Productivity growth: the effect of human
capital and international trade
Valentijn de Neve
supervisor: prof. M.P. Timmer
15 December 2010
Abstract
This thesis examines the role of primary and tertiary education on pro-ductivity growth as proposed by Vandenbussche, Aghion and Meghir (2006). The estimates are based on improved data on education and capital stocks and for a larger sample of countries. The dataset covers the period 1960 until 2000 for 144 countries.
Contents
1 Introduction 3
2 Literature review 4
2.1 The effect of education on productivity growth . . . . 4
2.2 The effect of international trade on productivity growth 7 2.3 Empirical evidence on the effect of education and inter-national trade on productivity growth . . . 9
3 The economic model 13 3.1 The economic environment . . . 13
3.2 Productivity growth . . . 14
3.3 Hypotheses . . . 17
4 Methodology 20 5 Data 24 5.1 TFP estimates . . . 24
5.2 Data on education and trade openness . . . 27
5.3 Data description . . . 28
6 Estimates 30 6.1 Empirical estimates . . . 31
6.1.1 The effect of the average years of education on productivity growth . . . 31
6.1.2 The effect of tertiary education on productivity growth . . . 33
6.1.3 The effect of international trade on productivity growth . . . 38
6.2 Reliability and Robustness of the estimates . . . 39
6.2.1 Assumptions underlying the regression analysis 39 6.2.2 Robustness of the results . . . 40
7 Conclusion 42 8 Appendix 50 8.1 Regression results . . . 50
8.2 Assumptions regression analysis . . . 52
8.3 Cross-correlation tables . . . 54
8.4 Outliers . . . 55
1
Introduction
The last decades showed large shifts in the relative size of economies. There was the rise of large developing countries, whereas certain re-gions such as Africa lagged behind. These large differences in eco-nomic growth have lead to numerous studies discussing variables that influence economic growth. Detailed growth accounting exercises in-dicate that the accumulation of labor and capital play an important role in explaining the variation in economic growth. However, most of the cross-country variation in economic growth is explained by differ-ences in Total Factor Productivity, TFP (Easterly and Levine, 2001). Therefore the main question is to explain what drives TFP growth. One of the important determinants of TFP growth is education. Van-denbussche, Aghion, and Meghir (2006) present a model in which productivity growth comes from the process of creative destruction in which new innovations replace old ideas. The replacement of old ideas occurs through the process of innovation and imitation. Imita-tion is mainly undertaken by low skilled labor whereas innovaImita-tion is mainly undertaken by high skilled labor, and the level of education is able to determine the skill level. Furthermore, innovation becomes more important the closer an economy’s productivity level is to the productivity level of the leading economy or the technological frontier. Therefore the role of education changes during the catch-up process. This thesis aims to contribute to the literature in several ways. First of all by testing the model proposed by Vandenbussche, Aghion, and Meghir (2006) on better data on education and TFP. Secondly, by in-vestigating if the proposed effects are also valid for a broader group of countries than those belonging to the OECD. Finally, its contribution consists of incorporating and testing the role of international trade on productivity growth since international trade can have an important effect on productivity growth as well. A better understanding of the role of education and international trade in the process of productivity growth can help to create better policies and thereby enhance produc-tivity growth.
be-comes smaller the closer the productivity level of the economy is to the frontier. Moreover the analysis shows that international trade has a positive effect on productivity growth the closer the productivity level of an economy is to the frontier. Although for economies lagging substantially behind in terms of productivity, the effect of interna-tional trade becomes negative.
In the next section the literature on the effect of education and in-ternational trade on productivity growth is analyzed. Subsequently in the economic model section the interaction between education, dis-tance to the frontier and international trade are formalized and result in the hypotheses. Thereafter these hypotheses are empirically tested and these findings will be summarized in the conclusion.
2
Literature review
In this research the model of Vandenbussche, Aghion, and Meghir (2006) is the core of the analysis of productivity growth. This litera-ture review focuses on how this model is embedded in the literalitera-ture and how the role of international trade can be analyzed within this model. Therefore the first part of this literature review will focus on the theoretical contributions on the effect of education and openness to international trade on productivity growth. The second part will focus on the empirical literature on these topics. Both parts start with characterizing the role of education and subsequently discuss the role of international trade.
2.1
The effect of education on productivity
growth
The most important debate about the effect of education on produc-tivity growth is whether education should be seen as an input to the economic process or that it should be seen as a facilitator of techno-logical progress. The neoclassical growth models and the AK model assume that education is an input to the process of economic growth, whereas in the new growth theories of the product variety model and the Schumpeterian growth models education is seen as a determinant of technological progress (Aghion and Howitt, 2009).
exoge-nously determined technological progress. This technological progress can be seen as a free good that is accessible to all at no cost (Fager-berg, 1994). Within this framework Mankiw, Romer, and Weil (1992) introduce human capital, proxied by educational attainment, as an extra input to the production process. Therefore education has an effect through the accumulation process, just like the other factors of production.
A disadvantage of the neoclassical growth model is that it is un-able to explain the process of technological progress that drives the productivity growth. Therefore in an attempt to explain this pro-cess within the economic model, Arrow (1962) endogenizes this by assuming that innovation is an externality that arises from learning-by-doing. When capital is accumulated, individuals create technolog-ical progress through working with the capital goods which results in this process of learning by doing. In contrast Lucas (1988) developed a model in which the creation and transmission of knowledge takes place through the accumulation of human capital. Therefore the rate of accumulation of human capital increases the rate of productivity growth.
In contrast Nelson and Phelps (1966) were the first to argue that the level of human capital determines the productivity growth, not the rate of human capital accumulation. The reason for this is that they consider human capital as a determinant of the ability to im-plement productivity-improving innovations. In their model, produc-tivity growth comes from the interaction between distance from the frontier and the level of human capital. Distance to the frontier refers to the relative difference between the productivity level of the home country and the country with the highest productivity level. The rea-son that they incorporate distance to the frontier is that the further an economy is away from the frontier, the more an economy can imitate and hence the higher productivity growth is. This analysis is taken one step further by Benhabib and Spiegel (2005) by extending the role of human capital. In their model human capital has not only an effect on the ability to implement productivity-improving imitations, but also on the ability to undertake innovation.
Schumpete-rian growth model originally proposed by Aghion and Howitt (1992) is that they state that productivity growth comes from the process of deliberate research and development activities undertaken by private companies.
more important the closer an economy is to the technological frontier, whereas the effect of primary education will become smaller the closer the economy is to the technological frontier.
This idea is formalized by a maximization problem within a Schum-peterian growth model. A firm can choose between imitating based on the global technology from the previous period, or innovating based on the local knowledge from the previous period. A successful inno-vator will earn monopoly rents in the subsequent period. The model of Vandenbussche, Aghion, and Meghir (2006) can be used to analyze the effect of changes in the level and composition of human capital. So far we have analyzed the process of productivity growth without considering the role of international trade. However, international trade can play a crucial role in the process of creative destruction, the concept which underlies the Schumpeterian growth models. Inter-national trade influences this process of productivity growth in three ways; through an increase in product market competition, influencing the incentives to innovate and through knowledge spillovers. All of these effects will be discussed in the next section.
