higher capital share could lead to social unrest and that a higher capital share of income fosters aggregate savings. The empirical analysis employs whether a change in the capital share of income has an effect on the real growth of the GDP per capita in the following year. No clear relation was found, but the results suggest that through different channels a change in the capital share of income may have a different effect on the economic growth.

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Contents

1. Introduction ... 5

2. Theoretical framework ... 10

2.1 The capital labour ratio ... 10

2.1.1. Capital in the 21st Century ... 10

2.1.2. Critical remarks on Piketty ... 12

2.2. Literature on the effects of income inequality on economic growth ... 13

2.3. Hypothesis ... 15

2.3.1 Existing theories ... 15

2.3.2. Suggested theory ... 16

3 Data ... 18

3.1. Trends in the Capital Share of Income and Economic Growth... 19

3.2. Variables ... 22 4 Methodology ... 24 5. Results ... 25 5.1 Regressions ... 25 5.2. Interpretation of results ... 31 6. Robustness check ... 33 7. Conclusions ... 35 8. Bibliography ... 37

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1. Introduction

This study is about the capital share of income and economic growth. A central theme in Thomas Piketty’s Capital in the 21st Century(2014) is the rising capital share of income. Piketty shows that economic growth leads to structural inequality. He states that in general the rate of return on capital (r) is greater than the economic growth(g). Piketty says that there are two fundamental laws of capitalism. The first fundamental law, which is true by definition, is α=r* β. The α is the share of income from capital and the β stands for the capital income ratio. The national income consists of capital income and labour income, and the α is the share of income from capital. The second fundamental law of capitalism is β = s/g. The capital income ratio is the savings rate (s) divided by the growth of the economy. Unlike the first fundamental law, which is always true by definition, the second fundamental law is the outcome of a dynamic process, described in his book. The fact that r>g leads to structural inequality.

The book of Piketty is about this inequality and the possibilities of the government to reduce this inequality. Piketty pays attention only to the distribution of wealth while he barely discusses the overall growth of the

economy. He proposes a number of regulations in his book in order to counteract this inequality. Piketty warns us for inequality-driven instability but ignores that also growth could raise welfare at the bottom in absolute terms. Piketty states that the capital share of income will rise much higher in the 21st century, but he

does not employ whether this affects the growth of the economy. This study investigates whether a change in the share of capital income in the national income has an impact on economic growth, because, if Piketty is right, this share will rise much in the 21st century.

The capital-labour split consists of the capital share of income and the labour share of income. Together they constitute the entire national income of a country. An increase in the capital share of income thus always implies a

decrease in the labour share of income and vice versa. For example, if a company makes sales, a part is paid to the employees and a part to shareholders. How big the part is which is paid to capital and labour, determines the capital-labour split. This paper focusses only on the macroeconomic level. The effects of a change in the capital-labour split at the national level on the growth of the GDP

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per capita is the relation of interest. Because the capital share of income is the exact opposite of the labour share of income, we only use the capital share of income in this paper. The figure below shows the capital-labour split for France and the UK for over 150 years.

Figure 1 shows that the capital share of income is slowly increasing in “normal” times, but drops heavily in times of war. Piketty states that the capital share of income will continue to increase in the 21st century until it reaches a level of

above 40% again.

There is no theory available about a causal relation between the capital-labour split, and the growth of the GDP. There are, however, several theories about a relation between income-inequality and its impact on economic growth. Cingano examines this relation in his article “Trends in Income Inequality and its Impact on Economic Growth.”(2014) He discusses several theories about the possible effects of inequality on economic growth and makes an empirical analysis of the relation between the GINI-coefficient and the economic growth and he finds that there is a negative relation between a higher income-inequality and economic

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growth. The GINI-coefficient represents the income distribution of a nation’s residents. The GINI-coefficient ranges from zero (when everybody has the same income) to 1 (when all income goes to only one person) and will always be somewhere in between. The relation between inequality (measured by the GINI-coefficient) and economic growth is relevant for the relation between the capital share of income and economic growth for two different reasons. First, a higher capital share of income leads to higher inequality within a country. Piketty

argues this in his book Capital in the 21st century. Because inequality has an effect

on economic growth, and the capital-labour split has a direct effect on inequality, it is to be expected that the capital-labour split will have an effect on the

economic growth. Secondly, there are different theories about inequality and its effects on economic growth and some of these theories will also apply on the relation between the capital-labour split and the economic growth. The human capital accumulation theory suggests that lower-income household will invest less in education, which eventually leads to a lower economic growth. The human capital accumulation can also apply on the relation between the capital-labour split and the economic growth. The incentive to get educated will be higher if more is paid to labour, compared to capital. On the other hand, there is a theory that higher inequality provides the incentive to work harder, invest and undertake risks. Over the last decades, there is a long-term trend towards higher inequality. At the moment, the income inequality is at its highest level since 30 years in most Organisation for Economic Co-operation and Development (OECD) countries. Figure 2 shows that in most countries the income inequality

(measured by the GINI-coefficient) started to grow since the 1980’s, and the inequality continued to grow, except during the crisis years.

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Figure 2, from the article of Cingano(2014)

Both the income inequality and the capital share of income have been rising over the last decades. It is, therefore, worth examining what the effect is of this

upward trend of inequality on the economic growth in the 21st century. This study examines in the theoretical framework, through which channels the capital share of income can affect economic growth. The different channels through which the capital share of income can have an effect on economic growth are: 1) The human capital accumulation theory. A higher capital share of income could lead to less investment in education, and this could reduce economic growth. 2) Social unrest theory. A higher capital share of income could lead to social unrest, and therefore reduce economic growth. 3) Aggregate savings theory. A higher capital share of income fosters aggregate savings, because the rich tend to consume less of their income. Through this channel a higher capital share of income could lead to a higher economic growth.

Contrary to previous studies, the focus in this paper is on the difference in the type of income. The GINI-coefficient does not distinguish what kind of income a person has (capital or labour). The mechanism of an increasing capital share of income of Piketty is explained in the literature review in section 2.1, followed by some critical remarks on his work. Several theories about the effect of inequality on economic growth are discussed in section 2.2. Cingano(2014) shows

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empirical evidence of the effects of inequality on economic growth and gives a theoretical explanation of these effects. The hypothesis in section 2.3 discusses how these effects and the different theories on inequality can be applied to the capital-labour split, and a theory is given in what other ways the capital income may affect economic growth.

