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University of Groningen

Faculty Economics and Business

The effect of foreign aid to education on economic

growth in Sub-Saharan Africa

Name: Sanne de Wit Student number: S2727374

Supervisor: G.H. Kuper Date of submission: March 6, 2019

Abstract

This thesis is aimed to investigate the relationship between foreign aid to education and economic growth in Sub-Saharan Africa. The analysis covers 46 countries over a time period of 1995-2017. The model that is used is based on the Solow growth model, in which lagged GDP per capita, population growth, investment and the education index are used as

explanatory variables. Furthermore, I control for the quality of institutions, trade, inflation, fertility, government consumption and the life expectancy. Moreover, an interaction

variable is included that tests the relationship between the quality of institutions and aid on economic growth. The model is tested with and without the use of instrumental variables to prevent endogeneity problems. The results of this research show a significant, positive relationship between foreign aid to education and economic growth in Sub-Sahara African countries. This effect is largened when the quality of institutions increases.

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Contents

Abstract ... 1

1. Introduction ... 4

2. Background ... 6

2.1 Theories of economic growth ... 6

2.1.1 The classical growth model ... 6

2.1.2 The neo-classical growth model ... 7

2.1.3 Endogenous growth models ... 8

2.1.4 Theories of foreign aid and economic growth ... 9

2.2 The definition of foreign aid ... 10

2.3 Foreign aid: Background and policy development ... 11

3. Literature review ... 14

3.1 Aid and growth: country heterogeneity? ... 14

3.2 Aid and growth: aid heterogeneity? ... 16

3.3 Aid, education and growth ... 17

3.4 Aid and endogeneity ... 18

4. Empirical model and methodology... 21

4.1 Data ... 21

4.1.1 Aid to education ... 21

4.1.2 Control and explanatory variables ... 22

4.2 The background of the model ... 25

4.3 The model... 26

4.3.1 The base model ... 27

4.3.2 The extended model ... 28

4.4 Methodology ... 30

5. Results ... 33

5.1. The base model ... 33

5.2 The extended model... 35

5.2.1 Equation 8 and 8a ... 35

5.2.2 Equation 9 and 9a ... 38

5.2.3 Equation 10 and 10a ... 41

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Abbreviations

2SLS – Two stage least squares

BLUE – Best Linear Unbiased Estimator ACH – Absolute convergence hypothesis CCH- conditional convergence hypothesis CRS – Credit Reporting System

DAC - Development Assistance Committee GDP – Gross Domestic Product

GEMR – Global Education Monitoring Report GNI – Gross National Income

IV – Instrumental Variable

NGOs – Non-governmental organizations ODA – Official Development Assistance

OECD - Organisation for Economic Cooperation and Development OLS – Ordinary least squares

R&D – Research and development SSA – Sub-Saharan Africa

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1. Introduction

In many economic theories, human capital is an essential ingredient for economic growth. Unquestionable, education is the key to increase human capital and therefore it is promising that worldwide more attention has been payed to provide universal primary education in developing countries. For example, the second goal of the United Nations Millennium Development Goals (2000) is to achieve Universal Primary Education, which means that the United Nations wants ‘to ensure that by 2015, children everywhere, boys and girls alike will be able to complete a full course of primary schooling’. Moreover, UNICEF claims that education is the key to meet all other Millennium Development Goals: ‘Educating children gives the next generation the tools to fight poverty and prevent diseases, including malaria and AIDS’. Between 2000 and 2015 the number of out-of-school children has decreased from 100 million to 61 million worldwide, which means that 91% of primary-school-age children were enrolled in school in 2015. The most challenging region is Sub-Saharan Africa (SSA), where only 79% of the children were enrolled in 2015 (UNICEF, 2016).

There is an ongoing discussion about the impact of foreign aid on economic growth,

especially in developing countries. The literature is divided into two main point of views; one that suggests that foreign aid contributes to economic growth, and contradictory, one that suggests that it does not. In his essay ‘Why Doesn’t Aid Work?’, Easterly (2006) supports the latter argument and suggests that evaluation of aid programs is very important in making foreign aid a success. One of the main principles of the Paris Declaration in 2005 is the establishment of a monitoring system to assess progress in recipient countries. To measure progress, not only the reduction of poverty and inequality, but also economic growth is considered as an important factor.

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ODA was invested in Africa (OECD, 2017). This indicates the emphasize of developed countries to help Africa to grow. Moreover, analysing the effect of this large investment in education in Africa is interesting, since initial education attainment and literacy levels are quite low in Africa compared to other regions. To study this effect, a regression analysis has been made on a data sample which includes 46 countries in Sub-Saharan Africa during the period of 1995-2017. The main finding of this paper is that foreign aid to education has a positive effect on economic growth. Furthermore, this positive effect is larger when the quality of institutions increases.

This thesis is organized as follows; the background of multiple economic growth theories and theories of the effect of foreign aid on economic growth is explained in the second section. The third section consists of a literature review that summarizes previous research about the effect of foreign aid on economic growth. The literature review will be followed by a section about the empirical model and methodology. In the fifth section, the results of the

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2. Background

In this section, important background theories and definitions are explained. First, the three most important economic growth theories are explained followed by a part that covers models about the relationship between foreign aid and economic growth. Next, the definition, the background and the development of foreign aid (to education) will be presented.

2.1 Theories of economic growth

There are numerous growth models that suggest why or why not economic growth occurs. Those models suggest potential factors that could encourage economic growth, for example capital, (the quality of) the labour force, technological improvement and resources.

Economists in the 1950s and 1960s thought that the main problem of developing countries was the lack of capital to invest and increase economic growth. They argue that

development assistance could be the key to promote economic growth in developing countries. The relationship between aid and economic growth goes through investment and undoubtedly, aid could fund investment (Gomanee et al. 2006). The first model that implies that savings contribute to economic growth is the Harrod-Domar model. This model is followed by one of the most important models of economic growth, the Solow-Swan model, which emphasizes how investments and capital support economic growth. This exogenous growth model is followed by multiple endogenous models that emphasize the importance of human capital accumulation and research and development (R&D) activities for economic growth. The studies that focus on the relationship between foreign aid and economic growth are mostly based on classical growth theories.

2.1.1 The classical growth model

One of the first explanations for economic growth is designed by among others Adam Smith in the 18th and 19th century. The classical growth theory can be summarized as follows; due

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per capita, the living standards will increase as well. The better living standards cause the population to grow and the workforce to expand. Since the amount of capital is fixed in the classic growth model, and the size of the labor force increases, labor productivity falls and GDP per capita will follow until the equilibrium level of GDP per capita is reached and the growth rate becomes zero. Summarized, the growth of the population will always cancel out the positive effects of technological improvement and GDP per capita will always return to the survival rate or stationary state. Nowadays, we know that this model is not valid in the real economy. During the 18th century, a lot of countries experienced a rise in GDP per capita

and population due to technological improvement, however the positive effects of the technological improvement were not cancelled out (Ucak, 2015).

2.1.2 The neo-classical growth model

To explain a permanent growth in GDP per capita, the neo-classical growth model is independently developed by Solow (1956) and Swan (1956). It is an exogenous growth model, which indicates that the government is unable to affect GDP per capita in the long run and the long run growth rate is not influenced by the savings rate. In this model, population growth and labor supply are exogenous in contrary to the classical growth theory. Furthermore, households save a constant percentage of their income. The long run growth rate of output is the sum of the population growth and labour-augmenting

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levels, and rich countries, those that have higher starting points due to higher capital, should convergence overtime and this is called the absolute convergence hypothesis (ACH). Barro and Sala-i-Martin (1995) test this hypothesis and find evidence that countries that were rich in the base year 1960 actually had higher growth rates than poor countries, which means that the ACH does not hold. However, there is another more sophisticated hypothesis that is called the conditional convergence hypothesis (CCH) which states that only truly similar characterized countries should converge. Again, Barro and Sala-i-Martin (1995) test this hypothesis with the use of twenty original OECD countries and found no evidence that could reject the CCH (Heijdra, 2017).