2.2
The effect of international trade on
pro-ductivity growth
International trade enhances the competition between foreign and do-mestic firms and thereby increases product market competition. This increased competition improves the process of output reallocation be-tween producers by selecting the more efficient firms and weeding out the less efficient ones. This process of market selection increases the overall productivity (Aghion and Howitt, 2009; Denicol`o and Zanchet-tin, 2010).
Acemoglu, Aghion, and Zilibotti (2006) argue that this market selec-tion process is more important in the process of innovaselec-tion than imi-tation. Furthermore the closer an economy is to the technology fron-tier, the more important innovation becomes for productivity growth. Therefore the market selection effect becomes more important the closer the economy is to the frontier.
These arguments show that international trade increases product mar-ket competition which increases productivity growth by selecting the most productive firms. Apart from this selection effect, increased com-petition influences the incentives to innovate, but the incentives de-pend on the economy’s position with respect to the frontier. The in-centive to innovate becomes larger for the relatively more productive firms as they will be able to escape competition through successful in-novation. The opposite is true for the relatively less productive firms; their incentives to innovate will be reduced due to the fact that even if they innovate successfully there is still a change of losing out to the leading firm. Therefore, a positive effect of the increased competition on the incentives to innovate is more likely the closer an economy is to the technological frontier (Aghion, Blundell, Griffith, Howitt, and Prantl, 2009).
The second effect of international trade on productivity growth is through knowledge spillovers. In the Schumpeterian model knowl-edge spillovers are present in the form of imitation. All firms are able to imitate based on all available technology from the world fron-tier of the last period. However, the ability to innovate depends on the national knowledge stock. Grossman and Helpman (1991) argue that the national stock of knowledge capital can be increased by hav-ing more interaction between domestic agents and their international counterparts. These contacts are increased by the level of commer-cial exchange in the form of international trade. Therefore Grossman and Helpman (1991) predict that international trade will increase the stock of knowledge capital and hence the efficiency of innovation and thereby productivity growth.
In contrast,Cameron, Proudman, and Redding (2005) argue that the level of international trade has not only an effect on innovation but also on imitation since it increases the absorptive capacity of an econ-omy and thereby the ability to imitate. In case that international trade mainly enhances the speed of imitation, the effect of interna-tional trade will be relatively larger for economies that have a larger distance to the frontier. In contrast, if the level of international trade mainly influences the speed of innovation, the effect will be relatively larger for economies that are close to the frontier.
in-ternational trade takes place, since the import of foreign intermediate goods creates the knowledge spillover effects.
To summarize, one can state that the effect of international trade within a Schumpeterian growth model has an ambiguous effect on productivity growth. The closer an economy is to the technological frontier, the more productivity growth will increase. This is due to the selection effect that is more important for innovation than for im-itation and due to the positive effect on the incentives to innovate for industries that are close to the frontier. Economies further away from the frontier may experience a different effect: the selection ef-fect increases productivity but the negative efef-fect on the incentives to innovate may reduce productivity growth. The effect of knowledge spillovers is ambiguous. On the one hand innovation and hence the spillovers become more important the closer a country is to the fron-tier. On the other hand, the size of the knowledge spillovers becomes smaller the closer the economy is to the frontier.
So far the effects of education and openness to international trade on productivity growth have been discussed on the basis of theoretical analysis and models. The next section examines empirical evidence on the relationship between education and productivity growth and the effect of international trade on productivity growth.
2.3
Empirical evidence on the effect of
edu-cation and international trade on productivity
growth
As mentioned before, education can either have an effect on productiv-ity growth as an input or as a determinant of the abilproductiv-ity to imitate and innovate. Regarding education as an input in the process of economic growth indicates that the change in the level of schooling influences productivity growth. In contrast recognizing education as a determi-nant of the ability to innovate and imitate implicates that the absolute level of schooling drives productivity growth.
the change in the level of education, but the level of education itself that determines productivity growth. Their analysis indicates that the level of education determines the ability of a country to imitate (catch-up) and to innovate. Barro and Sala-i Martin (1997) as well as Barro (1998) showed that both the initial schooling level and its interaction with a measure of the technology gap with the frontier are positively associated with subsequent productivity growth. Their work focuses on large cross-country datasets.
Important critique on these studies is that there are various mea-surement errors. In the dataset of Barro and Lee (1993), which is used in the growth regressions of Benhabib and Spiegel (2005), the heterogeneity of the population is not taken into account and thereby underestimating the level of education (Cohen and Soto, 2007). How-ever, in the new dataset of Barro and Lee (2010) the heterogeneity of the population is incorporated. Therefore this new dataset will be used in this thesis as is described in detail in the data section. Another critique on the measurement is that data on the years of edu-cational attainment do not incorporate the differences in the quality of education. Therefore researchers have also used results from interna-tional test scores on the mathematical, scientific and reading ability of students as a means of “quality adjusting” the crude schooling data. Results suggest that mathematics and science scores have a signif-icant partial correlation with growth (Hanushek and Kimko, 2000). De la Fuente and Dom´enech (2006) show for a subgroup of 21 OECD countries that the data used as measures for human capital is fairly unreliable. These measurement errors are also emphasized by Krueger and Lindahl (2001), who show that there is very limited information in the data on years of schooling that are used in growth regressions reported by for example Benhabib and Spiegel (1994). Furthermore, they notice that the effect of the level of education vanishes if the analysis is restricted to only the OECD countries.
In contrast Inklaar, Timmer, and Van Ark (2008) show for a sample of OECD countries that the effect of the level of education disappears once industry level data are used or a measure of productivity is used that corrects for the hours worked and the quality of the workforce. Therefore these findings lend support to the view that education can be seen as an input to the economic process.
There is thus evidence supporting the effect of the accumulation of education as well as the level of education on productivity growth. However, the results depend on the data used to measure human cap-ital and productivity growth.
The next question is whether the expected role of international trade on productivity growth is supported by empirical research. Evidence that international trade increases productivity by selecting the most effective firms is presented by Bernard, Jensen, and Schott (2006). They show that a decrease in the industry-level trading costs increase the productivity of an industry based on plant level data. Similar ev-idence is presented by Farinas and Ruano (2005). This supports the market selection effect, predicting that an increase in competition will increase overall productivity.
The evidence of competition on innovation is more complex. Study-ing the regulatory reform in OECD countries Nicoletti and Scarpetta (2003) found that entry liberalization has a positive effect on innova-tion. Based on very detailed industry level productivity growth and patent panel data for the UK in combination with the large number of policy reforms undertaken during the Thatcher era, they conclude that increased product market competition discourages innovation in laggard industries whereas it increases innovation in industries closer to the frontier (Nickell, 1996).
