Master Thesis in the Framework of the Double Degree Programme: M.A. International Economics (The University of Göttingen) M.Sc. International Economics and Business (The University of Groningen)

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Master Thesis in the Framework of the Double Degree

Programme:

M.A. International Economics

(The University of Göttingen)

M.Sc. International Economics and Business

(The University of Groningen)

Ageing countries: Can education moderate the effect of

ageing on labour productivity and economic growth?

Name Student: F.M. Steemers

Student ID number (Groningen): 1906658

Student ID number (Göttingen): 11403903

Student email: f.m.steemers@student.rug.nl

Date Paper: 15th of June 2015

Supervisor: Dr. A. A. Erumban

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Abstract

The share of elderly (people aged 65 and above) is getting larger in advanced countries and the same is expected to be seen in the rest of the world within some decades. At the same time advanced countries are close to experiencing a decreasing working-age population for the first time since the Second World War. This increasing dependency on a smaller working-population has raised concerns how society is going to maintain welfare growth. This thesis extends research in the field of ageing and growth by focussing on the moderating effect of education. Firstly, the combined effect of the share of elderly and their education on economic per capita growth is investigated. For the analysis, a sample of 71 countries is considered from 1970 to 2010 with 5-year gaps. Secondly, the effect of ageing on labour productivity growth is investigated after stratification by skill level. For this inspection, a sample of 15 advanced countries is considered from 1971 to 2005. Fixed effect panel data analysis is conducted and the robustness of the results is checked with the instrumental variable analysis. Results are inconclusive but provide some indication that education indeed moderates the effect of ageing on labour productivity and economic growth.

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Table of Tables

Table 1: Per capita growth rates and elderly dependency ratio for major economies from 1970 to 2000. ... 8

Table 2: Expected relationship of the independent variables with dependents ... 23

Table 3: Constructs, variables, and sources for model 1. ... 27

Table 4: Constructs, variables, and sources for model 2. ... 27

Table 5: Descriptive statistics of model 1. ... 33

Table 6: Descriptive statistics model 2. ... 34

Table 7: Regressions tested with corresponding statistics. ... 35

Table 8: FE regression analysis of model 1. ... 36

Table 9: FE regression analysis of model 2. ... 39

Table 10: IV regression of model 1. ... 40

Table 11: IV regression of model 2. ... 42

Table 12: Summary of empirical results. ... 43

Table 13: Countries used in model 1 and 2: ... 54

Table 14: Shapiro-Swilk normality and Jarque-Bera goodness-of-fit tests for model 1 and 2. ... 55

Table 15: Correlation matrices. ... 57

Table 16: Variation inflation factors for model 1 and 2. ... 58

Table 17: Modified Wald test for groupwise heteroscedasticity by region model 1 and 2. ... 59

Table 18: Shapiro-Swilk and Jarque-Bera normality tests for model 1 and 2. ... 59

Table 19: POLS regressions on model 1. ... 62

Table 20: POLS regression of model 2. ... 63

Table of Figures

Figure 1: Population pyramids of the less and more developed regions in 1970, 2013, and forecasts for 2050. ... 6

Figure 2: The demographic transition and population growth. ... 12

Figure 3: Labour productivity growth in the USA, Europe, and Japan from 1971 to 2013. ... 16

Figure 4: Histogram and PP-plot of the error (GDP per capita growth) in model 1. ... 55

Figure 5: Histogram and PP-plot of the error (GDP growth) in model 2. ... 56

Figure 6: Scatterplot of the fitted values for model 1 and 2. ... 59

Figure 7: Leverage plot for model 1. ... 60

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1 Introduction.

The world is at a unique point in time. The share of the working-age population (people from 15 to 64 years old) is shrinking in advanced economies and is expected to start declining in the developing countries as well within some decades (UN, 2013; the Conference Board, 2014). The baby-boom generation1 is retiring and leaves society with the concern how we can take care of this increasing share of elderly (people aged 65 and older). Societies may have troubles fighting poverty, especially among old people (Bloom, Canning, & Sevilla, 2001; UN, 2013), and to maintain and improve living standards for all people (Lee & Mason, 2010; UN, 2013). At the same time, there are also concerns on how the economy will react to the prospective decrease of the working-age population. This could have large impacts on the labour market.

In this thesis, I will investigate what the ageing of society will mean for labour productivity and economic growth. I will do this from two perspectives. Firstly, I will examine what the increasing share of elderly means for per capita income. The thesis will add to current literature by investigating if the education of elderly is moderating this relation. Secondly, I will focus on the expected decrease of the working-age population and its impact on labour shortages. Employment growth is expected to slow down, so growth will be more dependent labour productivity. Since ageing entails the change to an older labour force, I will examine how labour productivity changes over a lifetime. In that investigation, I will again focus on education and inspect if the relation of age and labour productivity is different dependent on the skill level of the worker. In the remainder of this introduction, I will explain how ageing relates to growth and why it might be relevant to investigate education in this context.

The global share of older people increased from 9.2 percent in 1990 to 11.7 percent in 2013 and will expectedly keep on growing toward a share of 21.1 percent in 2050. In absolute number this means an increase from 841 million old people in 2013 to more than 2 billion by 2050 (UN, 2013). There are large differences across regions. In figure 1, the so called population pyramids can be seen which show the rise of the share of elderly relative to the young and working-age population. As can be seen, developed regions are already experiencing large shares of elderly and a small working-age population. Less developed

1_{The baby-boom generation, also known as baby boomers, is generally used to indicate the people who lived in}

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Figure 1: Population pyramids of the less and more developed regions in 1970, 2013, and forecasts for 2050.

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regions2 are expected to experience the same by 2050 (UN, 2013). Ultimately all countries will turn from the demographic gift phase, recognizable for its relatively large working-age population, to the last phase of the demographic transition, the demographic burden which is identifiable for its relatively high share of elderly and small working-age population (Bloom & Sousa-Poza, 2013).

It might be interesting to take a closer look at some major economies. In table 1, the per capita growth rates and elderly dependency ratios3_{of China, Brazil, Germany, India, and the} USA can be seen. From this table the large differences in elderly dependency ratios are directly visible. On the one hand, there is Germany. From 2000 to 2010 Germany experienced the retirement of its baby-boom generation with now having an elderly dependency ratio of 31.5 percent. On the other hand, China and India are growing fast, seemingly benefiting from their low elderly dependency ratio. Nevertheless, having a low elderly dependency ratio is not necessarily a reason for rapid growth. Even though Brazil has had a relatively low elderly dependency ratio, their growth has been comparably low. Policy and labour market conditions seem important mediators. The implications of ageing are different among countries. For example, the USA is benefiting from migration. Large number of immigrants are keeping the dependency ratio of the USA relatively low. On the other hand, developing countries suffer from brain drain, the emigration of high-skilled workers to advanced ageing economies where better labour conditions are offered.