2.1.3 Endogenous growth models

The exogenous growth models lead to dissatisfaction of many economists. The rate of technological improvement is assumed to be determined exogenously, while there are many reasons to believe that it depends on economic decisions, like industrial findings that could be invented through funding. Among others, Paul (1986) establishes the first endogenous growth model that takes endogenous factors as determinants of economic growth into account. They develop the AK model, characterized by the absence of labour in the

aggregate production function and constant returns to capital (instead diminishing returns in the Solow/Swan models). The definition of capital differs in this model from the neo-classical growth model. In the Solow/Swan model, capital stands for physical capital, while in the AK model, capital is much broader and includes human capital as well. Constant returns to capital are the result of the increase in the marginal product of capital caused by the technological improvement. When people accumulate capital, they learn by doing which leads to efficiency and technological development (Howitt, 2008). The AK model is an endogenous growth model that highlights the importance of efficiency as a driver for economic growth, however other models have been developed that explain endogenously driven growth by other reasons.

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and effective labour. Particularly, this model can be interesting for this research, since it highlights the importance of education to increase economic growth. Investments of the government in developing countries are restrained by the absence of adequate domestic savings (explained in the next section). The lack of savings can be financed through foreign aid. With the use of foreign aid to education, the government invests in education, which leads to higher human capital and an increase in productivity. The model predicts an

increase in national savings, because the increase in productivity will result in an increase in savings.

Furthermore, Romer (1990a) describes another endogenous growth model, in which technological progress is the ultimate engine of economic growth. In his model, there are three sectors or production sides; the final-output sector, the intermediate good sector and the R&D sector. In the final-output sector the market is perfectly competitive, so zero profits are made. The goods that are sold are used for consumption or as input for the other two sectors. The market of the intermediate good sector is monopolistic, since products are different from each other. Each producer is quasi-monopolist with respect to their own product and therefore enjoys profits. However, to be an intermediate good producer, you must acquire a blueprint from the R&D sector. This blueprint is the technology for

transforming final goods into differentiated intermediate inputs. The R&D sector is

competitive and produces the aforementioned blueprints. The blueprints are protected by patents. All economic growth is due to innovation and technological improvements.

2.1.4 Theories of foreign aid and economic growth

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incentives to invest. If there is a lack of incentives, foreign aid only contributes to higher consumption, instead of investments (Boone, 1995).

The extension of the two-gap model includes another gap, the fiscal gap, and that not surprisingly is called the three-gap model. This fiscal gap is a subset of the savings gap and indicates the gap between government revenues and its expenditures. When government’s resources to invest and import are deficient (as result of debt service), the government is unable to encourage private investment. There is sufficient evidence to conclude that

expenditures of governments in Sub-Saharan African countries are restricted by foreign debt services (Tarp and Hjertholm, 2000). Furthermore, the dependency of developing countries to foreign aid to fill these gaps maintains not only because of the gaps explained above, but also due to the fact that aid is highly effective in raising growth in ‘good’ environments, but quite ineffective in ‘poor’ environments (Collier and Dollar, 1999). Poor environments, like Sub-Saharan Africa, are characterized by underdeveloped institutions which results in low education and technological development levels, poor economic and social infrastructure and political instability.

2.2 The definition of foreign aid

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contains over 150 countries or territories with per capita incomes below $12.276 in 2010 (OECD Net ODA, 2018). According to the DAC, ‘Aid activities include projects and programs, cash transfers, deliveries of goods, training courses, research projects, debt relief operations and contributions to non-governmental organizations’ (OECD DAC Glossary, 2018). Most of these aid activities fund projects that reinforce infrastructure, health and education

institutions, political stability and emergency help during humanitarian crises. The focus of this research is aid with educational purposes. Aid to education can be divided into five sub-sectors; primary education, secondary education, post-secondary education, education policy and administrative management, and education facilities, training and research.

2.3 Foreign aid: Background and policy development

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to flee from the wars and riots and depart to Europe. Germany, Greece and Italy reported that over 20% of their ODA in 2015 was spent on refugee costs (OECD Development, 2016). Furthermore, the drop of the line in 2007 and 2008 in the graph represent the financial crisis of that same period. During the crises, governments have smaller incomes and therefore lower budgets, which results in the decrease in development aid expenses.

Figure 1. Development of Official Development Assistance (ODA) 1960-2016 Source: OECD

Figure 2 illustrates the development of the part of the ODA that is invested in total

education. Since 1995, the amount of ODA invested in education has grown steady, both in the world and in Sub-Saharan Africa (SSA). As mentioned before, one of the Millennium Development Goals is to provide universal primary education in 2015. Although the goal is failed, it resulted in an increase in ODA to education. Since 2000, the governments of low-income countries have increased their spending on education, however the Global Education Monitoring Report (GEMR) estimate that low-income countries will face an annual financing gap that is equivalent to 42% of the total cost of providing quality pre-primary, primary and secondary education to all children (UNESCO, 2015a). Aid to education needs to be six times higher than 2012 levels for low-income countries (UNESCO, 2015b). Unfortunately, donors continue to place a lower priority on aid to education. The share of education in total aid

0 20000 40000 60000 80000 100000 120000 140000 160000 180000 19 60 19 62 19 64 19 66 19 68 19 70 19 72 19 74 19 76 19 78 19 80 19 82 19 84 19 86 19 88 19 90 19 92 19 94 19 96 19 98 20 00 20 02 20 04 20 06 20 08 20 10 20 12 20 14 20 16 O D A i n mi lli ons of cons ta nt 2 01 5 U S do lla rs Year

Total net Official Development Assistance

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(excluding debt relief) has fallen from 10% in 2009 to 6.9% in 2015. As mentioned before, 79% of primary-school-aged children attend school in Sub-Sahara African countries. More than half of the world’s out-of-school children live in Sub-Saharan Africa, and this region receives 26% of the total amount of aid to education in 2015. In Northern Africa and Western Asia live only 9% of out-of-school children, however those regions get 22% of the total amount of aid to education in 2015, a disproportionally high share. The countries with the highest contribution to the total aid to basic education are United States (2.9%), the United Kingdom (4.6%), Germany (2.4%), United Arab Emirates (6.3%) and Norway (7.5%). The percentages in bracket stand for the share of the total amount of aid of that country that is allocated to basic education (UNESCO, 2017).

Figure 2. Development of ODA to education 1995-2017 Source: OECD CRS 0 2000 4000 6000 8000 10000 12000 14000 16000 O D A t o educ at ion in mi lli ons o f cons ta nt 2 01 5 U S dol la rs Year

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3. Literature review

In this section, important research about the relationship between foreign aid (to education) and economic growth will be presented. The empirical results and methodological issues will be given as well.

The relationship between foreign aid and economic growth is a massively debated topic in not only academic articles, but also national institutions want to know whether their generous support is beneficial to the recipient country. While some studies conclude that there is a positive relationship between foreign aid and economic growth, others state that aid does not promote growth. Some have found evidence that only in an effective climate, so countries with powerful policies and developed institutions, aid contributes to economic growth. Others conclude that projects supported by foreign aid benefits citizens on

microeconomic-level, but there is no evidence of effectiveness on the macroeconomic-level. Despite the vast amount of literature, there is no agreement about the relationship between foreign aid and economic growth. Furthermore, some authors describe the problem of endogeneity on this relationship, however this problem can be addressed by using instrumental variables.

