University of Groningen
Faculty of Economics and Business
Economic growth and the role of human capital,
a cross-sectional study
B.W. Mather
2217910
July 2016
Under the supervision of
G.H. Kuper
Abstract
This paper examines the impact of human capital (in the form of education) on economic growth in the period 1990-2014 for the Sub-Saharan and the OECD region and examines if convergence takes place. The quality of education proves to have a positive outcome for growth in the OECD region. The results for the Sub-Saharan region are insignificant, whether quantity or quality is tested. Convergence was only confirmed for the OECD region, a finding consistent with the literature.
1
1.
Introduction
In September 2015, at the 70th Session of the United Nations General Assembly, the United Nations introduced a set of goals to end poverty, protect the planet, and ensure prosperity
for all as part of a new sustainable development agenda.
It is an ambitious agenda, covering 17 goals, the so-called “Sustainable Development Goals” or SDGs. Each goal has specific targets to be achieved over the next 15 years. One of the goals (SDG 4) is on Education: “Ensure inclusive and equitable quality education and
promote lifelong learning opportunities for all”.
Though access to schooling has increased over the past two decades in a number of developing countries, the economic gains are not yet visible. While the focus was on increasing the number of children attending school, educational outcomes were neglected (Hanushek and Woessmann, 2015). “An estimated 250 million children cannot read, write or count well, whether they have been to school or not. Across the world, 200 million young people leave school without the skills they need to thrive plus an estimated 775 million adults – 64 percent of whom are women – still lack the most basic reading and writing skills.”
(UNESCO, 2013)
Learning outcomes or cognitive skills were not asserted earlier, resulting in many students learning nothing. Results from international achievement tests show this unsettling outcome for many of the countries that did manage to improve in school access. Though it is a prerequisite, just being in school does not suffice. As cognitive skills boost economic growth, focussing solely on school accessis fruitless in trying to achieve economic growth (Hanushek and Woessmann 2015a). Focussing on quality, rather than quantity as put forward in the prior Millennium Development Goal1 concerning education, is of more importance to countries, according to Hanushek and Woessmann, as higher school access does not guarantee long-run economic growth and higher quality does.
Now could it be that the findings differ for different types of countries? Does quantity of education explain economic growth in developing countries better than quality of education, compared to developed countries? Might quality of education be a better determinant for economic growth in developed countries? With this thesis I hope to answer these questions. Two groups of countries will be compared: Sub-Saharan countries, representing developing countries and OECD countries, representing developed countries. A common starting point in
2
studies on economic growth is the Solow-Swann model, which predicts that over time
developing countries will “catch up”, so the gap between developing and developed countries will narrow. Developing and developed countries should converge in terms of income levels per capita. Does this convergence take place? And if so, how fast do the countries converge? Does human capital (in the form of education) influence convergence? These questions will also be clarified in this thesis.
3
2. Literature Review
2.1 Economic Growth and the role of Human Capital
The notion of human capital goes back at least to Adam Smith. He writes that part of the capital stock of a nation consists of “the acquired and useful abilities of all the inhabitants or
members of the society. The acquisition of such talents by the maintenance of the acquirer during his education, study, or apprenticeship, always costs a real expense” (Smith, 1776).
These talents add to the fortune of an individual and thus to that of the “wealth of nations” (Smith, 1776). Though later classical and neoclassical economists did take notion of human capital, they never incorporated the concept into their studies (Sobel, 1978), leaving it to researchers in other fields, like sociology. There was only one type of capital, physical capital. The expression “human capital” was not even in use. Rather one used the expression “human wealth”, as “human capital” was thought to be de-humanizing, reducing individuals to machines. Also in the light of slavery “human capital” was a controversial expression. Several factors induced the interest in human capital. Firstly, concerns about the level of education in the US compared to that of the USSR. Due to the success of the launching of the Sputnik, in 1957, the US felt the necessity to reform their education, focussing more on science and technology (as done in the USSR), in order to keep up. Secondly, international support and financial aid to developing countries was steadily growing, what factors could improve their development? Thirdly, what measures should the government take to increase economic growth at home? (Sobel, 1978).
4
only partially explain growth, a greater part remained a black box. A large residual of unexplained growth was labelled “technical change” or “measure of our ignorance”. (Abramovitz, 1956). But Schultz was convinced that part of the unexplained growth was due to improvements in the capital inputs, human and non-human. According to Schultz, the
quality of capital had increased, enhancing economic growth. Investments in human capital
(for instance through training and education) increased the productivity of human capital and one should weigh the costs of this investment against its returns. The investment involves costs and reduces earnings for an individual in the short term but increases earnings in the long-run. Not only were the private returns to education acknowledged in the early days, but also that society as a whole benefits from an educated workforce. Schultz refined his ideas over the years (Schultz, 1960; 1961a; 1961b; 1962; 1971), encouraging and inspiring others to further research in the field of human capital and its contribution to economic growth, like Mincer (1958; 1974) and Becker (1962) and the so-called “human capital revolution” emerged. While Schultz focussed on growth theory, Mincer and Becker focussed on income inequalities. According to Mincer and Becker, income inequalities were caused by differences in experience and by differences in formal schooling (education) and informal schooling (on-the-job training). Individuals decide whether to invest in themselves to become more productive by investing in human capital, adding to their human capital stock. A firm, after investing in training an employee, may not get its return on investment back, as sooner or later an employee may move to another firm. As a consequence the (profit seeking) firm will not make the investment (Le Chapelain, 2015).
Though why one should invest in education was a key point made, the how remained vague. What type of skills and knowledge contribute to economic growth? Even today this is a burning question, giving rise to further research. Nevertheless, the human capital revolution influenced a range of disciplines; agricultural economics, labour economics, development economics, business economics, the economics of education and urban economics (Vane et al. 2005).
