A Taxonomy of Country Performance Based on GDP and Innovation Indicators for the Group of Twenty (G20)

Abstract

This chapter proposes a taxonomy of country performance based on GDP and innovation indicators within G20 economies. This study considers the impact of GDP on the “development degree” (fi) for the G20 economies and investigates how the development of G20 economies relates to the innovation promotion factors extracted from the Global Innovation Index (GII) indicators, used as the secondary data for the period 2010–2016. Various variables are used, such as population (in millions), GDP (in USD billion), and seven indicators that are extracted from the GII data. Through the evaluation process, the seven indicators are divided into input and output data; five of them are the input data (institutions, human capital and research, infrastructure, market sophistication, and business sophistication), and the other two are the output data (knowledge and technology output and creative output). The taxonomy provides the identification of country performance and presents relevant information to policymakers, who seek to apply effective economic strategies and develop global policies.

1 Introduction

A group of world’s major economies, G20¹ (Group of Twenty), as a leading global forum, seeks to apply effective economic strategies and develop global policies. Thus, the group attempts to promote innovation and economic growth, by utilizing accumulative capabilities, based on existing resources. The most important resources are represented by some indicators to provide proper patterns toward methodical and stable development.

The G20 brings together substantially important advanced economies that account for over 85% of global GDP² and two-thirds of the world’s population (G20.org. Archived). Nowadays, economic growth has an impact on increasing competitiveness and innovation among nations like G20 countries and the European Union.³ G20 was formed in 1999 (consisting of 19 major economies plus the European Union⁴) for international collaboration in the promotion of global financial stability (Goedhuysa and Veugelers 2012).

During the depression years (especially from 2010 to 2012), the G20 economies faced many challenges that are manifested in GDP.⁵ An estimate of GDP growth for the G20 aggregate, on the basis of quarterly seasonally adjusted data (as reported by G20 members), is rendered by the OECD⁶ secretariat:

• Growth of real gross domestic product (GDP) in the G20 area⁷ was stable, at 0.9%, in the first quarter of 2017, according to provisional estimates and comprehensive information chosen from the OECD report (in 2016).

• Growth picked up in Korea (to 1.1%, from 0.5%) and, to a lesser extent, in Canada (to 0.9%, from 0.7%), Germany (to 0.6%, from 0.4%), and Italy (to 0.4%, from 0.3%). Real GDP also grew by 1.0% in Brazil.

• Growth was unchanged in India (at 1.5%), Indonesia (1.2%), Mexico (0.7%), the European Union (0.6%), and Japan (0.3%).

• On the other hand, economic growth slowed markedly in Turkey (to 1.4%, from 3.4%) and Australia (to 0.3%, from 1.1%).

• Growth also weakened in the United Kingdom (to 0.2%, from 0.7%), China (to 1.3%, from 1.7%), the United States (to 0.3%, from 0.5%), and France (to 0.4%, from 0.5%).

In South Africa, GDP declined further (to −0.2%, compared with a drop of 0.1% in the previous quarter).

Innovation policies and technology advancement create new economic benefits and opportunities to boost economic growth and lead to improvement in quality of life. A mix of innovative and highly productive industries promotes economic growth and stability, with information and communication technology playing a key role (Atkinson and Stewart 2012).

Indeed, recently an increasing general policy focus on innovation progress is observed, and not only innovation is remarked as the central phase in economic policymaking, but the perception of a coordinated, coherent, “whole-of-government” approach requirement is emphasized. This encompasses knowledge absorption and exploitation from R&D across countries and industries, and also fruitful cooperation among researchers and scientists (Van de Ven and Johnson 2006).

Access to knowledge depends on the type of research and development (R&D) activities and network governance among companies (Zalewski and Skawinska 2009). Many OECD member countries have adopted national strategic road maps to innovation and enhance its economic impacts (OECD 2017).⁸

Investing in the knowledge has produced a composite indicator of “investment in knowledge” made up of investment in R&D, investment in higher education, and investment in IT software. By this input measure, we can identify three groups of economies.⁹

• High knowledge investment economies of North America, OECD Asia, and Japan, investing around 6% of GDP

• Middle knowledge investment economies of Northern Europe and Australia, investing between 3% and 4% of GDP

• Low investment economies of Southern Europe, investing between 2% and 3% of GDP

In this decade, many transitions have occurred crucially in technology, and the developed economies achieved significant improvements. These countries generate strength and the ability to grow in the global economy. This capability in technology consists of many major elements, for instance, GDP growth, innovation, and entrepreneurship. In contemporary thinking on economic growth, one of the main views is that technological change inherently creates growth in economy (Hu and Png 2013).

The ICT sector for the European Union, the United States, and Japan is the largest R&D-investing sector.¹⁰ The most considerable percentage of incomes in the ICT industry businesses is spent on R&D in the European Union (Veugelers et al. 2012).

The innovation subindexes rendered by GII emphasize on institution, infrastructure, research, knowledge, and technology as the determining components, highly significant in promoting economic development (GII 2017).

The societies demonstrate evidences of expanding in many layers of the economy. The interest of economists in the sources of long-run economic growth has led to exploring the role of innovation in creating growth (Encaoua et al. 2000).