3.1 Aid and growth: country heterogeneity?

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aid normally goes to poorer countries (or with poor performance). They conclude that aid has no significant effect on growth, neither that aid works better in good policy or

geographical circumstances, nor that a certain form of aid is more beneficial to growth than others. Boone (1996) also conclude that there is no significant effect between aid and growth. By testing the effect of aid on poverty indicators, such as life expectancy, school attendance and infant mortality, he wants to test whether aid benefits the targeted poor. He concludes that human development indexes do not increase with aid, however the size of the government does is positively affected by aid. Furthermore, he concludes, contradictory to Rajan and Subramanian (2005), that short-term aid aimed to support new liberal regimes may be a more successful method to reduce poverty than current programs. More resolute, Burnside and Dollar (2000) state that ‘aid has a positive impact on growth in developing countries with good fiscal, monetary, and trade policies but has little effect in the presence of poor policies.’ To catch country heterogeneity, they include country specific fixed effects in their model. With the use of a panel data set that includes 56 countries between 1970-1993, both an OLS as a two stage least squares (2SLS) regression is made. Furthermore, the authors develop a policy index, using the budget surplus, inflation rate and an openness to trade dummy for each country, each having different weights. In their model, the policy index is interacted with the aid term to catch the differences in policy environments across the recipients. However, Ram (2004) conclude that there is little empirical evidence to support the view that aid results in more growth and greater poverty reduction in

developing countries with good policies. Hansen and Tarp (2001) examine the relationship between foreign aid and growth in real GDP per capita. They also conclude that aid increases the growth rate, but contradictory to Burnside and Dollar (2000), it does not depend on a good policy of the recipient country. Furthermore, they claim that there are decreasing returns to aid and that the estimated effectiveness of aid is highly sensible to the set of control variables, for example, when investment and human capital are controlled for, there is no evidence of a positive effect of aid. Furthermore Clemens et al. (2004) also claim that economic growth can be achieved without good institutions or policy climate.

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vulnerable to shocks, environmental disasters and political conflicts that result in a negative coefficient (Nilsson, 2013). In addition, Dalgaard et al. (2004) create a model which includes a ratio that represents the country’s share of land in the tropics and interact that ratio with aid. The authors conclude that aid has a stronger positive effect on economic growth in countries with a ratio of 0 (meaning no land in tropics) and that the opposite, so countries with a larger ratio, are characterized by a smaller effect of aid on economic growth. Furthermore, Collier and Hoeffler (2004) use an OLS regression together with robust standard errors to test if in post-conflict countries aid can contribute to growth. They find evidence that aid is efficient in encouraging economic growth in post-conflict countries.

3.2 Aid and growth: aid heterogeneity?

Research from the last decade focus more on the influence of different types of aid on economic growth rather than aggregate aid data. The problem of using aggregate data on aid is that it presumes that the impact of aid on growth is the same for all different types of aid. Some types of aid are not meant to increase growth, but for example to meet

humanitarian emergency needs after a nature disaster. Therefore, the separation of aid in different sub-categories is essential to investigate the heterogeneity of aid, instead of focusing on the country heterogeneity in section 3.1. The focus of this research is the subcategory foreign aid to education, however in this section all literature that focuses on aid heterogeneity is taken into account.

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four-year period, namely a $1 increase in short-impact aid results into a $8 increase in output and income. Furthermore, the authors test for country heterogeneity and find that this result is not dependent upon the recipient country’s level of developed institutions and policies. However, the authors find that the effect of aid on growth is stronger in countries with more developed institutions and higher life expectancies.

A paper that addresses the issue that the effect of foreign aid on growth could be somehow delayed is the research of Nilsson (2013). The aim of that study is to determine whether aid allocated into different sectors does affect growth differently in different time spans. The effect on growth is studied in short-term, 0 years, and long-term, 7 years. For aid that is invested in the social infrastructure, for example health, education, water, sanitation, the effect on growth is short-term. However, aid that is allocated to improving financial systems, transports, energy and communications, show a long-term effect on economic growth.

3.3 Aid, education and growth

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improvements in educational quality. However, aid to education can contribute to economic growth in recipient countries, since it facilitates the accumulation of human capital.

3.4 Aid and endogeneity

There are some empirical issues when the effect of aid on growth is studied, however the main problem is endogeneity. Endogenous variables are explanatory variables that are correlated with the equation’s error term and cause the OLS estimators to be biased and inconsistent. Endogeneity can arise from omitted variable bias, reverse causality and simultaneity, and measurement errors (Verbeek, 2012). In this research, endogeneity can arise due to reverse causality and omitted variable bias. Reverse causality means that not only the explanatory variable, aid in this case, influences the dependent variable, economic growth, but also the dependent variable (economic growth) also affects the independent variable (foreign aid). In this research, this problem could arise since countries with a lower economic growth are more likely to receive foreign aid. Furthermore, omitted variable bias can occur in this research, which means that a relevant explanatory variable that is

correlated with other regressors is omitted from the model. In this research, it could be that omitted variables exist, that influence both aid and growth. As mentioned before, it is likely that countries with lower economic growth will receive more aid or that donor countries have specific strategic interest when donating aid, which both result in the fact that aid is not exogenously given upon growth. Since this bias will be included in the error term, which leads the error term to be correlated with either the dependent and independent variable.

When one or more explanatory variables in a model are endogenous, so they are correlated with the error term, the OLS estimator is biased and inconsistent. To solve this econometric issue of endogeneity, an instrumental variable (IV) estimator could be used. An IV is a

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Dollar (2000) and included instrumental variables to test whether aid is more effective in countries with good policies and institutions. Burnside and Dollar (2000) did not use IV’s and as mentioned before, they concluded that aid is only effective in increasing economic

growth in countries with good policies and institutions. However, Dalgaard and Hanssen conclude that the results of Burnside and Dollar is not robust and obtain a positive effect of aid in any policy environment. Furthermore, Brückner (2013) also use an IV-estimator to overcome reverse causality and only find a significant positive effect when using this method. Moreover, Boone (1995) uses a two-step model to overcome the problem of endogeneity. When using a two-step model, first the effect of foreign aid on growth is estimated and then the residual variation in aid that is not caused by growth is estimated, which is used as an instrument.

However, there are also economists that are opposed using an estimator. Since an IV-estimator is only valid if the instrumental variable is uncorrelated with the error term and the instrumental variable is correlated with the endogenous variable. The new instrumental variable should affect economic growth through foreign aid. Some argue that there are no valid instruments that could replace foreign aid when testing the effect on growth. Some of the studies that use IV-estimators (Clemens et al. (2004), Hansen and Tarp (2000) and Boone (1995)), use lagged values of social and political indicators, like mortality rates and life expectancy, school enrolment rates, dummies for former colonies and population size. The use of lagged variables as instrumental variables could be useful in this research as well.

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4. Empirical model and methodology

In this section the data, estimation strategy and model that is used to test the effect of aid on growth is explained. This thesis focuses on Sub-Saharan Africa only, to lessen country heterogeneity issues.