5
2.2 The role of human capital in exogenous and endogenous growth models
Economic growth has become an increasingly popular topic of research over the past decades (figure A1, appendix A). Most (exogenous) growth research departs from the neoclassical Solow-Swan model. In particular the augmented Solow-Swan model, derived by Mankiw, Romer and Weil (1992), which is an improved model of the standard Solow-Swan model. The standard Solow-Swan model, including technology is based on a Cobb-Douglas production function with two inputs: physical capital and labour. Technology is added as a labour augumenting factor and is exogenously given.Over time, due to diminishing returns to capital countries converge to their steady state. After that stage long- run growth can only advance through the exogenous growth rate of technological progress.
The publication of the Solow-Swan model in 1956 and the increasing availability of statistical data gave rise to many empirical studies on convergence across and within regions and countries and the model remains popular.
Empirical research shows that the standard Solow-Swan model yields unrealistically high values for the speed of convergence. To resolve this problem, Mankiw, Romer and Weil (1992) improved the model by adding human capital in the form of education as an additional input to production (see appendix B for details on the standard Solow model and it’s extension). Human capital is assumed to have the same features as physical capital, it accumulatesby investing and depreciates at the same rate. Like in the standard Solow-Swan model, long-run growth is exogenous, its rate equalling the rate of technological progress. The inclusion of human capital to the model, yields more realistic outcomes for the speed of convergence. Furthermore, Mankiw, Romer and Weil find that by including human capital to the model, 80% of the cross-country variation in income per capita is explained by the model, in contrast to 59% for the model omitting human capital.
6
factors, from outside the model, the exogenous growth of technology. Instead of viewing technology as given (exogenous), technology is embodied (endogenous) in these models, hence the term endogenous growth models. Their focus is on increasing knowledge, which is the driver of growth. The models attempt to explain the sources of technological progress (part of the black box). One of these sources is human capital formation. An educated workforce is better at creating, utilizing and adopting new technology, boosting economic growth (Benhabib and Spiegel, 1994). Whether it’s technological imitation (which in particular can boost economic growth in developing countries) or technological innovation, both are futile without skilled labour (Aghion et al, 2009).
2.3 Measures of human capital
In both exogenous and endogenous growth models the importance of including human capital is clearly acknowledged. Either way, the significance of human capital (in the form of education) on the outcomes of a growth model depend heavily on the choice of measurement of human capital. Should one take quantity or quality of education into account, or both? Both can be measured in different forms and are constrained by the availability of data.
Mankiw, Romer and Weil (1992) proxy human capital by taking secondary school enrolment ratios2 as does Barro (1991). Though secondary education contributes more to growth than primary education (Krueger and Lindhal, 2001), this approach limits the countries one can study, as in developing countries, people may not get to pursue secondary education. In addition, it is questionable if current school enrolments (a flow variable) affect the current stock of human capital and the productivity of its owners, the current labour force (Woessmann, 2003). As it takes time for the effect of schooling to pay off, rather than affecting the current stock of human capital, it affects the future stock of human capital. Romer (1990) and Azariadis and Drazen (1990) proxy human capital using adult literacy rates. Their results show that this measure has little explanatory power for growth. This could be due to the fact that, across countries, different definitions for literacy are used. Another explanation may be that different types of skills and know-how are ignored, like logical and analytical reasoning, numeracy and technical and scientific know-how. These skills and knowledge clearly also contribute to labour productivity (Woessmann, 2003).
2
7
The most common used measure of human capital is average years of schooling, researched by Benhabib and Spiegel (1994), Barro and Sala-i-Martin (1995), Barro (1997; 2001), Gundlach (1995), Islam (1995), Krueger and Lindahl (2001), O’Neill (1995) and Temple (1999). The results are mixed, while some find a significant and positive impact of human capital on growth, other results are insignificant and in some cases even a negative impact (and significant) is found. One of the issues is that an additional year of schooling in one country may yield a different increase in skills and knowledge than in another country as the quality of education differs across countries. Another issue is that all years of schooling have the same weight, regardless how many years of schooling a person has already accumulated. The fact that not only formal schooling increases skills and knowledge is also not taken into account when taking average years of schooling as a proxy for human capital (Woessmann, 2003). This is a major flaw according to Hanushek and Woessmann (2015).
Lee and Barro (1997) recognize the issues with quantity measures of human capital and focus on the quality of education by using teacher salaries, pupil-teacher ratios, and educational spending per pupil, as measures for human capital. Another approach is to focus on research
and development indicators. To examine if an economy can turn scientific work into innovation, Soukiazis and Cravo (2008) use the number of articles, the number of patents and their ratio as measures of human capital. Expenditure per pupil, school capital per pupil, school weeks, pupil/teacher-ratio, teachers' training, age, gender, and length of service are measures used by Boppart et al. (2013).
In general, in most growth model research, human capital is poorly proxied, contributing to mixed and/or insignificant results.
Woessmann (2003) addresses the imperfections of several measures used in the literature. These imperfections mainly arise from the fact that the choice of a measure for human capital in growth models is not supported by economic theory. In an attempt to improve the specification of human capital, Woessmann combines an index of test scores with world average rates of returns to education at each level, backed up by economic theory.
Ironically the research of Hanushek’s and Woessmann (2008) is criticised by Breton (2011), in which they conclude that the quality of education determines economic growth rather than the quantity. Breton argues that “their growth model is misspecified and the test score data
8
Breton’s main argument is that the measures used for human capital, average years of schooling and average test scores, do not cover the same labour force (as they are measured for the same timeslots) and therefore the conclusion that quality and not quantity drives economic growth is invalid.
9
3. The Economic model
The point of departure of this research is the Solow-Swan model. According to Solow-Swan, countries with a lower initial level GDP should grow faster than countries with an initially higher level of GDP, due to the fact that diminishing returns to capital are assumed. Because poorer countries have a smaller initial capital stock, each additional unit of capital will have a higher return than in a richer country, allowing poorer countries to catch up.