Another study on U.K. firm patenting activity finds support for an inverted-U relationship between competition and productivity. Com-petition in the case of neck-and-neck industries results in more inno-vation and can be interpreted as increasing the incentives to innovate. However, competition in industries lagging behind in terms of produc-tivity results in less innovation taking place. This can be interpreted as a decrease in the incentives to innovate (Aghion, Bloom, Blundell, Griffith, and Howitt, 2005).
have a positive effect on the home country productivity depending on the extent to which international trade takes place (Coe and Help-man, 1995). Based on an extensive survey of the available empirical literature Keller (2004) comes to the same conclusion that undistorted trade regimes increase knowledge spillovers.
More specific Aghion, Fedderke, Howitt, Kularatne, and Viegi (2009) find, based on industry level data for South Africa, that the knowledge spillovers created through international trade have a relatively larger effect for industries that have a larger distance to the frontier than for the industries that are closer to the frontier. This supports the view that knowledge spillovers are more important for imitation then innovation, which is in line with Cameron, Proudman, and Redding (2005). They find evidence based on the analysis of 14 UK industries that the level of international trade mainly influences the ability to imitate and that it has only a minor effect on the ability to innovate. This would also indicate that knowledge spillovers have a larger effect for economies that are further away from the technological frontier. Summarizing, there is clear evidence that more international trade has a positive effect on the incentives to innovate for economies close to the frontier while the opposite is true for economies lagging behind in terms of productivity. Furthermore, the market selection effect coming from international trade seems to increase overall productiv-ity. The effect of knowledge spillovers is more difficult to assess, since there is both evidence of the positive effect of international knowledge spillovers on innovation as well as on imitation.
3
The economic model
In this section I will first describe the economic model that formalizes the process of productivity growth. Thereafter hypothesis are devel-oped based on the economic model. The economic model is based on the theoretical framework of Vandenbussche, Aghion, and Meghir (2006) with the inclusion of several simplifications as described by Aghion and Durlauf (2005). This model can be used to understand what the effect of the level and composition of human capital will be on productivity growth of the economy at different distances from the technological frontier. Moreover the model is extended in order to analyze the influence of international trade on productivity growth.
3.1
The economic environment
The basic model assumes that the world consists of a finite number of economies and that each economy is composed of several sectors. All individuals live for one period and there is a population size of 1 of workers which remains constant over time.
In the economy there is one good which is also used as an input for the production of intermediate goods. The final good is competitively produced according to the following Cobb-Douglas production func-tion.
Z 1 0
A(v)1−αx(i)αdi (1)
Where α is ∈ [0,1], AI,t is productivity in sector i, and xi,t is the flow
of intermediate goods used in the production of the final good. Since the final good sector is competitive, the price will equal the marginal cost. This means that the price of the final good will be:
pi,t =
∂yI,t
∂xi,t
is not worthwhile for the imitator to enter the market. χ indicates the relative cost disadvantage of the imitator and should be larger than 1 since that is the cost of the leading firm.
The corresponding monopoly profit in the intermediate sector is based on the limit price and the demand for intermediate products. The de-mand for intermediate good i can be derived from equation (2) and is:
xi,t = α
2
1−αAi,t (3)
The corresponding monopoly profits for intermediate sector i are: πi,t = (pi,t− 1)xi,t = δπi,t = δAi,t, where δ = (
1 α − 1)α
2
1−α (4)
The monopoly profits are the limit price multiplied by the quantity x(I, t). Substituting the quantity with equation (3) yields the results above.
3.2
Productivity growth
Intermediate firms can increase productivity either by imitating at the frontier or by innovating based upon existing technologies. Imitation can be performed by low skilled workers as well as high skilled work-ers. The difference is that high skilled labor is more productive in innovation than in imitation. Assuming that productivity growth is a linear function of innovation and imitation, the level of productivity can be described by:
AI,t= AI,t−1(i) + λ
h
uσm,i,ts1−σm,i,tA¯I,t−1+ γuφn,i,ts 1−φ n,i,tAI,t−1
i (5) ¯
Ai,t−1 is the world productivity frontier of industry i at t-1, Ai,t−1 is
the country’s technological frontier in industry i at t-1. um,i,t (resp.
sm,i,t) is the amount of unskilled (skilled) labor used in imitation in
sector i at time t, un,i,t(resp. sn,i,t) is the amount of unskilled (skilled)
labor used in innovation in sector i at time t. σ (resp. φ) is the elasticity of unskilled labor in imitation (resp. innovation) and γ > 0 measures the relative efficiency of innovation compared to imitation in generating productivity growth. λ > 0 measures the efficiency of the overall process of technological improvement.
uj,i,t ≡ uj,t and sj,i,t ≡ sj,t for all i and for j = m, n. Furthermore
assuming that there is a continuum mass of intermediate firms of 1, the equilibrium rate of productivity growth can be expressed as:
gt= Z 1 0 At(i) − At−1 At−1 di (6)
The goal is to arrive at an equation of productivity growth that simpli-fies the analysis of the effects of human capital on productivity growth. Based on the assumption that all firms face the same maximization problem the equilibrium rate of productivity growth can be written as:
g = λhuσm,ts1−σm,ta−1t−1+ γuφm,ts1−φm,ti (7)
Still assuming that there is a mass 1 of intermediate firms, it indicates that in equilibrium the level of unskilled labor is the amount employed in imitation plus the labor employed in innovation U = um,t + un,t.
The amount of skilled labor is simply the sum of the skilled labor em-ployed in imitation and innovation, S = sm,t+ sn,t.
The goal is to arrive at an equation that facilitates the derivation of the partial derivatives of low and high skilled labor with respect to productivity growth. Using these simplifications productivity growth can be expressed as proved by Vandenbussche, Aghion, and Meghir (2006) in the following way:
g/γλ =hφh(a)1−φU + (1 − φ)h(a)−φSi (8) Where: h(a) = (1 − σ)ψ(1 − a) (1 − φ)γa σ−φ1 (9) Where: ψ = σ(1 − φ) (1 − σ)φ (10)
increases the effect of market selection that is crucial to the process of innovation and thereby increases the productivity of innovation (Ace-moglu, Aghion, and Zilibotti, 2006). Furthermore international trade influences the incentives to innovate. The closer an industry is to the frontier, the larger the incentives become to innovate and thereby escape competition. Therefore a higher level of international trade in-creases the rate of innovation in economies close to the frontier, which results in higher productivity growth. However, in industries that lag behind international trade reduces the incentives to innovate, which results in a lower rate of innovation and hence reduces productivity growth.