4.1 Data

In this research, a panel data set of 46 countries in Sub-Saharan Africa is used, that are listed in table A1 in Appendix A. Sub-Sahara African countries that are characterized with high income, like Seychelles, were left out for obvious reasons. The dependent variable in this research is economic growth, measured by the relative change in the natural logarithm of GDP per capita between the current and previous period. Multiple explanatory variables are included based the growth theory of Solow and Swan. Furthermore, control variables are included in the regressions to overcome the problem of endogeneity due to omitted variables. The determination of control variables is based on earlier research and models. Data is retrieved from the Worldbank and the OECD DAC’s Creditor Reporting System (CRS). The Worldbank has a Development Data Group that coordinates statistical and data work and maintains databases. The data from the Worldbank comes from a country’s statistical system, and the quality of this data depends on the performance of those national statistical systems. The OECD DAC’s Creditor Reporting System is a database that captures aid

activities. The aid data is divided in recipient and donor countries, different sectors and type of aid.

4.1.1 Aid to education

In the sample used for this research, all aid to education provided by official donors is taken into account. Aid to education is the share of ODA that is invested in education in constant 2015 prices. The data is obtained from the Credit Reporting System of the OECD’s

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4.1.2 Control and explanatory variables

As mentioned before, the set of control variables is based on literature about the drivers of economic growth. In his paper ‘I Just Ran Four Million Regressions’ Sala-i-Martin (1997) runs millions of regressions with fixed effects to overcome the problem of omitted variable bias. For each regression, he tests how strong the regressions on itself is and investigate the sign of the coefficient to create a probability that explains which determinants explain growth. The determinants that affected growth the most are: political and economic stability, openness of the economy, property rights and law systems, low public intervention, and investment in capital, education and health. Barro (1991) explains that differences in GDP per capita growth rates could be positively explained by initial human capital, rule of law, international openness, and negatively on the ratio of government consumption to GDP, the fertility rate, and to the rate of inflation. Furthermore, he concludes that the relationship between investment and growth is positive but weak. Contradictory, Levine and Renelt (1992) conclude that the most robust cause of economic growth is the ratio of investment to GDP. Doppelhofer et al. (2004) use 32 explanatory variables in their regression to test the determinants of economic growth and rank them based on the robustness and conclude that initial log per capita GDP is the most important determinant. Based on those papers, a measure of institutional quality and investment as a share of GDP will be included as control variables in the model. Furthermore, an interaction term of aid and the quality of

institutions is included in the model, based on the research of Burnside and Dollar (2000). They state that foreign aid only has positive effects on economic growth in countries that have “good policies and institutions.”

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The data of the control and explanatory variables, log GDP per capita of the previous period, population growth, investment, inflation rates, trade, government consumption, inflation, the fertility rate, life expectancy at birth are obtained from the Worldbank (2018). The education index data is obtained from the UN Development Program. The data of the measure of quality of institutions that is used is collected from the Worldwide Governance Indicators (WGI) project (2018) supported by the Worldbank. The measure that is used is the rule of law variable, that indicates the ‘extent to which agents have confidence in and abide by the rules of society, and in particular the quality of contract enforcement, property rights, the police, and the courts, as well as the likelihood of crime and violence’ (WGI, 2018). The estimates can vary from -2.7 (weak) to 2.5 (strong) governance performance. The summary descriptive statistics of the variables that are used in this research are presented in Table B1 of Appendix B and a summary of the data is presented in Table 1.

Table 1. Summary of the data used for the analysis

Description Variable name Units Year Source Observations

Log GDP per capita

Logy Log, USD 1995-2017 Worldbank 995

Aid to education aid Log, USD 1995-2017 Worldbank 1,042

Aid to education aid % 1995-2017 Worldbank 990

Population growth

pop_grwth % 1995-2017 Worldbank 1,052

Education index edu Index 0-1 1995-2017 UN

Development Program

882

Investment/GDP investment % 1995-2017 Worldbank 927

Inflation in CPI inflation % 1995-2017 Worldbank 904

Trade/GDP trade % 1995-2017 Worldbank 944

Government consumption/GDP

govcon % 1995-2017 Worldbank 905

Fertility rate fertility Number of

children

1995-2016 Worldbank 1,012

Life expectancy at birth

lifeexp Years 1995-2016 Worldbank 1,012

Quality of institutions

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Table 1 summarizes the data used and the corresponding sources. Since the model of this research is based on a cross-section regression, economic growth is measured by the relative change in the natural logarithm of GDP per capita in constant US Dollars 2010 between the current and previous period, which is explained more extended in section 4.2. Furthermore, the cross-section model that is used by Barro (1991) is characterized by initial GDP per capita and initial human capital, measured by the human capital index.

Unfortunately, for the base year 1995, there is no data available of the human capital index, since this is a new measure. Instead, the education index is used, this is a measurement that includes the mean years of schooling for adults and the expected years of schooling for children, both weighted 50%. The data for the education index is obtained from the United Nations Development Programme (2018) and is scaled from 0-10, with 0 being a low education expectation and level. The lagged logarithm of GDP per capita is used to lessen the problem of large differences between countries instead of initial GDP per capita. Both initial GDP per capita and initial education index affect the growth rate in the long run. According to the convergence theory, countries that are already prosperous (high GDP per capita) tend to grow slower, whereas a developed work force (high human capital)

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4.2 The background of the model

The model1 that is used is based upon a Cobb-Douglas production function with constant

returns to scale. The production function in per capita terms is:

𝑦(𝑡) = 𝐴𝑘(𝑡)𝑎 (1)

in which A means the level of technology, y(t) = Y(t) / L(t) is the per capita income, and k(t) is the capital-labour ratio K(t) / L(t).  is a parameter that reflects the capital share of income. Furthermore, in this economy capital is accumulated by savings at a constant rate

0  s  1 and depreciation at a constant rate   0. Investments are equal to the savings rate times the total output. The labour force is growing at a constant rate n. The basic differential equation is obtained by setting the total savings (s*Y(t)) equal to the capital accumulation and write it in per capita form. The basic differential equation is:

𝑘̇ = 𝑠 ∗ 𝑦(𝑡) − (𝑛 + 𝛿)𝑘(𝑡) (2) If we put the production function in per capita form into the basic differential equation. The long run growth rate is obtained by dividing this equation by k, which results in the following equation

𝛾𝑘 = 𝑘̇𝑘= 𝑠 ∗𝑦(𝑡)𝑘 − (𝑛 + 𝛿) = 𝑠𝐴𝑘(𝑡)−(1−𝑎)− (𝑛 + 𝛿) (3)

The corresponding steady state is derived by setting 𝛾𝑘 equal to 0. The rate of growth of

output is derived as follows:

𝛾𝑦(𝑡) = 𝛼𝛾𝑘(𝑡) = −𝛽𝑎[log 𝑘(𝑡) − log 𝑘∗] = −𝛽 [log 𝑦(𝑡) − log 𝑦] (4)

The speed of convergence is defined by 𝛽 = (1 − 𝛼)(𝑛 + 𝛿). As can be seen, the speed of convergence depends on the population growth rate, the growth rate of labour-augmenting technical progress, the depreciation rate and the capital share of income. Equation 4 implies that if 𝛽 is positive, and countries are below their steady state income per capita, so

log 𝑦(𝑡) − log 𝑦∗ will be negative, their growth rates will be positive and the further away

from the steady state, the higher the growth rate. Furthermore, countries that have below steady state income per capita, will grow faster than countries that have above steady state income per capita, which is called the 𝛽-convergence. Structural differences between

1 The model that is explained in this section is obtained from ‘Limitations and implications of growth

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countries can result into different steady state income levels per country (Kuper et al., 1996). Since only Sub-Sahara African countries are included in this research, the steady-state levels will not be very different from each other.