Other important implications of ageing on growth are expected to come from changes in the financial markets and asset prices (e.g. Poterba, 2004), the savings rate (e.g. Bloom, Canning, & Fink, 2010), productivity (e.g. Lindh & Malmberg, 1999), and the labour market (Conference Board, 2014). Furthermore, it may lead to more fiscal pressure on the working population because of increasing taxes, pensions, and other support systems (Fougère & Mérette, 1999; UN, 2013; WEF, 2004). The impact of ageing on growth will be different among countries dependent on these areas.

2_{The UN (2013) uses 21 regions in its report and includes the following regions in less developed regions: all}

regions of Africa, Asia (excluding Japan), Latin America and the Caribbean, and Oceania (excluding Australia and New Zealand). The more developed regions include all other regions plus the three exclusions.

3_{The elderly dependency ratio is the people aged 65 years and above as share of the working age population}

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Table 1: Per capita growth rates and elderly dependency ratio for major economies from 1970 to 2000.

China Brazil Germany India USA

Growth rate of per capita income (in %)

1970 5.3 7.6 3.3 0.9 2.2

1980 6.6 0.5 1.6 0.9 0.8

1990 6.7 -1.7 3.2 3.3 1.4

2000 7.1 0.2 1.6 3.7 2.1

2010 8.3 2.2 1.0 5.2 -0.2

Old age dependency ratio (in %)

1970 7.1 6.9 21.5 6.0 15.8

1980 8.5 7.3 23.4 6.4 17.1

1990 8.9 7.4 21.7 4.4 18.9

2000 10.2 8.5 24.2 7.1 18.7

2010 11.4 10.2 31.5 7.8 19.5

Source: World Development Indicators (2015).

Note: 1) The dependency ratio old is the share of people aged 65 years and above dived by the working age population age 15 to 64 years. 2) The years are an average of 5 years; e.g. 1970 = 1968-1972.

Another important country characteristic that might also influence the impact of ageing on growth is education. Education should boost people’s physical or cognitive skills, and in this way, make people more productive. This means, people are able to do more with the same inputs or to produce the same in less time (Szirmai, 2005). Furthermore, education can facilitate or help persons develop creativity, and as a result, bring the economy to a higher level with improved technology and innovations (Fasko, 2001). The effect of education on growth has been widely investigated and a positive relation was found (e.g. Mankiw, Römer, & Weil, 1992). Lee and Mason (2010) connected education to ageing and growth. They argued that ageing leads to a growing transfer of resources from the working-population to the elderly, but that society should realize that ageing entails also increased human capital accumulation.

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My first objective is to investigate the influence of education on the increasing share of elderly. More specifically, I will examine the moderating effect of the education of elderly on the relation between the share of elderly and per capita income. By doing this, I will build on research that has investigated the effect of the share of young, working-age, and elderly on growth (Bloom & Williamson, 1998; Bloom & Finlay, 2009; Bloom, Canning, & Malaney, 2000; Fang & Wang, 2005). All have, however, not taken productivity differences among elderly into account. Thus, it might be interesting to know if the influence of elderly on growth is different dependent on their education. No research has yet investigated this relation. This investigation might be relevant since it can improve our understanding of the dependency effect of elderly on society.

My second objective is related to the expected decrease of the working-age population in advanced countries. This is expected to have a large impact on labour shortages. Since business can probably rely less on growth in employment, economic growth could slow down. However, since employment growth and labour productivity by definition add up to economic growth4, economic growth could be maintained by higher labour productivity growth (Conference Board, 2014; McGuckin & van Ark, 2005). Many have investigated the effect of ageing on labour productivity (e.g. Burtless, 2013; Lallemand & Rycx, 2009; Lindh & Malmberg, 1999; Malmberg, Lindh, & Halvarsson, 2008; Prskawetz et al., 2006; Werding, 2008). However, none of the authors have taken the skill level of the workers into account. This might be important. Workers perform different tasks, and therefore, it could be that the productivity of say low and high skilled workers are influenced differently by age (Lee & Mason, 2010; Skirbekk, 2008). Consequently, an investigation on skill-levels might lead to some interesting results that could not become visible in studies on aggregate population shares.

With the results of both investigations, I aim to answer the research question: “Can education moderate the effect of ageing on labour productivity and economic growth?” I will try to answer this question using the sub questions, 1) “Can the education of elderly moderate the relation between the share of elderly and economic growth per capita?”, and 2) “How does

4_{McGuckin and van Ark (2005) argue that employment growth is more precisely defined as the growth rate of}

the total hours worked. Labour productivity would then refer to the growth of output per hour worked. Referring to per capita income growth this would mean, ∆𝑙𝑛 𝑌

𝑝𝑜𝑝= ∆𝑙𝑛 𝑌 ℎ𝑜𝑢𝑟𝑠+ ∆𝑙𝑛 ℎ𝑜𝑢𝑟𝑠 𝑒𝑚𝑝 + ∆𝑙𝑛 𝑒𝑚𝑝 𝑝𝑜𝑝 , where Y is output

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labour productivity change over a lifetime for high-, medium-, and low-skilled workers?” This thesis’ overall objective is to add more understanding to the debate on ageing and growth by focussing on the moderating role of education. This will be done from a macro perspective.

To answer the first sub question, I use a world sample of 71 countries5 with data from 1970 to 2010. For the second sub question, I use 15 developed countries with data from 1970 to 2005.6 I conduct fixed effects (FE) panel data analysis and I check the robustness of the results with the instrumental variable technique by Baum, Schaffer, and Stillman (2010).

In the remainder of the thesis, I will first examine literature to explain the base of my research and I will pose my two hypotheses. Then in section 3, the methodology and the econometric specification are explained and data sources are provided. In section 4, the results will be reported. In section 5, I will relate the obtained results to other studies on ageing and growth and in section 6, the limitations and prospects for future research will be discussed. Section 7 closes with the conclusion.

2 Literature review and hypotheses.

The following literature review will give the reader a better understanding of the context in which the research question, “can education moderate the effect of ageing on labour productivity and economic growth?”, was built and why it might add valuable input to research on ageing and growth. In section 2.1, I will go firstly over the early thinkers on population dynamics and explain how the debate has developed up to now. After understanding this history, I will explain the concept of the dynamic transition and make a first connection between ageing and economic growth. Then in section 2.2, I focus on the relation between the increasing share of elderly and economic growth and elaborate why the education of elderly might be moderating this relation. In section 2.3, I switch the focus to the decreasing working-age population in advanced countries. I discuss the consequences of working-ageing on the labour market and make a first connection with labour productivity. In section 2.4, I will discuss the relation between age and labour productivity and explain the role the skill level of the worker might have in this relation.

5_{In appendix 1 can be found which countries are used.}

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2.1 Population dynamics: From Malthus (1798) to Bloom and Williamson (1998).