In the empirical part an Ordinary Least Squares regression with fixed effects for panel data, is done to test for the effect of the capital share of income on the economic growth for eight different countries from 1970-2010. In section 3 the dataset is presented and some trends in the independent variable of interest (the capital share of income) and the dependent variable (the growth of the GDP per capita) are given. The methodology is discussed in section 4 and the results and the analysis are given in section 5. The results do not show a clear relation between the capital share of income and the growth of the GDP per capita. Based on the regression in this model, there cannot be concluded that there is a causal relationship between a changing capital share of income and the growth of the GDP per capita. In the robustness check section (section 6) all models are tested on autocorrelation. Section 7 concludes.

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2. Theoretical framework

2.1 The capital labour ratio

2.1.1. Capital in the 21st Century

Piketty’s Capital in the 21st Century consists of four parts. The first three parts are a scientific analysis of capital and income. In these three parts, Piketty shows that modern economic growth leads to structural inequality. Part four is more political. In this part, he gives some solutions to reduce this inequality. This paper focusses only on the first three parts of the book. The central thesis in these parts is that the rate of return on capital (r) is greater than the rate of economic growth (g). He gives a theory why capitalist societies lead to structural inequality, and supports this with a lot of empirical evidence. This chapter

summarizes the main mechanism developed by Piketty.

Piketty has done research for over fifteen years to collect as much data as possible. He has been analysing a lot of tax returns. He studies this data on the economy in the long term, to answer two central questions in his book:

1) How important is capital today?

2) What is the role of capital in the distribution of wealth?

The book begins with some definitions. If a company makes money, always a part of it is paid in wages and a part of it is paid as profit. The difference is income from work and income from capital. These are the two ways to make money in an economy, through labour or capital. In the long term, the

distribution of labour income and capital income is not very stable.

Piketty looks at two different ratios: the ratio between capital and income and the ratio between capital and labour. Capital is every form of property (real estate, financial capital and business assets) that a person can possess and can be traded on the market. National wealth or national capital is the total market value of all property of all residents and government added together. This consists of all financial and non-financial assets together.

The first fundamental law of capitalism is

α=r* β (1)

The β stands for the capital-income ratio. This is the national capital divided by the national income. So if β is 600%, the total market value of all the capital in a country is six times the national income. The r is the rate of return on capital.

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The rate of return on capital consists of profits, dividends, interest and rents. So if r is 5%, the average return on capital is 5% in that country. The α stands for the share of income from capital. So if for example the β is 600% and r is 5%, α will be 30%. This means that 30% of the national income will be capital income and 70% will be labour income. The equation is an analytical equation and is always true by definition. The share of income that is capital income rather than labour income is determined entirely by how much capital there is and what its average return is. The average β in developed countries is in between 500% and 600%. Globally, there is an extreme difference in production per country. Piketty says it is difficult to predict the exact growth rate of the GDP in the 21st century. The second fundamental law of capitalism is

β = s/g (2)

The ratio between capital and income depends on the savings rate (s) and the growth of the economy (g). For example, if the savings rate (s) is 12%, and the growth rate is 2%, the ratio between capital and income will be 12%/2%=600%. This is to be understood as follows: A country that saves a lot and grows slowly, builds on a huge capital stock. If the growth rate is low, the capitals that have been accumulated in the past are of great importance. Important to note is that small changes in the growth rate could cause for major changes in the ratio between capital and income. Unlike the first fundamental law, which is always true by definition, the second fundamental law is the outcome of a dynamic process. β= s/g moves to an equilibrium, but does not explain the short-term shocks. It is important to note that the second fundamental law is independent of the reasons for the inhabitants of a country to build up capital. The law β = s/g is always applicable. From equation 2 follows that a higher savings rate results in a higher capital stock, and that this thus results in a higher capital share of income. The ratio between capital and income will increase substantially in the 21st century. According to Piketty, the β will be around 700% in 2090.

Piketty says that the rate of return on capital is always between 3% and 6%. The rate of return is relatively stable in the long term. The β, however, is increasing. That means, given the first fundamental law, the α will increase. In other words, the share of income from capital will increase in the 21st century. He notes that

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because of the increase in capital, the return on capital is likely to drop. However, the β will rise faster than r will decrease and thus the α will also rise.

Piketty is saying that rate of return on capital (r) is greater than the rate of economic growth. The rate of return on capital consists of profits, dividends, interest and rents. Economic growth is measured in the national income.

The amount of available capital has decreased dramatically in the first half of the 20th century, because of the first and second world war (a lot of capital was destroyed). This has also led to a reduction of the capital-labour-split (see figure 1).

2.1.2. Critical remarks on Piketty

The claim that if r>g implies that wealth will accumulate, leading to structural inequality, is based on the fact that the return on capital is never consumed but always reinvested (Homburg, 2015). Wealth can even decrease if not all of the return on the capital is reinvested. Homburg also shows in his article that the capital-income ratio is not always increasing. He refers to the same figure used in this introduction (figure 1). He states that this graph does not show an upward trend in the capital share of income. Capital income shares were lower in 2010 than in 1820 and 1900, reaching record lows in the 1970s and 1980s. The statement of Piketty that the capital share of income will rise to historically high levels in the 21st century is just speculation. Homburg states that both the theory

of Piketty is not correct and that his own data prove that the capital share of income is not always rising.