Besides that, it is necessary to adjust equation (4), so it can be used in a panel analysis. Initial log GDP per capita or the steady state value cannot be used in a panel analysis, since those are fixed effects. In the new suitable equation, the difference between log output per capita,

log y(T), and log output per capita of the previous period, log y(T-1), also called the relative

change in log y, is explained by country specific details, a, and the log GDP per capita of the previous period, log y(T-1) and an error term u.

log 𝑦(𝑇) − log 𝑦(𝑇 − 1) = 𝑎 − (1 − 𝑒−𝛽) log 𝑦(𝑇 − 1) + 𝑢(𝑇) (5)

4.3 The model

The studies that test the effect of aid on growth use different methods and models to estimate the coefficients. Moreover, the effect of aid on growth does not have a

theoretically defined relationship on which the regression could be based upon. This results into a flexible choice of empirical model. The main aim of this study is to test the effect of foreign aid to education on economic growth, which results in a model that is depicted in equation (6).

100 ∗ ∆ log 𝑦𝑖,𝑡= 𝛽𝑖+ 𝛽𝑡+ 𝛽1log 𝑦𝑖,𝑡−1+ 𝛽2𝑝𝑜𝑝_𝑔𝑟𝑤𝑡ℎ𝑖,𝑡+ 𝛽3𝑒𝑑𝑢𝑖,𝑡+

𝛽4𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡𝑖,𝑡+ 𝛽5𝑎𝑖𝑑𝑖,𝑡+ ∑𝛽𝑛𝑐𝑛,𝑖,𝑡+ 𝜀𝑖,𝑡 (6)

The relative change between the current and previous period in the natural logarithm of GDP per capita of country i at time t is explained by: explanatory variables based on Solow (1956) and Swan (1956), namely the lagged value of log GDP per capita, population growth, the education index, and investments of country i at time t, the key explanatory variable aid of country i at time t, and a vector of n control variables c in country i at time t. Furthermore, 𝛽𝑖 + 𝛽𝑡 are the individual and period fixed effects, respectively. Since most explanatory

values are percentages, the dependent variable is multiplied by 100. To adjust for any

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correlation between errors of the same country in different time periods, so to avoid problems with heteroskedastic error terms. In the next section, the base model and

extended model will be explained. As mentioned before, there are researchers in favour of the use of instrumental variables and against. It is possible that the estimates are biased due to the endogeneity of the aid-growth relationship, however the use of instrumental

variables will avoid this problem of endogeneity. In this research, for variables that could be endogenous, lagged variables will be used as instrumental variables, based on Hansen and Tarp (2001) and Boone (1995). Instrumental variables should be uncorrelated with the error term, and influence the dependent variable, economic growth, through the endogenous variables that they replace. The education index, investment, aid, trade, government consumption, the fertility rate and life expectancy are all variables that could be

endogenous, and the lagged values of those variables could be relevant instruments in this research. All models will be estimated with and without the use of instrumental variables.

4.3.1 The base model

The first model that is regressed is a base regression and lacks additional control variables and is based upon the economic growth theory of Solow and Swan. This version of the Barro (1991) model only includes the log GDP per capita of the previous period, population

growth, the education index, and investments. Investments are used as a proxy for savings, since in the Solow Swan model, they are assumed to be equal. According to the exogenous growth theory of Solow and Swan, long run growth is affected by population growth

(determines the amount of labour available) and savings (leads to an increase in the capital stock). In this model, rapid population growth leads to smaller amounts of capital per worker, which decreases economic growth. A higher savings rate increases the amount of capital per worker, which increases productivity and therefore economic growth.

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Furthermore, equation 7a states the equation that will be estimated with the use of instrumental variables for education and investment.

100 ∗ ∆ log 𝑦𝑖,𝑡 = 𝛽𝑖+ 𝛽𝑡+ 𝛽1log 𝑦𝑖,𝑡−1+ 𝛽2𝑝𝑜𝑝_𝑔𝑟𝑤𝑡ℎ𝑖,𝑡+ 𝛽3𝑒𝑑𝑢𝑖,𝑡+

𝛽4𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡𝑖,𝑡+ 𝜀𝑖,𝑡 (7)

100 ∗ ∆ log 𝑦𝑖,𝑡 = 𝛽𝑖+ 𝛽𝑡+ 𝛽1log 𝑦𝑖,𝑡−1+ 𝛽2𝑝𝑜𝑝_𝑔𝑟𝑤𝑡ℎ𝑖,𝑡+ 𝛽3𝑒𝑑𝑢𝑖,𝑡−1+

𝛽4𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡𝑖,𝑡−1+ 𝜀𝑖,𝑡 (7a)

4.3.2 The extended model

In addition to the recipient’s country features, measured by the catch-up variable of log GDP per capita, the education index, population growth and investments, control variables are included to determine if other factors besides foreign aid influence economic growth in equation (8), (9) and (10). In equation (8), the control variables that are based on Sala-i-Marin (1997) are included in the model. The variable qlty_inst reflect the quality of property rights and law systems as well as the political and economic stability and trade reflects the openness of the economy. Both trade and the quality of institutions should have a positive effect on economic growth. Many economists study the effect of the quality of institutions on economic growth and while there is no real consensus, most of the researches claim that favorable institutions positively affect economic growth (Siddiqui and Ahmed, 2013).

Furthermore, there is enough evidence that the openness to trade positively affects

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100 ∗ ∆ log 𝑦𝑖,𝑡 = 𝛽𝑖+ 𝛽𝑡+ 𝛽1log 𝑦𝑖,𝑡−1+ 𝛽2𝑝𝑜𝑝_𝑔𝑟𝑤𝑡ℎ𝑖,𝑡+ 𝛽3𝑒𝑑𝑢𝑖,𝑡+ 𝛽4𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡𝑖,𝑡+ + 𝛽5𝑎𝑖𝑑𝑖,𝑡+ 𝛽6𝑞𝑙𝑡𝑦_𝑖𝑛𝑠𝑡𝑖,𝑡+ 𝛽7𝑡𝑟𝑎𝑑𝑒𝑖,𝑡+ 𝛽8𝑞𝑙𝑡𝑦_𝑖𝑛𝑠𝑡𝑖,𝑡∗ 𝑎𝑖𝑑𝑖,𝑡+ 𝜀𝑖,𝑡 (8) 100 ∗ ∆ log 𝑦𝑖,𝑡 = 𝛽𝑖+ 𝛽𝑡+ 𝛽1log 𝑦𝑖,𝑡−1+ 𝛽2𝑝𝑜𝑝_𝑔𝑟𝑤𝑡ℎ𝑖,𝑡+ 𝛽3𝑒𝑑𝑢𝑖,𝑡−1+ 𝛽4𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡𝑖,𝑡−1+ + 𝛽5𝑎𝑖𝑑𝑖,𝑡−1+ 𝛽6𝑞𝑙𝑡𝑦_𝑖𝑛𝑠𝑡𝑖,𝑡+ 𝛽7𝑡𝑟𝑎𝑑𝑒𝑖,𝑡−1+ 𝛽8𝑞𝑙𝑡𝑦_𝑖𝑛𝑠𝑡𝑖,𝑡∗ 𝑎𝑖𝑑𝑖,𝑡+ 𝜀𝑖,𝑡 (8a)

In equation (9), the control variables suggested by Barro (2003) are added to the model. These are the ratio of government consumption to GDP, the fertility rate and the inflation rate. According to the exogenous growth theory of Solow and Swan, a fiscal policy crowds out the physical capital stock in the long run and a temporary tax cut increases consumption, however decreases savings and investments and therefore has no real effect. Therefore, I expect government consumption to have a negative coefficient and negatively affecting economic growth. The fertility rate indicates the number of children a woman will have if she lives through her fertile years. A higher fertility rate implies a higher population growth and therefore the relationship between the fertility rate and economic growth should be negative. If general prices increase more than income does, households will have a relative smaller budget and consume and save less. If savings decrease, the capital stock per worker will decrease which negatively influences economic growth. In equation 9a the instrumental variables are included to replace the endogenous variables.

