Human capital & economic growth : reviewing the augmented Solow-Swan Growth Model

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Human Capital & Economic Growth:

Reviewing the augmented Solow-Swan

Growth Model

Name: Kevin Teeling

Date: 29.06.2016

Thesis Supervisor: Oana Furtuna

Student number: 10418539

University: Universiteit van Amsterdam

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Statement of Originality

This document is written by student Kevin Teeling, who declares to take full responsibility for the contents of this document.

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

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

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Abstract

This paper investigates the inclusion of human capital as a variable in the augmented Solow Growth Model. It is based upon Mankiw, Romer and Weil (1992) and uses a similar approach with newer, improved quality data and variables. The empirical analysis involves a cross-section regression of the data for three different samples. The results found generally support the results found by MRW and the continued inclusion of human capital in the (augmented) Solow Growth Model.

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List of Abbreviations

There are several abbreviations used in this paper. In addition to being introduced where they first appear in the text of this paper, these are also listed here for ease of reference:

- Augmented SGM: refers to the human-capital augmented Solow Growth Model - GDP: Gross Domestic Product

- MRW: refers to the Mankiw, Romer and Weil’s 1992 paper A Contribution to the Empirics of Economic Growth, published in The Quarterly Journal of Economics (see References for full reference)

- OECD:Organisation for Economic Cooperation and Development - PWT: Penn World Table

- RQ: Research Question

- SGM: refers to the Solow Growth Model - WB: World Bank

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Introduction

Economic growth is one of the fundamental elements that governments seek to achieve, on the basis that it will lead to economic development. In particular, the study and modeling of growth is important in macroeconomics, more specifically in the field of development economics. One of the main models used to describe and study economic growth is the Solow Growth Model (SGM). A key addition to the original SGM that was developed in 1956 came in 1992, when Mankiw, Romer and Weil (henceforth referred to as MRW) introduced human capital into the model and tested this empirically. Human capital itself has long been considered as a factor affecting economic growth, and its role may have changed with recent developments in the global economy such as the Internet and the growth of the service economy. Reflected in the increasing value placed on education, human capital is playing an increasing role in economic growth. Given that the data used by both MRW 1992 and Islam 1995 was for the years 1960-1985, and the increased availability of more and better quality data, combined with the potential changes in the role of human capital, it is important to investigate whether this can help in not only confirming or casting doubt on the continued validity of the augmented SGM. As such, this research paper carries out an empirical investigation on the inclusion of human capital in the SGM, based mainly on the methodologies of MRW and Islam (1995). Although both those papers discuss the issue of convergence by comparing the SGM to alternative growth models, this is not investigated here. This paper focuses solely on the inclusion of human capital.

There are two key aspects to this paper: Firstly this paper deals with issues concerning the modeling of economic growth- focusing on the Solow Growth Model. Secondly, issues concerning human capital- in particular its measurement and its effect economic growth.

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Keeping this in mind, the purpose of this research paper is to investigate and answer the following research question (RQ):

RQ: To what extent do the findings of Mankiw, Romer and Weil in their 1992 paper with regard to the inclusion of human capital continue to hold?

The methodological approach taken to answering this research question is based on that of MRW, using a single cross-section regression of the panel data. This involves taking an average of the data over time (1960-2014) for all variables with the exception of two- for these only the data from the final year (2014) was used due to this better fitting the theory underpinning the model. The data used is over a longer time period and is of improved quality than that used by previous studies of human capital in the SGM.

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Theory and Literature

Overview

This section introduces the relevant theory and literature for this research. There are four parts to this section: Firstly, the two key research papers, including the MRW paper, treating similar topics are discussed, with a general overview of each paper’s approach and results being provided. Secondly, the continued relevance of the SGM is addressed by examining its assumptions as well as alternative growth models. Thirdly, theory specific to human capital is discussed, including the motivation for including human capital in the SGM and issues relating to the measurement of human capital. Finally, motivation for carrying out this further research is provided, and it is explained why existing literature does not already adequately address the research question of this paper.

Key Papers

There are two main research papers that investigate the role of human capital in economic growth within the context of its inclusion in the Solow Growth Model (SGM). The first of these is the 1992 MRW paper upon which this research paper is itself based. MRW test two aspects of the SGM in their paper: In the first part of their paper, the one most relevant for this research, they address whether the addition of human capital can improve the fit of the SGM to cross-country data. Secondly, they investigate how the SGM compares to endogenous growth models via its usefulness in investigating convergence (MRW, 1992, p. 407). Convergence is the ability of less economically developed countries to grow faster than more economically developed countries and reach the same level of GDP as the more developed countries.

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The first part of the MRW paper investigates the inclusion of human capital in the Solow Growth Model, as a complement to the physical capital already included in the first version of the model (1992, p. 408). The MRW paper investigates this due to perceived weaknesses in the SGM that exaggerate the effects of population growth and savings when fitted to the data (MRW, 1992, p. 408). The methodology followed by MRW in their paper is to carry out a regression using three country samples (1992, p. 408). The first of these three samples consists of all countries for which data is available, except those for which oil production consists of a significant part of their GDP (MRW, 1992, p. 413). The second sample excludes from the first sample those countries with poor data and those with a population less than one million people (MRW, 1992, p. 413). The final sample excludes all non-OECD countries from the second sample (MRW, 1992, p. 413). The data comes included in these samples is dated from 1960 to 1985 and is annual (MRW, 1992, p. 412). They model the data using a version of the SGM that includes human capital and compare it to the modeled data where human capital is not included (MRW, 1992, pp. 413-416). MRW find that including human capital does indeed improve the model (MRW, 1992, p. 408). They also find that including human capital reduces what was a high estimate of alpha, the share of physical capital in income, (0.59 as opposed to theoretically predicted 0.33), providing further evidence for including human capital (MRW, 1992, p.415). In the second part of their paper, MRW find that the critique of the SGM with regards to its use in modeling convergence is unfounded (MRW, 1992, p. 407).

The second paper is a further study based on the MRW one that is carried out by Islam (1995). Islam mainly focuses on convergence (1995, p. 1127). As such the results Islam finds are not directly relevant to our research question, as their research question differs. However the methodology, in particular the econometric approach, as well as the fact that Islam’s paper aims to address some of the concerns associated with MRW’s approach, makes

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it a relevant paper for the literature review. The paper investigates convergence by emulating MRW’s 1992 research but uses a panel data approach instead of the single cross-country regressions used by MRW (Islam, 1995, p. 1127-1128). The basis for using panel data in Islam is that country-specific differences, which result in different aggregate production functions, can be better accounted for by using a panel data approach, in this way addressing omitted variable bias occurring with the MRW approach (1995, pp. 1127-1135). These country-specific differences include the effects specific to each individual country, such as differences in institutions and technologies, as a result of the characteristics of each country, that cannot easily be measured and are as a result not directly observed, and therefore not included in single cross-country regressions (Islam, 1995, p. 1128). As a result of these country specific effects being correlated with the explanatory variables in an aggregate production function, there is an omitted variable bias when using single cross-country data (Islam, 1995, p. 1128). Islam finds that accounting for these effects leads to significantly different results (1995, p. 1127). For example, changes in capital are found to have a lower impact on the level of output when using panel data (Islam, 1995, p. 1128). Islam argues that these lower values are more realistic (1995, p. 1128). Using a variety of estimators, the approach used by Islam is to use a dynamic panel data model (1995, p. 1127). Islam explains that an alternative way to account for some of the country specific factors would be to group countries with similar characteristics together for the analysis (1995, p. 1149).

