What Can We Learn from Global and Regional Rankings of Countries?

Abstract

We use principal component analysis (PCA) to extract the essential information contained in 10 different country rankings, measuring different country characteristics such as GDP per capita, human development, quality of governance, environmental quality and business environment. Globally, the first principal component accounts for about 82 per cent of the variation across countries, and the first three principal components account for over 92 per cent. The percentages are similar for regions such as Europe, North America and Asia, but lower for South America and Africa, but even in the last of these regions, the first three principal components account for 86 per cent of the variation. Excluding GDP per capita does not change our results appreciably. The analysis suggests that various different indices may add relatively little new information to more basic measures of development. Regional comparisons suggest that Asia’s economic structures, as implied by the rankings, may be closer to those of Europe and North America than South America and Africa.

JEL Codes: C38, O1, O57

Keywords

Global rankings principal component analysis economic development governance environment

I. Introduction

The most basic measure of economic welfare is GDP per capita, and this has long been used to track a nation’s economic performance over time. As the promotion of economic development became a task in which international institutions played a role, comparisons of the economic performance of different countries also became commonplace, again using GDP per capita, but with adjustments for differences in the domestic purchasing power of individual currencies.¹ Somewhat later, conceptual arguments with respect to the limitations of GDP as a measure of wellbeing led to the creation of the Human Development Index (HDI), itself with GDP per capita as a component.²

A related development in cross-country comparisons came with attempts to explain economic outcomes through empirical analyses such as cross-section and panel regressions (Barro & Sala-i-Martin, 1995). For these regressions, indices of governance quality were developed to provide explanatory power. In a similar vein, though initially not motivated by the idea of developing explanatory variables for regressions, indices of ‘economic freedom’, ‘ease of doing business’ and ‘growth environment’ have also been created.³ All of these are typically conceived of as capturing factors that affect the growth performance of nations, as measured by GDP per capita. Most recently, measures of performance with respect to the goal of environmental sustainability have also surfaced.⁴ Many of the measures of economic performance and/or social outcomes, or of conditions underlying future performance, are themselves aggregate indices of several underlying components. Each of these indices has its own measurement scale, but what receive attention are the national rankings generated by the calculation of the indices. For example, a country may rank highly in terms of an ‘economic freedom’ index, and this is compared to its GDP per capita rank, or its HDI rank may be contrasted with its GDP per capita rank, and so on.

The influence of these different country rankings seems to be increasing, making understanding their information content even more important. Several articles by Kelley and Simmons (2014, 2015a, 2015b) examine the influence of global indices such as ease of doing business and trafficking in persons on international relations and ‘soft power’. The OECD’s Programme for International Student Assessment (PISA), which measures 15-year-olds’ academic performance across dozens of countries (The Economist, 2014), is another example of an influential global performance indicator (GPI).

The plethora of increasingly influential indices and national rankings, the complexity of their calculation, and overlaps in the information they contain, suggest that it would be useful to see if one can extract the essential information contained in these multiple indicators. This study examines the relative contribution of 10 ranking indicators. The benefits of doing so are three-fold. First, one obtains a more parsimonious measure of how individual nations compare in terms of economic conditions (whether initial situations or outcomes). Second, one gains insight into the relationships among the many overlapping indices that have been created. Third, our exercise can yield summary indicators that are useful for regression analyses that seek to explain economic growth in quantitative terms.

The rest of this article is organized as follows: Section II reviews the related literature, including a discussion of the evolution of some of the different indices used to rank country performance; Section III describes the data sources, which are a variety of international organizations as well as private sector entities; Section IV explains the econometric methodology employed, namely principal component analysis (PCA); Section V reports the estimated results and discusses the findings, emphasizing the concentration of information in the varied indices, as expressed in the small number of principal components that account for most of the cross-country variation and Section VI provides a summary conclusion.

II. Review of Related Literature

The assessment of global ranking of countries has been of long interest to the economists and policy makers. According to Kelley and Simmons (2014), ‘In the last 15 years more than 8 new state-focused GPIs have been added on average each year, and today over 160 of these chart anything from gender equity to happiness’. Kelley and Simmons (2014) provide a useful literature review that the reader is referred to, and which is not repeated in this section. The following discussion can be considered to be complementary.