A critique of David Weil (2015) at the work of Piketty is that he does not

distinguish between capital and wealth. The definition that Piketty uses of capital is “the market value of tradeable assets.” This is problematic because new types of wealth, like human capital, are now a significant fraction of the total wealth. The constancy of the wealth/income ratio in the book of Piketty is thus an illusion. These new types of capital are far more equal than the capital he measures, and can’t be inherited. He says that Piketty did not pay attention to this new types of capital, but that he nevertheless has made a great contribution to the role of capital in the economy: “The fact that Piketty misses out on some dimensions of wealth does not undermine the value of the exercise conducted in his

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book and supporting articles, however. Over recent decades, the dynamics of market wealth on which he focuses probably have indeed been the biggest part of the story of wealth evolution.” (Weil, 2015)

2.2. Literature on the effects of income inequality on economic growth

There are different theories about how inequality may affect economic growth. A theory, first formulated by Simon Kuznets in the 1950s and further investigated by Barro(2000), says that during times of economic growth, inequality first increases and later decreases, known as the Kuznets Curve. This is due to the fact that in growing economies, a shift takes place from an agriculture economy to an industrial economy. The inhabitants of a country who move first to the industrial sector experience a rise in their income. This leads to inequality first, but after some time the wages in the different sectors will be equal.

There are some theories that say that inequality reduces economic growth and some theories that say that inequality affects growth in a positive way. The theories differ through what channels inequality influences economic growth. Theories that say that inequality affects growth in a negative direction:

1) Greater inequality could become unacceptable to voters who want to reduce the inequality, which may lead social polarization and to social unrest. Property and contractual rights are less secure in more polarized societies, due to the fact that current government policies protecting property and contractual right, are more likely to change drastically. Income inequality, therefore, is inversely related to the security of contractual and property rights. Through this channel inequality reduces growth. (Keefer & Knack, 2000).

2) The human capital accumulation theory could also be a reason for a negative effect of inequality on economic growth. In the face of capital market

imperfections, the distribution of wealth affects the investment of people in human capital, like education. Growth is thus affected by the initial

distribution of wealth. Individuals need to inherit enough to be able to invest in human capital. A large middle class has, because of this reason, a positive effect on economic growth (Galor & Zeira, 1993). With a high inequality, poor

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individuals may not be able to make investments in human capital. This leads to a lower economic growth in the future. The ability of different individuals to invest depends on their wealth level; so poor people may not be able to invest in education. This is especially the case nowadays because

technological innovation requires replacing less skilled workers by better-educated workers (Zeira, 1998). Both within countries and globally, human capital inequality (the distribution of education) has an inverted U-shape curve over time. This corresponds with the Kuznets curve. During times of economic development inequality, and human capital inequality increases first, and then starts decreasing after some time (Morrisson, et al., 2013). Theories that says inequality affects economic growth in a positive way: 1) Inequality provides an incentive to work harder or to seek more and better

education. If much more is paid to people who work hard or who are better educated, this provides an incentive to get educated and to work hard. A greater difference in wages can therefore ensure that people work harder and is thus better for economic growth. (Lazear and Rosen, 1981).

2) A higher inequality fosters aggregate savings because the rich consume less of their income. Higher incomes save relatively more, compared to lower incomes. Inequality leads therefore to a higher savings rate, which has a positive effect on economic growth. (Bourguignon, 1981).

Some work suggests that the inequality could lead to a lower economic growth in poor countries, but to a higher economic growth in richer countries. Inequality tends to have a negative effect on growth when the GDP per capita is below $2000 (1985 US dollars) and a positive effect when the GDP per capita is above $2000. (Barro, 2000). Barro also suggests that there is a little overall relation between income inequality and the growth rate.

Cingano(2014) investigates the gap between the rich and the poor in the OECD countries. At the moment, this gap is at the highest level in 30 years. The lower incomes grew much slower than the top incomes. This led to a gap with the richest 10 percent earning 9.5 times the income of the poorest 10 percent. He says that the income inequality has a negative effect on the economic growth, especially the gap between the low-income households and the rest of the population. This income inequality varies widely between the different OECD

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countries though. Since the 1990s and the 2000s also the traditionally low-inequality countries witnessed a widening gap between the poor and the rich. During the recession, the inequality increase came to a halt, but after the

recession the inequality is on the rise again. Policies to reduce income inequality could lead to a higher economic growth in the long run. He therefore suggests that inequality must be countered not only from a social point of view but also from an economic point of view.

The empirical evidence is ambiguous, because of the poor quality of the available data and a lack of time series variation. The data of income distribution from different countries is heterogeneous. The inequality measures usually differ as to coverage, reference unit, weighting and definition of income. Different indicators show a different picture. Cingano(2014) comes with a new approach and new evidence. It is important to note however that he only looks at the countries in the Organisation for Economic Co-operation and Development (OECD) countries. He looks at the Solow growth model with an interval of five years. He uses a GMM analysis that shows that inequality has a negative impact on economic growth. Lowering inequality by 1 GINI point would translate in an increase in cumulative growth of 0.8-percentage points in the following five years. Some theories say that it might be a nonlinear relationship, but when the coefficient GINI^2 was added no such nonlinearity was found. Lowering inequality by reducing the top income has a smaller positive impact than an increase in the lowest incomes. This corresponds to the human accumulation theory (lower incomes will invest less in education). Income inequality is negatively related with educational attainment. Reducing not only the inequality of the lowest 10% incomes but of the bottom 40% incomes will positively affect economic growth.

2.3. Hypothesis 2.3.1 Existing theories

There isn’t theory available on the relation between the capital share of income and economic growth. Piketty(2014) shows however that a higher capital share of income leads to a higher inequality in the long run. Cingano(2014) shows that a higher inequality leads to a lower economic growth, so the hypothesis is that a higher capital share of income will lead to a lower economic growth. The human

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capital accumulation theory is also directly applicable for the capital-labour split. Employees cannot invest in education, if little is paid to labour (Galor and Zeira, 1993). A higher capital share of income will therefore lead to less investment in human capital. A high capital share, on the other hand, fosters aggregate savings because the rich consume less of their income. (Bourguignon, 1981). The theory that a higher inequality provides an incentive to work harder, does not apply here (Lazear & Rosen, 1979) A higher capital share does not mean that by working harder you do get paid more, but only that more is paid to capital. It may even reduce the motivation to work hard, because working hard pays relatively less than owning capital.