As part of the empirical analysis, Islam first carries out the same analysis by using single cross-country regressions as MRW do, in order to compare the effect on results due to sample and variable differences (1995, p. 1140). The results found are comparable to those of MRW (1995, p. 1140). Islam also does this using a pooled OLS estimation of the five-year intervals that are used in the panel data approach, achieving again very similar results (1995, p. 1141-1142). Islam interprets this as meaning that using shorter time intervals does not alter

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the results found (1995, p. 1142). Islam then introduces a dynamic panel data approach, and in implementing this the data is divided into several time periods (1995, p. 1137). Islam takes one year time periods to be too short, as irregularities may result having an exaggerated effect (1995, p. 1139). Instead, five year time periods are used to calculate the average population growth and savings rates (Islam, 1995, p. 1139-1140). As Islam explains, there are several ways to estimate panel data that has ‘individual effects’ (1995, p. 1137). Islam argues that using a fixed effects approach in estimation is the most relevant approach in this case, because estimators under the random effects approach rely on the assumption that the unobserved ‘individual’ effects are uncorrelated with the model’s included exogenous variables, and that the omitted variable bias that Islam seeks to correct in using a panel data approach would be the result of such a correlation between the unobserved effects and the included exogenous variables (1995, p. 1138). Islam carries out the empirical analysis using two different estimators, the Least Squares Dummy Variable (LSDV) estimator and the Minimum Distance (MD) estimator (1995, p. 1138). Overall, Islam finds results to those found by MRW, although human capital is less significant than in the MRW paper, particularly when using the dynamic model that is introduced, and is not significant for all samples (1995, pp. 1151-1152).

Relevance of the SGM

Assumptions of the SGM

The SGM as used by MRW relies on several assumptions. Firstly, the SGM assumes that countries are in their steady states in the final year of the analysis (MRW, 1992, p. 422). Secondly, the rate of population growth, technological growth rate and savings rate are taken to be exogenous (MRW, 1992, p. 409). Moreover, investment consists of a constant fraction

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of GDP, and growth rates of technology and depreciation rates are taken as constant across countries (MRW, 1992, p. 410). The latter two can be taken as reasonable assumptions because for the growth rate of technology new knowledge spreads across borders, and for the depreciation rates, because there is no available method of estimating depreciation rates specific to each country, nor is there any indication that depreciation rates in different countries would be significantly different were measurement possible (MRW, 1992, p. 410). Nevertheless, the level of technology does differ across countries due to for instance institutional and geographical differences (MRW, 1992, p. 411). This can then be represented by constant and a variable representing country-specific shocks (MRW, 1992, p. 411). It is also assumed that the population growth and savings rates are not dependent on this variable (MRW, 1992, p. 411). Although this could lead to omitted variable bias, this is a common assumption to make with most growth models and it is also made to allow the judgment of how much endogenous growth models can account for things that the SGM may not be able to account for, and finally it allows for checking whether using OLS introduces biases (MRW, 1992, pp. 411-412). This assumption then allows equation 2 to be estimated using Ordinary Least Squares (OLS) (MRW, 1992, p. 412).

Alternatives to the SGM

There is a lot of controversy linked to the best way of modeling human capital in economic growth (Hanushek et al., 2000, p.1187). In addition to exogenous growth models such as the SGM, there are also alternatives ways of modeling. For example, endogenous growth models are a popular approach to investigations of economic growth (MRW, 1992, p. 421). There is competition between exogenous growth models such as the SGM and endogenous ones (Islam, 1995, p. 1127). A key feature of endogenous growth models is that the returns to the factors of production that can be replicated are taken to be constant or

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increasing (MRW, 1992, p. 421). Assuming this implies that a higher level of savings rates will always lead to a higher growth rate (MRW, 1992, p. 421). Unlike endogenous growth models, the SGM predicts ‘steady state levels of income’ (MRW, 1992, p. 423). MRW argue that when examining the models with regard to the rate of return on capital, the SGM is preferable to the endogenous models because these assume that returns to scale are constant for the factors of production that can be reproduced and therefore don’t allow for differences in return on capital between countries based on their income levels, despite empirical evidence suggesting that the lower the income level of a country, the higher the return on capital there (1992, p. 432). MRW indicate that the SGM might be construed as weaker since it does not account for the movement of international capital or for differences in the rates of return between countries (1992, p. 430). However, they do not see these providing cause to discard the use of the SGM, because amongst other reasons the link between real interest rates and the capital’s marginal product relies on the situation of perfect capital markets where investors ‘optimise’ (1992, p. 430). MRW provide plausible examples of situations where this may not be the case (1992, p. 431). Overall, MRW find in their research that the SGM is relevant (1992, p. 414).

Human Capital

Effect of human capital on economic growth

Becker (1962) identifies human capital as one of the factors that can lead to increases in future real income (p. 9). As such, he identifies human capital investment as the increasing of resources within people (Becker, 1962, p. 9). He associates the increase of human capital with additional knowledge, education (either via schools or training provided by jobs) and health (Becker, 1962, p. 9).

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The motivation for including human capital in the SGM contains two elements: the establishment of a causal link between human capital and economic growth, and the motivation for the SGM in particular being possibly improved via the inclusion of human capital in it.

Most findings from international cross-country studies of economic growth show that human capital is significant (Hanushek et al., 2000, p. 1184). MRW state that human capital has for a long time been regarded as important for economic growth (1992, p. 415). Hanushek et al. find that differences in the quality of the labour force do affect economic growth (2000, p. 1204). According to Hanushek et al. human capital can lead to the faster adoption of ideas and more invention, resulting in, for instance, improved research and development, and thus leading to higher economic growth (2000, p. 1184). Hanushek et al. explain that human capital can lead to economic growth because higher levels of human capital in the workforce lead to higher labour productivity, resulting in movement toward a higher equilibrium growth level (2008, p.627). They explain that education can lead to increased human capital (Hanushek et al., 2008, p. 627). Hanushek et al. also explain that increased human capital can also aid in adaption of new technologies as well as increased innovation, thus leading to higher levels of economic growth (Hanushek et al., 2008, pp. 627-628). Hanushek et al. indicate that a large number of research papers investigating the effect of schooling on economic growth using cross-country regressions have found schooling to be significant (2008, p. 629). In their research, Hanushek et al. use newer data to regress schooling against economic growth, and find it to be significant, although this does not hold when they add further variables into their model (2008, p. 631). According to Barro (2001), some theories suggest that the growth rate of the economy is linked specifically to the human to physical capital ratio (p.12). Barro finds that, holding constant real GDP per capita, higher levels of human capital are associated with a higher human to physical capital ratio, and that

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this ratio results in increased economic growth (2001, p. 14). Barro explains that a higher level or stock of human capital allows advanced technology to be adopted more easily (2001, p. 14). Barro also finds that increasing the level of human capital (relative to the level of physical capital) is more difficult for countries than changing the level of physical capital is (2001, p.14). This means that, for example, countries with high human to physical capital ratios can grow their economies quickly by increasing the level of physical capital (Barro, 2001, p. 14). MRW explain that the returns on physical capital are greater the higher the level of human capital, because higher capital accumulation can result from a higher income level (caused by higher rates of saving) without the share of income attributed to human capital changing (1992, p. 417)

The main motivation for including human capital in the SGM in particular is that the effects of population growth and savings are exaggerated in the standard SGM when data is used (MRW, 1992, p. 408). This is due to human capital being an omitted variable in the standard SGM (MRW, 1992, p. 416). This is firstly as a result of human capital accumulation being correlated to the population growth and saving rates, leading to biases in these variables’ estimated coefficients (MRW, 1992, p. 408). Moreover, at every human capital accumulation rate, both a decrease in population growth and an increase in savings will lead to higher income levels, which also means more human capital (MRW, 1992, p. 408). MRW find that including human capital does indeed improve the model (MRW, 1992, p. 408). Omitting human capital from the SGM leads to biases in the variables for population growth and savings (MRW, p. 418).