In the development economics literature, real income or real GDP per capita is still the best known and most widely utilized economic indicator to measure development. It is considered that if GDP per capita increases over a long period of time, it would imply that the country is moving towards a higher standard of living and achieving economic goals. Nevertheless, real GDP per capita by itself may not be an adequate indicator of development, where development should cover several aspects such as poverty reduction, employment and income distribution. Therefore, the literature moved on to measure development by taking into consideration of wellbeing and basic human needs. Hicks and Streeten (1979) were early in pointing out that there was growing interest in finding better measure of development, including modifications of gross national product (GNP), social indicators and associated systems of social accounts, and composite indices of development. A review of these approaches and concepts, suggested that the use of social and human indicators was the most promising supplement to GNP, particularly if analysed in areas central to the basic needs approach. Even though the basic needs approach is considered superior as it spells out human needs, it is criticized on the ground that it does not include security, justice and human rights which are an important measures of quality of life.

Economists formulated the HDI, which intends to address the issue of not only how much GDP growth but what kind of growth. The HDI is a new way of measuring development by combining indicators of life expectancy (a proxy indicator for health care and living conditions), educational attainment and real GDP per capita into a composite HDI, published by United Nations Development Programme (UNDP). The innovation of this index is the creation of a single statistic which was to serve as a frame of reference for both social and economic development. Booysen (2002) points out that the HDI index is simple to calculate and transparent, and hence attract the attention of politicians, policy markets and the public. As broadly the same HDI methodology is used each year one can argue that between-country comparisons are valid (Ogwang, 2000).

However, there are a number of critiques⁵ of the quality of the data upon which the HDI is based. In addition, the index is based on a national average which ignores the within-country variation. For instance, the use of the real GDP per capita component as a proxy for average income can be suspect. Sagar and Najam (1998) point out that the HDI index does not allow for perhaps major differences in income distribution within a country. They argue that the UNDP reports have lost touch with their original vision and the index fails to capture the essence of the world it seeks to portray. In addition, the index focuses almost exclusively on national performance and ranking, but does not pay much attention to development from a global perspective. Morse (2003) finds that even the simple and highly aggregated HDIs are supposed to help with an understanding and presentation of such change, it may also mislead and need to be handled with care. Morse (2003) recalculates the HDI using various methodologies employed by the UNDP, the results reveal that the volatility of recalculated HDI ranks and original ranks is substantial. Such movement can easily be accounted for by changes in the HDI methodology rather than genuine progress in human development.

Another important aspect of measuring development is environmental sustainability. This concept has evolved into a definition of the three pillars of sustainability, namely, social, economic and environmental. The HDI has neglected links to sustainability by failing to investigate the impact on natural system of the activities that potentially contribute to national income, and hence to HDI. For example, the distribution of environmental performance of countries varies greatly. A country can improve its performance on the HDI in part by converting their natural resources to income. Even though the human development achievement of this country may seem impressive, its environmental quality might not sustainable. In recent years, there has been an increasing interest in examining the linkages among environment, human development and economic growth. Costantini and Monni (2008) examine the causal relationships among these three variables and their empirical results confirm the importance of investments for human well- being and high institutional quality in order to build a sustainable development path. Achieving a higher standard of living and maintaining natural resources could be complementary goals rather than competing ones, by mutually reinforcing development and economic growth.

It is now widely accepted that factor accumulation and technological change alone cannot adequately explain differences in economic development across countries. Institutional quality and governance are emerging as key determinants of economic growth in recent literature. Many studies have been conducted to examine the effects of these indicators on economic performance, using various indicators such as corruption, economic freedom index, rule of law, etc. For example, Mauro (1995) points out that low institutional quality that includes high levels of corruption will hinder economic performance. Mendez and Sepulveda (2006), and Mobolaji and Omoteso (2009) also show that corruption has a significant impact on economic growth. Economic freedom indices developed by Fraser Institute and Heritage Foundation are also utilized to analyse the role of freedom in influencing economic development (Haan & Strum, 2000).