2.3.2. Suggested theory

Besides the theories of inequality and its effects on economic growth, a higher capital share of income may also influence economic growth in other ways. Possible ways in which a higher capital share of income may reduce growth:

1. Capital owners will not have an incentive to work at all. If you can live well from a capital income, there is no reason to work. Even a small rise in capital income can result in that capital holders will work less in

subsequent years. In earlier times there were classes in society who never had to work but could live entirely on private means. If capital owners will work less, that will slow down economic growth.

2. In accordance with the theory of Keefer(2000) a higher capital share of income could lead to an even higher unrest than just income inequality. If a company makes a lot of profit, but the workers get paid little compared to shareholders, there is a risk of dissatisfaction among the employees and possibly strikes.

Possible ways, in which a higher capital share of income may increase growth:

1. In accordance with the theory of Bourguignon (1981), inequality fosters aggregate savings. A higher capital share of income may foster aggregate savings even more, because more is paid to capital. Capital owners will likely again invest in capital. If relatively more is paid to capital, there is a higher incentive to invest in capital.

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2. A higher capital income may lead people to be more willing to take risks and start new businesses. This is due to the fact that it is worth more in this case, to be a shareholder than to work for someone else.

The ways in which the capital share of income can affect economic growth, can differ in various situations. It could be that there is a difference between emerging and rich countries, in accordance with the theory of Barro(2000). Some effects can take several years, like the human accumulation theory, while higher aggregate saving could lead directly to higher investments.

Both existing theories of inequality, as the expected effects of a change in capital income, seem to indicate mostly that there will be a negative relationship

between the capital share of income and income growth. This paper focusses only on the effects in rich countries.

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3 Data

The analysis in this paper makes use of the data from the website of Thomas Piketty. From his website is the data of the net capital Share of Income (after taxes) of eight different countries (The United States, Japan, Germany, France, the United Kingdom, Italy, Canada & Australia) from 1970 till 2010. The series of the capital-labour split are not perfectly comparable over time and across

countries, but the rise of the capital share in these eight rich countries is relatively robust, however. There is much fewer data available on emerging countries. The capital share of income measured by Piketty consists basically of everything that is not earned from wages, that is corporate capital income (net corporate profits), housing capital income (net rents), capital share of self-employment net income and net foreign capital income. The capital share of income is measured after taxes.

The data of the economic growth and the control variables are from the World Data Bank and the OECD income distribution database: The GDP per capita is measured by the GDP divided by the midyear population. The real growth is measured by the annual percentage growth of the GDP per capita, corrected for inflation. Gross Fixed Capital Formation consist of all acquisitions of new or existing fixed assets minus the disposals of fixed assets. The growth of the Gross Fixed Capital Formation is the average annual growth of gross fixed capital formation based on constant local currency. Gross fixed capital formation includes land improvements (fences, ditches, drains, and so on); plant,

machinery, and equipment purchases; and the construction of roads, railways, and the like, including schools, offices, hospitals, private residential dwellings, and commercial and industrial buildings. The inflation as measured by the annual growth rate of the GDP implicit deflator shows the rate of price change in the economy as a whole. The GDP implicit deflator is the ratio of GDP in current local currency to GDP in constant local currency.Real interest rate is the lending interest rate adjusted for inflation as measured by the GDP deflator. 1

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3.1. Trends in the Capital Share of Income and Economic Growth

The capital share of income fluctuates over time, but tend to increase. Figure 1 in the introduction shows that the capital share of income used to be much higher in the 19th century for France and the United Kingdom. In figure 3 you can see that in most countries there was a drop in the capital share of income from 1970 till 1976, but from 1976 till 2010 there is a growing trend in the capital share of income. Piketty(2014) argues that this is only the beginning and predicts that this growing trend will only increase in the 21st century, until there are large inequalities differences.

The biggest drop in the capital share of income is in Japan in the early 70s. This is probably because Japan experienced tremendous growth in the late 60s, which led to a high capital share of income, but this growth stagnated in the early 70s. The profits of all companies in Japan were in previous years still very high, but in the early 1970’s they became much less in a short time, leading to the big drop.

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Figure 4 shows the real growth rates of the GDP per capita from 1970 till 2010. The growth rate fluctuates between -5% and 5%. Most countries had a drop in their growth at the financial crisis in 2008.

The graphs show that both the capital share of income and the growth of the GDP per capita fluctuate over the years, but that the growth of the GDP per capita is most of the times positive. The graphs show that the capital share of the different countries move together and that the growth of the GDP per capita of different countries roughly move together. Figure 5 shows the independent variable of interest; the change of the capital share in percentage points, measured by 𝐶𝐶𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝑆𝑆ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑡𝑡− 𝐶𝐶𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝑆𝑆ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑡𝑡−1

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This graph shows that the capital share of income changes every year for all countries and that it moves roughly between -4 and +4 percentage points

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Especially the housing capital income is stable in the long run and is increasing slowly. Net foreign capital income used to be a significant part of the total capital income, but this has become considerably less in the second half of the 20th century. This is due to the decolonization in that period. Most of the fluctuations of the capital share of income, come from fluctuations in the share of corporate capital income. This is due to the fact that rents are much more rigid than profits. Most of the fluctuations in the variable of interest, the change in the capital share of income, are therefore results of fluctuations in the profit of companies. the long-term upward trend of the capital share income, is largely the result of the rising housing capital income.

3.2. Variables

The dependent variable is the real growth rate of the GDP per capita(%), as a measure of economic growth. The GDP per capita is measured by the GDP,

divided by the population of that year. The real growth rate of the GDP per capita is the growth rate of the GDP per capita, corrected for inflation. Because the growth of the GDP may have a direct influence on the capital share of income, there could be reversed causality. Therefore, the change of the capital share of income of the year before the GDP is used, measured in percentage points. This is the one-period lagged value of the capital share of income minus the two-period lagged value of the capital share of income. The control variables used in the model are the inflation rate (measured by the GDP deflator), the real interest rate and the growth rate of the Gross Capital Formation. In all models, the change of capital share of income from the year before is used, so with the term

change of capital share is meant the one-period lagged value of the capital share

minus the two-period lagged value of the capital share. As discussed in section 2, the impact of a change in the capital share of income on the growth of the GDP can go through different channels (Human Capital accumulation or aggregate savings). For this reason, a change in capital share of income can have a different effect over the different years. An accumulation of aggregate savings could have a direct effect on the capital share of income, but it could take several years for

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the human capital accumulation to have an effect. Therefore, the difference in the capital share of income of previous years is also taken into account.