Measuring human capital

Islam (1995) explains that there are difficulties associated with measuring human capital empirically (p. 1150). Moreover, they find that good data is no longer available that

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would enable the use of MRW’s proxy for human capital, and instead use the measure provided by Barro and Lee in their 1993 paper (Islam, 1995, p. 1150). Most studies use quantity of schooling as a measure of human capital (Hanushek et al., 2000, p. 1184). According to Hanushek et al., human capital is in most instances measured using a proxy of either primary or secondary schooling enrollment rates (2000, p. 1184). These are not good measures for human capital accumulation when countries undergo changes in demography or their educational systems (Hanushek et al., 2000, p.1184). Nor are they good measures of the human capital levels in the labour force (Hanushek et al., 2000, p. 1184). Hanushek et al. also indicate the potential of omitted variable bias caused by country-specific factors affecting both schooling results and economic growth (2000, p.1185). Hanushek et al. also argue that the quality of education should be accounted for (2000, p. 1184). Additionally, Hanushek et al. note that most growth models require increasing levels of human capital for continued increases in economic growth (2000, p. 1185). However, the quantity of schooling is unlikely to increase indefinitely (Hanushek et al., 2000, p. 1185). Hanushek et al. identify that increased levels of economic growth may result in higher investment in schooling, leading to better results in measures of schooling quality and thus introducing reverse causality/endogeneity into growth models that include human capital (2000, p. 1185). However, the quantity of schooling may also not be an adequate measure of human capital (Hanushek et al., 2000, p. 1184). Hanushek et al. find that mathematics and science skills represent a significant part of human capital when examining the labour force (2000, p. 1184). Hanushek et al. find that the quality of the labour force is as important as quantity of education (2000, p. 1184). Hanushek et al. find that cognitive skills are much more important than schooling in leading to economic growth (although cognitive skills are linked to schooling quantity and quality) (2008, p. 608). Hanushek et al. explain that it is well known that cognitive skills, thus human capital, are not only developed via schooling, but can

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originate from other places such as family or other people, and that culture can have an effect (2008, p. 609). Furthermore, the development of cognitive skills is also influenced by country specific factors such as the level of security and for example a functioning system of property rights and rule of law (2008, p.609). Human capital could also be considered to include non-cognitive skills such as interpersonal skills (Hanushek et al., 2008, p. 612).

Motivation for research

There are several ways in which this paper improves upon the existing research on the role of human capital in the SGM. Firstly, prior papers such as MRW and Islam are based upon data from the years 1960-1985. As such the data does not necessarily reflect the current role of human capital in the economy, which may have changed. Using newer data can help address this issue. Moreover, the newer data might be expected to be of higher quality, and better ways of estimating or measuring in particular the human capital variable are now available. The measure for human capital used in this paper is taken from the Penn World Table (2016). Furthermore, other papers that do use newer data do not use the SGM, and many of these papers, as well as for example Islam, are not focused on the inclusion of human capital in the model, but rather on issues such as convergence.

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Model(s)

This section of the paper introduces the models for the empirical analysis. These show how human capital is integrated into the SGM.

There are two models that are relevant for the empirical analysis: the standard SGM and the augmented one that includes human capital. The standard SGM is taken as given in the MRW paper: ln[𝑌(𝑡) 𝐿(𝑡)] =ln𝐴(0) + 𝑔𝑡 + 𝛼 1 − 𝛼ln(𝑠) − 𝛼 1 − 𝛼ln(𝑛 + 𝑔 + 𝛿) (1) (MRW, 1992, p. 410) where 𝑌 is output, 𝑡 is time, 𝐿 is labour, 𝐴 is the level of technology, 𝑔 is the growth rate of the level of technology, 𝛼 is the share of physical capital in income, 𝑠 is the fraction of output invested, 𝑛 is the growth rate of the labour force and 𝛿 is the depreciation rate(MRW, 1992, pp. 409-412).

A(0) also reflects differences in country-specific resources such as geography, institutions and natural resources (MRW, 1992, p. 410-411).

Equation 1 (MRW Equation 6) can be rewritten to form Equation 2 (Equation 7 in MRW), which is used in the analysis for the original SGM:

ln(𝑌 𝐿) = 𝑎 + 𝛼 1 − 𝛼ln(𝑠) − 𝛼 1 − 𝛼ln(𝑛 + 𝑔 + 𝛿) + 𝜖 (2) (MRW, 1992, p. 411)

where 𝑌 is output, 𝑡 is time, 𝐿 is labour, 𝑎 is a constant, 𝑔 is the growth rate of the

level of technology, 𝛼 is the share of physical capital in income, 𝑠 is the fraction of output

invested, 𝑛 is the growth rate of the labour force, 𝛿 is the depreciation rate and 𝜖 represents country –specific shocks (MRW, 1992, pp. 409-412).

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In order to investigate the effect of human capital on growth, human capital must be introduced to the SGM. The approach here is also the same as that used in the original MRW paper. MRW introduce two possible forms of the same equation, each form enabling a slightly different measure of human capital to be introduced into the SGM. The first of these, Equation 3 (Equation 11 in MRW), uses the rate of human capital accumulation (MRW, 1992, p. 418). MRW use this form of the equation in their analysis (MRW, 1992, p.419):

ln[𝑌(𝑡) 𝐿(𝑡)] = 𝑙𝑛𝐴(0) + 𝑔𝑡 − 𝛼 + 𝛽 1 − 𝛼 − 𝛽ln(𝑛 + 𝑔 + 𝛿) + 𝛼 1 − 𝛼 − 𝛽ln(𝑠𝑘) + 𝛽 1 − 𝛼 − 𝛽ln(𝑠ℎ) (3) (MRW, 1992, p. 417) where 𝑌 is output, 𝑡 is time, 𝐿 is labour, 𝐴 is the level of technology, 𝑔 is the growth rate of the level of technology, 𝛼 is the share of physical capital in income, 𝛽 is the share of human capital in income, 𝑛 is the growth rate of the labour force, 𝛿 is the depreciation rate, 𝑠𝑘 is the investment in physical capital as a share of income and 𝑠ℎ is the investment in human capital as a share of income (MRW, 1992, pp. 409-418).