Combining the market selection effect and the effect on the incentives to innovate of international trade implies that the rate of innovation depends on the level of international trade and the distance to the frontier. This can be formalized by stating that the rate of innovation depends on p(at−1 − ω), where p is a measure of the level of
inter-national trade. ω denotes the minimum level of relative productivity that an economy has in order to benefit from the effect of international trade. This specification results in the situation that the level of in-ternational trade has a negative effect on productivity growth below a productivity level ω and has a positive effect above that level of pro-ductivity. Economies with a relative low level of productivity will not profit from the positive effect of international trade on innovation and the market selection effect will only lead to a decrease of productivity of domestic firms. However, the closer an economy is to the frontier the more international trade can have a positive effect on productivity growth. Therefore international trade increases productivity growth relatively more the closer an economy is to the frontier
to the frontier changes. The size of knowledge spillovers is larger the further an economy is from the frontier, whereas the closer an econ-omy is to the frontier the more important the innovation becomes that relies on the knowledge stock. Unfortunately the inclusion of this knowledge spillover effect lies outside the scope of this thesis but would be interesting for further research.
Since knowledge spillovers are excluded from the analysis the results of the effect of international trade have to be interpreted with caution. In the interpretation it will be difficult to infer whether the effect of international trade comes from changing incentives to innovate and the market selection effect, or from knowledge spillovers.
In this section the economic model was presented that describes pro-ductivity growth, in the next section the hypothesis regarding produc-tivity growth will be derived based on equations(8) and (11).
3.3
Hypotheses
Based on the model above the hypothesis regarding productivity growth can be derived. The first subject is the relationship between human capital and productivity growth. As can be seen from the equation there is a level effect as well as a composition effect of human cap-ital on productivity growth. The level effect refers to the effect of varying the aggregate level of human capital, while holding its distri-bution between skilled and unskilled labor at a constant rate. The composition effect denotes the effect of changing the relative shares of skilled and unskilled labor. This has a different effect on productivity growth depending on the economy’s position relative to the technolog-ical frontier. Finally the effect of international trade will be discussed in relation to the distance to the frontier of an economy. These effects will be formalized and discussed in more detail in this section in order to hypothesize on them.
below: ∂g ∂(S) = (1 − φ)h(a) −φ γλ > 0 (12) ∂g ∂(U ) = (φ)h(a) 1−φγλ > 0 (13)
Since both equations are > 0, an increase in the average level of skilled or unskilled labor will increase productivity. Intuitively this does make sense, a higher average level of skilled (resp. unskilled) labor increases the ability to innovate (resp. imitate) and hence increases productiv-ity. This assumption is also in line with the results of Benhabib and Spiegel (2005) , stating that a higher level of average human capital increases productivity growth. Therefore the hypothesis is:
H1: An increase in the average level of human capital increases pro-ductivity growth
The second relationship is the composition effect. Equations (12) and (13) indicated that a marginal increase in either skilled or unskilled labor increases productivity growth, but that the size of the effect de-pends on the economy’s position relative to the technological frontier. To understand the interaction between the distance to the frontier and the increase in skilled labor the following partial derivative as derived by Vandenbussche, Aghion, and Meghir (2006) can be studied:
more innovation activities take place and the more valuable skilled labor can be. One can imagine that an economy has to have a certain level of development and activities to fully profit from skilled labor. In a similar fashion Aghion and Howitt (2009) prove that ∂a∂U∂2g < 0. This indicates that the effect on productivity growth of an increase in the level of unskilled labor becomes smaller the closer an economy is to the frontier. This can be explained by looking at the fact that the closer an economy is to the frontier, the less opportunities there are for imitation and the lower the value of unskilled labor can be in productivity growth. However, in the case that a country is far from the technological frontier, there is more room for imitation and therefore low skilled labor can generate more productivity growth. Consequently hypothesis 2 reads:
H2a: An increase in the stock of skilled human capital enhances pro-ductivity growth relatively more the closer the economy is to the world technology frontier.
H2b: An increase in the stock of unskilled human capital enhances pro-ductivity growth relatively less the closer the economy is to the world technology frontier.
The third effect that is discussed is the impact of the level of interna-tional trade on productivity growth. As described in the literature re-view and formalized within the economic model the effect of the level of international trade varies with the distance to the frontier of an economy. In the modeling of the effect of international trade I assume that international trade decreases productivity growth for economies that have a large distance to the frontier, while it increases produc-tivity growth for economies that are closer to the frontier. Moreover, I assume that the closer an economy is to the frontier, the more in-ternational trade increases productivity growth. These effects can be illustrated by the following partial derivatives based on equation (11):
Consequently hypothesis 3 reads:
H3: The level of international trade increases productivity growth rela-tively more the closer an economy is to the world technological frontier.
4
Methodology
In this section the procedure to create the empirical results is dis-cussed. The economic model defines the relationship between produc-tivity growth, human capital, distance to the frontier and international trade. In order to test these relationships three different equations are estimated on a cross sectional dataset covering the years 1960-2000. Based on this dataset two observations are created for each country (if available), one for the period 1960-1980 and one for the period 1980-2000. Then the TFP growth rate of 1960-1980 (resp. 1980-2000) is regressed on the initial values of human capital and distance to the frontier of 1960 (resp. 1980). In the equation t is used for the TFP growth rate and refers to the growth rate between t and t − 1, t − 1 refers to the 20 years before t as is the case for all dependent variables with a lag.
The main reason to test the relationships on a cross-section instead of a panel dataset is that the proposed relationships are long run effects. Therefore the estimates have to reveal the long run effects whereas the year-to-year changes are less relevant. Secondly, by using cross sectional estimates the problems associated with endogeneity and the need for using instrumental variables are reduced.
The economic model defines the relationship from the level of human capital and distance to the frontier running to TFP growth. However, there may be a problem of endogeneity, the problem that the rela-tionship runs into two directions. For example one can argue that the relationship runs from the TFP growth to the level of human capital, since relative wealthier countries can spend more on education and consequently have a higher level of human capital. Similarly one can state that due to lower TFP growth rates an economy has a larger distance to the frontier and that therefore the relationship runs from lower TFP growth to the distance to the frontier.
capital and the distance to the frontier to TFP growth. But in order to minimize the endogeneity in the measurement, the estimates are conducted in a cross-section and with lagged values for the indepen-dent variables of education and distance to the frontier (Benhabib and Spiegel, 1994).
The same endogeneity problem may be present in estimating the effect of international trade. More international trade can cause productiv-ity growth. However the relationship may also hold the other way around, a booming economy may also import and export more. Based on the economic model and corresponding theory there are strong ar-guments to believe that the relationship runs from international trade to productivity growth. Furthermore the problem of endogeneity in the data is reduced by using the lagged values of international trade. The distance to the technological frontier is measured as the TFP level of a country with respect to the US. This implicates that the US is seen as the technological frontier and therefore has in theory the highest TFP level of all countries. However in practice there are economies with a TFP level that is higher than that of the US. In the model the distance to the frontier is measured as the logarithm of the TFP level of the home country minus the logarithm of the TFP level of the US. This results in a negative a for all economies with a TFP level that is lower than the US, for an a of zero for the US and a positive a for all economies with a TFP level that is higher than that of the US. Estimating the model with the distance to the frontier defined as the TFP relative to the US can therefore influence the estimated effect of the distance to the frontier. Therefore in the robustness checks a specification is estimated that excludes all observations with a TFP level higher than that of the US. The estimates indicate that it does not change the results in an important manner.