100 ∗ ∆ log 𝑦𝑖,𝑡 = 𝛽𝑖+ 𝛽𝑡+ 𝛽1log 𝑦𝑖,𝑡−1+ 𝛽2𝑝𝑜𝑝_𝑔𝑟𝑤𝑡ℎ𝑖,𝑡+ 𝛽3𝑒𝑑𝑢𝑖,𝑡+ 𝛽4𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡𝑖,𝑡+ + 𝛽5𝑎𝑖𝑑𝑖,𝑡+ 𝛽6𝑞𝑙𝑡𝑦_𝑖𝑛𝑠𝑡𝑖,𝑡+ 𝛽7𝑡𝑟𝑎𝑑𝑒𝑖,𝑡+ 𝛽8𝑞𝑙𝑡𝑦_𝑖𝑛𝑠𝑡𝑖,𝑡∗ 𝑎𝑖𝑑𝑖,𝑡+ 𝛽9𝑔𝑜𝑣𝑐𝑜𝑛𝑖,𝑡+ 𝛽10𝑓𝑒𝑟𝑡𝑖𝑙𝑖𝑡𝑦𝑖,𝑡+ 𝛽11 𝑖𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛𝑖,𝑡+ 𝜀𝑖,𝑡 (9) 100 ∗ ∆ log 𝑦𝑖,𝑡 = 𝛽𝑖+ 𝛽𝑡+ 𝛽1log 𝑦𝑖,𝑡−1+ 𝛽2𝑝𝑜𝑝_𝑔𝑟𝑤𝑡ℎ𝑖,𝑡+ 𝛽3𝑒𝑑𝑢𝑖,𝑡−1+ 𝛽4𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡𝑖,𝑡−1+ + 𝛽5𝑎𝑖𝑑𝑖,𝑡−1+ 𝛽6𝑞𝑙𝑡𝑦_𝑖𝑛𝑠𝑡𝑖,𝑡+ 𝛽7𝑡𝑟𝑎𝑑𝑒𝑖,𝑡−1+ 𝛽8𝑞𝑙𝑡𝑦_𝑖𝑛𝑠𝑡𝑖,𝑡∗ 𝑎𝑖𝑑𝑖,𝑡+ 𝛽9𝑔𝑜𝑣𝑐𝑜𝑛𝑖,𝑡−1+ 𝛽10𝑓𝑒𝑟𝑡𝑖𝑙𝑖𝑡𝑦𝑖,𝑡−1+ 𝛽11 𝑖𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛𝑖,𝑡+ 𝜀𝑖,𝑡 (9a)

In equation (10), the last control variable is included, which is a social variable, namely life expectancy at birth. If the life expectancy of a country increases, overall health of the

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more productive, which increases GDP per capita. So, the coefficient of life expectancy should be positive. Furthermore, in equation 10a the instrumental variables are included.

100 ∗ ∆ log 𝑦𝑖,𝑡 = 𝛽0+ 𝛽1log 𝑦𝑖,𝑡−1+ 𝛽2𝑝𝑜𝑝_𝑔𝑟𝑤𝑡ℎ𝑖,𝑡+ 𝛽3𝑒𝑑𝑢𝑖,𝑡+ 𝛽4𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡𝑖,𝑡 + + 𝛽5𝑎𝑖𝑑𝑖,𝑡+ 𝛽6𝑞𝑙𝑡𝑦_𝑖𝑛𝑠𝑡𝑖,𝑡+ 𝛽7𝑡𝑟𝑎𝑑𝑒𝑖,𝑡+ 𝛽8𝑞𝑙𝑡𝑦_𝑖𝑛𝑠𝑡𝑖,𝑡∗ 𝑎𝑖𝑑𝑖,𝑡 + 𝛽9𝑔𝑜𝑣𝑐𝑜𝑛𝑖,𝑡+ 𝛽10𝑓𝑒𝑟𝑡𝑖𝑙𝑖𝑡𝑦𝑖,𝑡+ 𝛽11 𝑖𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛𝑖,𝑡+ 𝛽12𝑙𝑖𝑓𝑒𝑒𝑥𝑝𝑖,𝑡+ 𝜀𝑖,𝑡 (10) 100 ∗ ∆ log 𝑦𝑖,𝑡= 𝛽0+ 𝛽1log 𝑦𝑖,𝑡−1+ 𝛽2𝑝𝑜𝑝_𝑔𝑟𝑤𝑡ℎ𝑖,𝑡+ 𝛽3𝑒𝑑𝑢𝑖,𝑡−1+ 𝛽4𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡𝑖,𝑡−1+ + 𝛽5𝑎𝑖𝑑𝑖,𝑡−1+ 𝛽6𝑞𝑙𝑡𝑦_𝑖𝑛𝑠𝑡𝑖,𝑡+ 𝛽7𝑡𝑟𝑎𝑑𝑒𝑖,𝑡−1+ 𝛽8𝑞𝑙𝑡𝑦_𝑖𝑛𝑠𝑡𝑖,𝑡∗ 𝑎𝑖𝑑𝑖,𝑡+ 𝛽9𝑔𝑜𝑣𝑐𝑜𝑛𝑖,𝑡−1+ 𝛽10𝑓𝑒𝑟𝑡𝑖𝑙𝑖𝑡𝑦𝑖,𝑡−1+ 𝛽11 𝑖𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛𝑖,𝑡+ 𝛽12𝑙𝑖𝑓𝑒𝑒𝑥𝑝𝑖,𝑡−1+ 𝜀𝑖,𝑡 (10a) 4.4 Methodology

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estimators are significantly different. The null hypothesis is unlikely to hold and therefore almost certainly a fixed effects model will be used.

Unfortunately, the dataset is unbalanced, since it misses certain values for countries over time. Therefore, it is impossible to perform a Hausman test to test if a fixed or a random effects model should be used to test the equations. However, as mentioned before, it is very likely that the fixed effects model should be used for this economic growth analysis. The fixed effects model will be estimated, using both individual fixed effects and period fixed effects. In the aforementioned equations, these effects are included as 𝛽𝑖 + 𝛽𝑡, respectively

the individual fixed effects and period fixed effects. Furthermore, to adjust for correlation between errors of the same country in different years and arbitrary heteroskedasticity, cluster-robust standard errors are used in all models (Griffiths et al, 2012).

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Table 2. Results of the Dickey Fuller test for stationarity

Before the models can be estimated, the panel data must be checked on collinearity between the explanatory variables. Collinearity is the existence of strong correlation of the explanatory variables, which could affect the least squares estimation harmfully. The results of the correlation estimation of the explanatory variables is depicted in table C1 in Appendix C. In order to use the panel data, the correlation between the variables should be less than an absolute value of 0.9, otherwise the separate effects of the explanatory variables cannot be distinguished. As can be seen in table C1, there are no values above 0.9, so there is no problem of collinearity. Correlation can either be positive or negative, indicating the relationship between two variables.

Variable P-value Stationary?