Since many indicators display a strong correlation with economic development, an interesting issue arises here is to evaluate the most important measures or the priorities of these indicators to represent the global ranking. Peniwati and Hsiao (1987) offer a composite index that touches more on the quality of life to measure the degree of development of the nations of the world. The indicators employed are GNP per capita, physical quality of life, percentage of national income received by the poorest 40 per cent, population density in agricultural areas, political rights and civil liberties, number of telephones per capita and number of drug-related offenses. Their results using absolute measurement and 26 nations reveal that the United States ranked second to Australia. This finding demonstrates that even though the income is still the best known and most widely used economic indicator to measure development, the global ranking tends to differ if taking into consideration of other relevant indicators.

Hossein and Kaneko (2011) attempt to develop macro composite sustainability indicators of 132 countries using four dimensions, namely, institutional, economic, social and environment. They find that the total sustainable development of the countries can be viewed in institutional, economic and social dimensions when environmental conditions deteriorate every year. They also discover that when institutional, environmental and economic pillars are strongly correlated, economic development cannot solely explain environmental deterioration. On the other hand, Oral and Chabchoub (1997) try to replicate the World Competitiveness Report (WCR) rankings based on their mathematical programming approach. They show that one does not need to use all of the indicators in order to replicate the WCR ranking, and in fact 27 indicators are unnecessary. Therefore, choosing the right indicators to reduce the dimension of all the relevant indicators are crucial in deriving a key indicator.

One of the techniques in the literature that can reduce the dimension of possibly correlated variables into a set of values is PCA. It is a straightforward, non-parametric method for extracting pertinent information from confusing data sets. It presents a roadmap for how to reduce a complex data set to a lower dimension to disclose the hidden, simplified structures that often underlie it. In addition, this method tends to identify patterns in data, and express the data in a way to highlight their similarities and dissimilarities, as well as allows the use of variables which are not measured in the same units. Hossein and Kaneko (2011) point out that the main advantages of PCA are (a) PCA is a weighting approach that may be used as an alternative to the more subjective weighting systems like public opinion polls, and (b) PCA is a useful tool for improving the efficiency of indicators. PCA has been used in the analysis of colleges and universities rankings (Webster, 2001), macro composite sustainability indicators (Hossein & Kaneko, 2011) and even in ranking economists (Seiler & Wohlrabe, 2012).

III. Data

We use the following rankings data for our analysis.

Rankings

Ease of Doing Business created by the World Bank measures whether the business environment is promoting to the starting and operation of a firm and it is based on the average of 10 sub-indices. Higher rankings show better regulations for business and property rights. It measures regulations that affect business directly and do not measure general conditions like the strength of the financial system or proximity to large markets since it is limited in scope. Ease of doing business index has been used widely by academic paper and its effect on economic growth has been claimed as very strong.

Index of Economic Freedom created by the Heritage Foundation and the Wall Street Journal measures the degree of economic freedom of nations. Economic freedom index is based on the average of 10 broad components such as monetary freedom, labour freedom and, etc. and higher rankings indicate freedoms of movement of labour, capital and goods, better protection of property ownership and less constraint on economic liberty.

Growth Environment Scores (GES) index created by Goldman Sachs represents a measure of growth conditions which aims summarizing the overall growth environment and gauges the ability of nations to achieve sustainable economic growth over the long run. Countries are given an overall GES score which is an average of 13 components such as inflation, government deficit and investment rate. Higher rankings indicate the likelihood of potential growth.

HDI created by United Nations is composite measure of development and it includes three component indicators as life expectancy, income and education. HDI is expressed as a value between 0 and 1 which a higher value shows a higher level of development. It also provides an alternative to conventional way of evaluating countries based on income.

Index of Carbon Dioxide (CO₂) emissions per capita created by the US Department of Energy is a measure of metric tons of CO₂ emission from the burning of fossil oils and cement manufacture.

Index of Ratings (riskiness) created by The Economist Intelligent Unit is a measure whether a country is unable to meet its loan obligations. It is crucial for creditors to consider the sovereign risk quality of a country before the credit quality of a firm. Higher rankings indicate the capacity and commitment to fulfil obligations where lower rankings indicate very capacity and commitment to fulfil obligations.

Index of Government Effectiveness (Gov) created by the World Bank measures ‘the quality of public services, the quality of the civil service and the degree of its independence from political pressures, the quality of policy formulation and implementation, and the credibility of the government’s commitment to such policies’. Higher rankings indicate a better governance quality and performance.