Malthus (1798) is seen by many as one of the first who discussed the effect of population on economic growth. He and subsequent researchers who followed his line of argument, maintained the view that population growth has a negative effect on growth. The Malthusian view argued that with higher wages people start to consume much more. People were believed to marry earlier, having more children, and hence, keeping per capita income at a similar level. The well-known Solow (1978) growth model can be seen as modernisation of the Malthusian view. Population growth is considered as depressing since more people leads to capital dilution. Besides the Malthusian view, Smith (1776) developed another, less adopted, view on population growth. Smith and his followers believed technical change to be endogenous. In other words, population growth was believed to induce technological change since people had to be creative in feeding the larger population. Hence, population growth is regarded as a positive driver of growth (Malmberg & Lindh, 2002; Ray, 1998).7

Research has often found contradictory effects (Ray, 1998) or often no effect of population growth on economic growth at all (Malmberg & Lindh, 2002). However, in the 1990s an important insight has been brought into the debate on demographics and growth. Even though conventional theories of economic growth considered the size and the growth rate of the population, changes of the age structure on growth have been neglected (Williamson, 1998; Bloom et al., 2001). The age structure, which can be defined as the way in which the population is distributed across different age groups, has improved our understanding of the relation between population dynamics and growth (Malmberg & Lindh, 2002; Ray, 1998).

Bloom and Williamson (1998) explain the changing age structure as the demographic transition which they define as society’s change from high fertility and mortality rates to low rates for both over the course of development. In figure 2, the concept of the demographic transition can be seen and is described step by step. Typically, the mortality rate starts declining first, after which the fertility rate follows, lagging a certain period of time behind. Bloom and Williamson (1998) theorised that in the initial phases of the demographic transition, income per capita growth decreases as a result of an increased youth dependency. With a low mortality rate but still high fertility growth, the share of the working-age population declines relatively to the non-working-age population. This means that relatively more people are now dependent

7_{Malmberg and Lindh (2002) and Ray (1998) provided interesting summaries on the history of research in the}

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on the same total income which hampers economic growth. After about two decades, assuming the fertility rate has decreased meaningfully, the youth dependency burden falls. Consequently, this new large young population can become active in the labour market. From this point, the economy benefits from the demographic gift with a higher share of working-aged. Society can save and invest more, and as a result, income can grow faster. Some decades later, the baby boomers turn old. Hence, the share of elderly rises relatively to the share of active labourers. This means that the demographic gift phase will turn into a burden as the current population has to take care of the back then fast growing generation.8

Figure 2: The demographic transition and population growth.

Source: Bloom and Williamson (1998).

8_{Declining fertility and mortality rates can be explained by many reasons. Most importantly seem to be}

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Bloom and Williamson (1998) considered a world sample of 71 economies from 1965 to 1990 to test the theory of the demographic transition. Their aim was to explain an important part of the rapid growth in East-Asia. They theorised that rapid growth in East-Asia could for a large part be explained by their demographic gift phase. They divided the population in three shares, namely the young (aged 0 to 14 years), the working-age population (15 to 64 years), and the elderly (aged 65 and above). They found that from 1965 to 1990 about 2 percent of growth in East-Asia could be attributed to their large working-age population. Since East-Asia grew on average about 6 percent in that period, it shows the importance of the gift phase. In similar studies, Bloom et al. (2000) and Fang and Wang (2005) argued as well for the importance of the working-age population for growth. Malmberg and Lindh (2002)9_{and Lindh} and Malmberg (2008)10 took a slightly different approach. They divided the working-age population further into age groups to differentiate which working-aged contribute most. The age group 50 to 64 was found to be most productive with the age groups 0 to 14 and 65 and above contributing less to per capita growth.

Now, however, the focus of the demographic transition is changing. Where Bloom and Williamson (1998) and Bloom et al. (2000) examined the positive growth effects coming from an increasing working-age population, recently research has started to stress the increasing share of elderly (Bloom & Finlay, 2009). With a relatively smaller working-age population, this would mean that growth slows down according to theory. Nevertheless, even if ageing is irreversible, there may be reasons for optimism.

2.2 Behavioural changes: The role of education on ageing and growth.

A first reason for optimism is that not all research has found that a growing elderly population is hampering growth. For example, Bloom and Williamson (1998). They found that an increasing elderly population does not impede economic growth. An insignificant (positive) effect was found. The authors argued that this might be explained by positive effects coming from savings and part-time work which together would have offset the negative dependency effect. Furthermore, society is expected to adjust to ageing in order to preserve economic

9_{Malmberg and Lindh (2002) inspected the relation in the Western world using 14 OECD countries and used}

pre-war data from 1850 to 1950. The authors found a strong positive effect for the middle-aged group (50-64 years) on economic growth per capita; nevertheless, the negative effect of the share of elderly (65+) was imprecise and less robust.

10_{Lindh and Malmberg (2009) found a humped-shaped relationship between the age structure and economic}

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growth. Hence, these so-called behavioural changes might be another reasons why ageing might not decelerate economic growth.

Examples of such behavioural changes are increased female labour force participation (e.g. Klasen & Lamanna, 2009), more openness to international trade, and improvements of institutions (Bloom & Finlay, 2009; Bloom et al. 2010). Still, there might be another behavioural effect of great importance. Lee and Mason (2010) argue that even though ageing leads to a growing transfer of resources from the working population to the elderly, society will benefit from increased human capital accumulation. Since ageing means that fertility is low, the authors argue that with lower fertility the educational investments per child increase. Hence, the younger generation can enter the workforce with higher productivity, and in this way, add more to growth.

In addition, education might have more effects which are yet unobserved. Where Lee and Mason (2010) discussed that society would adjust to ageing by increasing human capital investments, I argue that the education of elderly can be another reason to expect less growth declines. Research on the demographic transition has only consulted population shares, and hence, not taken any heterogeneity among the elderly into account. By treating every individual as equal, results might be biased (Lee & Mason, 2010). It could be that certain old people are contributing more to growth than other elderly. Following that reasoning, I suspect that the education of elderly might explain such a difference within the group of elderly. Therefore, I ask the question, “Can the education of elderly moderate the relation between the share of elderly and economic growth per capita?”

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more dependent years), I expect that the positive effects will outweigh the negative. Hence, I state the following hypothesis:

H1: The education of elderly mitigates the negative effect of the share of elderly on economic growth per capita.

2.3 Labour shortages in the ageing advanced countries.

In the previous part, the focus has been on the influence the increasing share of elderly will have on economic growth per capita. In this next part, however, I want to switch the focus towards the expected decrease of the working-age population. The Conference Board (2014) showed that the growth rate of the working-age population is almost turning negative in most advanced economies11. The Netherlands, Germany, Poland, France, Greece, and Japan have already experienced declines in the working-age population in the period 2010 to 2013. By 2030 the baby-boom generation is assumed to be retired in all advanced nations (Conference Board, 2014).