The second equation introduced by MRW, shown as Equation 4 here (Equation 12 in MRW), uses the level of human capital (MRW, 1992, p. 418). As our analysis uses data representing a proxy for the human capital stock (level), as opposed to the rate of human capital accumulation as the proxy that MRW use, Equation 4 and not Equation 3 will be used in the empirical analysis for this paper:

ln[𝑌(𝑡) 𝐿(𝑡)] = 𝑙𝑛𝐴(0) + 𝑔𝑡 + 𝛼 1 − 𝛼ln(𝑠𝑘) − 𝛼 1 − 𝛼ln(𝑛 + 𝑔 + 𝛿) + 𝛽 1 − 𝛼ln(ℎ∗) (4) (MRW, 1992, p. 418) where 𝑌 is output, 𝑡 is time, 𝐿 is labour, 𝐴 is the level of technology, 𝑔 is the growth rate of the level of technology, 𝛼 is the share of physical capital in income, 𝑠_𝑘 is the investment in physical capital as a share of income, 𝑛 is the growth rate of the labour force, 𝛿 is the depreciation rate, 𝛽 is the share of human capital in income and ℎ∗ is the level of human capital (MRW, 1992, pp. 409-418).

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Methodology

Overview

This section outlines the methodology for the empirical analysis carried out in this paper. This section is composed of two parts. The first part introduces the data and the variables used in the empirical analysis, including calculations and sources. The second part introduces the regressions used and the estimation approaches, including the steps carried out and any tests carried out.

Data and Variables

The data are obtained from two sources: the Penn World Table and the World Bank. The first source, the Penn World Table is also used by MRW, although they refer to it as the Real National Accounts of Summers and Heston (1992, p. 412). The Penn World Table provides a large amount of macroeconomic data that has been made comparable between countries (PWT, 2016). The PWT, when first introduced as the Summer and Heston Real Nation Accounts, was instrumental in introducing global cross-country data that resulted in lots of new research and empirical analysis, and has been used in several key papers (Islam, 1995, p. 1138-1139). Although MRW also used data from PWT, the Table has since been updated, and the data used here are from version 9.0, which was published in early June 2016 (PWT, 2016). As such the data and variables can be expected to have been updated and improved.

The second source is the World Bank, again also used by MRW (1992, p. 412). The World Bank provides data relevant for development for a large number of countries globally (World Bank, 2016).1

1

An alternative source for the World Bank Data (population aged 15-64) would have been the United Nations (UN).

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The data used is for the years 1960-2014, a longer period than that used by MRW due to the inclusion of more recent data. The analysis is carried out using three different country samples, following the example of MRW. Islam (1995) also maintains the three country samples used by MRW, although a couple of small changes in the countries included are made due to the unavailability of some data (p. 1139).

Excluded from all three samples are those countries that have had a command economy (MRW, 1992, p. 412). In a command economy, the means of production are owned by the government and the level production of goods is dictated by the government. As a result, models such as the SGM are not applicable to countries with command economies. The list of countries included in each sample can be found in the Appendix.

The first sample includes all countries where there is available data, with the exception of those where the oil production industry is central to the economy, as standard growth models are not expected to apply given that they do not account for the measured GDP in such countries (MRW, 1992, p. 413). MRW explain that this is because most of the GDP that is recorded in such oil producing countries does not represent value added, but rather the extraction of oil resources (1992, p. 413).

The second sample of countries further removes those with small populations or those that received a low data quality ranking in the data used by MRW (MRW, 1992, p. 413). Here the same countries are excluded as in MRW, as it is seen as unlikely that data quality would be significantly lower for any country for the newer data when compared with the original data used.

The third sample of countries includes only the OECD countries included in the second sample (MRW, 1992, p. 413). The OECD countries used in this analysis are the same as those used in the MRW paper, as these are the countries that have been in the OECD for the entire data period. The only exception to this is (West) Germany, which though included

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in the MRW paper is excluded here, as it has since unified with East Germany, which was earlier a command economy. The third sample is created and used because OECD data may be seen as better quality data and therefore including data from countries that were not members for the entire timespan of the data might diminish this quality. This means that of the current 34 OECD countries, only 21 are included.

The variables to be included in the regression are introduced in Table 1. The variables are indicated in the Table, including how they are calculated and where the data for each variable originates from, for equations 2 and 4 respectively. For both equations 2 and 3, the sum of the growth rate of technology and the depreciation rate is assumed to be 0.05 (MRW, 1992, p. 413). This assumption is that made by MRW using their data and prior research and it is still used here, as MRW find that moderate changes to this figure do not

significantly alter the estimation results (1992, p. 413). Moreover, 𝑔 + 𝛿 are assumed to be

constant across countries (MRW, 1992, p. 410). The same assumption as MRW of the sum of the growth and depreciation rates being 0.05 and of these being constant over time and across countries is also made by Islam (1995, p. 1139). Human capital is measured using the proxy provided by the Penn World Table.

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Table 1: Variables for Equations 2 and 4 Variable

(theory):

Variable (empirical measure) :

Components: Sources: Calculations (if any):

𝑌 𝐿 Real GDP divided by working-age population in same year (MRW, 1992, p .413) Real GDP at constant 2005 national prices (in mil. 2005US$) Penn World Table (PWT) rgdpna

Step 1: Express population ages 15-64 as a fraction

𝑆ℎ𝑎𝑟𝑒 𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑎𝑔𝑒𝑠 15 − 64 =

(𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑎𝑔𝑒𝑠 15 − 64 %

100% )

Step 2: Calculate working age population

𝑊𝑜𝑟𝑘𝑖𝑛𝑔 𝑎𝑔𝑒 𝑝𝑜𝑝. = (𝑠ℎ𝑎𝑟𝑒 𝑝𝑜𝑝. ) ∙ (𝑃𝑜𝑝. )

Step 3: real GDP per working-age person

𝑅𝑒𝑎𝑙 𝐺𝐷𝑃 𝑊𝑜𝑟𝑘𝑖𝑛𝑔 𝑎𝑔𝑒 𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 Population (in millions) PWT pop Population ages 15-64 (% of total) World Bank (WB) SP.POP.1 564.TO.Z S Equation 2: 𝑠 Equation 4: 𝑠𝑘 Average share of real investment (including government investment) in real GDP (MRW, 1992, pp. 412-413) Real domestic absorption at constant 2005 national prices (in mil. 2005US$) PWT rdana

Step 1: Calculate real investment

𝑟𝑒𝑎𝑙 𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 = 𝑟𝑒𝑎𝑙 𝑑𝑜𝑚𝑒𝑠𝑡𝑖𝑐 𝑎𝑏𝑠𝑜𝑟𝑝𝑡𝑖𝑜𝑛 −

𝑟𝑒𝑎𝑙 𝑐𝑜𝑛𝑠𝑢𝑚𝑝𝑡𝑖𝑜𝑛

Step 2 : Calculate share of real investment in GDP

𝑆ℎ𝑎𝑟𝑒 𝑜𝑓 𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 𝑖𝑛 𝑟𝑒𝑎𝑙 𝐺𝐷𝑃 =𝑟𝑒𝑎𝑙 𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 𝑟𝑒𝑎𝑙 𝐺𝐷𝑃 Real consumption at constant 2005 national prices (in mil. 2005US$) PWT rconna Real GDP at constant 2005 national prices (in mil. 2005US$) PWT rgdpna

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24 Variable (theory): Variable (empirical measure) :

Components: Sources: Calculations (if any):