As described in the hypothesis section, both the average level and the composition of human capital are assumed to have an effect on TFP growth. To analyze the effect of the average level of human capital and the effect of the composition of human capital, different empirical specifications are required. The effect of the average level of human capital is tested in equation (17).
is high skilled. The remaining fraction of the labor force belongs to the labor that is low skilled. The composition effect is then tested by investigating what the effect is of a change in the percentage of in-habitants that studied beyond secondary school, or in other words the change in the fraction of the labor force belonging to the high skilled labor.
A disadvantage of this specification is that only estimating the effect of a change in the fraction of the population that attained education beyond secondary schooling, the effect of the average level of human capital as discussed in hypothesis 1 is ignored. For example, if the fraction of high skilled labor increased, but the average number of years of primary schooling also increased, then this last effect is ig-nored.
In order to tackle this problem the composition effect is also tested us-ing a specification in which the number of years of primary schoolus-ing and the number of years of tertiary schooling are explicitly included. In this way stock of low skilled human capital and high skilled human capital are allowed to vary independently. Thereby the composition effect as well as the role of changes in the level of human capital is incorporated.
A disadvantage of this specification is that there is a high expected correlation between primary and tertiary schooling, since all individ-uals that attained tertiary schooling had to attain primary schooling first. The high correlation will increase the test statistic and thereby lead to a lower significance of the results.
The effect of the level of human capital is tested in equation (17) and the effect of the composition of human capital is tested both in equation (18) and in equation (19). In contrast, the role of interna-tional trade is included in all of these three equations in the same way. The effect of changes in the average level of human capital is esti-mated by:
gj = β0+ β1aj+ β2Hj + β3ajHj+ β4Oj+ β5ajOj+ j (17)
In this equation gj is the average TFP growth rate of a country over
twenty years. Furthermore aj is the initial value of the natural
O stands for the level of international trade as measured by the level of imports and exports divided by national income.
The effect of the composition of human capital based on change in the fraction of high skilled human capital is estimated by the following equation:
gj = β0+ β1aj+ β2Fj + β3ajFj+ β4Oj + β5ajOj+ j (18)
In this equation all symbols are the same as in the previous equation. Only F is new and stands for the share of individuals that have studied beyond high school, expressed as a percentage of the total population. The effect of the composition of human capital in combination with the level effect of human capital is estimated by the following equation:
gj = β0+ β1aj + β2Y earsPj+ β3Y earsTj+
β4aj∗ Y earsPj + β5aj∗ Y earsTj+ β6Oj+ β7aj ∗ Oj+ j
(19) All the symbols are the same as in the equations above, only YearsP and YearsT are new. YearsP measures the average years of primary schooling of the population whereas YearsT measures the average years of tertiary schooling of the population.
All three equations above have interaction variables. Interpreting the coefficients of interaction models requires a little more analyses. Spe-cific standard errors have to be estimated since they are a function of the moderating variable, in order to be able to understand the signif-icance of the results (Hill, Griffiths, and Lim, 2008).
This can be illustrated with an example. Consider equation (17) that is used to test the relationship between the aggregate level of human capital interacted with the distance to the frontier on TFP growth. The marginal effect of the level of human capital on TFP growth be-comes a function of the distance to the frontier (a). More formally:
∂g
∂H = β2 + β3aj,t. The size of the marginal effect now depends on
a and the corresponding test statistics also becomes a function of a. The standard error becomes:
p
In order to simplify the interpretation of the marginal effect, I will create graphs with the marginal effect and the corresponding signifi-cance for different levels of the moderating variable (a). This graph has to be created for the relevant interval of the modifying variable (Brambor, Clark, and Golder, 2006). In this case the relevant domain is determined by a, the natural logarithm of the distance to the fron-tier. In this I will create the graphs for economies with a TFP level of 1 until 150% of the US.
5
Data
The dataset is constructed based on three different sources and incor-porates TFP levels, education data and a measure of trade openness. The first subsection describes how the TFP levels are calculated. In the second subsection the data sources on education and international trade are discussed. In the last subsection the dataset is described and the detection of outliers is examined.
5.1
TFP estimates
In this subsection the construction of the TFP levels is explained. First the method is discussed and subsequently the necessary data are described. The TFP levels are obtained based on the standard Cobb-Douglas production function:
Y = AKαL1−α (21)
In this equation Y stands for output, A for TFP, K for the capital stock, L for the amount of labor and α is the output share of capital. Under the assumption of constant returns to scale 1 − α is the output share of labor.
The following equation is used to obtain the natural logarithm of the TFP level of the home country with respect to the US:
ln(Ah/AU S) = ln(Yh/YU S)−(1−α)ln(Lh/LU S)−αln(Kh/KU S) (22)
used to obtain the TFP growth rate:
ln(At/At−1) = ln(Yt/Yt−1)−(1−α)ln(Lt/Lt−1)−αln(Kt/Kt−1) (23)
In this case t − 1 is a lag of 20 years as is discussed in the methodology section. In the estimates I choose to set the output share of labor (α) at 0.7. Gollin (2002) finds that the labor share lies between .05 to about 0.8 based on international cross-section estimates. However, after some adjustments they argue that the labor shares lie between .65 and .80. The main argument not to rely on estimated labor shares based on national accounts is that the estimates fail to incorporate the earnings of the entrepreneurs and the self employed. This leads to severe underestimation of the labor shares, especially in developing countries. Furthermore Gollin (2002) finds that the adjusted estimates indicate that factor shares are approximately constant across time and space. Therefore, it is plausible for this aggregate study to assume a constant labor share.
Nevertheless an important argument that opposes using constant la-bor shares is that lala-bor share tends to decline for developed countries (Inklaar, Timmer, and Van Ark, 2008). There is thus room to create a better dataset by incorporating the heterogeneity of the labor shares, but that lies outside the scope of this thesis. Therefore a constant labor share of 0.7 is assumed which is also in line with Benhabib and Spiegel (2005); Vandenbussche, Aghion, and Meghir (2006); Erumban (2008).