Empirical research shows that this “absolute convergence” is not realized, but for similar countries convergence is observed, which is referred to as conditional convergence. This type of convergence takes place for countries that are structurally the same; having the same production function, saving rate, population growth rate and the same rate of technological progress. In order to test if convergence takes place, and under what conditions, several variations of the Solow-Swan model, will be examined for both regions together and separately. The equation used is a variant of the Barro regression, which is derived from the Solow-Swan model. It’s a commonly used equation in (cross-country) empirical studies on growth determinants and the subject of convergence:
[(1
𝑇)(𝑙𝑜𝑔𝑦𝑖(𝑇) − 𝑙𝑜𝑔 𝑦𝑖(0)] = 𝛽0+ 𝛽1𝑙𝑜𝑔𝑦𝑖(0) + 𝛽2𝑙𝑜𝑔(𝑛𝑖 + 𝑔 + 𝛿) + 𝛽3𝑙𝑜𝑔𝑠𝐾𝑖+ 𝑒𝑖 (1)
Where the dependent variable is calculated by dividing the difference in income per capita in period T and the income per capita in period 0 by the number of periods considered. 𝑦𝑖 is
real GDP per capita. 𝑙𝑜𝑔𝑦𝑖(𝑇) − 𝑙𝑜𝑔𝑦𝑖(0) is the growth rate from period 0 to period T.
𝑌𝑖(0) is the initial income level in country i, 𝑛𝑖 is the average population growth rate over the period studied, 𝑠𝑘𝑖 is the average savings rate over the same period, 𝑔 is the rate of technological progress, 𝛿 is the depreciation rate and 𝑒𝑖 is an error term.
3.1 Hypotheses
To examine unconditional convergence, we assume that the population growth rate and the savings rate are the same for all regions. This implies that in equation (1), (𝑛𝑖 + 𝑔 + 𝛿) and 𝑠𝑘𝑖 are both constant and are included in the intercept 𝛽0 and we have a simple OLS
10
Hypothesis 1: There is no relationship between initial GDP and average GDP growth per capita.
Three additional models will be tested. Model 2 will test the presence of conditional convergence in the standard Solow-Swan model. In model 2, the following “Solow-Swan variables” are added to model 1: the savings rate, the population growth rate, the rate of technological progress and the depreciation rate. Again, for convergence to take, 𝛽1 must be negative. So hypothesis 2 is identical to hypothesis 1:
Hypothesis 2: There is no relationship between initial GDP and average GDP growth per capita
The third and fourth model add human capital measures to the model. Incorporating human capital, equation (1) changes to:
[(1
𝑇)(𝑙𝑜𝑔𝑦𝑖(𝑇) − 𝑙𝑜𝑔 𝑦𝑖(0)] =
𝛽0+ 𝛽1𝑙𝑜𝑔𝑦𝑖(0) + 𝛽2𝑙𝑜𝑔(𝑛𝑖 + 𝑔 + 𝛿) + 𝛽3𝑙𝑜𝑔𝑠𝐾𝑖+ 𝛽4𝑙𝑜𝑔𝑠𝐻𝑖 + 𝑒𝑖 (2)
In addition to testing the same hypothesis as in model 1 and model 2, the impact of quantity of human capital (model 3) and impact of quality of human capital (model 4) on growth in the two regions will be examined through the following hypotheses:
Hypothesis 3: The quantity of human capital has no impact on economic growth in the OECD region
Hypothesis 4: The quantity of human capital has no impact on economic growth in the Sub-Saharan region
Hypothesis 5: The quality of human capital has no impact on economic growth in the OECD region
11
3.2
Assumptions made in the model
Apart from the assumption on diminishing returns to capital, mentioned in the previous paragraph, the following assumptions are made:
12
4. Data
To evaluate the impact of human capital on economic growth in developed countries and developing countries, a cross sectional study amongst two regions, OECD countries and Sub-Saharan countries (appendix C) will be carried out. As the starting point of this research is the Solow-Swan model including technology, the variables from this model are used. These variables are: average (real) GDP growth, initial level of GDP, average savings rate, average population growth, rate of technological progress and the depreciation rate. Other variables included are: average enrolment rates in primary education as a proxy for quantity of education and average adult literacy rates as a proxy for quality of education.
The variables of interest are all collected from the World Bank database, except for most of the OECD literacy rates, which are from the UIS3. Due to missing data on the initial level of income, four OECD countries (Estonia, Hungary, Slovak Republic and Slovenia) and four Sub-Saharan countries (Eritrea, São Tomé and Principe, Somalia and South Sudan) are not included in the research of this paper, leaving 74 countries in total. The period studied is 1990-2014. This time frame is chosen, as starting in 1990, more economic data became available and 2014 is the most recent year data was collected for. As convergence is of interest, a shorter time span would not make sense.
The specifics on the variables used will be further described in the following paragraphs. Summary data and an overview of the variable labels and their official definitions from the World Bank can be found in appendix D.
4.1 Variables of the model
4.1.1 Average GDP growth
In order to measure economic growth, in terms of purchasing power, real GDP per capita was collected. The (Solow-Swan) assumption made is that everyone works, so GDP per capita is the same as GDP per worker. The average growth rate is calculated by subtracting the (log) initial level of GDP per capita in 1990 from the (log) GDP per capita in 2014 and dividing by the number of periods. This method was chosen as there were quite some missing data throughout the period under consideration. A disadvantage of this calculation is that fluctuations influencing the economy during the period are not taken into account.
3
13
4.1.2 Initial level of GDP
In order to measure convergence, you need an initial period to start with, this is the initial level of GDP per capita in the year 1990. Due to countries not yet in existence that year, a number of countries had to be dropped from the sample. Looking at the descriptive statistics of the gdp per capita in 1990, for the two regions, the relative dispersion of the Sub-Saharan region is much higher that of the OECD region.
4.1.3 Average savings rate
The savings rate was proxied by gross fixed investment as a percentage of GDP, as savings equal investment. For most Sub-Saharan countries investment/gdp ratio’s were not available that is the reason for choosing this measure. The average savings rate was calculated, taking all years into account. In particular for this measure the descriptive statistics reveal the huge differences in values for the Sub-Saharan region.
4.1.4 Average population growth, rate of technological progress and the rate of depreciation
The average population growth was calculated by averaging the annual population growth, taking all years into account. There were no missing data. The rate of technological progress and the depreciation rate assumed to add up to 5 percent (a common assumption used in the literature) and are assumed to be the same for all countries.