𝑛 Average rate of growth of the working-age population (working age =15-64) (MRW, 1992, pp. 412) Population (in millions) PWT pop

Step 1: Express population ages 15-64 as a fraction

𝑆ℎ𝑎𝑟𝑒 𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑎𝑔𝑒𝑠 15 − 64 =

(𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑎𝑔𝑒𝑠 15 − 64 %

100% )

Step 2: Calculate working age population

𝑊𝑜𝑟𝑘𝑖𝑛𝑔 𝑎𝑔𝑒 𝑝𝑜𝑝. = (𝑠ℎ𝑎𝑟𝑒 𝑝𝑜𝑝. ) ∙ (𝑃𝑜𝑝. )

Step 3: Calculate pop. Growth

𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑔𝑟𝑜𝑤𝑡ℎ Population ages 15-64 (% of total) WB SP.POP.1 564.TO.Z S 𝑔 + 𝛿 Assumption : 𝑔 + 𝛿 = 0.05 Equation 4: h*

Proxy for the level/stock of human capital Index of human capital per person, based on years of schooling (Barro/Lee, 2012) and returns to education (Psacharopoulo s, 1994) PWT hc

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25

Estimation and Regressions

The empirical approach taken in this paper consists follows a similar methodology to that taken by MRW in the first part of their paper, using a single cross-section regression on the data using averages over time. The dependent variable as well as the human capital variable are not averaged over time, instead the final year data is used for them. This is because in the version of the SGM used, economic growth is assumed to be at its steady state level, while the measure of human capital used measures the level of human capital as opposed to the rate of human capital accumulation. Any large changes from the results of MRW should already be visible using the same methodology as them. This provides evidence for or against further investigation. The regression software used is Stata (version 14).

The single cross-section regressions are carried out for all three samples over the time period 1960 to 2014, using both the original SGM and the augmented SGM. The results are then compared to those of MRW (and Islam). The results are compared to the expected ones provided by theory, as well as to those found in the original study. In particular, knowing the values of certain coefficients that are implied by theory provides reason to regress the original SGM. In using newer data it can be seen how additional and more recent data affects the results.

Each of the regressions is carried out both restricted and unrestricted, with the restriction taking coefficients on the savings rate and the population growth rate to have opposite signs, and to have the same magnitude (MRW, 1992, p. 413). Heteroskedasticity robust standard errors are used. Errors are assumed to be heteroskedastic because the variance of some of the factors included in the error terms of the models, such as country-specific factors, the level of technology, and the level of the dependent and independent variables at earlier points in time, are likely to be correlated with the level of the independent variables, such as the level of investment and population growth rates. For example, countries with less

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stable or developed institutions and government might be likely to experience higher variation in the level of investment than those countries with more developed institutions.

Results and Analysis

Overview

This section consists of three parts. The first part examines the effect of including human capital in the SGM by comparing the two regressions for each sample, including comparing the values to the theoretical ones suggested by the SGM. The second part compares the results of the analysis to those of MRW, to see how the results obtained with the newer data and methodology compare to the results of MRW. Finally, the third part evaluates the approach taken in this analysis. The results from the three samples are presented in Table 2, with the full Stata output available in the Appendix.

Effect of including human capital in the SGM

Samples 1 and 2 both exhibit similar results in the empirical analysis. There are three key theoretical values predicted by the SGM. Firstly, SGM predicts the share of (physical) capital in income, alpha, to be close to one third (MRW, 1992, p. 410). The results for the non-augmented model indicate that for both samples 1 and 2, the implied alpha is approximately 0.55, above the theoretical value of one third. This high value may be due to the omitted variable bias caused by not including human capital as an independent variable in the regression. The results from the analysis show that in the human capital augmented SGM, the implied values of alpha in both samples are reduced to 0.12 in sample 1 and to 0.17 in sample 2. Although the value of the implied alpha in both samples does decrease when human capital is added to the model, the values are much lower than the theoretical value of

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one third, and are not closer to one third than the initial value of approximately 0.55. Therefore on the basis of the implied value of alpha in samples 1 and 2, there is no strong evidence to support the inclusion of human capital.

Secondly, linked to the value of alpha, MRW suggest in their paper that the share of human capital in income, beta, should be expected to be between one third and one half in the SGM (MRW, 1992, p. 417). The results for the samples 1 and 2 are within this range, at 0.496 and 0.423 respectively. This supports the augmented model.

Thirdly, given the predicted value for alpha of one third, the SGM also predicts the coefficient on savings (which represents the elasticity of income per capita with respect the savings rate) to be close to one half, and the coefficient of the population growth rate (and growth rate of technology and depreciation rate) to be close to negative one half (MRW, 1992, p. 410). The results from the empirical analysis indicate that including human capital in the augmented SGM has a similar effect on sample 1 as it does on sample 2. The inclusion of human capital significantly reduces the magnitude of the coefficients for saving and for population growth in both samples, with the magnitude of each coefficient being roughly halved in both samples as a result of the inclusion of human capital as a variable. This leads to the coefficients moving closer to their theoretical values, with the coefficient for saving being reduced from 0.865 to 0.338, and from 0.862 to 0.452 in samples 1 and 2 respectively. Similarly, the coefficient for population growth is reduced in magnitude from -4.03 to -1.59 in sample 1 and from -3.64 to -1.58 in sample 2. In both samples including human capital leads to a value of the coefficient for population growth that is closer to the theoretical one, a positive indication with regard to the inclusion of human capital in the SGM. The coefficient for human capital in both samples is 2.80 and is significant. Furthermore, the R2 increases

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capital improves the fit of the regression, this also includes the effect of including an additional variable.

Overall, despite the low values for the implied alpha in samples 1 and 2 following the introduction of human capital, the results broadly appear to support the inclusion of human capital in the SGM.

The results in sample 3 differ from the results in the first two samples. Sample 3 is the smallest of the three samples, including only 21 countries. However, these are the OECD countries, and therefore the quality of the data for sample 3 might be considered higher than that of samples 1 and 2. Moreover, the OECD countries, being amongst the most developed, might be considered the most likely countries to be in their steady states for the final year of the data, therefore meeting one of the assumptions of the SGM. The value of the implied alpha in sample 3 is, at 0.18, much lower in the original model than the values for samples 1 and 2. The implied value for alpha in sample 3 is also lower in the augmented model than in the original one. This results in a negative value for the implied alpha in the augmented model for sample 3, which is even further from the theoretically predicted value. This does not appear to support the inclusion of human capital in the SGM. The implied value for beta in sample 3 is indicated to be 0.93, higher than expected by theory. However, the theoretical expectations for the value of beta are based upon the ratio of the minimum wage to the average wage in manufacturing (MRW, 1992, p. 417). Given that these estimated theoretical values of beta are subject to change, or to error, the implied beta in sample 3 in reality being higher than expected may not necessarily be unrealistic.

In contrast to samples 1 and 2, including human capital in the SGM for sample 3 leads to an increase in the coefficients for saving and for population growth, while the coefficient for human capital is lower than in samples 2 and 3, at a around 2.00. It must be noted that in sample 3, the standard errors are much larger relative to the coefficients than in the other two

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samples, in particular the standard error for the coefficient for population growth. This makes the result less significant or reliable. However, one reason for the increase in the value of this coefficient as a result of the addition of human capital to the model may be that it is the result of less demographic variation between countries in the sample- unlike samples 1 and 2, sample 3 consists only of developed countries, that tend to experience lower rates of population growth than developing countries. Developed countries may experience an increase in income as a result of increased population growth, due to their declining population levels. Therefore despite the higher expected quality of the data in sample 3, the limited range may result in weaker regressions.