The following data is used to construct the TFP levels:
Output: The output data comes from Erumban (2008) and is based on the PWT 6.2 which provided the data on Gross Domestic Prod-uct (GDP) in 2005 $ purchasing power parities. In this case Y = P OP ∗ rgdp, in which P OP is the population and rgdpl is the real GDP per capita using Laspeyres index.
these investments up and assume that they have homogenous marginal productivities and depreciation rates. For example Benhabib and Spiegel (2005) assume a constant depreciation rate of 3 % whereas Vandenbussche, Aghion, and Meghir (2006) assume 6 %. A constant depreciation rate rests on the assumption of constant marginal pro-ductivities and depreciation rates of the different types of capital as-sets. However, in reality equipment machinery tends to have higher marginal productivities and faster depreciation. Aggregating all types of capital can lead to an underestimation of the actual contribution of capital to output growth in the case of a rising share of equipment of total capital (Erumban, 2008).
That the contribution of capital is understated can be demonstrated by some empirical considerations with respect to the different types of assets. First of all the share of ICT capital, which depreciates much faster than the other types of capital, has increased substantially in most OECD countries (Inklaar, Timmer, and Van Ark, 2008; Jor-genson, 2001). Secondly, developed countries have a larger share of equipment in total assets than developing countries (Erumban, 2008). Both considerations lead to an underestimation of the contribution of capital to productivity growth and possibly to an overestimation of the importance of capital for developing countries.
A second advantage is that Erumban (2008) constructs measures of the initial capital stocks which are not available in the Penn World Tables. Estimates of the aggregate capital stocks without incorpo-rating initial stocks will underestimate the contribution of capital to output growth. Therefore using the data on aggregate capital stocks of Erumban (2008) will lead to more accurate TFP estimates.
5.2
Data on education and trade openness
The education data are obtained from Barro and Lee (2010) and con-tain data for 146 countries for the years 1950 until 2010. The data are disaggregated by 5-year age intervals. This dataset is the improved version of the older dataset which is for example used by Vanden-bussche et al. (2006) and Benhabib and Spiegel (2005). An advantage of using this new dataset is that it has been improved by taking into consideration the heterogeneity of the age structure of the population. This resolves one of the important flaws of underestimating the level of education. Cohen and Soto (2007) argue that on average older indi-viduals have lower levels of education, but also lower life expectancies. Not incorporating this heterogeneity of the age groups will then un-derestimate the aggregate level of educational attainment. Another improvement is that they use more information from consistent cen-sus data.
A disadvantage as already discussed in the literature review is that this dataset only measures years and levels of education, but has little information on the quality of education. On the other hand a disad-vantage of using estimates based on for example test scores is that the data is not available for the whole dataset in terms of number of countries and years. Nevertheless Vandenbussche et al. (2006) and Benhabib and Spiegel (2005) show that the data based on schooling attainment exhibits useful information in the context of productivity growth.
In order to understand the data used the relevant educational vari-ables are described below:
Average years of schooling attained: contains the average years of schooling all inhabitants of a country have had above the age of 25. The years of education include in this case primary, secondary and tertiary education.
Percentage of tertiary schooling attained: contains the percentage of inhabitants above 25 of the total population that have studied beyond secondary school.
Average years of tertiary schooling: contains the average years of ter-tiary schooling all individuals above 25 have attained.
International trade: is based on Heston, Summers, and Aten (2009) and measured by the percentage of imports and exports with respect to national income. One of the disadvantages of this measure of inter-national trade there is a high level of endogeneity as discussed in the methodology section. This effect is partly removed by using lagged values. However, there are more advanced measures of international trade that suffer less from this problem such as for example Sachs and Warner (1995) who take also into account the geographic characteris-tics as the size and the location of the country. Such a measure would be more accurate, but lies outside the scope of this thesis.
5.3
Data description
In this section the steps to create a clean dataset are reported first. Thereafter the method to detect outliers is discussed.
In the original dataset some observations have a value of exactly 0 for the percentage of the population that attained tertiary education and for the average years of tertiary schooling. Most likely these are errors in the measurement and are therefore excluded from the anal-ysis1. Excluding these observations results in the cleaned dataset.
In table 1 the summary statistics of the cleaned dataset are pre-sented. A more detailed look at the summary statistics shows that the average TFP growth roughly equals 17% over a period of 20 years and therefore equals a yearly growth of about 0.8%. The minimum and maximum values of the TFP growth are respectively -1.06, which indicates a decline of 106% in twenty years and 1.17, which equals a growth of 117% in twenty years. Similarly the average distance to the frontier is -.93, which equals roughly 40% of the TFP level of the US. Looking at the minimum and maximum statistics of the distance to the frontier which are -3.01 and 1.50 and respectively correspond to a TFP level of 5% and 448% of the US.
1From the analysis are removed for the year 1960 the observations of Burundi, Morocco,
Table 1: Summary statistics
Variable Mean Std. Dev. Min. Max. N
TFP growth 0.172 0.346 -1.064 1.169 203
Distance to the frontier -0.929 0.709 -3.007 1.498 203
Years of schooling 4.092 2.738 0.079 11.936 203
% attained tertiary education 4.078 5.008 0.1 30 203
Average years of primary schooling 2.997 1.868 0.045 7.58 203
Average years of tertiary schooling 0.133 0.162 0.002 0.962 203
Openness to trade 0.063 0.081 0.001 0.529 203
There are 15 observations with a higher TFP level than the US and most of them are heavy oil exporting economies. Since the revenues of their natural resources are part of their GDP the calculated TFP lev-els give a distorted picture. Therefore, in the section dealing with the robustness of the estimated results both the exclusion of oil producing countries as well as the exclusion of all observations with a TFP level that is higher than the US is tested.
There is a large variety in the education data. The differences be-tween the minimum and maximum years of schooling is large as well as the attainment of tertiary education. The percentage that attained tertiary education is expressed as a percentage of the total population thas is 25 years or older. The average years of schooling, primary schooling and tertiary schooling are also calculated as an average of all inhabitants of a country that are 25 or older.
observation is an outlier and ranks the observations. Thereafter the relative most outlying observations are eliminated at a predetermined point. Identifying the outliers with this method does not result in es-timates with residuals that are normally distributed. A reason could be that there are groups of outliers present. A disadvantage of indi-vidual outlier detection is that groups of outliers may not be detected. Sometimes groups of outliers can mask the presence of an individual outlier (Rousseeuw and Van Zomeren, 1990; Sturm, De Haan, and Ludwig-Maximilians, 2000). In that case deleting only the individual outliers may have little effect. Therefore methods testing the influ-ence of groups of observations can lead to better results. A method that tests the presence of individual outliers as well as the presence of groups of outliers is proposed by Verardi and Croux (2009). This method tests with an iterative process the effect of omitting different groups of observations. Since this method relies on the specification of the estimate, for each specification the group of outliers is detected with this method. The estimates excluding these outliers result in es-timates with residuals that are normally distributed. In the appendix the list of excluded observations for each equation is presented. The amount of outliers that are detected is relatively large, about 10 percent of the observations is excluded from the analysis. This large number of outliers can indicate that there is an omitted variable in the analysis. An examination of the list of outliers shows that there are relatively a large number of countries that are often considered to have relative weak institutions. Aghion and Howitt (2009) indicate that the quality of the institutions is an important determinant of pro-ductivity growth. Therefore the high number of outliers could be due to the absence of the effect of institutional quality in the estimates.