4.1.5 Average enrolment ratios in primary education
The average enrolment ratios in primary education from 1980 to 2004 were calculated as a proxy for the quantity of human capital. Primary education has been chosen over secondary education as this study includes developing countries. In these type of countries, people may not get to pursue secondary education. As for the choice of the time period 1980 to 2004, the reasoning is as follows: pupils are (approximately) aged 6 to 12 years. A pupil aged 6 in the year 1980 will be 16 in the year 1990, contributing to growth in that year, which is the start of period researched. Now in developing countries individuals may not enter the workforce that young of age, but in developing countries this is quite common.
4.1.6 Average adult literacy rates
14
PISA4 are not available. Average adult literacy rates were calculated for 1990-2014, it is a fair assumption that these rates effected growth in that same period. That is why the adult rates are chosen, they include everyone of 15 years of age and older. Take notice that adult literacy rates, as defined by the World Bank, do not merely relate to reading and writing, they include simple numeric skills as well (appendix D, table D3).
For most of the periods, average enrolment ratios in primary education were available, for adult literacy rates this was not the case. For most OECD countries, the literacy rates are missing in the World Bank databank. The reason is that these countries do not collect standard literacy data, but focus on more advanced literacy skills (UNESCO, 2015). For OECD countries that had no literacy data, estimates from the UIS5 were used. The UIS databank contains literacy estimates for regions classified by the World Bank. Among these World Bank regions is the region “High income countries”. As the missing literacy data are all from high-income countries, as classified by the World Bank (see table C1, appendix C) the estimates from the UIS are used to proximate the missing literacy rates. The literacy rates estimates in the UIS databank are given for the period 1995-2004 and the period 2005-2014. The averages of these estimates were calculated and used for the missing values of the OECD countries.
4.2 Limitations of the data
As for some of the variables the averages are not calculated over the full period, due to missing data, the averages may over- or underestimated. Average GDP growth does not reflect fluctuations in the data over time, which could influence convergence. Different countries measure and define human capital in different ways, for instance, literacy is in some countries a self-declaration, and people may be hesitant to admit that they can not read or write. School systems vary over the globe, in some countries students start school later or earlier than they the age of six. As mentioned in the literature review, enrolment in school does not guarantee that actual learning took place. The estimated literacy rates of the high-income OECD countries produced by the UIS may be lower than in reality for some of the countries.
4
Programme for International Student Assessment 5
15
5. Empirics
Including specific variables, the general model, described in equation (1) takes the following functional form:
[(1
𝑇)(𝑙𝑜𝑔𝐺𝐷𝑃𝑖,2014− 𝑙𝑜𝑔 𝐺𝐷𝑃𝑖,1990 )] = 𝛽0+ 𝛽1𝑙𝑜𝑔𝐺𝐷𝑃𝑖,1990+ 𝛽2𝑙𝑜𝑔(𝐺𝑃𝑂𝑃𝑖+ 0.05) +
𝛽3𝑙𝑜𝑔𝑆𝐴𝑉𝑖+ 𝑒𝑖 (3)
The coefficients 𝛽1 and 𝛽2 are expected to have a negative sign. The higher the initial level of
GDP per capita, the smaller the growth rate of GDP per capita. Higher population growth will decrease the growth rate of GDP per capita. Coefficient 𝛽3 is expected to have a positive sign, a higher savings rate implies a higher growth rate of GDP per capita.
For models 3 and 4, including human capital, we expect 𝛽4 to have a positive sign, human capital should boost economic growth. Model 3 includes enrolment rates as a proxy for the quantity of human capital:
[(1
𝑇)(𝑙𝑜𝑔𝐺𝐷𝑃𝑖,2014− 𝑙𝑜𝑔 𝐺𝐷𝑃𝑖,1990 )] = 𝛽0+ 𝛽1𝑙𝑜𝑔𝐺𝐷𝑃𝑖,1990+ 𝛽2𝑙𝑜𝑔(𝐺𝑃𝑂𝑃𝑖+ 0.05) +
𝛽3𝑙𝑜𝑔𝑆𝐴𝑉𝑖+ 𝛽4𝑙𝑜𝑔𝐸𝑁𝑅𝑂𝑖+ 𝑒𝑖 (4)
Model 4 includes literacy rates as a proxy for the quality of human capital:
[(1
𝑇)(𝑙𝑜𝑔𝐺𝐷𝑃𝑖,2014− 𝑙𝑜𝑔 𝐺𝐷𝑃𝑖,1990 )] = 𝛽0+ 𝛽1𝑙𝑜𝑔𝐺𝐷𝑃𝑖,1990+ 𝛽2𝑙𝑜𝑔(𝐺𝑃𝑂𝑃𝑖+ 0.05) +
𝛽3𝑙𝑜𝑔𝑆𝐴𝑉𝑖+ 𝛽4𝑙𝑜𝑔𝐿𝐼𝑇𝑅𝑖+ 𝑒𝑖 (5)
All variables are measured in natural logs.
16
There should be no linear relationship among the explanatory variables. To check for multicollinearity, correlation matrices were constructed (appendix G, tables G1-G3). Overall the outcomes indicate weak to moderate correlation (0-0.8). There are two that are high: literacy rates and initial gdp per capita for the OECD region (0.88) and literacy rates and enrolment rates for the Sub-Saharan region (0.88). Another striking outcome is that the correlation for savings and gdp growth per capita is much higher (and positive) for the Sub-Saharan region than for the OECD region, for which the correlation is small (and negative).
17
6. Results
A simple first step to see if convergence takes place is to plot GDP growth rates of countries against their initial levels of per capita GDP. If convergence occurs, countries with an initially low level of capital stock should grow faster than countries with a higher capital stock in the initial period. This implies a negative relationship between the initial income and the growth rate. Average per capita GDP growth for the years 1990-2014 is regressed on the per capita levels of income in the year 1990, for both regions (figure 1).