This trend has raised concerns on potential labour shortages. Shortages were already expected some years ago, but this was postponed by the financial crisis of 2008 and its aftermath. Now, advanced countries are starting to experience a tight labour market12. As a result, businesses are expected to have more difficulties to recruit strong human capital labourers and to control wages. Shortages can in the first place be avoided by recruiting unemployed people. However, the rate of unemployment in advanced countries is getting close to the natural rate of unemployment13_{. This means that future shortages cannot simply be solved} with more labour. This is not necessarily the case for every occupation. Occupations in for example science, engineering, and mathematics are not expected to be troubled with labour shortages. Nevertheless, the general tendency indicates a future with labour shortages (Conference Board, 2014).

11_{The Conference Board (2014) investigated and defined the following countries as advanced economies: North}

America - USA, Canada; Asia-Pacific – Taiwan, Australia, Japan, South Korea, New Zealand; Europe – Austria, Belgium, Denmark, Finland, France, Germany, Greece, Iceland, Ireland, Italy, Luxembourg, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland, UK. Source: OECD and the Conference Board.

12_{A tight labour market is defined as the labour market conditions that make it difficult for employers to find}

qualified job candidates due to fact job vacancies are receiving a relatively small number of qualified applicants (Conference Board, 2014).

13_{The natural rate of unemployment is defined as the expected rate at which a country is producing at full}

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Labour shortages would mean that the role of employment growth in economic growth will get smaller. By definition employment (total hours worked) and labour productivity (output per hour worked) growth add up to economic growth. This means that to maintain economic growth, labour productivity is expected to become most important. Nevertheless, perspectives are not optimistic. This can be seen in figure 3. The labour productivity growth rates of Europe and Japan show a continuous downward trend (with a small exception in the 1980s for Japan). Furthermore, since 2000 the USA has also been experiencing lower labour productivity growth every year (Conference Board, 2014).

Figure 3: Labour productivity growth in the USA, Europe, and Japan from 1971 to 2013.

Source: The Conference Board (2014).

2.4 Labour productivity and an ageing labour market.

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productivity. Therefore, my aim is to find out how labour productivity develops over a lifetime. I will focus on labour productivity and not economic growth since the latter takes the non-working population also into account.

A well-known study of ageing and labour productivity was conducted by Lindh and Malmberg (1999). The authors used an augmented Solow model including human capital, inspired by Mankiw, Romer, and Weil (1992), in which their dependent variable was the growth rate of real GDP per worker. They subdivided the working population into young, middle, and old aged labourers. Using OECD data from 1950 to 1990, Lindh and Malmberg (1999) found that a larger share of middle-aged (50-64 years) population is linked to a higher per worker growth rate. McMillan and Baesel (1990) and Andersson (1998) found similar results. Summarizing a wide range of studies, Prskawetz et al. (2006)14 found in line with Lindh and Malmberg (1999) an inverted U-shaped relationship between age and productivity. The highest productivity is on average found somewhere between 35 and 65 years old.

On the other hand, Burtless (2013) argues that ageing has not had a decreasing effect on labour productivity. Based on hourly wages, extracted from the Current Population Survey in the USA, he showed that the age group 60 to 74 is most productive. Prskawetz et al. (2006), however, argue that wages do not indicate someone’s productivity. They argue that employees benefit from delayed payment. This means, higher wages create loyalty to the firm and is a compensation for high productivity in the younger years of the career.

Lindh and Malmberg (1999) and Prskawetz et al. (2006) allowed for a human capital effect coming from experience. This means that one cannot only argue that shifts in the age structure affect the physical capital stock through the savings rate, but furthermore, that age dynamics do also cause changes in human capital coming from the accumulation of experience (Brunow & Hirte, 2006; Lindh & Malmberg, 1999; Prskawetz et al., 2006). This argument, however, is based on the whole population without taking any heterogeneity of skills into account. As a result, some important differences within the age groups may not have been observed. Following that argument, I argue in this thesis that research may have ignored that the skill level of the worker might be a determinant of the accumulation of experience. If this reasoning is true, previous research on labour productivity and ageing may have been biased

14_{Prskawetz and Lindh wrote a book published in 2006 on the impact of population ageing on innovation and}

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by not stratifying age groups by skill level. Following this reasoning I want to find out if age has a different influence on productivity dependent on the skill set of the worker. The sub question that I try to answer is: “How does labour productivity change over a lifetime for high-, medium-high-, and low-skilled workers?”

Only Ilmakunnas and Miyakoshi (2013)15_{have investigated the influence of age on} labour productivity for different skill groups. The authors built their results on a Cobb-Douglas equation and they used the EU KLEMS16_{database including 13 OECD countries. They used} three age groups, 15 to 29 years, 30 to 49 years, and 50 years and above, and two skill groups, low-skilled and high-skilled17. They did not find convincing results for the influence of age on labour productivity in the low-skilled group. In the high-skilled group, however, ageing seems to have an effect on productivity but the shape of the effect is not totally clear. The results suggest that there is either a positive effect or an inversed U-shaped effect of age on labour productivity.

Since little research has been conducted on the combination of age and skill on labour productivity, it is somewhat difficult to provide the hypothesis with a strong academic base. The mechanism that affects this lower productivity is not yet clear. Productivity changes over a lifetime may come from, among many other reasons18, work experience, cognitive functioning, physical abilities, stamina, energy, and health (Skirbekk, 2008; Prskawetz et al., 2006). Skirbekk (2008) argued that productivity reductions at older ages are most severe in occupations where problem solving, learning, and speed matter more. For tasks where experience and verbal abilities are more important, there is little or even no decrease in productivity found.

In building the hypothesis, I will focus on three skill groups, namely low-, medium-, and high-skilled workers. By doing this I follow O’Mahony and Timmer (2009) who based the skill groups on educational attainment. For the high-skilled, I expect that experience is most important and will outweigh potential negative effects of ageing. Therefore, I expect that for high-skilled workers productivity increases during a life-time. For low- and medium-skilled, I

15_{Ilmakunnas and Miyakoshi (2013) focussed in their research on TFP, ageing, and skill levels; however, they}

also run regressions on labour productivity.

16_{For more information on the EU KLEMS, see www.euklems.net and O’Mahony and Timmer (2009).} 17_{Ilmakunnas and Miyakoshi (2013) built the high-skilled group from the medium- and high-skilled groups}

provided by the EU KLEMS since they believed the high-skilled group was too small.

18_{Skirbekk (2008) names as well that productivity changes over time due to family and care obligations,}

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expect an inversed U-shaped relation between age and labour productivity. The group of low- and medium-skilled workers are relatively larger than the high-skilled group, and therefore, I expect that the inversed U-shaped relation that was found by research (Lindh & Malmberg, 1999; Prskawetz et al., 2006) was driven by the low- and medium skilled. Hence, the following hypothesis is stated:

H2: Age has an inversed U-shaped relation with labour productivity in the group of low- and medium-skilled workers, and a positive relation in the group of high-skilled workers.