Real annual growth (%)of the GDP per capita = 𝐺𝐺𝐺𝐺𝐺𝐺𝑃𝑃𝑡𝑡 Capital share of income = 𝐶𝐶𝑆𝑆𝑡𝑡

Gross Capital Formation = 𝐺𝐺𝐶𝐶𝐹𝐹𝑡𝑡

Inflation measured by the GDP deflator = 𝐼𝐼𝐼𝐼𝐼𝐼𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝐼𝐼𝐼𝐼𝑡𝑡

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4 Methodology

To study the effect of a change in the Capital Share of Income on the Economic growth, panel data of eight different countries is used. The results show an Ordinary Least Squares regression with fixed effects for panel data. For the country-fixed effects, dummy variables for the countries are used. Because global economic shocks could affect the GDP per capita for all countries, time fixed effect dummy variables are included. In all models standard robust errors are used.

There are two different dependent variables in the different regressions. First, the real annual growth (%) of the GDP per capita (𝐺𝐺𝐺𝐺𝐺𝐺𝑃𝑃𝑡𝑡). Models with the 𝐺𝐺𝐺𝐺𝐺𝐺𝑃𝑃𝑡𝑡 as the dependent variable are autocorrelated, as is shown in the

robustness check section. Therefore also the change of the real annual growth (%) of the GDP per capita (𝐺𝐺𝐺𝐺𝐺𝐺𝑃𝑃𝑡𝑡− 𝐺𝐺𝐺𝐺𝐺𝐺𝑃𝑃𝑡𝑡−1) is used as the dependent variable. It is difficult to interpret the results with this as the dependent variable, because it is a change of a percentage change. It does solve the problem of

autocorrelation and the results suggest a relationship but this should be further investigated.

To test whether the capital share of income has an effect on the growth of the GDP per capita, different regressions are used. Both the absolute change in the capital share of income (𝐶𝐶𝑆𝑆𝑡𝑡−1− 𝐶𝐶𝑆𝑆𝑡𝑡−2) and the relative change as a percentage change ((𝐶𝐶𝑆𝑆𝑡𝑡−1−𝐶𝐶𝑆𝑆𝑡𝑡−2)

𝐶𝐶𝑆𝑆𝑡𝑡−2 ), are looked at.

Because the growth of the GDP per capita is autocorrelated, reversed causality could be a problem. The growth of the GDP per capita may have a causal effect on the capital share of income. To test whether this is the case, a regression is run with the change in capital share as the dependent variable and the growth of the GDP as the independent variable.

Because time-series data is used, all models are tested for autocorrelation in the robustness check section. Autocorrelation can make the estimators less efficient. Each model is tested by a Woolridge test for autocorrelation.

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5. Results

5.1 Regressions

Table 1 shows the result for the regression:

GGDPt= β0+ 𝛽𝛽1(𝐶𝐶𝑆𝑆𝑡𝑡−1− 𝐶𝐶𝑆𝑆𝑡𝑡−2) + 𝛽𝛽2𝐺𝐺𝐶𝐶𝐹𝐹𝑡𝑡+ 𝛽𝛽3𝐼𝐼𝐼𝐼𝐼𝐼𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝐼𝐼𝐼𝐼𝑡𝑡+ 𝑐𝑐𝐼𝐼𝑐𝑐𝐼𝐼𝑎𝑎𝑎𝑎𝑐𝑐𝐼𝐼𝑎𝑎𝑐𝑐𝑎𝑎𝑐𝑐𝑎𝑎𝐼𝐼𝐼𝐼𝑎𝑎𝑐𝑐𝑎𝑎𝑐𝑐 + 𝑎𝑎𝑎𝑎𝑡𝑡𝑎𝑎𝐼𝐼𝑎𝑎𝑐𝑐𝑎𝑎𝑐𝑐𝑎𝑎𝐼𝐼𝐼𝐼𝑎𝑎𝑐𝑐𝑎𝑎𝑐𝑐 + 𝜖𝜖𝑖𝑖

(3) In this regression, the growth of the GDP is the dependent variable and the independent variables are the change in capital share, the Gross Capital Formation, and Inflation. Dummy variables are included for the country-fixed effects and the time fixed effects.

This regression shows that there is no significant correlation between the change of the capital share of income and the growth of the GDP, if the gross capital formation is included in the model (model 2 and 3). This corresponds with the theory that a higher capital share of income fosters aggregate savings, and thus more is invested in capital (Bourguignon, 1981). Including the gross capital formation, has as a result that the effect of an increase in the capital share of income is therefore no longer noticeable.

In table 1 the change in the capital share of income is in percentage points. Table 2 shows the results of a regression with a relative change in the capital share:

GGDPt = β0+ 𝛽𝛽1�𝐶𝐶𝑆𝑆𝑡𝑡−1𝐶𝐶𝑆𝑆−𝐶𝐶𝑆𝑆𝑡𝑡−2

𝑡𝑡−2 � + 𝛽𝛽2𝐺𝐺𝐶𝐶𝐹𝐹𝑡𝑡+ 𝛽𝛽3𝐼𝐼𝐼𝐼𝐼𝐼𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝐼𝐼𝐼𝐼𝑡𝑡+

𝑐𝑐𝐼𝐼𝑐𝑐𝐼𝐼𝑎𝑎𝑎𝑎𝑐𝑐𝐼𝐼𝑎𝑎𝑐𝑐𝑎𝑎𝑐𝑐𝑎𝑎𝐼𝐼𝐼𝐼𝑎𝑎𝑐𝑐𝑎𝑎𝑐𝑐 + 𝑎𝑎𝑎𝑎𝑡𝑡𝑎𝑎𝐼𝐼𝑎𝑎𝑐𝑐𝑎𝑎𝑐𝑐𝑎𝑎𝐼𝐼𝐼𝐼𝑎𝑎𝑐𝑐𝑎𝑎𝑐𝑐 + 𝜖𝜖𝑖𝑖

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No significant relation was found between a relative change of the capital share of income and the real annual growth of the GDP per capita, if the gross capital formation is included.