Index of Control of Corruption (Cor) created by the World Bank measures ‘the perceptions of the extent to which public power is exercised for private gain, including both petty and grand forms of corruption, as well as “capture” of the state by elites and private interests’. Higher rankings indicate the nations’ like- lihood of controlling corruptions.

Corruption Perception Index (Cor_Ind) created by Transparency International measures the corruption perceived by the public sector where corruption is defined as misusage of entrusted power for individual interest. Corruption Perception Index has been used widely since perceptions have been a reliable estimate of corruption. Countries are assigned a value between 0 and 10 where higher rankings indicate less perceived corruption.

Index of GDP per capita is a standard economic measure that serves as an approximation of the values of the goods produced per person within a country. Each country maintains national income accounts, and international organizations compile and standardize them. We use the IMF numbers.

IV. Methodology

When there are a large number of variables it is not easy to display the relationship between those variables. One may wish to reduce the number of variables that can explain all of the original variables. PCA enables one to have a new set of variables to take the advantage of redundancy of information, which means some of the variables are correlated with one another. One can simplify the problem by replacing the large number of variables with a new artificial variable (called principal component). Each principal component is a linear combination of the original variables and all the principal components are orthogonal to each other, so there is no redundant information.

Let us assume, we have k explanatory variables in a functional relationship, which can be explained as

z_{1} = a_{1} x_{1} + a_{2} x_{2} + \dots + a_{k} x_{k}

z_{2} = b_{1} x_{1} + b_{2} x_{2} + \dots + b_{k} x_{k}

z_{k} = k_{1} x_{1} + k_{2} x_{2} + \dots + k_{k} x_{k}

Now we choose values of z₁ such that variances are maximized subject to the

1 = a_{1}^{2} + a_{2}^{2} + \dots + a_{k}^{2}

This restriction is known as the normalization condition and it is necessary that the values of z₁cannot increase indefinitely. z₁ is called the first principal component and it is the linear function of the explanatory variables x_i that has the greatest variance. The first principal component should be able to explain variations better than any other linear combination of explanatory variables subject to the normalization rule. We may also consider linear combinations z₂ which is the second principal component and orthogonal to z₁ subject to the condition that

1 = b_{1}^{2} + b_{2}^{2} + \dots + b_{k}^{2}

(3)

This procedure is repeated until we have k linear functions z₁, z₂, …, z_k which principal components of x_is. The variances of the principal component are ordered as

var (z_{1}) > var (z_{2}) > \dots > var (z_{k})

Each principal component is a linear combination of the original variables with coefficients equal to the eigenvectors of the correlation or covariance matrix. The principal components are sorted in descending order by their eigenvalues which are equal to the variance of the components.

V. Results

Tables 1 and 2 summarize the results from the application of PCA to the global and regional rankings. While Table 1 presents the eigenvalues and proportions of variance explained by principal components, Table 2 details the variables with factor loadings for the first two principal components. The eigenvalues indicate that the first principal component explains about 80 per cent of the standardized variance in global and regional rankings except Africa and the second principal component explains another 6–7 per cent. It is clear that majority of the variability in rankings can be explained by the first two principal components. For instance, in the global ranking the first and second components explain 82.1 and 6.9 per cent of the total variance of 10 rankings, respectively. They together account 89 per cent of the variance in the rankings. A similar pattern exists for regional rankings as well. The total variance explained by the first two components range from a low of 80.1 per cent to a high of 89.1 per cent. Therefore, the dimensionality of the rankings can be reduced from 10 to 2.

Table 1.
Principal component analysis: Eigenvalues and Proportion explained

Principal Component Global
Africa
Asia
Europe
S. America
N. America

Eigen % Eigen % Eigen % Eigen % Eigen % Eigen %

1st 8.214 82.143 6.297 62.966 8.248 82.478 8.044 80.442 5.545 61.615 8.050 80.500