3 Methodology.

In this section 3.1, I will elaborate on the two models that are used to answer the two hypotheses. To be clear, for each hypothesis a different equations is set up. Then, in the sections 3.2 and 3.3 the dependent, independent, and control variables are discussed and I will elaborate on the choice of measurement. In section 3.4, I report which data I will use and in section 3.5 I will elaborate on the econometric specifications that are adopted to test the two models.

3.1 Model of estimation.

3.1.1 Equation 1 for the inspection of hypothesis 1.

The first hypothesis, the education of elderly mitigates the negative effect of the share of elderly on economic growth per capita, will be tested with the following model:

Equation 1: 𝑙𝑛∆ 𝐺𝐷𝑃𝑝𝑐𝑖𝑡 = 𝛽0𝑖 + 𝛽1 𝑙𝑛∆( 𝐸𝑚𝑝 𝑃𝑜𝑝)𝑖𝑡+ 𝛽2 𝑝𝑜𝑝(0 − 14)𝑖𝑡+ 𝛽3 𝑝𝑜𝑝(65 +)𝑖𝑡 + 𝛽4 𝑆𝑐ℎ𝑜𝑜𝑙𝑖𝑛𝑔(65 +)_𝑖𝑡+ 𝛽5 𝑝𝑜𝑝(65 +) ∗ 𝑆𝑐ℎ𝑜𝑜𝑙𝑖𝑛𝑔(65 +)_𝑖𝑡 + 𝛽6 𝑙𝑛 𝐻𝐶𝑖𝑡+ 𝛽7 𝐺𝐷𝑃𝑝𝑐𝑟𝑎𝑡𝑖𝑜𝑖𝑡 + 𝛽8 𝑂𝑝𝑒𝑛𝑒𝑠𝑠𝑖𝑡+ 𝛽9 𝑃𝑟𝑜𝑝. 𝑟𝑖𝑔ℎ𝑡𝑠𝑖𝑡 + 𝛽10 𝐼𝑛𝑣.𝑖𝑡+ 𝜀𝑖𝑡

where 𝑙𝑛∆𝐺𝐷𝑃_𝑝𝑐 is the growth rate of GDP per capita, 𝑙𝑛∆(𝐸𝑚𝑝

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country, 𝑂𝑝𝑒𝑛𝑒𝑠𝑠 is openness to trade measured as an index from 0 to 10, 𝑃𝑟𝑜𝑝. 𝑟𝑖𝑔ℎ𝑡𝑠 is property rights measured as an index from 0 to 10, and 𝐼𝑛𝑣. is investment as a percentage of GDP. The share of the population 15 to 64 years old is used as reference group since it would add up to 1 together with the population aged 0 to 14 years and the population aged 65 years and above.

The model is based on research conducted in the field of the demographic transition and growth (e.g. Bloom & Williamson, 1998). In line with this research, I expect that the share of elderly has on average a lower contribution to per capita income growth compared to the population aged 15 to 64 which is the reference group. To measure the mitigating effect of elderly education on the relation between the share of elderly and growth, I will include an interaction term. The interaction term that is built of the education of elderly and the share of elderly. The interaction term will have a negative coefficient if education of elderly mitigates the negative effect of the share of elderly on per capita growth. This means that if the share of elderly is low, the effect of the education of elderly is too small to be observed, but the further the share of elderly increases the more important elderly education becomes to mitigate the negative effect. There might be as well a main effect of elderly education though I do not expect this. The main effect of elderly education would already be captured by the variable human capital. Nevertheless, elderly education is of course included in the model to avoid estimation problems of the interaction variable.

By including the growth rate of the people engaged as share of the total population, I am able to make a distinction between employment growth and labour productivity growth. In addition, relevant control variables are included to be able to increase the explanatory power of the model and the chance of correct interpretation of the variables of interest.

3.1.2 Equation 2 for the inspection of hypothesis 2.

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where 𝑙𝑛∆ 𝐺𝐷𝑃 is the growth rate of GDP, 𝐻 − 𝑆(30 − 49) is the share of high-skilled workers in the specific age group, 𝐻 − 𝑆(30 − 49) is the share of medium-skilled workers in the specific age group, , 𝐻 − 𝑆(30 − 49) is the share of low-skilled workers in the specific age group, 𝑙𝑛∆ 𝐻𝑂𝑈𝑅𝑆 𝐻 − 𝑆 is the growth rate of the total hours worked by the high-skilled engaged workers, 𝑙𝑛∆ 𝐻𝑂𝑈𝑅𝑆 𝑀 − 𝑆 is the growth rate of the total hours worked by the medium-skilled engaged workers, and 𝑙𝑛∆ 𝐻𝑂𝑈𝑅𝑆 𝐿 − 𝑆 is the growth rate of the total hours worked by the low-skilled engaged workers. The share of workers aged 15 to 29 in the high-, medium-, and low-skilled groups is used as reference group to avoid that the shares add up to 1.

The model is based on the approach used by Ilmakunnas and Miyakoshi (2013). They used the level of gross value-added as outcome variable and indicator for growth. Besides that they used only low- and high-skilled (which consisted of medium- and high-skilled) age shares. The model that I use is slightly different. In my model, GDP growth is used as outcome variable.By including the growth rate of the hours worked by high-, medium- and low-skilled workers I can capture the effect of labour productivity growth. All that can be explained after the growth rate of total hours worked are taken into account can be attributed to labour productivity growth. By including the high-, medium, and low-skilled age groups I can see if their impact on labour productivity growth differs relatively to each other. This estimation method makes it necessary to assume that workers in the different age groups are comparable. Capital growth is added to control for productivity effects coming from capital alone. In addition, openness is added to control for productivity differences coming from international trade.

3.2 Dependent variables.

3.2.1 Model 1: The growth rate of GDP per capita.

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standard of living due to its high correlation with measures of welfare and happiness. Therefore, in line with their arguments, GDP per capita is used as proxy for the standard of living. Since GDP per capita is the most common welfare measure, problems of missing data are avoided. Growth rates are taken since ageing is a dynamic effect. If one would only look at the level of GDP per capita, the effects of ageing may not become visible. Constant GDP per capita in 2005 US dollar prices are used to make comparisons across countries and over time possible.

3.2.2 Model 2: The growth rate of GDP.

In model 2, I will use the growth rate of GDP as outcome variable. Note that GDP growth is not the outcome variable of main interest, this is labour productivity growth. However, by first letting GDP growth be explained by employment growth, all variation left can be attributed to labour productivity growth. Furthermore, by using GDP growth the thesis can inspect the relation of the labour shares on economic growth as well. In this way, more information can be obtained and results might be easier to interpret. Hence, constant GDP in 2005 US dollar prices is used as outcome variable

3.3 Independent and control variables.

In this subsection, I elaborate on the independent variables that are used in the regressions. Controls are used to capture all other effects on growth that are not seized by the independent variables of interest. Without these controls, the independent variables used may turn out to be significant or insignificant where actually their effect is different. The interpretation of the coefficients would then be untrustworthy (Hill, Griffiths, & Lim, 2012). For the ease of reading, all independent and control variables are reported in table 2, including their constructs and their expected relationship with economic growth or labour productivity.