The effects of change in the capital share of income through the channel of human capital accumulation, could take several years. For that reason, the difference in the capital share of income of previous years is also taken into account. Table 3 shows the output with the change of the capital share of income over several years:

GGDP = β0+ 𝛽𝛽1(𝐶𝐶𝑆𝑆𝑡𝑡−1− 𝐶𝐶𝑆𝑆𝑡𝑡−2) + 𝛽𝛽2(𝐶𝐶𝑆𝑆𝑡𝑡−2− 𝐶𝐶𝑆𝑆𝑡𝑡−3) + 𝛽𝛽3(𝐶𝐶𝑆𝑆𝑡𝑡−3− 𝐶𝐶𝑆𝑆𝑡𝑡−4) + 𝛽𝛽4(𝐶𝐶𝑆𝑆𝑡𝑡−4− 𝐶𝐶𝑆𝑆𝑡𝑡−5) + 𝛽𝛽5𝐺𝐺𝐶𝐶𝐹𝐹𝑡𝑡+ 𝛽𝛽6𝐼𝐼𝐼𝐼𝐼𝐼𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝐼𝐼𝐼𝐼𝑡𝑡+

𝑐𝑐𝐼𝐼𝑐𝑐𝐼𝐼𝑎𝑎𝑎𝑎𝑐𝑐𝐼𝐼𝑎𝑎𝑐𝑐𝑎𝑎𝑐𝑐𝑎𝑎𝐼𝐼𝐼𝐼𝑎𝑎𝑐𝑐𝑎𝑎𝑐𝑐 + 𝑎𝑎𝑎𝑎𝑡𝑡𝑎𝑎𝐼𝐼𝑎𝑎𝑐𝑐𝑎𝑎𝑐𝑐𝑎𝑎𝐼𝐼𝐼𝐼𝑎𝑎𝑐𝑐𝑎𝑎𝑐𝑐 + 𝜖𝜖𝑖𝑖

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No significant correlation was found with a change in the capital share of income from previous years. Model 1-3 in table 1 and model 4-6 in table 2 and model 7-10 in table 3 are autocorrelated (see section 6). Autocorrelation makes the estimators not efficient. This autocorrelation could also mean there is reversed causality in the model. Because the growth of the dependent variable (the

growth of the GDP) is autocorrelated, an increase in the growth of the GDP could be explained out of the lagged growth of the GDP. The lagged growth of the GDP can have a causal effect on the change in the capital share of income, leading to a biased estimator. Figure 4 and figure 5 show the dependent variable (the growth of the GDP) and the independent variable of interest (the change in the capital share of income). These figures show that both the growth of the GDP and the change in the capital share of income are mostly positive. This may partly explain the positive correlation, since both variables are mostly positive.

To solve the problem of autocorrelation, a test with lagged dependent variables is run. Table 4 shows the output of the same OLS-regression as equation 4, with different lagged values of the growth of the GDP included.

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𝛽𝛽5(𝐶𝐶𝑆𝑆𝑡𝑡−1− 𝐶𝐶𝑆𝑆𝑡𝑡−2) + 𝛽𝛽6(𝐶𝐶𝑆𝑆𝑡𝑡−2− 𝐶𝐶𝑆𝑆𝑡𝑡−3) + 𝛽𝛽7(𝐶𝐶𝑆𝑆𝑡𝑡−3− 𝐶𝐶𝑆𝑆𝑡𝑡−4) + 𝛽𝛽8(𝐶𝐶𝑆𝑆𝑡𝑡−4− 𝐶𝐶𝑆𝑆𝑡𝑡−5) + 𝛽𝛽9𝐺𝐺𝐶𝐶𝐹𝐹𝑡𝑡+ 𝛽𝛽10𝐼𝐼𝐼𝐼𝐼𝐼𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝐼𝐼𝐼𝐼𝑡𝑡+

𝑐𝑐𝐼𝐼𝑐𝑐𝐼𝐼𝑎𝑎𝑎𝑎𝑐𝑐𝐼𝐼𝑎𝑎𝑐𝑐𝑎𝑎𝑐𝑐𝑎𝑎𝐼𝐼𝐼𝐼𝑎𝑎𝑐𝑐𝑎𝑎𝑐𝑐 + 𝑎𝑎𝑎𝑎𝑡𝑡𝑎𝑎𝐼𝐼𝑎𝑎𝑐𝑐𝑎𝑎𝑐𝑐𝑎𝑎𝐼𝐼𝐼𝐼𝑎𝑎𝑐𝑐𝑎𝑎𝑐𝑐 + 𝜖𝜖𝑖𝑖

Including the lagged values of the Growth of the GDP doesn’t solve the problem of autocorrelation (see section 6).

A model with the difference in growth is expected to solve the problem of autocorrelation. The dependent variable in this model is the change in the growth of the real GDP per capita; the growth of the real GDP per capita minus the lagged value of the real GDP per capita. Table 4 shows the output of the with the change of the growth of the GDP as the dependent variable:

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29 GGDPt− GGDPt−1 = β0+ 𝛽𝛽1(𝐶𝐶𝑆𝑆𝑡𝑡−1− 𝐶𝐶𝑆𝑆𝑡𝑡−2) + 𝛽𝛽2(𝐶𝐶𝑆𝑆𝑡𝑡−2− 𝐶𝐶𝑆𝑆𝑡𝑡−3) + 𝛽𝛽3(𝐶𝐶𝑆𝑆𝑡𝑡−3− 𝐶𝐶𝑆𝑆𝑡𝑡−4) + 𝛽𝛽4(𝐶𝐶𝑆𝑆𝑡𝑡−4− 𝐶𝐶𝑆𝑆𝑡𝑡−5) + 𝛽𝛽5𝐺𝐺𝐶𝐶𝐹𝐹𝑡𝑡 + 𝛽𝛽6𝐼𝐼𝐼𝐼𝐼𝐼𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝐼𝐼𝐼𝐼𝑡𝑡+ 𝑐𝑐𝐼𝐼𝑐𝑐𝐼𝐼𝑎𝑎𝑎𝑎𝑐𝑐𝐼𝐼𝑎𝑎𝑐𝑐𝑎𝑎𝑐𝑐𝑎𝑎𝐼𝐼𝐼𝐼𝑎𝑎𝑐𝑐𝑎𝑎𝑐𝑐 + 𝜖𝜖𝑖𝑖 (7)