Figure 1 GDP per capita growth (1990-2014) versus log GDP per capita 1990, OECD countries
and Sub-Saharan countries
Figure 1 confirms that the GDP growth rate per capita is inversely related to the initial level of GDP per capita, more so for the Sub-Saharan countries than for the OECD.
But the estimation results for model 1 (tables F2 and F3, appendix F) show that for the regions together and Sub-Saharan countries the outcomes are insignificant. There is no convergence among the two regions and the poorer countries do not catch up. For the OECD regions the value of the slope is statistically significant at the 1 percent level and indicates that a 1 % decrease in the initial GDP results in an increase of 0.0065 % in the GDP growth rate per capita (ceteris paribus). The coefficient of determination is also the highest for this region, indicating that almost 35 % of the variation in GDP growth per capita is explained by
18
the variation in the income per capita in 1990. So the null hypothesis of no convergence is rejected. The finding of what is known as “club convergence” among the OECD countries is consistent with findings in the literature (e.g. Barro and Sala-i-Martin6, 1995); convergence only occurs among the more developed countries.
Adding more variables to the model increased the explanatory power (increase in r-square) of the model, in particular for the two regions together and the Sub-Saharan region. However, the coefficient 𝛽1 remains insignificant for the Sub-Saharan region, so the hypothesis of no convergence can not be rejected. For both the regions together and the Sub-Saharan countries the coefficient of log savings is positive and significant as predicted by the Solow-Swan model, if human capital variables are added this remains the case. For the OECD region log savings is negative and insignificant.
Literacy rates prove to be highly significant for growth for the OECD region. A 1 % increase in the literacy rates results in a 0.12 % in the GDP growth rate per capita (ceteris paribus). Overall, model 4 gives the best results for the OECD region with the highest value for R2, and the highly significant outcome for the coefficient of initial gdp per capita.
The importance of the significance of enrolment rates in the Sub-Saharan region is flawed as, at least for this region, the model is misspecified.
Hypothesis 1, that there is no relationship between initial GDP and average GDP growth per capita is rejected for the OECD region, a significant negative relationship exists.
Hypothesis 2, that there is no relationship between initial GDP and average GDP growth per capita when Solow-Swan variables are included in the model is rejected for the OECD region a significant negative relationship exists.
Hypothesis 3, that the quantity of human capital has no impact on economic growth in the OECD region is not rejected. Hypothesis 4, that the quantity of human capital has no impact on economic growth in the Sub-Saharan region is not rejected. Hypothesis 5, that the quality of human capital has no impact on economic growth in the OECD region is not rejected. Hypothesis 6, the quality of human capital has no impact on economic growth in the Sub- Saharan region is not rejected.
6
19
7. Conclusion
The developing countries did not catch up. Part of the problem, apart from possible flaws in the data, is that developing countries can not easily adapt new technologies, while in the Solow-Swan model this is assumed free and accessible for all economies. In practice this is not (yet) the case. Developing countries are hindered in their development by poor institutions, political barriers, sluggish laws and corruptness. While the flow of knowledge should be “flowing freely” between borders, it is actually in one direction; high-educated workers from developing countries move elsewhere. As expected, convergence is confirmed only for the OECD countries. That the quality of education has an impact on growth is confirmed for the OECD region, that quantity of education matters (more) for growth in Sub-Saharan is not confirmed. As mentioned in the introduction, the economic gains are not visible yet. Other factors appear to be of greater importance for economic growth in the Sub-Saharan region. The United Nations should continue their efforts to improve the quality and access to education as should governments.
Why should the government invest in human capital?
Though the outcomes of empirical research on the contribution of human capital to economic growth are mixed, governments Government should prioritize investing in human capital, as there are not only private gains, due to higher wages, but society as a whole can benefit, due to the presence of positive externalities. Research shows that higher educated individuals are likely to commit less crimes (Lochner and Moretti, 2004), are more involved in and aware of politics (Milligan, Moretti and Oreopoulos, 2004) and are less likely to engage in risky behaviour (Jensen and Lleras-Muney, 2010). There are spill-over effects for the workforce; high educated workers increase the productivity of their co-workers (Moretti, 2004). Higher educated individuals have a better health as do their children (Chou et al, 2007) and their children are likely to have a higher level of education. The last two points are of particular importance to developing countries.
20
capital of their employees. These two reasons are both strong incentives for government intervention. The government could provide student loans, in order to facilitate students to pursue an education.
Failure to maximize family utility is another problem. Especially in early childhood decisions on education are made by parents. They decide on the amount and level of education a child receives. They may choose an education that does not match their child’s abilities
And lastly, free or subsidized education improves income mobility. As education is a normal good (more income will increase demand), children from high-income families can profit from get a better education, while children from low-income families can not.
Limitations
Data availability has a been limitation in this study. But even if I would have had no missing data, maybe there simply is not enough in order to study convergence. In the end there are only so many countries in the world and a limited time span of data exists. Now the first issue is a given fact and can’t be resolved, but for the second one, time will tell, more observations will increase the reliability of the results (Temple, 1999).
The difficulty to find an appropriate proxy for human capital is another (well documented) limitation I faced. An additional problem related to this is the fact that different countries do measure human capital in different ways and that school systems vary over the globe, which makes comparison difficult.
Further research
Finding an appropriate measure for human capital is an ongoing investigation. And which other measures to include in the growth model? You don’t want to end up running “Four
million regressions”.
21
References
Abramovitz, M.(1956). Resource and Output Trends in the United States Since 187. American
Economic Review, May 1956 (Papers and Proceedings) Vol. 46, p. 11
Aghion, P. et al (2009). The Causal Impact of Education on Economic Growth: Evidence
from U.S. Brookings Papers on economic activity
Azariadis, C. and Drazen, A. (1990). Threshold externalities in economic development. Quarterly Journal of Economics, 105(2), pp. 501–526
Barro, R. J. (1991). Economic Growth in a Cross Section of Countries. Quarterly Journal of Economics, 106, 2, pp. 407–443
Barro, R. J. (1997). Determinants of Economic Growth: A Cross-Country Empirical Study. Cambridge, MA: MIT Press.
Barro, R. J. (2001). Human Capital and Growth. American Economic Review, Papers and Proceedings, 91, 2, pp. 12–17.