2nd 0.689 6.886 1.711 17.110 0.552 5.519 0.869 8.688 2.427 26.966 0.787 7.870

3rd 0.351 3.513 0.639 6.389 0.378 3.778 0.582 5.824 0.395 4.389 0.436 4.364

4th 0.281 2.813 0.521 5.214 0.297 2.972 0.183 1.825 0.248 2.756 0.364 3.637

5th 0.159 1.591 0.349 3.492 0.172 1.717 0.129 1.289 0.156 1.729 0.204 2.038

6th 0.122 1.224 0.177 1.774 0.144 1.441 0.094 0.936 0.138 1.532 0.084 0.837

7th 0.078 0.779 0.132 1.316 0.078 0.782 0.043 0.426 0.052 0.577 0.034 0.339

8th 0.051 0.506 0.077 0.771 0.073 0.729 0.034 0.344 0.037 0.412 0.021 0.205

9th 0.032 0.317 0.066 0.657 0.044 0.443 0.015 0.148 0.002 0.024 0.016 0.156

10th 0.023 0.228 0.031 0.312 0.014 0.142 0.008 0.078 0.006 0.055

Principal Component	Global	Africa	Asia	Europe	S. America	N. America
1st	8.214	82.143	6.297	62.966	8.248	82.478	8.044	80.442	5.545	61.615	8.050	80.500
2nd	0.689	6.886	1.711	17.110	0.552	5.519	0.869	8.688	2.427	26.966	0.787	7.870
3rd	0.351	3.513	0.639	6.389	0.378	3.778	0.582	5.824	0.395	4.389	0.436	4.364
4th	0.281	2.813	0.521	5.214	0.297	2.972	0.183	1.825	0.248	2.756	0.364	3.637
5th	0.159	1.591	0.349	3.492	0.172	1.717	0.129	1.289	0.156	1.729	0.204	2.038
6th	0.122	1.224	0.177	1.774	0.144	1.441	0.094	0.936	0.138	1.532	0.084	0.837
7th	0.078	0.779	0.132	1.316	0.078	0.782	0.043	0.426	0.052	0.577	0.034	0.339
8th	0.051	0.506	0.077	0.771	0.073	0.729	0.034	0.344	0.037	0.412	0.021	0.205
9th	0.032	0.317	0.066	0.657	0.044	0.443	0.015	0.148	0.002	0.024	0.016	0.156
10th	0.023	0.228	0.031	0.312	0.014	0.142	0.008	0.078			0.006	0.055

Source: Authors’ calculations.

A useful method to determine the number of PCA to retain is the Kaiser criterion. Kaiser (1960) suggests choosing principal components that have eigenvalues greater than 1, λ = 1. However, this criterion needs to be relaxed when some important components are discarded. For instance, in the European ranking, the first principal component explains about 80 per cent of the total variance. The second component account for about 9 per cent of the variability but its eigenvalue is 0.87, which is smaller than the Kaiser criterion. The global, Asian and North American rankings also follow a similar characteristic and thus, discarding the second eigenvalue would increase the unexplained variability. Jolliffe (1972) relaxes the Kaiser criterion and recommends to use λ = 0.7 as a threshold. Following Jolliffe (1972), the first two principal components should be retained that also aligns with the principle that majority of variance should be explained by these components. Figure 1 plots the eigenvalues for the global and regional rankings.

Table 2 presents the factor loadings for the retained principal components. The striking point is that either for global or regional rankings, all variables have positive contribution on the first principal component. With some exceptions, the loading factors are approximately equal and fluctuate around 0.3. GES variable has a relatively high correlation with the first component in both global and regional rankings. In contrast, GDP’s correlation is smaller, except for North America. The Gov variable also has a high correlation in all rankings and generally succeeds GES in magnitude. The variable that has the third highest correlation is Cor or Cor_Ind, except in South America. In South America, the Freedom variable has the third highest correlation. It is important to remember that the correlation between Cor and Cor_Ind is very high. For South America, the two variables are perfectly correlated, and thus only one of them is used for the estimation. When two perfectly correlated variables are used in the estimation, one ends up having a singular correlation matrix, which makes impossible to test the sampling adequacy. By looking at GES, Gov and Cor (or Cor_Ind) variables, we can have a rough idea about the ranking of any country across all indices.

Table 2.