Model 15-20 of table 5 show that a change in the Capital Share of income and the one-period lagged change in capital share are negatively correlated with the change of growth of the GDP the year after. Model 18 (this is the model with the highest adjusted R-squared) shows that an increase in the capital share with one percentage point, leads to a reduction of the economic growth of 0,222 in the following year and a reduction of 0,262 in the year thereafter. The models in table 5 are not autocorrelated (see section 6), and the correlation is significant, but it is difficult to give an interpretation of the results. The models in table 5 give the results of an effect on the change of a percentage change. Model 18 suggests that an increase of 1 percentage point from t-2 to t-1 in the capital share leads to a change of the growth from t-1 to t with -0,222. From this model you

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can’t tell however whether this change in the capital share led to a higher economic growth in t-1 or to a decrease of the economic growth in t. This model does suggest there is a relation but you can’t tell, however, exactly how they are related.

The growth of the GDP could have an effect on the capital share of income. To test whether economic growth leads to a change in the capital share of income, a regression is run with the change in capital share as the dependent variable. Table 6 shows a regression with the change in capital share as the dependent variable and the growth of the GDP per capita as independent variables. The change in the capital share is measured by the capital share minus the lagged value of the capital share.

𝐶𝐶𝑆𝑆𝑡𝑡− 𝐶𝐶𝑆𝑆𝑡𝑡−1= 𝛽𝛽0+ 𝛽𝛽1𝐺𝐺𝐺𝐺𝐺𝐺𝑃𝑃𝑡𝑡+ 𝛽𝛽2𝐺𝐺𝐺𝐺𝐺𝐺𝑃𝑃𝑡𝑡−1+ 𝛽𝛽3𝐺𝐺𝐺𝐺𝐺𝐺𝑃𝑃𝑡𝑡−2+ 𝛽𝛽4𝐺𝐺𝐺𝐺𝐺𝐺𝑃𝑃𝑡𝑡−4+ 𝛽𝛽5𝐺𝐺𝐺𝐺𝐺𝐺𝑃𝑃𝑡𝑡−5+ 𝛽𝛽6𝐺𝐺𝐶𝐶𝐹𝐹 + 𝛽𝛽7𝐼𝐼𝐼𝐼𝐼𝐼𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝐼𝐼𝐼𝐼 + 𝛽𝛽6𝑎𝑎 +

𝐶𝐶𝐼𝐼𝑐𝑐𝐼𝐼𝑎𝑎𝑎𝑎𝑐𝑐 𝐼𝐼𝑎𝑎𝑐𝑐𝑎𝑎𝑐𝑐 𝑎𝑎𝐼𝐼𝐼𝐼𝑎𝑎𝑐𝑐𝑎𝑎𝑐𝑐 + 𝑎𝑎𝑎𝑎𝑡𝑡𝑎𝑎𝐼𝐼𝑎𝑎𝑐𝑐𝑎𝑎𝑐𝑐𝑎𝑎𝐼𝐼𝐼𝐼𝑎𝑎𝑐𝑐𝑎𝑎𝑐𝑐 + 𝜀𝜀𝑖𝑖

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The growth of the GDP has a positive effect on the capital share of income from that year. As figure 7 shows, most fluctuations in the capital share, are due to fluctuations in the corporate capital share of income. Because of the economic growth, the dividends rise first. This explains the positive coefficient of the economic growth in that same year (0,378 in model 25). Wages are more rigid than dividends and it may take a few years before wages go up. This could explain why the one-period lagged and the two-period lagged growth of the GDP in model 25 have a negative effect on the Capital Share of income. Wages will go up two years after economic growth, leading to a higher labour share of income, and thus a lower capital share of income.

5.2. Interpretation of results

Models 1-8 suggest there is no significant relation between an increase in the capital share of income and the growth of the GDP per capita when the gross capital formation is included. Model 9 and model 10 suggest there is a positive relation between the capital share of income and the growth of the GDP per capita. This relation cannot be trusted, however, because of the problem of autocorrelation. Figure 3 and figure 4 show that both the GDP and the capital share of income are on an upward trend, and that could be the reason that they are positively correlated. Important to note is that including the growth of the gross capital formation has the effect that the estimator of a change in the capital share of income is no longer significant. This is consistent with the theory that a higher capital share of income will lead to the fact that there will be more invested in the following year, due to more aggregate savings. (Bourguignon, 1981) Including the growth of the gross capital formation in the model has as a result that this effect is explained by that estimator. An increase in the capital share of income leads to higher aggregate savings and therefore a higher gross capital accumulation. This explains the fact that there is a positive correlation in model 1 and model 4, where the gross capital formation is not included.

There is no autocorrelation if we look at the change of the growth of the GDP. However, the outcome of these models(15-20) is difficult to interpret. These models suggest that a rise in the capital share of income, results in less growth

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than the previous year, but we can’t tell if there is a positive or a negative relation with the growth of the GDP. The difference in model 15 and 16 shows that a higher capital share income, has as a result that more is invested in capital. Table 6 shows that economic growth will result in a higher capital share of income in the same year, but in a reduction of the capital share of income the year thereafter. This is most likely due to the fact that dividends (income on capital) rise first in times of economic growth, and wages (income on labour) rise only after a year.

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6. Robustness check

The tables in this section show the results for the Woolridge test for

autocorrelation in panel data. For every test the null hypothesis is that there is no autocorrelation and the alternative hypothesis is that there is autocorrelation. The null hypothesis is rejected when the p-value of the test is below 10%.

Table 7 shows the results of the Woolridge test for the models used in table 1, and table 8 shows the results for the models used in table 2.