Barro, R.J. and Sala-i-Martin, X. (1995). Economic Growth. McGraw-Hill, New York The MIT Press, Cambridge, Massachusetts,London, England
Becker, G. (1962). Investment in Human Capital: A Theoretical Analysis. Journal of Political Economy, vol. 70, p. 9
Benhabib, J. and Spiegel, M. M. (1994). The Role of Human Capital in Economic
Development:Evidence from Aggregate Cross-Country and Regional U.S. Data. Journal of
Monetary Economics, 34, 2, pp. 143–173.
Boppart, T., Falkinger, J., Grossmann, V., Woitek, U. and Wüthrich, G. (2013). Under which
conditions does religion affect educational outcomes? Explorations in Economic History, vol.
50, 2, pp. 242-266
Breton, T.R. (2011). The quality vs. quantity of schooling: What drives economic growth?. Economics of Education Review 30, pp. 765-773
Le Chapelain, C. and Mateos S. (2015). Human Capital, give us the theoretical foundations
please. 64th Annual meeting of the French Economic Association, Rennes
Chou, S. et al. (2007). Parental Education and Child Health: Evidence from a natural
experiment in Taiwan. NBER Working Paper No. 13466
Denison, E. F. (1962). The sources of economic growth in the United States and the
alternatives before us. Committee for Economic Development, New York.
Gundlach, E. (1995). The Role of Human Capital in Economic Growth: New Results and
Alternative Interpretations. Weltwirtschaftliches Archiv, 131, 2, pp. 383–402
Hanushek, E.A. and Woessmann, L. (2008). The Role of Cognitive Skills in Economic
Development, Journal of Economic Literature, 46.3, pp. 607-668
Hanushek, E.A. and Woessmann, L. (2015). Universal basic skills should become the primary
22
Heijdra, B. J.(2009) Foundations of Modern Macroeonomics, second edition, Oxford University Press, Oxford
Islam, N. (1995). Growth Empirics: A Panel Data Approach. Quarterly Journal of Economics, 110, 4, pp. 1127–1170
Jensen, R. and Lleras-Muney, A. (2010). Does staying in school (and not working) prevent
teen smoking and drinking, Working paper, UCLA, 2010
Krueger, A.B. and Lindahl, M. (2001). Education for Growth: Why and For Whom? Journal of Economic Literature, Vol. 39, No. 4 (Dec., 2001), pp. 1101-1136
Lee, J.-W. and Barro, R. J. (1997). Schooling quality in a cross-section of countries. Working Paper 6198, National Bureau of Economic Research, Cambridge, M.A
Lochner, L.and Moretti, E. (2004). The Effect of Education on Crime: Evidence from Prison
Inmates, Arrests, and Self-Reports. American Economic Review Vol.94, pp. 155-189
Mankiw, Romer and Weil (1992). A contribution to the Empirics of Economic Growth, Quarterly Journal of Economics, May 1992, pp. 407-347
Milligan, K., Moretti, E. and Oreopoulos, P. (2004). Does education improve citizenship?
Evidence from the United States and the United Kingdom. Journal of Public Economics
Vol.88, pp. 1667-95
Mincer, J. (1958). Investment in Human Capital and Personal Income Distribution. Journal of Political Economy Vol.66, No.4, pp. 281-302
Mincer, J. (1974). Schooling, Experience and Earnings. New York: National Bureau of Economic Research.
Moretti, E. (2004). Workers Education, Spillovers, and Productivity: Evidence from
Plant-Level Production Functions. American Economic Review 94, pp. 656-690
O’Neill, D. (1995). Education and Income Growth: Implications for Cross-Country
Inequality, Journal of Political Economy, 103, 6, pp. 1289–1301
Romer, P. M. (1990). Endogenous technological change. Journal of Political Economy 98, S71-S102
Schulz, T.W. (1958). The Emerging Economic Scene and Its Relation to High School
Education. Francis S. Chase and Harold A. Anderson (eds.), The High School in a New Era,
University of Chicago Press
Schultz, T.W. (1960). Capital Formation by Education. Journal of Political Economy, 68, December, pp. 571–583.
Schultz, T.W. (1961a). Investment in Human Capital. American Economic Review, 51, March, pp. 1–17.
Schultz, T.W. (1961b). Investment in Human Capital: A Reply. American Economic Review, 51, December, pp. 1035–1039.
23
Schultz, T.W. (1971). Investment in Human Capital: The Role of Education and Research. Free Press, New York
Smith, Adam (1776). An Inquiry into the Nature and Causes of the Wealth of Nations. 1776. Reprint, New York: T. Nelson and Sons, 1870.
Sobel, I. (1978). The Human Capital Revolution in Economic Development: Its Current
History and Status. Comparative Education Review, 22(2), pp. 278-308
Solow, R. M. (1957). Technical change and the aggregate production function. Review of Economics and Statistics 39(3): pp. 312-20
Soukiazis, E. and Cravo, T. (2008). Human Capital and the Convergence Process Among
Countries. Review of Development Economics, 12: pp. 124–142.
Temple, J. (1999). A Positive Effect of Human Capital on Growth. Economics Letters, 65, 1, pp. 131–134.
UNESCO (2013), The Global Learning Crisis, UNESCO Publishing, France
UNESCO (2015), Adult and Youth literacy, UIS Fact Sheet September 2015, no. 32, p. 3 Vane, H. R. and C.Mulhearn (2005). The Nobel Memorial Laureates in Economics: An
Introduction to Their Careers. Edgar Elgar Publishing Limited, Cheltenham, UK
24
Appendix
A25
Appendix B
The Solow-Swan model 7
The standard Solow-Swan model, including technology is based on a Cobb-Douglas production function with three inputs, physical capital (K), technology (A) and labour (L): Y(t) = K(t)αK [A(t)L(t)]1- αK 0 < αK < 1 (1)
Where Y(t) is output at time t, αK is the physical capital’s share of income. The model does
not explain technology but shows how it enhances labour in the development of growth (Harrod neutral), increasing the efficiency of labour.