6
Estimates
relatively more the closer an economy is to the technological frontier. In the first subsection the results of the empirical estimates will be discussed in more detail. In the subsequent subsection the robustness and reliability of the estimates is examined.
6.1
Empirical estimates
As described in the methodology section there are three different equa-tions that are estimated to test the proposed relaequa-tionships. The first equation (17) incorporates the effect of the average level of educa-tion whereas equaeduca-tion (18) and (19) include the effect of primary and tertiary education. These three equations are estimated both on the complete dataset as well as on the OECD sample and are presented in table 2.
6.1.1 The effect of the average years of education on productivity growth
Hypothesis 1 states that the aggregate level of human capital is ex-pected to have a positive effect on productivity growth. This effect is tested by estimating equation (17). The results are presented in table 2. Column 1 displays the estimates based on the complete sample and column 2 shows the estimates based on the OECD sample. The graphs plotting the marginal effect are presented in figure 1 (a) for the estimates based on the complete sample and in figure 1 (b) for the estimates based on the OECD countries.
The estimates for the whole sample confirm that the aggregate level of human capital has a positive effect on productivity growth. An increase in the average years of education increases TFP growth, but the effect decreases the closer the economy is to the frontier. The results based on the OECD sample are insignificant 2 in the relevant domain.
Table 2: Overview empirical estimates of ∆ TFP
(1) (2) (3) (4) (5) (6) Complete sample OECD Complete sample OECD Complete sample OECD Years of schooling 0.0361∗∗∗ -0.0192
(3.19) (-1.41)
Distance to the frontier -0.213∗∗∗ 0.264 -0.103∗∗ -0.276 -0.175∗∗∗ 0.166
(-3.43) (1.12) (-2.14) (-0.92) (-2.69) (0.81) Distance to the frontier *
average years of schooling -0.0421∗∗∗ -0.0772∗∗∗
(-3.28) (-3.14)
openness to trade 3.262∗∗∗ -0.854 2.753∗∗∗ 3.297 3.305∗∗∗ 1.737
(4.94) (-0.29) (3.86) (1.09) (4.71) (0.59) Distance to the frontier *
openness to trade 2.066∗∗∗ -9.524 1.632∗∗∗ -0.541 1.924∗∗∗ 0.472
(4.68) (-1.48) (3.25) (-0.06) (3.94) (0.08) % attained tertiary education 0.00111 0.000696
(0.22) (0.13) Distance to the frontier *
% attained tertiary education -0.0482∗∗∗ 0.00135
(-5.28) (0.06)
Average years of primary schooling 0.0493∗∗∗ -0.0515∗∗
(2.62) (-2.23) Average years of tertiary schooling -0.0834 0.313∗∗
(-0.52) (2.27) Distance to the frontier *
average years of primary schooling -0.0109 -0.198∗∗∗
(-0.59) (-5.00) Distance to the frontier *
average years of tertiary schooling -0.885∗∗∗ 1.837∗∗∗
Figure 1: Marginal effect average years of education on productivity growth
(a) Whole sample (b) OECD countries
The estimates vary in the size of the estimated effect and the domain in which the estimates are significant. The results based on the complete sample indicate that the effect is positive and significant for economies with a TFP level with respect to the US which is lower than 122%. The size of the marginal effect depends, as also indicated by the graph, on an economies position relative to the technological frontier. For example a country with a TFP level of 60% with respect to the US would have based on the estimates of the complete sample an increase of TFP growth over 20 years of 3.2% in case the average years of education increases by one year.
The estimates based on the OECD sample are insignificant above a TFP level of 59% with respect to the US. Since most OECD countries are above that relative level of TFP, these estimates are insignificant in the relevant domain. Concluding one can state that there is clear evidence for hypothesis 1 that the level of human capital increases productivity growth based on the complete sample. However based on the estimates of the OECD sample nothing can be concluded since the effect is insignificant.
6.1.2 The effect of tertiary education on productivity growth
Figure 2: Marginal effect % that attained tertiary education on productivity growth
(a) Whole sample (b) OECD countries
Figure 3: Marginal effect average years of primary education on productivity growth
Figure 4: Marginal effect average years of tertiary education on productivity growth
(a) Whole sample (b) OECD countries
population that attained tertiary education and equation (19) that includes both the average years of primary schooling and the average years of tertiary schooling. The results are presented in table 2. The estimates of equation (18) based on the complete sample are in row 3 and the estimates based on the OECD countries in column 4. These estimates based on the complete sample indicate that the fraction of the population that studied beyond secondary school has a positive effect on productivity growth, but that the effects are decreasing in a. This can also be seen in the graph of figure 2. Thus the closer an economy is to the frontier, the smaller the effect of education becomes. This is the opposite of what one would expect based on the hypoth-esis. The estimates based on the OECD sample are insignificant for all relevant levels of a and therefore indicate that the fraction of the population that studied beyond secondary school does not have an impact on productivity growth.
tertiary schooling on productivity growth. A more detailed look at the estimates based on the complete sample show that the effect of education becomes insignificant beyond a TFP level of 85% compared to the US. The size of the effect again depends on the relative level of the economy with respect to the frontier as can be seen in figure 2 (a). An increase of 1% that attained tertiary schooling will increase productivity growth with 0. 9% growth over 20 years for an economy with a TFP of 60% compared to the US.
Concluding one can state that based on the estimates hypothesis 2a has clearly to be rejected.
A reason that the level of tertiary education increases productivity growth at a decreasing rate, instead of at an increasing rate the closer an economy is to the frontier could be that high skilled labor does play an important role in the process of imitation. The central as-sumption in the economic model is that the elasticity of high skilled labor is higher in innovation than in imitation. In the case that high skilled labor is crucial and very productive in imitation, the elasticity of high skilled labor is no longer higher in innovation than in imita-tion. Therefore the level of high skilled labor can increase productivity growth relatively less the closer an economy is to the frontier as the results indicate. Essentially this indicates that the model of Vanden-bussche, Aghion, and Meghir (2006) has to be reconsidered.
is indicated by graph 2 (a). For a country with a TFP level which is 60% of the US an increase of 1 year of the average years of primary schooling attained will increase TFP growth with 2.7% over a period of twenty years.
The estimates based on the OECD sample indicate that primary schooling only has a positive effect on productivity growth in case an economy has a TFP level that is lower than 59% with respect to the US. The effect of 1 year increase of average years of primary schooling attained in an economy that has a TFP level of 60% of the US is minimal as can be seen in figure 3 (b). Based on the estimates of the whole sample there is clear evidence for hypothesis 2b, that an increase in low skilled human capital has a positive but decreasing effect with respect to an economy’s distance to the frontier. Based on the OECD sample the evidence is mixed. The positive effect of the level of primary education on productivity growth is as expected decreasing the closer an economy is to the frontier, but in contrast to the hypothesis the effect becomes negative for economies with a TFP level that is higher than 60% of the US.