3.3.1 Model 1: The share of elderly, elderly education, and growth. 3.3.1.1 Independent variables of interest.

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Table 2: Expected relationship of the independent variables with GDP per capita and labour productivity growth.

Construct to measure Independent variable Expected relation

with:

H1: GDPper capita growth

H2: Labour productivity growth Share of elderly Share of population over 64 years (% of whole pop) Negative

Education of elderly Average years of total schooling of people aged 65 years and above

Positive Share of educated elderly

(interaction term of share of elderly and education of elderly)

Interaction variable of the average years of total schooling of people 65 years and above and the share of population over 64 years (% of whole pop)

Mitigates negative effect (Negative regression coefficient) Share of young people Share of population aged 0 to 14 years old. Negative

Growth of the working population

Growth rate of persons engaged as share of the total population

Positive Human capital Combination of average years of schooling and rates

of return on education

Positive Convergence of growth Ratio GDP per capita constant 2005 prices in US

dollar (USA=1)

Negative Investment rate Gross capital formation (% of GDP) Positive Protection of doing business Index of property rights Positive

Openness to trade Index of trade regulations Positive Positive Age in the group of high-skilled

workers

Hours worked by high-skilled in the age groups (15 to 29, 30 to 49, and 50 and above) as share of all hours worked by the high-skilled

Positive Age in the group of

medium-skilled workers

Hours worked by medium-skilled in the age groups (15 to 29, 30 to 49, and 50 and above) as share of all hours worked by the medium-skilled

Inversed U-shaped relation

Age in the group of low-skilled workers

Hours worked by low-skilled in the age groups (15 to 29, 30 to 49, and 50 and above) as share of all hours worked by the low-skilled

Inversed U-shaped relation

Growth of physical capital The growth of the capital stock at constant 2005 national prices (US dollar)

Positive Growth of hours worked per

skill group

Growth of hours worked by high-, medium, and low-skilled

Positive

3.3.1.2 Control variables.

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Bloom & Williamson, 1998; Kögel, 2004) I expect a negative effect of the young population on economic growth.

Employment/population growth: I add the growth rate of the persons engaged (all active workers, also self-employed) as share of the total population to capture the effect of employment growth. Since I use GDP per capita growth as the dependent variable, I only need to divide the growth rate of the people engaged by the growth rate of the population. This is similar to the approach of Bloom and Williamson (1998) who used the growth rate of the working-age population to measure employment growth and the growth rate of the population to measure the growth of the dependent population. However, my measurement is better. Firstly, I use the number of people engaged instead of using the working-age population as proxy (also recommended by Bloom & Williamson, 1998). Secondly, multi-collinearity is reduced by accommodating the employment and population growth in one term. I expect that employment growth has a positive impact on economic growth.

GDP per capita ratio: To tackle convergence of growth and productivity among

countries, the real GDP per capita ratio relative to the USA is added. Obviously, the USA will have ratio 1. Mankiw et al. (1992) argue that countries are facing decreasing returns to scale. Consequently, countries having a relatively lower GDPper capita are able to grow faster. Hence, a negative coefficient is prospected.

Human Capital: In addition, human capital is added to detect the growth effects coming from the higher educated. In this thesis, human capital is measured as a combination of the average years of schooling (Barro & Lee, 2013) and the rate of return for completing different sets of years of education (Psacharopoulos & Patrinos, 2004), constructed in the Penn Tables 8.0. Similarly as with the years of schooling of people aged 65 and above, this measure is limited because it does not take any variation of the returns over time and across countries into account. Furthermore, as mentioned earlier, cognitive skills are not necessarily measured (Hanushek and Woessman, 2012). The natural logarithm is taken to reduce collinearity with the education of elderly. Human capital is expected to have a positive effect.

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legal system, legal enforcement of contracts, regulatory restrictions on the sale of real property, reliability of police, business costs of crime. The prediction is that property rights has a positive effect on growth.

Openness: To differentiate between countries’ engagement in international trade, an index (from 0 to 10) for openness to trade is added. Some research has proxied openness with exports and imports as a percentage of GDP. However, measuring openness in this way will lead to a downward bias in larger countries. Larger countries have less need to cross the border in search for intermediates or final products simply because it is produced within the nation. Hence, in this thesis openness is measured by averaging the following sub-indexes: Tariffs (measured by revenue from trade taxes (% of trade sector); mean tariff rate; standard deviation of tariff rates), Regulatory trade barriers (measured by non-tariff trade barriers; Compliance costs of importing and exporting), black market exchange rates, and controls of the movement of capital and people (measured by foreign ownership/investment restrictions; capital controls; freedom of foreigners to visit).

3.3.2 Model 2: Age, skill-level, and labour productivity. 3.3.2.1 Independent variables.

Shares of high-, medium-, and low-skilled workers: I will use shares to investigate the relation of age on labour productivity in different skill groups. This effect will be measured by using information on the hours worked per skill and age group. Shares are taken with the result that the age groups in the high-skilled, medium-skilled, and low-skilled group add up to 1. The age groups 15 to 29, 30 to 49, and 50 and above are taken. By omitting the group aged 15 to 29, the other age groups will be compared to this reference group. Taking three skill groups seems to be the most precise indication to find differences among occupations, especially for an investigation using world data. However, note that skill groups only can present a general picture and does not need to be relevant for every occupation. The high-, medium-, and low-skilled are defined differently for each country. The choice is for all dependent on the level of education, but since education differs among countries the definitions differ slightly (Timmer, O’Mahony, van Ark, 2008).

3.3.2.2 Control variables.

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capital productivity. Therefore, I add capital growth in constant 2005 prices (US dollar). I expect a positive effect. Openness is as well added. For an explanation see the previous model.

3.4 Data collection.

In this thesis, I use for both investigations two different models. For the investigation of hypothesis 1 a database is constructed consisting of several other databases. Data is obtained from the World Bank’s World Development Indicators (2015), the Penn World Tables 8.0, the Barro and Lee (2013) dataset on educational attainment, and the Economic Freedom Database (2014). In table 3, one can see from which database exactly the variables are taken. All databases report data for a world sample. Barro and Lee (2013) and the Economic Freedom Database (2014) only provide data on 5-year intervals. Furthermore, the Economic Freedom Database (2014) only provides estimates from 1970 onwards. Hence, the period 1970 up to 2010 is investigated taking 5-year intervals. Optimally, this would mean 9 within estimations per country; nevertheless, the databases do not all report data for the same countries, and in addition, data is been missing for some countries. This problem of missing data is partly reduced by averaging yearly data in 5-year intervals. This thesis constructs averages by using the years around the 5-year intervals, e.g. the average of 1978 to 1982 is reported as the value for 1980. Nevertheless, this does not fully solve the problem, and therefore, only countries with a minimum of 6 observations are included in the merged dataset. After the exclusion of oil nations, which are expected to distort the regressions for their large fluctuating growth rates, this thesis ends up with 71 countries with 575 observations. In appendix 1 table 13 the countries used are reported.