Principal component analysis: Coefficients

Principal Component	Global		Africa		Asia		Europe		S. America		N. America
Principal Component	1st	2nd	1st	2nd	1st	2nd	1st	2nd	1st	2nd	1st	2nd
GDP	0.323	0.350	0.277	0.494	0.324	0.339	0.332	0.112	0.233	0.489	0.341	0.176
Business	0.305	–0.216	0.291	–0.347	0.293	–0.007	0.294	–0.371	0.344	–0.213	0.276	0.533
Freedom	0.312	–0.328	0.333	–0.200	0.316	–0.147	0.305	–0.178	0.372	–0.250	0.310	–0.159
GES	0.335	0.151	0.352	0.148	0.331	0.029	0.348	–0.021	0.395	0.052	0.339	–0.046
HDI	0.320	0.355	0.296	0.406	0.333	0.187	0.323	0.121	0.302	0.435	0.330	0.081
CO₂	0.283	0.611	0.321	0.385	0.290	0.672	0.169	0.876	0.069	0.617	0.289	0.523
Risk	0.289	–0.150	0.269	0.095	0.301	0.043	0.317	0.114	0.339	–0.267	0.294	–0.195
Gov	0.333	–0.193	0.342	–0.299	0.324	–0.375	0.347	–0.060	0.406	–0.049	0.343	–0.069
Cor	0.328	–0.254	0.335	–0.325	0.322	–0.299	0.343	–0.093	0.396	–0.080	0.331	–0.245
CorInd	0.330	–0.277	0.335	–0.238	0.324	–0.381	0.345	–0.107			0.301	–0.525

Source: Authors’ calculations.

Figure 1.

Source: Authors’ calculations.

On the other hand, the second principal component does not pose a clear picture about the factor loadings. Indices have both positive and negative contributions on the second component that contradicts the first component. One common thing about the loading factors is that CO₂ variable has the highest and positive correlation with the second component. HDI also has a high and positive correlation in four rankings. Indices with negative correlations do not have a high loading factor in general. While business has a high and negative correlation in Europe, Cor_Ind has a similar property in North America. Factor loadings of all indices are plotted in Figure 2.

Figure 2.

Source: Authors’ calculations.

The final thing to check is whether PCA can be applied efficiently to our dataset. In order to do so, we use the Kaiser–Meyer–Olkin (KMO) measure of sampling adequacy to test whether PCA is able to extract useful information. If the variables in the dataset share a common variation, KMO will be close to 1, and otherwise 0. In the literature, a KMO value of 0.5 is generally considered as the smallest value to apply PCA. In our case, the KMO value is very high, except for South America. While the KMO value for South America is 0.5, it ranges from a low of 0.76 to a high of 0.91 for other rankings. Therefore, we can assert that PCA has extracted adequate useful information from our dataset.

As a robustness check, we exclude the GDP variable from our dataset and re-apply PCA using other nine indices. The reason behind the exclusion of GDP per capita is the potential feedback between GDP per capita and other indices, since GDP is the most comprehensive measure of economic activity. For instance, the GES index measures growth conditions, and thus the probability of feedback between the two is very high. Re-estimated eigenvalues and factor loadings without the GDP index are presented in Tables 3 and 4. As Table 3 details, the first principal component of all rankings except for Africa and South America explain around 80 per cent of the total variation. In addition, the first two components of all rankings except Africa account for around 90 per cent of the total variance in the data. In Africa, the first two components explain 80 per cent of the total variance and it is still accepted as an adequate ratio. Therefore, the first two components are retained. Most of the second eigenvalues are lower than the Kaiser criterion, λ = 1. However, the Jolliffe (1972) criterion is satisfied except for Asia and eigenvalues are plotted in Figure 3. As detailed in Table 4, factor loadings of indices on the first principal component have a similar pattern. GES and Gov have a high correlation with the first component and CO₂ has the highest correlation with the second component. All factor loadings are plotted in Figure 4. Finally, the KMO values are very high and very similar to our first estimations. Therefore, excluding GDP per capita does not make any difference to our initial estimation, and thus supports the robustness of our results.

Table 3.