Given this, overall, samples 1 and 2 appear to support the inclusion of human capital in the SGM, while sample 3 does not.

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Table 2: Estimation results for Samples 1, 2 and 3 (Standard errors are presented in brackets)

Model Variable Sample 1 93 observations Sample 2 72 observations Sample 3 21 observations Without human capital With human capital Without human capital With human capital Without human capital With human capital Unrestricted ln(𝑠) 0.865 (0.157) 0.338 (0.083) 0.862 (0.204) 0.452 (0.128) 0.441 (0.388) 0.502 (0.271) ln(𝑛 + 𝑔 + 𝛿) -4.03 (0.586) -1.59 (0.346) -3.64 (0.553) -1.58 (0.311) 0.376 (1.035) 0.981 (0.677) ln(ℎ∗₎ _{_} _2.82 (0.215) _ 2.61 (0.194) _ 2.01 (0.35) Constant 0.406 (1.748) 3.47 (0.84) 1.61 (1.70) 3.94 (0.801) 12.7 (3.13) 12.1 (2.24) R2 0.591 0.876 0.611 0.868 0.050 0.644 Restricted ln(𝑠) − ln(𝑛 + 𝑔 + 𝛿) 1.20 (0.160) 0.312 (0.0822) 1.21 (0.234) 0.426 (0.110) 0.220 (0.328) -0.275 (0.226) ln(ℎ∗_{) − ln(𝑛 + 𝑔 + 𝛿)} _ 2.44 (0.150) _ 2.17 (0.137) _ 1.50 (0.44) Constant 8.51 (0.186) 0.685 (0.487) 8.66 (0.270) 1.61 (0.433) 10.7 (0.5) 5.35 (1.49) R2 0.503 0.863 0.509 0.853 0.036 0.447 Implied 𝛼 0.545 0.120 0.547 0.172 0.181 -0.026 Implied 𝛽 _ 0.496 _ 0.423 _ 0.93

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Comparison of results with MRW

Comparing the results obtained for the estimation of the original SGM against those obtained by MRW, the coefficient for savings is found to be smaller in magnitude but of the same sign. In both samples 1 and 2, the coefficient for savings is 0.86, which compares to 1.42 and 1.31 in samples 1 and 2 respectively that MRW obtain. In sample 3, the coefficient is very similar to that from MRW, 0.44 compared to 0.50.

The coefficient for population growth also produces results that are much larger in magnitude, but of the same sign, as those found in MRW (For sample 1, -4.03 compared to -1.97 in MRW and for sample 2, -3.63 compared to -2.01 in MRW). As with the coefficient for savings, the difference between the two results is reduced in the third sample, with 0.37 here compared to -0.76 in MRW.

When adding human capital to the model, the coefficient for human capital is found to be 2.8 in sample 1, 2.6 in sample 2 and 2.0 in sample 3. This is a much higher value than that found by MRW, who find a value of 0.66, 0.73 and 0.76 for each of the three samples respectively. However, as a result of the level rather than the stock of human capital being used, and because this analysis used the proxy provided by the PWT as opposed to that calculated by MRW, the magnitude of the coefficient itself may not be directly comparable to that of the variables in the MRW paper.

The R2 obtained for the unrestricted estimations of Samples 1 and 2 are both around

0.60, which matches with the values for samples 1 and 2 in MRW. It must be noted, however,

that MRW use an adjusted R2, therefore somewhat reducing the ability to compare the figures

directly. Finally, sample 3 both here and in MRW is found to have an R2 value (adjusted R2 in

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Lastly, the implied value of alpha for the original SGM, the share in income of (physical) capital, has similar results as in MRW for samples 1 and 2. For sample 3, the implied value of alpha is twice as large in MRW.

Overall, the results found are broadly similar to those found by MRW, and differences in magnitude are likely to be the result of differences in how specific variables are measured, or the units they are measured in. Moreover, fewer countries in total were used in each sample than in MRW, also affecting the results. This is apparent as the same pattern emerges in the results found in this paper and those in MRW.

Evaluation of empirical approach

There are several factors that weaken the strength of the results. Firstly, in using a single-cross section approach similar to that of MRW, omitted variable bias may occur as a result of individual country effects. Secondly, theory on human capital suggests that there may be endogeneity, whereby higher levels of economic growth result in higher human capital. Although to some extent lagged variables were used (the averages of the independent variables were for over the years before each data point), this does not fully address concerns regarding endogeneity. This is because the level of economic growth at any point in time is correlated to the level of economic growth at any earlier point in time. Therefore the level of economic growth in 2014, is correlated with the level of economic growth in 1959, for instance. The level of economic growth is 1959 also be correlated to the independent variables such as human capital used in the regression for data from 1960 onwards. As a result, lagging the variables does not fully remove endogeneity. Thirdly, autocorrelation occurs as a result of the time-series characteristic of the panel data being taken into account. Some of these issues could be addressed using the dynamic panel model introduced in the Appendix and using LSDV or MD estimation techniques as done by Islam. These would

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address some of the time-invariant fixed effects that are not accounted for when suing a single cross country regression approach rather than a panel data estimation approach. However, both these alternative estimators also fail to address some of the endogeneity and autocorrelation issues mentioned here.

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Conclusion

The research question that this paper aimed to answer was: To what extent do the findings of Mankiw, Romer and Weil in their 1992 paper with regard to the inclusion of human capital continue to hold?

This research paper began by approaching this examining the key papers treating a similar topic, discussing the relevance of the SGM, examining how human capital is related to economic growth as well as exploring issues related to the measurement of human capital. The empirical approach taken emulated the approach of MRW, but using newer and improved data. The empirical analysis involved the introduction of human capital into the SGM using data from 1960-2014. The data for the majority of the variables was averaged over this time period in order to allow for a single section OLS regression on the cross-country panel data. Moreover, the data was split into three samples of countries

Overall, the results support those found by MRW, and therefore the continued inclusion of human capital in the SGM. The introduction of human capital into the SGM is found to decrease the coefficients for the other independent variables, bringing them closer in line to their theoretically expected values. However, a further analysis into the results from sample 3 may be beneficial to find the reason for the different results in the OECD sample.

Suggestions for further research include using the newer data within a dynamic panel data estimation approach, with lagged variables and to continue the research from this paper and investigate the effect of the newer data on the results for convergence.

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References

Barro, Robert J. (2001). Human Capital and Growth. American Economic Review. Vol.91. No. 2. pp.12-17

Barro, Robert J. and Jong, Wha Lee. (December 1993). International comparisons of educational attainment. Journal of Monetary Economics. Vol. 32,Issue 3 pp. 363-394 Becker (1962). Investment in Human Capital: A Theoretical Analysis. Journal of Political Economy. Vol.70, Series 5, p. 9

Hall, Robert E. and Jones, Charles, I. (Feb., 1999). Why Do Some Countries Produce So Much More Output Per Worker Than Others? The Quarterly Journal of Economics. Vol. 114, No. 1. pp. 83-116

Hanushek, Eric A., and Dennis D. Kimko. (December 2000). Schooling, labor force quality, and the growth of nations. American Economic Review . Vol. 90, no. 5. pp. 1184–1208. Hanushek, Eric A., and Woessmann, Ludger. (September 2008). The role of cognitive skills in economic development. Journal of Economic Literature. Volume 46, no. 3. pp. 607–668. Mankiw, Gregory, Romer, David and Weil, David. (May 1992). A Contribution to the Empirics of Economic Growth. The Quarterly Journal of Economics. Vol. 107, No. 2. pp 407-437.