The initial levels of labour and technology are taken as given and both grow exogenously at constant rates:
𝐿̇(t) = nL(t) (2)
𝐴̇(t) = gA(t) (3)
Physical capital depreciates at rate δ’:
𝐾̇(t) = sY(t) – δK(t) (4)
(as savings equal investment, S(t) = I(t), sY(t) = δK(t) + 𝐾̇(t))
For the (physical) capital stock per effective worker: 𝐾̇(𝑡) 𝐴(𝑡)𝐿(𝑡)
=
𝑠
𝑌(𝑡) 𝐴(𝑡)𝐿(𝑡) - δ 𝐾(𝑡) 𝐴(𝑡)(𝐿(𝑡)(5) 𝑘̇(t) + nk(t) + gk(t) = sy(t) - δk(t)
(6) Re-arranging terms and writing sy(t) as a function of k(t), gives the fundamental differential equation:
𝑘̇(t) = sf(k(t)) - (δ + n + g)k(t) (7) This equation shows that the rate of change of the capital stock per effective worker (= capital intensity) is the difference between the actual investment per effective worker and the amount of investment required to maintain a constant level of capital stock per effective worker.
26
The growth rate 𝑘̇(t)/k(t) implies that countries with a low capital stock and low output (per capita) will grow faster than countries with a high capital stock and high output (per capita) and eventually converge. According to empirical research by Barro and Sala-i-Martin, the model shows conditional convergence, that is, countries that are structurally alike (country differences in n and s are controlled for, g and δ were assumed to be constant across countries) do converge to the same steady state. More empirical studies confirm the existence of conditional convergence rather than absolute convergence, where all countries or regions converge to the same steady state, regardless their initial state.
When 𝑘̇(t) = 0, actual investment sf(k(t)) equals required investment (δ + n + g)k(t). There are two steady state equilibria, k*
= 0 and k*
> 0. The steady state k*
= 0 is ignored, as this steady state is unstable and has no economic meaning. If actual investment exceeds required investment, k < k*, the capital stock rises. If actual investment is smaller than
required investment, k > k*,the capital stock falls. So starting from a value of k larger than 0,
the model predicts that the economy eventually will converge to its steady state, k(t) k*.
Now if convergence takes place, how long will it take? The speed of convergence is given by:
β = (1 – α) (δ + n + g) (8)
One can also calculate what is known as the “half life” if β is known. The convergence rate β , defines how long it will take to half the gap to steady state, this gap it should be closed in ln2/β years.
Using given parameters, Barro and Sala-i-Martin (1995) conclude that the speed of convergence (5-6%) does not match with empirical evidence, it is too fast. A realistic speed of convergence, around 2%, demands the capital share, αk, to be unrealistically high, while it is
estimated to be 1/3. Mankiw, Romer and Weil (1992) suggest adding human capital (H) in the form of education as an additional input to production in the model. As there is more capital and capital accumulation takes time, this will slow the speed of convergence and improve the standard model:
Y(t) = K(t)αK H(t) αH [A(t)L(t)]1- αK -αH 0 < αK, αH, αK + αH < 1 (9)
Where αH is the human capital’s share of income, so αH= 0 represents the standard model.
With a higher value of α (= αK + αH ) convergence will take more time (human capital is
27
With the inclusion of human capital the conditions of the model do not change, both types of capital are assumed to show diminishing returns (αK + αH < 1).
28
Appendix C
Australia HI Hungary HI Poland HI
Austria HI Iceland HI Portugal HI
Belgium HI Ireland HI Slovak Republic HI
Canada HI Israel HI Slovenia HI
Chile HI Italy HI Spain HI
Czech Republic HI Japan HI Sweden HI
Denmark HI Korea, Rep. HI Switzerland HI
Estonia HI Luxembourg HI Turkey UMI
Finland HI Mexico UMI United Kingdom HI France HI Netherlands HI United States HI Germany HI New Zealand HI
Greece HI Norway HI
Table C1 OECD countries and their income classification
http://www.oecd.org/about/membersandpartners/list-oecd-member-countries.htm
Behind the countries are the income classifications, according to the World Bank Atlas method:
29
Angola UMI Gabon UMI Nigeria LMI
Benin LI Gambia, The LI Rwanda LI
Botswana UMI Ghana LMI São Tomé and
Principe
LMI
Burkina Faso LI Guinea LI Senegal LMI
Burundi LI Guinea-Bissau LI Seychelles HI
Cabo Verde LMI Kenya LMI Sierra Leone LI
Cameroon LMI Lesotho LMI Somalia LI
Central African Republic
LI Liberia LI South Africa UMI
Chad LI Madagascar LI South Sudan LI
Comoros LI Malawi LI Sudan LMI
Congo, Dem. Rep. LI Mali LI Swaziland LMI
Congo, Rep LMI Mauritania LMI Tanzania LI
Côte d'Ivoire LMI Mauritius UMI Togo LI
Equatorial Guinea HI Mozambique LI Uganda LI
Eritrea LI Namibia UMI Zambia LMI
Ethiopia LI Niger LI Zimbabwe LI
Table C2 Sub-Saharan Africa, 48 countries and their income classification
http://data.worldbank.org/region/SSA
Behind the countries are the income classifications, according to the World Bank Atlas method:
LI = Low-income country, GNI per capita equal or less than $1,045
30
Appendix D
Variable | Obs Mean Std. Dev Min Max
ggdp 30 .0069638 .0036745 .0014736 .0156267 lgdp90 30 4.354839 .3329548 2.888377 4.751566 lngdelta 30 .0584597 .0071766 .0500529 .0824138 .0824138 lsav 30 .2255247 .0209128 .1853712 .2884669 lenro8004 30 2.007556 0243362 1.943005 2.086432 llitr 30 1.983839 .0307216 1.831272 1.998235
Table D1 OECD countries, summary data of the log variables
Variable | Obs Mean Std. Dev Min Max
ggdp 44 .0069384 .011635 -.0104641 .0623715 lgdp90 44 3.317673 .3932439 2.574049 4.290025 lngdelta 44 .0747627 .0069237 .0568865 .0865172 lsav 44 .227756 .1402176 .0565122 .9686766 lenro8004 44 1.896813 .1595462 1.463747 2.157673 llitr 44 1.749967 .1850025 1.290073 1.99326
31
Variable name description Units
region Country classification, Sub-Saharan or OECD gdp90 GDP per capita based on purchasing power parity
(PPP) in the year 1990. PPP GDP is gross domestic product converted to international dollars using purchasing power parity rates. An international dollar has the same purchasing power over GDP as the U.S. dollar has in the United States. GDP at purchaser's prices is the sum of gross value added by all resident producers in the economy plus any product taxes and minus any subsidies not included in the value of the products. It is calculated without making deductions for depreciation of fabricated assets or for depletion and degradation of natural resources. Data are in constant 2011 international dollars.