Principal component analysis: Eigenvalues and Proportion explained

Principal Component	Global		Africa		Asia		Europe		S. America		N. America
Principal Component	Eigen	%	Eigen	%	Eigen	%	Eigen	%	Eigen	%	Eigen	%
1st	7.374	81.933	5.863	65.147	7.397	82.193	7.172	79.684	5.300	66.252	7.122	79.131
2nd	0.605	6.725	1.293	14.368	0.498	5.532	0.859	9.546	1.842	23.029	0.762	8.463
3rd	0.351	3.896	0.637	7.074	0.378	4.197	0.529	5.878	0.372	4.656	0.432	4.804
4th	0.276	3.061	0.521	5.792	0.242	2.684	0.165	1.832	0.175	2.182	0.330	3.663
5th	0.139	1.540	0.273	3.033	0.171	1.903	0.119	1.324	0.155	1.940	0.203	2.256
6th	0.122	1.359	0.174	1.933	0.144	1.595	0.088	0.975	0.114	1.421	0.083	0.925
7th	0.062	0.689	0.129	1.438	0.077	0.850	0.043	0.472	0.038	0.472	0.034	0.376
8th	0.047	0.526	0.070	0.781	0.058	0.644	0.017	0.192	0.004	0.048	0.020	0.223
9th	0.025	0.272	0.039	0.434	0.036	0.404	0.009	0.098			0.014	0.159

Source: Authors’ calculations.

Figure 3.

Source: Authors’ calculations.

Table 4.

Principal component analysis: Coefficients

Variable	Global		Africa		Asia		Europe		S. America		N. America
Variable	1st	2nd	1st	2nd	1st	2nd	1st	2nd	1st	2nd	1st	2nd
Business	0.326	–0.153	0.316	–0.367	0.312	0.097	0.316	–0.334	0.334	–0.152	0.291	0.583
Freedom	0.332	–0.311	0.354	–0.146	0.334	–0.150	0.328	–0.136	0.363	–0.213	0.334	–0.103
GES	0.353	0.221	0.358	0.276	0.350	0.095	0.368	–0.009	0.369	0.150	0.359	–0.033
HDI	0.332	0.396	0.287	0.537	0.348	0.181	0.337	0.107	0.249	0.558	0.349	0.095
CO₂	0.293	0.717	0.311	0.486	0.301	0.731	0.178	0.911	0.021	0.726	0.302	0.541
Risk	0.306	–0.130	0.274	0.179	0.320	0.184	0.333	0.109	0.336	–0.264	0.312	–0.195
Gov	0.354	–0.156	0.370	–0.243	0.346	–0.350	0.368	–0.046	0.385	0.023	0.366	–0.047
Cor	0.349	–0.232	0.361	–0.310	0.342	–0.307	0.364	–0.083	0.385	–0.002	0.354	–0.219
Cor Ind	0.351	–0.258	0.355	–0.235	0.344	–0.376	0.366	–0.093	0.385	–0.002	0.324	–0.508

Source: Authors’ calculations.

Figure 4.

Source: Authors’ calculations.

As a final robustness check, we categorize all countries into three groups as high, mid and low GDP per capita instead of global and regional rankings. Tables 5 and 6 present the estimation results for eigenvalues and factor loadings. The striking difference after the new classification is the loss of explanatory power in the first two principal components. In the previous estimations, the first two components account for almost 90 per cent of the total variance. However, they only explain 77, 68 and 67 per cent of the total variation for high, mid and low per capita GDP rankings. There is a significant drop in the explanatory power especially for mid and low per capita GDP countries. When we focus on the first three components, they are able to explain around 80 per cent of the total variation. Second eigenvalues are greater than two and even third eigenvalues barely satisfy the Kaiser criterion. Eigenvalues are plotted in Figure 5. For the sake of consistency, we retain the first two principal components. When factor loadings are investigated, we can still see the similar pattern about GES and Gov indices. CO₂ also has a similar pattern and has a really high correlation with the second component. However, the third component does not pose a clear picture, since indices have both positive and negative correlations and the size of the correlation changes for different groups. Factor loadings of all indices are plotted in Figure 6. KMO values are above 0.75 for all groups, and that is a sign that the change in classification does not deteriorate the efficiency of PCA. Based on this final check, we still observe a similar pattern as before, supporting the robustness of our estimations.

Table 5.

Principal component analysis: Eigenvalues and Proportion explained

Principal Component	High		Mid		Low
Principal Component	Eigenvalue	%	Eigenvalue	%	Eigenvalue	%
1st	6.527	65.269	4.948	49.478	4.585	45.847
2nd	1.137	11.372	1.874	18.741	2.107	21.070
3rd	0.907	9.070	0.984	9.840	0.953	9.530
4th	0.659	6.588	0.716	7.160	0.830	8.301
5th	0.234	2.342	0.509	5.092	0.544	5.443
6th	0.210	2.102	0.422	4.219	0.390	3.902
7th	0.160	1.604	0.193	1.931	0.184	1.841
8th	0.097	0.969	0.175	1.747	0.162	1.618
9th	0.050	0.500	0.124	1.240	0.133	1.332
10th	0.018	0.184	0.055	0.553	0.112	1.117

Source: Authors’ calculations.