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Table 3: Constructs, variables, and sources for model 1.

Construct to measure Variables Sources

Standard of living GDP per capita growth, constant 2005 prices (in US dollar) Penn World Tables 8.0

Education of elderly Average years of total schooling of people 65 and above Barro & Lee (2013)

Share of elderly Share of the population aged 65 and above (% of total pop) World Development Indicators (2015) Share of young people Share of the population aged 0 to 14 years (% of total pop) World Development Indicators (2015) Human capital Combination of average years of schooling and rates of return on education Penn World Tables 8.0

Growth of the working population Growth rate of persons engaged as share of the total population Penn World Tables 8.0

Convergence of growth Ratio GDP per capita constant 2005 prices in US dollar (USA=1) World Development Indicators (2015) Openness to trade Index of trade regulations Economic Freedom Data (2014) Protection of business Index of property rights Economic Freedom Data (2014) Investment rate Gross capital formation (% of GDP) World Development Indicators (2015)

Table 4: Constructs, variables, and sources for model 2.

Construct to measure Variables Sources

Economic growth GDP growth in constant 2005 prices (in US dollar) Penn World Tables 8.0

Age in the group of high-skilled workers Hours worked by high-skilled workers in the age groups 15 to 29, 30 to 49, and 50 and above as share of all hours worked by high-skilled workers (in %)

EU KLEMS (2008) Age in the group of medium-skilled workers Hours worked by medium-skilled workers in the age groups 15 to 29, 30 to 49,

and 50 and above as share of all hours worked by medium-skilled workers (in %)

EU KLEMS (2008) Age in the group of low-skilled workers Hours worked by low-skilled workers in the age groups 15 to 29, 30 to 49, and 50

and above as share of all hours worked by low-skilled workers (in %)

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have data on the same time-period.19 The EU KLEMS provides data per industry but I use the data that is provided for all industries combined. Furthermore, from this database I use the hours worked by age/skill groups as a percentage of the total hours worked. These shares are reshaped to end up with the hours worked of an age group as a percentage of the total hours worked of that skill group. By doing this I follow Ilmakunnas and Miyakoshi (2013). To illustrate: In Australia 1982 the medium-skilled aged 15 to 29 are responsible for 12.41 percent of total hours worked, the skilled aged 30 to 49 for 17.77 percent, and the medium-skilled aged 50 and above for 8.14 percent. This means that the medium-medium-skilled aged 15 to 29 are responsible for 32 percent of total hours worked in the group of medium-skilled, the group aged 30 to 49 for 46 percent, and the older group for 21 percent.

3.5 Econometric specification.

There are several ways to investigate the validity of the hypotheses in the constructed panel dataset. In this thesis, panel data analysis will be used to test both hypotheses. Panel data is expected to be the most appropriate form of analysis. Firstly, in this way the dynamic effects of ageing can be best taken into account. Secondly, I am interested in cross-sectional differences as comparison could provide valuable information.

3.5.1 Pooled ordinary least squares and fixed effects estimation.

As base of the econometric specification, the panel dataset will be evaluated using pooled ordinary least square (POLS) first. In pooled ordinary least square, all observations on different countries are simply pooled together without considering differences among countries which may induce different coefficients (Hill et al., 2012).

Models that take country differences into account, and may therefore be more appropriate, are either the fixed effects (FE) or random effects (RE) estimator. The FE estimator, also called the within-estimator, has the advantage of controlling for time-invariant omitted variables. In other words, assuming there do not exist any omitted variables that change over time, then any changes in the dependent variable over time cannot be caused by omitted variables. Country heterogeneity is captured by the intercept. The disadvantage of the FE model

19_{The following countries and years are taken from the EU KLEMS database: Australia: 1983 to 2005, Austria:}

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is that it is inefficient when variables have only little variance over time. Furthermore, time-invariant variables, for example region dummies, cannot be added to this model. A solution would be to use the RE model which provides more information, and is therefore, more efficient. It allows for constant correlation over time and time-invariant variables can be included. In the RE model, country heterogeneity is captured by the slope and the intercept. However, the RE estimator is more likely to suffer from endogeneity (endogeneity is further discussed in section 3.5.3) due to an extra time-invariant error term. Hence, RE may be more efficient but also less consistent (Hill et al., 2012).

To test if the FE assumption of heterogeneity in the intercept is correct, the FE model is compared to POLS using an F-test. In addition, with the Hausman (1978)20_{test the estimation} of the RE model is compared to the FE model. After conducting both tests, it seems that the FE model is the most suitable estimator in every regression. Both test statistics are reported in table 7 which can be found in the results section.

3.5.2 Assumptions of the fixed effects estimator.

To secure consistency of the FE estimator, the datasets are investigated on possible violations of the FE assumptions, namely the normality of the error, multi-collinearity, heteroscedasticity, and autocorrelation. Formal tests and visual investigations show that the error might not be perfectly normally distributed in both GDP and GDP per capita growth. Nevertheless, Lumley, Diehr, Emerson, and Chen (2002) argue that in large datasets, also used in this thesis, normality of the error is less of a problem. Hence, no real harm is done to the unbiasedness and reliability of the coming regressions.

Secondly, there do not seem to be large problems of multi-collinearity for the variables of interest. Nevertheless, some small notes. Elderly education has a variation inflation factor (VIF) exceeding the rule of thumb of 4, but its VIF of 5 seems acceptable. Furthermore, in model 2 the high-, medium-, and low-skilled shares have among each other fairly high correlations. This could be a problem, but since the VIFs are below 4 for all, I do not foresee large problems. In addition, omitting one skill-group would not be an improvement since the effect of the omitted group could then be captured by one of the other two skill groups. Note

20_{The Hausman test’s (1978) null hypothesis states that there are no systematic differences between the}

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that since reference categories (age shares) and an interaction term is used, correlations and VIFs are inflated. Nevertheless, Allison (2012) argues that in these cases multi-collinearity is not a problem. See appendix 2 table 15 and 16 for respectively the correlation matrices and the VIFs.

Lastly, in both models heteroscedasticity and autocorrelation are found, and therefore, the thesis follows Hoechle (2007) who argues that with autocorrelation and heteroscedasticity it is best to analyse with clustered standard errors by country. A sophisticated analysis with figures and tests of all FE assumptions can be found in appendix 2.

3.5.3 Endogeneity and instrumental variable approach. 3.5.3.1 Endogeneity.

Growth regressions often suffer from the problem of identification. In other words, the variables that are measured and investigated in the econometric analysis do not report trustworthy coefficients. The reason is endogeneity. To put it more formally, endogeneity may distort the regressions by violating the assumption of no interaction between the error term and the independent variables. Endogeneity can come from three sources, namely reverse causality, an omitted variable, and a measurement error (Hill et al., 2012; Wooldridge, 2002).