Constant 2011 international $
gdp14 See above, for the year 2014. Constant 2011 international $ ggdp GDP per capita growth rate 1990−2014, based on
gdp90 and gdp14
Percentage points per year
gpop Annual population growth rate for year t is the exponential rate of growth of midyear population from year t-1 to t, expressed as a percentage . Population is based on the de facto definition of population, which counts all residents regardless of legal status or citizenship.
Percentage points per year
sav Gross fixed capital formation (% of GDP) averaged over 1990-2014
Percentage points per year
ngdelta Average population growth rate (=average gpop 1990-2014) + rate of technological progress + depreciation rate.
Percentage points per year
enro8014 Total enrollment in primary education, regardless of age, expressed as a percentage of the population of official primary education age. GER can exceed 100% due to the inclusion of over-aged and under-aged students because of early or late school entrance and grade repetition.
Percentage points per year
litr Percentage of the population age 15 and above who can, with understanding, read and write a short, simple statement on their everyday life. Generally, ‘literacy’ also encompasses ‘numeracy’, the ability to make simple arithmetic calculations. This indicator is calculated by dividing the number of literates aged 15 years and over by the
corresponding age group population and multiplying the result by 100.
Percentage points per year
32
Table D4 Summary statistics of the original variables OECD region
Variable Obs Mean Std. Dev. Min Max
gdp 90 30 26679.02 11437.1 773.3517 56437.29 gdp14 30 38037.8 16124.11 1689.437 91368.11 gpop 30 .8459727 .7176612 .0052867 3.241381 sav 30 22.55247 2.091278 18.53712 28.84669 enro8004 30 101.911 5.805579 87.70112 122.0203 litr 30 96.55868 5.907259 67.80663 99.59441
Table D5 Summary statistics of the original variables Sub-Saharan region
Variable Obs Mean Std. Dev. Min Max
33
Appendix E
Figure E1 Residual plot model 3 both regions
Figure E2 Residual plot model 3 OECD
34
Figure E3 Residual plot model 3 Sub-Saharan
Figure E4 Residual plot model 4 both regions
35
Figure E5 Residual plot model 4 OECD
Figure E6 Residual plot model 4 Sub-Saharan
36
Appendix F
Table F1 Estimates for both regions combined, all 4 models, robust standard errors
Model 1 Model 2 Model 3 Model 4
lgdp90 -.0010572 -.0044076* -.0044368* -.0051353* lsav .0393653 ** .0392868*** .0383558** lngdelta -.0137055 -.0136274 -.0106133 lenro8004 .0003278 llitr .0047909 constant .0109006 -.0173995 -.0178874 -.0247399 R2 0.0052 0.4338 0.4338 0.4372 no. of obs. 74 74 74 74
***p-value < 0.01 **p-value < 0.05 *p-value < 0.1
Table F2 Estimates for the OECD, all 4 models, robust standard errors
Model 1 Model 2 Model 3 Model 4
lgdp90 -.0065137*** -.0055238** -.0055098 -.0143188*** lsav -.001861 -.0017271 -.0038757 lngdelta .0119111 .0111052 .0251851* lenro8004 -.0055071 llitr .1218422*** constant .0353299 .0244343 .0358642 -.1863986 R2 0.3484 0.3681 0.3693 0.5772 no. of obs. 30 30 30 30
***p-value < 0.01 **p-value < 0.05 *p-value < 0.1
Table F3 Estimates for the Sub-Saharan, all 4 models, robust standard errors
Model 1 Model 2 Model 3 Model 4
lgdp90 -.0015404 -.0071458* -.0071233** -.0074606* lsav .0407001** .0407301** .0403741** lngdelta -.0254359 -.0255441 -.0230348 lenro8004 -.000142** llitr .0017445 constant .0120488 -.0003985 -.0001489 -.0040739 R2 0.0027 0.4798 0.4798 0.4803 no. of obs. 44 44 44 44
37
Appendix G
ggdp lgdp90 lsav lngdelta lenro8004 llitr ggdp 1.0000 lgdp90 -0.0723 1.0000 lsav 0.6208 0.2166 1.0000 lngdelta 0.0126 -0.8178 0.1954 1.0000 lenro8004 0.1954 0.5768 0.3911 -0.5175 1.0000 llitr 0.1056 0.7594 0.3392 -0.7054 0.8734 1.0000
Table G1 Correlation matrix all regions
ggdp lgdp90 lsav lngdelta lenro8004 llitr ggdp 1.0000 lgdp90 -0.5902 1.0000 lsav -0.1423 -0.3360 1.0000 lngdelta 0.4329 -0.5340 -0.2103 1.0000 lenro8004 -0.1881 0.2014 0.1081 -0.3262 1.0000 llitr -0.3360 0.8803 0.1965 -0.5987 0.2962 1.0000
Table G2 Correlation matrix OECD
ggdp lgdp90 lsav lngdelta lenro8004 llitr ggdp 1.0000 lgdp90 -0.0521 1.0000 lsav 0.6617 0.2016 1.0000 lngdelta -0.0780 -0.5315 -0.1634 1.0000 lenro8004 0.1685 0.5522 0.3753 -0.4537 1.0000 llitr 0.1523 0.5918 0.3297 -0.5524 0.8797 1.0000