The effect of tertiary education is different for the estimates based on the complete sample and the OECD countries. The estimates based on the whole sample indicate that an increase in the average years of tertiary education has a positive effect on TFP growth, but that the effect decreases in a. This is in contrast with hypothesis 2a which states that the effect will become larger the closer a economy is to the frontier.
coun-tries.
The estimates of equation (18) and (19) based on the complete sample show no evidence in favor of hypothesis 2a that the effect of skilled labor increases the closer an economy is to the technological frontier. The estimates based on the OECD countries of equation (18) are in-significant for all observations and of equation (19) for most OECD countries. Therefore the provided estimates fail to support hypothesis 2a. However, interesting is that the estimates of (19) reveals a posi-tive and increasing effect in a of tertiary education for economies that have a similar TFP level to that of the US.
6.1.3 The effect of international trade on productivity growth
Figure 5: Marginal effect international trade on productivity growth
(a) Whole sample (b) OECD countries
The effect of international trade on productivity growth is included in equations (17), (18) and (19) and lead to very similar results. All these estimates based on the complete dataset show that international trade has a positive effect on productivity growth and the effect be-comes larger the closer an economy is to the frontier. All estimates based on the OECD countries show no significant result for the effect of international trade on productivity growth. Therefore the rest of this section will focus on the size of the effect of international trade on productivity and its significance in the different estimates based on the complete dataset.
equation (18) will be described here. This equation correctly includes the effect of skilled labor as described in the economic model and does not have the disadvantage of a high correlation between the average years of primary and tertiary schooling as is the case in equation (19). The estimate of equation (18) reveal that the effect of international trade depends on the economy’s distance to the frontier a. An econ-omy with a TFP level below 9% with respect to the US international trade has a significantly negative effect on productivity growth as can be seen from figure 5 (a). Nevertheless, since the effect of interna-tional trade increases the closer an economy is to the frontier, the effect becomes significantly positive for economies with a TFP level beyond 24% of the US. The effect of an increase of for example the level of international trade from 10% to 11% of the GDP, increases productivity with 1.9% over a period of twenty years for a country that has a TFP level of 60% with respect to the US.
The estimates based on the complete sample provide clear evidence in favor of hypothesis 3, that the effect of international trade depends on the distance to the frontier, and that the closer a country is to the technological frontier the larger a positive effect of international trade is. However, it is puzzling why there is no significant effect in the estimates based on the OECD countries. A possible explanation could be that the measure of international trade that is used is too crude is to find an effect. A better measure of international trade would incorporate the country specific characteristics that influence the level of trade.
6.2
Reliability and Robustness of the estimates
In order to rely on the estimates presented in the preceding section, the assumptions that underlie the regression analysis have to be examined. This is done in the first subsection. In the subsequent section the robustness of the estimates is examined.
6.2.1 Assumptions underlying the regression analysis
the fit of the models increases once the interaction effect of education and distance to the frontier and the interaction effect of international trade and distance to the frontier are introduced. An important note is that especially the normality of the residuals depends on the out-lier selection method. As discussed in the methodology section this could indicate an omitted variable, as for example the quality of the institutions.
6.2.2 Robustness of the results
The next step is to check the robustness of the results. ‘The estimates of equation (17), (18) and (19) are robust to all the additional checks. Since all three equations are robust and lead to similar results the focus of this section will be to describe the effect of the robustness checks on equation (18). This equation estimates the proposed economic model without suffering from high multicollinearity as is the case with (19). The estimates of the three additional robustness checks are presented in table 3. First of all the observations with a TFP level that is above the level of the US are excluded, these estimates are in column 6. This indicates whether choosing the US as the frontier leads to an under-estimation of productivity growth as is discussed in the methodology section. Secondly the oil producing countries are excluded from the analysis, these results are presented in column 7. Finally, region dum-mies are included and these estimates are presented in column 8. Countries that have abundant natural resources tend to grow differ-ently (Sachs and Warner, 1995). Therefore it is important to test what the effect is of omitting the observations of economies that rely heavily on the export of natural resources. In order to do so the oil exporting countries as defined by the IMF are excluded3. The IMF definition includes countries whose net oil exports represent a minimum of two-thirds of total exports and are at least equivalent to approximately one percent of world exports of oil.
Excluding the oil exporting countries does decrease the fit of the model. This is counterintuitive; one would expect that excluding economies that grow different in a way which is not explained by the estimated model, would increase the fit of the model.
It is even more interesting to assess whether excluding the oil pro-ducing countries alters the effects found in the previous estimates and
3Bahrain, Iraq, Libya, Kuwait, Oman, Qatar, Saudi Arabia and the United Arab
whether this changes the results. These effects can best be studied by looking at the graphs plotting the marginal effect of - in this case - the percentage of the population that attained tertiary education. These graphs are provided in the appendix in figure 6. Based on these graphs the conclusion is robust that the effect of tertiary education on productivity growth becomes smaller the closer an economy is to the frontier. The effect does not change when the economies with a TFP level that is higher than the US are excluded, the oil exporting countries are excluded or when region dummies are introduced. The significance becomes only a little smaller in case the economies with a TFP level that is higher than the US are excluded. Consequently one can conclude that there is robust evidence in opposition of hypothesis 2a.
7
Conclusion
In this thesis the effect of education and international trade on pro-ductivity growth is investigated. This is done based on the theoretical model proposed by Vandenbussche, Aghion, and Meghir (2006). This model is extended to incorporate the role of international trade in the process of productivity growth. The most important results are that the role of skilled labor as proposed by Vandenbussche, Aghion, and Meghir (2006) does not hold for a broader group of economies and is insignificant for the OECD countries. The second conclusion is that besides the effect of education the level of international trade is an important determinant of productivity growth. Including both edu-cation and the level of trade in the model leads to significant results and increases the model fit.
The core of the theoretical model proposed by Vandenbussche, Aghion, and Meghir (2006) is that low and high skilled labor have a different role in the production process. High skilled labor is more important for innovation and low skilled labor is more important for the process of imitation. Consequently high skilled labor increases productivity growth relatively more the closer an economy is to the frontier, since most growth has to come from innovation. In contrast low skilled la-bor increases productivity relatively more the further an economy is from the frontier since most productivity growth comes from imitation. These hypothesis are tested by estimating the effects of educational at-tainment on productivity growth on an improved dataset with respect to Vandenbussche, Aghion, and Meghir (2006). The dataset includes more countries and improved education data. Furthermore improved data on capital stocks is used, that remove the underestimation of the contribution of capital to productivity growth in the advanced coun-tries.