The first form of endogeneity is reverse causality, also called simultaneity, in which not only the independent variable influences the dependent variable, but also the other way around. Reverse causality distorts the value of the coefficient. Reverse causality can be solved with the use of an instrument. An instrumental variable is a variable that is strongly correlated with the independent but not at all with the dependent variable (Hill et al., 2012).

Besides reverse causality, a second form of endogeneity may come from an omitted variable. An omitted variable is correlated with the independent, but also with the dependent variable. In that case, not the independent variable in the model but the omitted variable is actually causing the outcome variable to change. Finding this form of endogeneity is difficult but first-differencing the data, as done with the FE model, at least tackles the problem of omitted time-invariant variables (Hill et al., 2012).

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term. Since the independent variable is in that case correlated with the error, there exists endogeneity. As a result, the measurement noise will have a downward bias on the coefficient of the proxy (Wooldridge, 2002).

In growth regressions, endogeneity can be caused in numerous ways and it is difficult to rule out endogeneity entirely (Griliches and Mairesse, 1998; Bond, Hoeffler, and Temple, 2001). Being aware of the difficulty to solve the problem of identification, I stress that I do not expect to solve endogeneity completely, but I hope I can make a first step in reducing the problem by using the instrumental variable technique.

3.5.3.2 Instrumental variable approach.

The approach that will be used in this thesis is the two stages least square instrumental variable approach (Baum et al., 2010). In economic growth regression, actually all variables may be endogenous. Using the test for endogeneity21 (Baum et al., 2010), however, shows that only GDP per capita ratio and investment are expected to cause real problems in model 1. The results of the endogeneity test are given in the regression tables in section 4. By treating the endogeneity of GDP per capita ratio and investment, the econometric model might behave differently. This could result in a change in the variables of interest as well.

Of course, identifying the problem is only the first step. The most difficult step probably is to find a proper instrument that is strongly correlated with one of these endogenous variables, but does not cause the dependent to change. No perfect instrument seems to be available for any of the two endogenous variables. Therefore, the variables will be instrumented by their lag. In this way, I try to solve or at least strongly reduce simultaneity. I expect that for example the economic growth rate of 2010 (an average of 2008 to 2012) will not be influenced strongly by the GDP per capita ratio and investment of 2005 (built from the observations from 2003 to 2007).

In model 2, the endogeneity test (Baum et al., 2010) shows that the growth rate of capital is expected to be endogenous22_{. Since yearly data is used more caution is advised.} Capital growth might be influenced by its first and second lag, and in this way, the lags would

21_{The test for endogeneity, endog, tests the null hypothesis which states that the independent variable(s) is}

exogenous. The test corrects for heteroscedasticity and autocorrelation (Baum, Schaffer, & Stillman, 2010).

22_{Endogeneity of the hours worked of the low-skilled might also be a problem; however, no proper instrument}

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still have an effect on growth. Hence, the endogeneity problem would not be reduced. Therefore, I will instrument capital growth with its third lag.23

To test the validity of the instruments, three test are conducted. In the first test, I check if the instrument is underidentifying 24 the econometric model. In the case of underidentification, the instruments have no power at all and one should consider using different instruments. The second test investigates if the instruments are strong enough.25 Stock and Yogo (2005) argue that in the case of weak instruments estimators can perform poorly. The third test, the Sargan-Hansen test26_{, checks if the instruments are not overidentifying the} model. In the case of overidentification, it is just the numerous amount and not the actual explanatory power of the instruments that leads to the rejection of underidentification and weak identification. The Sargan-Hansen test reports obviously a value of zero since only on instrument per variable is used. All tests are passed by all instruments and indicate that the instruments are strong (Baum et al., 2010). In the IV regression tables 10 and 11, the IV statistics are shown.

3.5.4 Influential observations.

In addition, I check for influential observations using Cook’s distance (Cook, 1977). There are multiple reasons why an observation could be deemed as influential or outlier. A measurement error would be of course a reason to drop the observation; however, the observation might also contain real and valuable information. Influential points might change the estimations considerably which could change the conclusion (Wooldridge, 2002). The outliers are those observations for which Cook’s distance exceed the commonly used threshold of 4 divided by the number of observation. In model 1 and 2, respectively 6.1 and 6.6 percent of the observations are deemed influential (based on the regressions including all variables). To check for their possible influence, estimation are also run excluding the outliers. The results are

23_{The third lag is expected to be a better instrument for the capital growth since the test Kleibergen-Paap F-test}

showed very large value for the second and first lag. An F-value of 190 for the second lag and 850 for the first lag was found and might indicate that the first and second lag do not solve or even reduce the problem of endogeneity.

24_{The test of underidentification checks the null hypothesis that the instruments are strong enough. In case of}

rejection of the null hypothesis, the instruments seem to be relevant. Because of heteroscedasticity and autocorrelation in the model, the Kleibergen-Paap rk Lagrange Multiplier statistic is reported.

25_{In case of identically and independent distributed (i.i.d.) errors, the Cragg-Donald Wald F statistic needs to be}

consulted. As in thesis, the assumption of i.i.d. errors is dropped, the Kleibergen-Paap rk Wald F statistic is used to test for weak identification. The Stock-Yogo critical values are used as benchmark.

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reported in the robustness check in section 4.3. A leverage plot can be found in appendix 2 figure 7 and 8.

4 Results.

4.1 Descriptive statistics.

In table 5, the descriptive statistics can be found for model 1. Only the most relevant variables are discussed. GDP per capita growth has a mean of 2 percent and a standard deviation of 3. The maximum value of 13 percent growth is reported by Gabon in 1975, and the lowest of -8 percent by Iran in 1980. The share of the population aged 65 and above has a share of 7.7 percent with a standard deviation of 4.8. Japan reports the largest share of elderly; 23 percent in 2010. Uganda has the smallest share of elderly; 2.4 percent in 2010. The population aged 0 to 14 has a relatively large mean value with 33 percent (of the total population) and its standard deviation is 10. Kenia reported the highest share of young people in the population; 50 percent in 1980. Hong Kong has the smallest share of young people with only 12 percent in 2010. The working-age population grows on average with 1 percent with a standard deviation of 1. Uruguay had the fastest growing working population in 2005 with almost 7 percent. In Ireland, the working population is shrinking; a 5 percent decrease in 2010. Lastly, elderly are on average 4.5 years educated. There is a standard deviation of 2.9. In Switzerland the elderly are best educated. In 2010 its elderly had on average more than 13 years of total schooling. In Mali, however, the elderly are poorly educated with less than 1 year of schooling on average in 1980 which is still in 2010 the case.

Table 5: Descriptive statistics of model 1.

Master Thesis in the Framework of the Double Degree Programme: M.A. International Economics (The University of Göttingen) M.Sc. International Economics and Business (The University of Groningen)