Delta log y 0.000 Yes

Log(y)-1 0.8435 No

Aid (log) 0.000 Yes

Aid (as % of GDP) 0.000 Yes

Population growth 0.000 Yes

Education index 0.0014 Yes

Investment 0.0028 Yes

Inflation 0.000 Yes

Trade 0.00913 Yes

Government consumption 0.0020 Yes

Fertility rate 0.000 Yes

Life expectancy 0.000 Yes

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5. Results

In this section, the regression results of the aforementioned equations are summed up and explained. First, the simple model is regressed with a fixed effects model. Afterwards, the other equations are regressed with a fixed effects model. Furthermore, the robustness of the results is discussed.

In this section the results of the fixed effects model, both period and individual effects are presented. First the base model is estimated without IV and afterwards with IV. Next, the extended model is estimated, first without IV and afterwards with IV. An instrumental variable should be valid and relevant. Since multiple IV’s are used in each regression, it is not possible to check if they are relevant, however it is possible to test if it is valid. Relevance implies that the instruments are correlated with the regressors that they are supposed to be instrumenting. This is done by a J-statistic. The null hypothesis states that the instrumental variable is valid and that the instrumental variables are uncorrelated with the error term, and the alternative hypothesis states that the instrumental variables are correlated with the residuals and that the variables are not valid. The regression results are presented in

corresponding tables. For all tables, *, **, *** express significance at a 10%, 5% and 1% respectively. The numbers between the brackets are the corresponding t-statistics.

5.1. The base model

First, the base model that is based on the theory of Solow and Swan is regressed. The regression results are shown in table 3.

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The second column shows the results of the base model that includes instrumental variables for the education index and investment, which are the lagged values of the education index and investment. The results of this regression still show insignificant estimates for

population growth, education index and investment. Furthermore, the p-value of the J-statistic rejects the null hypothesis of valid instruments. So, the instrumental variables that are used are correlated with the error term and therefore not valid. In the next section, the results of the extended model will be presented.

Table 3. Results of the regression of the base model Explanatory variable (1) (LS) (2) (IV) Log y-1 -13.219*** (-3.749) -10.513*** (-5.117) Pop_grwth 0.325 (0.382) 0.433 (0.538) Edu 11.957 (0.968) 5.516 (0.454) Investment 0.044 (0.940725) 0.131 (2.445) Constant 87.172*** (3.492) 68.745*** (4.761) N 765 762 Adjusted R2 0.420 0.404 F-statistic 9.479 9.728 Prob(J-statistic) 0.000

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5.2 The extended model

After regressing the base model, the extended model will be estimated. Equations 8 until 10a will be tested and the results will be presented in table 4-6. Column (1 and 2) presents the results of the model in which aid as a share of GDP in included and in column (1a and 2a) aid as the natural logarithm of the total amount of dollars a country received is included. This structure will be the same for equation 8-10a.

5.2.1 Equation 8 and 8a

As mentioned before, first the model is regressed without IV, but with least squares. In equation 8, explanatory variable aid and control variables for the quality of institutions, trade and an interaction term are included in the model. As we can see in column (1) of table 4, the coefficients for population growth, education and investment are insignificant,

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Column (1a) includes the natural logarithm of the amount of foreign aid to education a country received instead of aid as a percentage of GDP. The results of this regression differ not that much from the results in (1) however, the coefficient of quality of institutions and the interaction term became insignificant. Still, aid has a positive effect on economic growth if aid is included as natural logarithm of the amount a country received.

The second column represents the results of the model that includes instrumental variables for the education index, investment, aid and trade. The p-value of the J-statistic of column (2) is rather high, which means that it is not possible to reject the null hypothesis that states that the instruments are valid. The instruments are not correlated with the residuals and are valid. This model did not generate significant estimates for most variables, however aid, the quality of institutions and the interaction term did generate significant results. When the lagged value of aid is used as an instrument, aid still has a significant positive result on economic growth. Column (2a) shows the results of the regression in which aid is included as the natural logarithm of the amount of money a country received. In this case, the

instrumental variables are not valid, since the p-value indicates that the null hypothesis can be rejected. Next, the results of equation (9) and (9a) will be discussed.

Table 4. Results of the regression of equation 8 and 8a Explanatory

variable

(1) (LS) (1a) (LS) (2) (IV) (2a) (IV)

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Aid (log, USD) 0.482** (2.271) 0.473** (2.167) Qlty_inst 3.942** (2.546) 3.301 (0.449) -68.679* (-1.861) 2.666 (0.358) Trade 0.027* (1.719) 0.031** (2.062) -0.240 (-0.544) 0.085*** (5.284) Qlty_inst*aid 0.471*** (4.247) 0.130 (0.315) 31.564** (2.023 0.138 (0.339) Constant 91.728*** (6.151) 95.298*** (6.858) -281.027 (-1.556) 87.417*** (4.948) N 634 634 629 630 Adjusted R2 0.293 0.264 -79.384 0.228 F-statistic 4.983 4.432 31874.82 4.816 Prob(J-statistic) 0.9636 0.000

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5.2.2 Equation 9 and 9a

The table below represents the regression results of equation 9 and 9a, which includes additional control variables for government consumption, inflation and fertility. In column (1), the results of the regression with least squares and with aid as a share of GDP is presented. As can be seen in the table, aid, trade and the quality of institutions have a positive effect on economic growth. If the amount of trade as a share of GDP increases with 1 percentage point, the relative change of the natural logarithm of GDP per capita between the current and previous period is expected to increase with 0.046 percentage point. The natural logarithm of GDP per capita of the previous period, government consumption and inflation have a negative effect on economic growth. In his research, Barro (2003) concludes that government consumption and inflation have a negative influence on economic growth and the results of this research are in line with his conclusion. If the share of government consumption to GDP increases with 1 percentage point, the relative change of the natural logarithm of GDP per capita of the current and the previous period is expected to decrease with 0.197 percentage point. The negative coefficient of log(yt-1) is in line with expectation as

mentioned before. The coefficient of the interaction term is significant at a 1% level and therefore interpretable. The positive sign indicates that the positive effect of aid on

economic growth increases when the quality of institutions is higher. If aid to GDP increases with 1 percentage point, the relative change between the natural logarithm of GDP per capita is expected to increase with 0.78+0.72*quality of institutions, the marginal effect of foreign aid to education. The coefficients of the population growth, education index, investments and the fertility rate are insignificant. In column (1a) aid is included in the model as natural logarithm of the total amount of aid received. The results of this regression do not differ much from the results in column (1), however the coefficients of the quality of institutions and government consumption became insignificant.

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natural logarithm of GDP per capita between two periods. Column (2a) represents the results of the regression in which instrumental variables are used and aid is included as a logarithm of the total amount received. The instruments are not valid, since the null

hypothesis of valid instruments can be rejected. Next, the results of equation (10) and (10a) will be discussed.