These test show there is autocorrelation in model 1-6, and the results in table 9 show that this also the case when the lagged values of the change in the capital share are included (Model 7-10)

Including the lagged values of the growth of the GDP per capita could solve the problem of autocorrelation but table 10 shows that when this is done, there is still autocorrelation (in model 11-14)

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Table 11 shows us that there is no autocorrelation in model 16-18. Model 18 has the lowest F-value, while it has the highest adjusted R-squared.

These tests show that all models face the problem of autocorrelation, except the models with the change in the growth of the GDP per capita as the dependent variable.

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7. Conclusions

Piketty states that a higher capital share of income leads to a higher inequality, and Cingano(2014) shows that a higher inequality results in a lower economic growth. Based on these theories an increase in the capital share of income will result in a decrease of the economic growth. The capital share of income (and thus a decrease in the labour share of income) could have a negative effect on the economic growth for two other reasons. First, in accordance with the human capital accumulation theory, if more is paid to capital compared to labour, there is no incentive to invest in education. Second, if more is paid to capital there is no incentive to work at all for capital owners.

Based on the models in this paper, it is hard to say anything about the effect of a change in the capital share of income on the economic growth. It is clear that a higher capital share of income provides an increase in the investments in capital. Through this channel a higher capital share of income can have a positive effect on economic growth. As Bourguignon (1981) says, more inequality leads to higher savings and more investments. This is probably all the more true considering the capital share of income. Owners of capital will likely reinvest more of their earned money. Because of the autocorrelation in model 1-15, it is difficult to determine the effect of a change in capital income on economic growth.

The difference in the estimator of the change in the capital share of income, in table 4, suggests that a higher capital share of income has a positive effect because of the increased investment in capital, but a negative effect due to other reasons. Further research is needed to determine what these reasons may include. This could be the Human Capital Accumulation theory (Galor & Zeira, 1993) or it may be because capital owners tend to work less hard. Economic growth first creates a rising capital share of income. If we look at equation 1, α=r* β, this is probably the result of a higher return on capital. This becomes less after a few years, because wages go up. Here the assumption is made that in times of economic growth, dividends rise faster than wages. This corresponds to the Kuznets curve. Economic growth leads to inequality first, but after a few years to equality (Barro, 2000). Another reason why this share rises first but then seems to decline, is that the economic growth creates excess savings.

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Because of this excess savings, the return on capital drops after a few years. According to Piketty(2014), however, the total amount of capital will always rise faster than the rate of return on capital will decrease. An increasing capital share of income can have an effect on economic growth in different ways. This study shows that there is not a direct clear correlation. Further research is needed to determine what the effects will be in the short and long term.

Further research is needed to determine whether there really is a causal relation between a rising capital share of income and the effect on economic growth. A model has to be developed that takes into account the problem reversed causality. It is also worth examining the effect of the capital share of income in the long run. This paper only examines the relation between a change in the capital share and the economic growth. A high share of capital income for several years could also have a negative effect on the economic growth. This does not mean that in those years the capital share of income increases. The models in this paper do not account for that effect. If such a model is made, it should be taken into account that the relationship may not be linear. It is possible that a certain ratio between capital income and labour income is optimal for economic growth. Further research will also be needed to show the differences in the short term and long term. This study did not investigate the differences in the various types of capital income. Figure 6 shows that the housing capital share of income is mainly on the rise. The research in this paper has looked only at the

macroeconomic level. An investigation at the microeconomic level will better be able to determine the effects of a higher capital share of income within a

company. Found results do not mean that measures must be taken to prevent a higher capital income, because such measures could also have a direct negative effect on economic growth. Piketty argues in his book for regulations to reduce inequality, but research is needed to test whether these regulations may have a direct effect on economic growth.

This study only investigated eight rich countries. The effects may be different in other countries and may vary over time. There is currently little data available about the structure of the national income of other countries.

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8. Bibliography

Barro, R. J., 2000. Inequality and Growth in a Panel of Countries. Journal of

economic growth, 5(1), pp. 5-32.

Bloome, D., 2013. Income Inequality and Intergenerational Income Mobility in the United States. Russel.

Bourguignon, F., 1981. Pareto superiority of unegalitarian equilibria in

Stiglitz'model of wealth distribution with convex saving function. Econometrica:

Journal of the Econometric Society , pp. 1469-1475.

Cingano, F., 2014 . Trends in Income Inequality and its Impact on Economic Growth. OECD Social, Employment and Migration Working Papers , Volume 163 . Galor, O. & Zeira, J., 1993. Income Distribution and Macroeconomics. The Review

of Economic Studies, 60(1), pp. 35-52.

Homburg, S., 2015. Critical remarks on Piketty’s Capital in the Twentyfirst.

Applied Economics, 47(14), pp. 1401-1406.

Keefer, P. & Knack, S., 2000. Polarization, politics and property rights. World

Bank Policy Research Working Paper, Issue 2418.

Lazear, E. P. & Rosen, S., 1979. Rank-Order Tournaments as Optimum Labor Contracts. Journal of, 89(5), p. 841–64.

Lee, B. R. a. J., 2013. A new data set of educational attainment in the world, 1950– 2010. Journal of, Volume 104, pp. 184-198.

Morrisson, Christian & Murtin, F., 2013. The Kuznets curve of human capital inequality: 1870–2010. The Journal of Economic Inequality, 11(3), pp. 283-301. Piketty, T., 2014. Capital in the 21st Century. London: Harvard University Press . Weil, D. N., 2015. Capital and Wealth in the 21st Century. National Bureau of

Economic Research, Volume w20919.

Zeira, J., 1998. Workers, Machines, and Economic Growth. The Quarterly Journal

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The distinction for Elder Douglas Headworth between First Nations traditional food practices and sport hunting is premised around the role of traditional foods as a way

Using in-situ electron microscopy, we observe and quantify how gold and silver nanocrystals nucleate from a supersaturated aqueous gold and silver solution in

Concessionaire model for food and beverage operations in South African national parks | iii period of three weeks and consisted of four sections, namely a demographic section, a

Biomaterials Innovation Research Center, Division of Engineering in Medicine, Brigham and Women's Hospital, Harvard Medical School, Cambridge, MA 02139, USA.. Harvard-MIT Division