Nazrul Islam. (November, 1995). Growth Empirics: A Panel Data Approach. The Quarterly Journal of Economics. Vol. 110. No. 4, pp. 1127-1170.

Penn World Table (June 2016). http://www.rug.nl/research/ggdc/data/pwt/pwt-9.0 University of Groningen.

United Nations Statistics. (June 2016). http://unstats.un.org/unsd/methods/m49/m49alpha.htm

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Appendix

Appendix: Methodology

Samples

The oil producing countries that MRW exclude in Sample 1 are Bahrain, Gabon, Iran, Iraq, Kuwait, Oman, Saudi Arabia, and the UAE (MRW, 1992, p. 413). MRW also exclude Lesotho because there is an indication of labour income from abroad constituting a large fraction of GNO (MRW, 1992, p. 413).

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37 Country List: Sample 1

Note: Data has been provided according to country codes (ISO3 3166-1 alpha- 3) as opposed to country names for ease of use.

Country Code 1. ARG 2. AUS 3. AUT 4. BDI 5. BEL 6. BEN 7. BFA 8. BGD 9. BOL 10. BRA 11. BRB 12. BWA 13. CAF 14. CAN 15. CHE 16. CHL 17. CIV 18. CMR 19. COD 20. COL 21. CRI 22. CYP 23. DNK 24. DOM 25. DZA 26. ECU 27. EGY 28. ESP 29. ETH 30. FIN 31. FJI 32. FRA Country Code 33. GBR 34. GHA 35. GMB 36. GRC 37. GTM 38. HKG 39. HND 40. HTI 41. IDN 42. IND 43. IRL 44. ISL 45. ISR 46. ITA 47. JAM 48. JOR 49. JPN 50. KEN 51. KOR 52. LKA 53. LUX 54. MAR 55. MDG 56. MEX 57. MLI 58. MOZ 59. MRT 60. MUS 61. MWI 62. MYS 63. NER 64. NGA Country Code 65. NIC 66. NLD 67. NOR 68. NPL 69. NZL 70. PAK 71. PAN 72. PER 73. PHL 74. PRT 75. PRY 76. RWA 77. SEN 78. SGP 79. SLV 80. SWE 81. SYR 82. TGO 83. THA 84. TTO 85. TUR 86. TZA 87. UGA 88. URY 89. USA 90. VEN 91. ZAF 92. ZMB 93. ZWE

Countries included now but not included in MRW paper:

BRB, CYP, FJI, GMB, ISL, LUX

Countries not included now but that were included in MRW paper:

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Country Code 1. ARG 2. AUS 3. AUT 4. BEL 5. BGD 6. BOL 7. BRA 8. BWA 9. CAN 10. CHE 11. CHL 12. CIV 13. CMR 14. COL 15. CRI 16. DNK 17. DOM 18. DZA 19. ECU 20. ESP 21. ETH 22. FIN 23. FRA 24. GBR Country Code 25. GRC 26. GTM 27. HKG 28. HND 29. HTI 30. IDN 31. IND 32. IRL 33. ISR 34. ITA 35. JAM 36. JOR 37. JPN 38. KEN 39. KOR 40. LKA 41. MAR 42. MDG 43. MEX 44. MLI 45. MWI 46. MYS 47. NGA 48. NIC Country Code 49. NLD 50. NOR 51. NZL 52. PAK 53. PAN 54. PER 55. PHL 56. PRT 57. PRY 58. SEN 59. SGP 60. SLV 61. SWE 62. SYR 63. THA 64. TTO 65. TUR 66. TZA 67. URY 68. USA 69. VEN 70. ZAF 71. ZMB 72. ZWE

None

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Country Code 1. AUS 2. AUT 3. BEL 4. CAN 5. CHE 6. DNK 7. ESP 8. FIN 9. FRA 10. GBR 11. GRC 12. IRL 13. ITA 14. JPN 15. NLD 16. NOR 17. NZL 18. PRT 19. SWE 20. TUR 21. USA

None

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40

Appendix: Results and Analysis

Sample 1

Sample 1, original SGM, unrestricted:

Sample 1, restricted original SGM:

_cons .4058761 1.747671 0.23 0.817 -3.066178 3.87793 lnn1960201~d -4.03347 .586333 -6.88 0.000 -5.198322 -2.868617 lns19602014 .8653834 .1566307 5.52 0.000 .5542091 1.176558 lnyl2014 Coef. Std. Err. t P>|t| [95% Conf. Interval] Robust Root MSE = .77991 R-squared = 0.5907 Prob > F = 0.0000 F(2, 90) = 92.36 Linear regression Number of obs = 93 . regress lnyl2014 lns19602014 lnn19602014gd, robust

_cons 8.508257 .1861173 45.71 0.000 8.138558 8.877956 lnsm~19602014 1.198803 .16042 7.47 0.000 .8801487 1.517458 lnyl2014 Coef. Std. Err. t P>|t| [95% Conf. Interval] Robust Root MSE = .85507 R-squared = 0.5026 Prob > F = 0.0000 F(1, 91) = 55.84 Linear regression Number of obs = 93 . regress lnyl2014 lnsminuslnngd19602014, robust

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41 Sample 1, augmented SGM, unrestricted:

Sample 1, restricted augmented SGM:

_cons 3.470481 .8407678 4.13 0.000 1.799893 5.141068 lnhc2014 2.823365 .2146535 13.15 0.000 2.396853 3.249877 lnn1960201~d -1.593428 .3463035 -4.60 0.000 -2.281526 -.9053306 lns19602014 .3378459 .083058 4.07 0.000 .1728114 .5028805 lnyl2014 Coef. Std. Err. t P>|t| [95% Conf. Interval] Robust Root MSE = .432 R-squared = 0.8758 Prob > F = 0.0000 F(3, 89) = 265.74 Linear regression Number of obs = 93 . regress lnyl2014 lns19602014 lnn19602014gd lnhc2014, robust

_cons .6846557 .487482 1.40 0.164 -.2838123 1.653124 lnhcminu~2014 2.441467 .1495174 16.33 0.000 2.144425 2.738509 lnsm~19602014 .3116214 .0822489 3.79 0.000 .1482195 .4750233 lnyl2014 Coef. Std. Err. t P>|t| [95% Conf. Interval] Robust Root MSE = .45113 R-squared = 0.8631 Prob > F = 0.0000 F(2, 90) = 377.13 Linear regression Number of obs = 93 . regress lnyl2014 lnsminuslnngd19602014 lnhcminuslnngd2014, robust

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42 Sample 2

Sample, 2 restricted original SGM:

_cons 1.614353 1.701951 0.95 0.346 -1.780945 5.009652 lnn19602014gd -3.638491 .5529453 -6.58 0.000 -4.741587 -2.535396 lns19602014 .8619311 .2041474 4.22 0.000 .4546681 1.269194 lnyl2014 Coef. Std. Err. t P>|t| [95% Conf. Interval] Robust Root MSE = .66595 R-squared = 0.6114 Prob > F = 0.0000 F(2, 69) = 67.29 Linear regression Number of obs = 72 . regress lnyl2014 lns19602014 lnn19602014gd, robust

_cons 8.659061 .2699372 32.08 0.000 8.120688 9.197433 lnsmi~19602014 1.207046 .2339238 5.16 0.000 .7404998 1.673592 lnyl2014 Coef. Std. Err. t P>|t| [95% Conf. Interval] Robust Root MSE = .74328 R-squared = 0.5090 Prob > F = 0.0000 F(1, 70) = 26.63 Linear regression Number of obs = 72 . regress lnyl2014 lnsminuslnngd19602014, robust

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_cons 3.939038 .8010059 4.92 0.000 2.340655 5.53742 lnhc2014 2.606526 .1938602 13.45 0.000 2.219684 2.993368 lnn19602014gd -1.581114 .3108123 -5.09 0.000 -2.20133 -.9608973 lns19602014 .4521252 .1284379 3.52 0.001 .1958314 .708419 lnyl2014 Coef. Std. Err. t P>|t| [95% Conf. Interval] Robust Root MSE = .39126 R-squared = 0.8678 Prob > F = 0.0000 F(3, 68) = 220.60 Linear regression Number of obs = 72 . regress lnyl2014 lns19602014 lnn19602014gd lnhc2014, robust

_cons 1.614159 .4325302 3.73 0.000 .7512852 2.477033 lnhcminus~2014 2.168268 .1366673 15.87 0.000 1.895624 2.440912 lnsmi~19602014 .4262836 .1099242 3.88 0.000 .2069909 .6455763 lnyl2014 Coef. Std. Err. t P>|t| [95% Conf. Interval] Robust Root MSE = .40982 R-squared = 0.8529 Prob > F = 0.0000 F(2, 69) = 283.18 Linear regression Number of obs = 72 . regress lnyl2014 lnsminuslnngd19602014 lnhcminuslnngd2014, robust

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44 Sample 3

Sample 3, restricted original SGM:

_cons 12.67239 3.126104 4.05 0.001 6.104688 19.24009 lnn19602014gd .3756207 1.034974 0.36 0.721 -1.79878 2.550021 lns19602014 .4414548 .3881826 1.14 0.270 -.3740866 1.256996 lnyl2014 Coef. Std. Err. t P>|t| [95% Conf. Interval] Robust Root MSE = .3352 R-squared = 0.0494 Prob > F = 0.5336 F(2, 18) = 0.65 Linear regression Number of obs = 21 . regress lnyl2014 lns19602014 lnn19602014gd, robust

_cons 10.66883 .5041215 21.16 0.000 9.613693 11.72397 lnsminuslnngd19602014 .2204184 .3278315 0.67 0.509 -.4657408 .9065776 lnyl2014 Coef. Std. Err. t P>|t| [95% Conf. Interval] Robust Root MSE = .32854 R-squared = 0.0360 Prob > F = 0.5095 F(1, 19) = 0.45 Linear regression Number of obs = 21 . regress lnyl2014 lnsminuslnngd19602014, robust

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_cons 12.10684 2.237002 5.41 0.000 7.387181 16.8265 lnhc2014 2.011662 .3549154 5.67 0.000 1.262856 2.760468 lnn19602014gd .9807806 .6767421 1.45 0.165 -.4470204 2.408582 lns19602014 .5020809 .2711458 1.85 0.082 -.0699867 1.074148 lnyl2014 Coef. Std. Err. t P>|t| [95% Conf. Interval] Robust Root MSE = .21114 R-squared = 0.6438 Prob > F = 0.0000 F(3, 17) = 20.78 Linear regression Number of obs = 21 . regress lnyl2014 lns19602014 lnn19602014gd lnhc2014, robust

_cons 5.345119 1.492988 3.58 0.002 2.208467 8.48177 lnhcminuslnngd2014 1.501838 .4416284 3.40 0.003 .5740106 2.429664 lnsminuslnngd19602014 -.275063 .2261636 -1.22 0.240 -.7502151 .2000891 lnyl2014 Coef. Std. Err. t P>|t| [95% Conf. Interval] Robust Root MSE = .25562 R-squared = 0.4472 Prob > F = 0.0007 F(2, 18) = 11.08 Linear regression Number of obs = 21 . regress lnyl2014 lnsminuslnngd19602014 lnhcminuslnngd2014, robust

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46 Dynamic Model

Although not used for the empirical analysis in this particular research, the models introduced by Islam are introduced here, to show how the SGM can be rewritten as a dynamic model.

Islam takes the equation that MRW introduce in their investigation of convergence and uses it as a basis for a panel data model that accounts for the individual country effects (1995, p. 1128). ln𝑦(𝑡₂) = (1 − 𝑒−𝜆𝜏) 𝛼 1 − 𝛼ln(𝑠) − (1 − 𝑒−𝜆𝜏) 𝛼 1 − 𝛼ln(𝑛 + 𝑔 + 𝛿) + 𝑒−𝜆𝜏ln𝑦(𝑡1) + (1 − 𝑒−𝜆𝜏)𝑙𝑛𝐴(0) + 𝑔(𝑡₂− 𝑒−𝜆𝜏𝑡₁) (5) (Islam, 1995, p. 1136) where ln𝑦(𝑡𝑖) is the income per capita at time 𝑡𝑖 (Islam, 1995, p. 1136), 𝑡 is time, 𝛼 is the share of capital in income, 𝑠 is the investment in capital as a share of income, 𝑛 is the growth rate of the labour force, 𝑔 is the growth rate of the level of technology, 𝛿 is the

depreciation rate, 𝐴 is the level of technology, and 𝜆 is the convergence rate towards steady

state (MRW, 1992, pp. 409-423).

Islam also shows how human capital can be included in the SGM (Islam, 1995, p. 1150). This is displayed in equation 6:

ln𝑦(𝑡₂) = (1 − 𝑒−𝜆𝜏) 𝛼 1 − 𝛼[ln(𝑠) −ln(𝑛 + 𝑔 + 𝛿)] + (1 − 𝑒−𝜆𝜏) 𝜑 1 − 𝛼ln(ℎ∗) + 𝑒−𝜆𝜏_ln𝑦(𝑡 1) + (1 − 𝑒−𝜆𝜏)𝑙𝑛𝐴(0) + 𝑔(𝑡2− 𝑒−𝜆𝜏𝑡1) (6) (Islam, 1995, p. 1136) where ln𝑦(𝑡_𝑖) is the income per capita at time 𝑡_𝑖 (Islam, 1995, p. 1136), 𝑡 is time, 𝛼 is the share of physical capital in income, 𝑠 is the investment in capital as a share of income, 𝑛 is the growth rate of the labour force, 𝑔 is the growth rate of the level of technology, 𝛿 is the depreciation rate, ℎ∗_{is the steady state level of human capital and}_{𝜑 represents the exponent} in the augmented production function of the human capital variable (Islam, 1995, p. 1150), 𝐴

is the level of technology, and 𝜆 is the convergence rate towards steady state (MRW, 1992,

Human capital & economic growth : reviewing the augmented Solow-Swan Growth Model