Table 5. Results of the regression of equation 9 and 9a Explanatory

variable

(1) (LS) (1a) (LS) (2) (IV) (2a) (IV)

Log y-1 -12.178*** (-5.166) -15.457*** (-5.367) 10.493 (0.924) -13.275*** (-3.289) Pop_grwth 0.431 (0.499) 0.468 (0.524) 0.838 (0.484) 0.309 (0.354) Edu 12.632 (0.936) 7.722 (0.577) 32.407 (0.681) 29.769 (1.552) Investment 0.064 (1.382) 0.046 (1.067) 0.641 (1.591) 0.075 (0.970) Aid (% of GDP) 0.782*** (2.797) 29.819** (2.500)

Aid (log, USD) 0.484**

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Fertility 1.580 (0.901) 1.256 (0.695) -2.549 (-0.351) 3.383 (1.250) Constant 72.767*** (3.531) 92.022*** (4.209) -104.127 (-1.204) 53.320* (1.831) N 540 540 534 535 Adjusted R2 0.339 0.275 -19.023 0.133 F-statistic 5.181 4.093 71.850 5.012 Prob(J-statistic) 0.122 0.00000

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5.2.3 Equation 10 and 10a

In table 6, the results of the regression that estimate equation 10 and 10a are summarized. In these equations, life expectancy is included in the model to capture the effect of health on economic growth. In column (1) aid is included as the share of GDP. The coefficients for population growth, education index, investment, fertility and life expectancy are

insignificant. The coefficient for the natural logarithm of GDP per capita of the previous period is still negative, as expected. Furthermore, there is still evidence of a positive

relationship between the quality of institutions and economic growth. The marginal effect of aid is calculated by 0.801+0.725*quality of institutions, implying a positive influence of the quality of institutions on the effect of foreign aid on economic growth. So, the effectiveness of aid in promoting economic growth is higher in countries with better institutions than for countries with lower quality of institutions. Furthermore, if trade as a share of GDP increases with 1 percentage point, economic growth or the relative change in the natural logarithm between GDP per capita of the current and previous period is expected to increase with 0.047 percentage point. This means that trade has a positive effect on economic growth. In contrast, government consumption has a negative effect on economic growth. Inflation has a negative effect on economic growth as well, both in line with expectations. In column (1a), aid is included as the natural logarithm of the total amount that a country received in a certain year. The marginal effect of aid in this model is 0.49+0.53*quality of institutions. So, if the natural logarithm of aid increases with 1, the relative change of the natural logarithm of GDP per capita between the current and previous period is expected to increase with 0.49+0.53*quality of institutions. The results are quite similar to (1). However, the

coefficients for the quality of institutions and government consumption are insignificant in this equation.

In column (2), instrumental variables for education index, investment, aid, trade,

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Table 6. Results of the regression of equation 10 and 10a Explanatory

variable

(1) (LS) (1a) (LS) (2) (IV) (2a) (IV)

Log y-1 -11.608*** (-4.910) -14.931*** (-5.148) 13.233 (1.172) -12.483*** (-3.063) Pop_grwth 0.452 (0.498) 0.489 (0.524) 0.914 (0.572) 0.335 (0.359) Edu 12.233 (0.909) 7.409 (0.554) 30.773 (0.664) 29.481 (1.547) Investment 0.066 (1.463) 0.048 (1.130) 0.651* (1.658) 0.084 (1.128) Aid (% of GDP) 0.801*** (2.771) 28.772** (2.504)

Aid (log, USD) 0.487**

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Life expectancy -0.137 (-1.095) -0.125 (-0.924) -0.896* (-1.752) -0.190 (-1.145) Constant 77.916*** (3.822) 96.600*** (4.357) -66.135 (-0.816) 60.063** (2.207) N 540 540 534 535 Adjusted R2 0.339 0.275 -17.609 0.130 F-statistic 5.134 4.052 66.291 4.991 Prob(J-statistic) 0.099 0.000

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6. Discussion

In this section, the results of the regressions will be summarized and discussed. Possible explanations for the results obtained will be given as well.

It is difficult to determine the robustness of the model and the reliability of the results. Problems of endogeneity, for example omitted variables are a serious threat to this research that aims to examine the relationship between foreign aid to education and economic growth. However, with the use of instrumental variables I hope to lessen the problem of endogeneity. Unfortunately, most of the time, the instrumental variables that are used are not valid, since they are correlated with the error term. Another action that was taken to increase the robustness of the results is the use of various control variables. Those control variables increase the observed effects and therefore should decrease the problem of endogeneity and increase the reliability of the estimates. However, not all control variables show significant results in the different models and regressions, so it is still likely that the results suffer from endogeneity issues, caused by omitted variables. Furthermore, before regressing, the data has been tested on stationarity and collinearity.

The aim of this paper is to investigate whether foreign aid to education influences economic growth and the results of chapter 5 suggest that there is a significant positive effect of aid on economic growth. The result of this research is in line with the results of Asiedu (2014), who shows that aid invested in primary education has a positive effect on economic growth, however aid to post-primary has no or even a reverse effect on economic growth.

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the results of Burnside and Dollar (2000) and Clemens et al. (2004), who conclude that aid is the most effective in countries with good policies and institutions.

A lot of economic growth theories are based on the assumption that savings increase economic growth, like the Harrod-Domar model. The increase in savings will result into an increase in investments and therefore the capital stock. The larger capital stock stimulates economic growth. The coefficient of investment was significant once, however its positive sign does not come as a surprise and is in line with many economic models of economic growth. Furthermore, the negative coefficient of the lagged variable of log GDP per capita is also in line with expectations. According to the absolute convergence hypothesis, countries with similar technological improvements, population growth rates and savings propensities, should converge to the same growth rate. The Solow Swan model predicts that poor

countries would grow relatively faster to reach the same capital-labour ratio. So, countries with lower lagged log GDP per capita are expected to grow faster, implying a negative relationship. Unfortunately, the education index and population growth showed no significant coefficients, so the results are uninterpretable.

Furthermore, the results of the regressions imply that the quality of institutions is expected to improve economic growth as well. The results of this research show a positive

relationship between trade and economic growth as well. This result is in line with research that study the effect of trade on economic growth. Zahonogo (2016) conclude that the relationship between trade and economic growth is positive in Sub-Sahara African countries, especially since the openness to trade concerning imports has a positive effect on growth in those countries. In addition, life expectancy and inflation both have negative coefficients. The negative coefficient for inflation is in line with expectations, since the increase in prices result into a decrease in purchasing power. If people can buy less with the same budget, they will save less to make up the loss in purchasing power. The decrease in savings will lead to a decrease in capital and therefore less output. The coefficient for government

consumption is negative, which implies that an increase in government consumption leads to a decrease in economic growth. Dao (2012) conclude that overall government

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7. Conclusion

Foreign aid, measured by Official Development Assistance, devoted to the educational sector grows rapidly since 2000. From just under 6 billion US dollars in 2000, aid to education more than doubled to 13 billion US dollars in 2010. Sub-Sahara Africa has accounted for a substantial share of foreign aid to education, between 17 and 22 per cent over this period (OECD, 2017). As one of the first, Uzawa (1965) argues that the

technological progress that supports economic growth is not a ‘manna from heaven’, but instead the outcome of educational purposes that intend to build human capital. Many economists support Uzawa’s view that knowledge may have a positive effect on

technological progress and productivity and therefore support economic growth. As Sub-Sahara Africa is characterized by low initial school attainment levels and low levels of GDP per capita, it could be interesting to investigate the effect of the large investments made in education on economic growth.

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The results of this research show evidence of a positive effect of aid to education to economic growth in Sub-Sahara African countries. Aid is included in the model as a percentage of GDP and as the natural logarithm of the total amount of aid that a country received in US Dollars. An increase in both aid variables lead to an increase in the relative change of the natural logarithm of GDP per capita between the current and the previous period. Furthermore, the interaction variable that is included to capture the interaction between aid and the quality of institutions on economic growth shows a positive significant coefficient as well. This implies that the positive effect of aid to education on economic growth is even bigger in countries with higher values for the quality of institutions. This result is in line with Burnside and Dollar (2000) and Clemens et al. (2004). Furthermore, trade has a positive effect on economic growth as well. The natural logarithm of GDP per capita of the previous period, government consumption and inflation have a negative effect on economic growth according to the results of the regressions made in this research.

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