Table 6.

Principal component analysis: Coefficients

Variable	High			Mid			Low
Variable	1st	2nd	3rd	1st	2nd	3rd	1st	2nd	3rd
GDP	0.280	–0.014	0.647	0.207	0.498	–0.419	0.310	0.368	0.241
Business	0.301	0.333	–0.385	0.335	–0.096	0.481	0.258	–0.218	–0.496
Freedom	0.311	0.337	–0.354	0.382	–0.168	–0.030	0.188	–0.352	–0.167
GES	0.376	–0.025	–0.042	0.357	0.184	0.239	0.396	0.203	–0.115
HDI	0.309	–0.207	0.270	0.244	0.491	–0.315	0.337	0.410	–0.095
CO₂	–0.071	0.845	0.383	0.055	0.503	0.634	0.323	0.432	–0.027
Risk	0.257	–0.090	0.266	0.221	–0.298	–0.067	0.188	–0.217	0.797
Gov	0.374	–0.092	–0.118	0.423	–0.040	–0.045	0.376	–0.227	0.089
Cor	0.378	–0.020	0.002	0.334	–0.295	–0.012	0.350	–0.316	–0.045
Cor Ind	0.380	–0.008	–0.054	0.412	–0.095	–0.165	0.359	–0.315	0.009

Source: Authors’ calculations.

Figure 5.

Source: Authors’ calculations.

Figure 6.

Source: Authors’ calculations.

VI. Conclusion

In this study, we analysed 10 common indices used in economics to understand where a country stands in terms of economic activity and development. Utilizing the method of PCA, we solved the dimensionality problem associated with a proliferation of indices, and reduced the number of dimensions from 10 to 2. We find that the first two principal components are able to account for around 90 per cent of the total variance. One main finding is that there is a consistency in the correlation of variables with the first component. All indices have a positive contribution and the indices that have the highest correlation with the first component are GES, Gov and Cor (or Cor_Ind). Therefore, looking at these indices can provide a rough picture about where a country stands in indices. However, the second component has different implications. Only CO₂ has a high and positive correlation with the second component and other variables have both positive and negative correlation in different rankings. Regional comparisons suggest that Asia’s economic structures, as implied by the rankings, may be closer to those of Europe and North America than South America and Africa.

We also check whether PCA is able to extract useful information based on the KMO criterion. Our calculations point that the KMO value is 0.5 for South America and ranges between 0.7 and 0.9 for other rankings. Since the minimum KMO value to use PCA is 0.5, we can conclude that PCA is efficiently applied to our dataset.

As a robustness check, we make two alterations. First, we exclude the GDP variable from our dataset due to endogeneity between GDP and other indices. Second, we classify countries into three groups instead of splitting them into global and regional groupings. The exclusion of GDP does not make any difference. First, two components are retained and they still have a similar explanatory power. While GES and Gov have a high correlation with the first component, CO₂ has a high correlation with the second component. However, reclassification of countries reduces the explanatory power of the first two components. Instead, we retain the first three components. Likewise, we still observe the same pattern for GES, Gov and CO₂. Either of the changes does not deteriorate the test of sampling adequacy. In summary, we show that our estimations are robust and the pattern does not change.

An evident area for further research is to have time-series data. In our study, we collected indices from a single year. The indices can be obtained for a time interval and analysed whether our findings would still be valid for different time periods. Another area of research would be to include FDI data and use principal components instead of indices as regressors. The determinants of FDI have been extensively studied in the literature but using principal components would make an important contribution. Analysing the relationship of measures of trade openness as well as capital openness might provide further insight into the reasons for Asia’s economic structures, as implied in the PCA, are more similar to those of Europe and North America than the other two regions, Africa and South America. Patterns of trade and investment, including global production networks, may be part of the answer.

Declaration of Conflicting Interests

The authors declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The authors received no financial support for the research, authorship and/or publication of this article.

Footnotes

Acknowledgements

We are grateful to the referee and editor of the journal for helpful comments and suggestions. We alone are responsible for remaining shortcomings.

Notes

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