R&D as the efficient force behind innovation supports economic growth. This goal achieved through effective communication, knowledge sharing, valuable information utilization, and use of appropriate channels of communication depends mainly on workforce abilities and skills, e.g., social capital, collaboration, and co-creation of both individuals and organizations. Trust within individuals and organizations is determinant in its effectiveness (Romuald and Eulalia 2009). Organizations operating on the R&D innovate a new product or process, thus extending markets and sales, promoting investment, and ultimately creating position for vocations. These firms and organizations take advantage of shared knowledge and expertise and are often the first to modify new products and generative technologies.¹¹ Figure 1 depicts the area of a business that would benefit most from innovation.

Fig. 1

The area of a business that would benefit most from innovation (% of respondents). Source: www.cbi.org.uk (Annual Conference London 2016) (authors’ own figure)

2 Methodology

Innovation in the GII (Global Innovation Index) consists of two categories, input and output data. Input’s subindexes include institutions, human capital and resources, infrastructure, market sophistication, and business sophistication factors. Output’s subindexes are knowledge, technology outputs, and creative outputs (Framework of the Global Innovation Index 2016). GII as a renowned international index which is published annually, in its 2017 report, included 127 countries which stand for 92.5% of the world population and 97.6% of world’s GDP. GII overall index is the simple statistical average of five input indexes and two output ones, which are summarized in Table 1.

Table 1 Input and output indexes which constitute the overall GII

The GII indexes (2010–2017) corresponding to the G20 countries, together with two additional indicators, i.e., population and GDP, are compared by application of “numerical taxonomy” analysis (using matrix operations) during 2010–2016. Figure 2 depicts a description of the methodological steps.

Fig. 2

Description of methodological steps. Authors’ own figure

This method of analysis forms matrices containing dimensionless elements (replacing quantities with different units of measurement or dimensions), enabling comparison of indicators by computing dimensionless numbers for matrix elements (Forouharfar et al. 2018; Sazegar et al. 2018).

A method of selecting from a data matrix the characters most likely to lead to valid conclusions is put forward, based on the concept of a uniquely derived character and its logical consequences (Le Quesne 1969). As explained in the next section (and subsections), following final measurements, a development factor (fi) is obtained with a quantitative value between zero and unity, such that an economy with a factor value less than others and closer to zero would be more developed than those closer to unity (Forouharfar et al. 2018; Sazegar et al. 2018).

3 Computations of Comparative Indexes

The computations proceed in seven steps described in the following subsections (Le Quesne 1969; Phillips 1983; Forouharfar et al. 2018; Sazegar et al. 2018).

3.1 Step 1: Development of the Data Matrix

Consider:

$$ {X}_{oj}=\left({\sum}_{i=1}^n{X}_{ij}\right)/n $$

(1)

The purpose of step 1 was to develop a matrix with “n” members (1, 2, 3, …, n) to represent the variables as a group. The variables were shown with “m” (as an indicator of each study). The matrix, as it was shown in Eq. (1), consisted of “i” rows and “j” columns. Thus, the data matrices of the G20 countries were formed by using the GII’s indexes data from 2010 to 2016, as shown in Tables 2, 3, 4, 5, 6, 7, and 8. It should be noted that each indicator (for the scores of the indexes and subindexes) was normalized. In the tables that follow, the subindexes of the innovation input and output for each year are placed in columns. Additionally, population, GDP, and five subindexes of institution, human capacity, infrastructure, market sophistication, and business sophistication (1–7), besides the two subindexes of knowledge (scientific outputs) and creative outputs (8–9), comprise the (GII) innovation input index and innovation output index, respectively.

Table 2 GII’s data matrix for G20 countries in 2010

Table 3 GII’s data matrix for G20 countries in 2011

Table 4 GII’s data matrix for G20 countries in 2012

Table 5 GII’s data matrix for G20 countries in 2013

Table 6 GII’s data matrix for G20 countries in 2014

Table 7 GII’s data matrix for G20 countries in 2015

Table 8 GII’s data matrix for G20 countries in 2016

Considering that the European Union (EU) is also a G20 member, consisting of 28 countries, the data for the EU was obtained as an average of each indicator for the EU members within the time span of 2010–2016.

3.2 Step 2: Forming the Standard Matrix

Since the indicators have different units of measurement (dimensions), a “standard matrix” is formed, containing dimensionless elements Z_ij:

$$ {S}_j=\sqrt{\sum_{i=1}^n\Big({X}_{ij}-{\overline{X_j\Big)}}^2/n} $$

(2)

$$ {Z}_{ij}=\left(\ {X}_{ij}-{X}_{oj}\right)/{S}_j $$

(3)

“X_ij” is a data matrix, “X_oj” is an average matrix (Eq. 1), and “S_j” denotes the standard deviation for “j” indicators, which are derived from the GII reports for 2010–2016. Thus, in this data analysis, “i” represents the G20 countries in the above time period. The corresponding standard matrices were computed and presented in the tables that follow. Moreover, eliminating the discrepancy between the indicators’ units (by generating scale-free indexes) renders average = 0 and standard deviation = 1 in the Z matrix. Thus, “Z” matrix acceptability could be controlled for the required computations, as shown in Tables 9, 10, 11, 12, 13, 14, and 15.

Table 9 Standard matrix for 2010

Table 10 Standard matrix for 2011

Table 11 Standard matrix for 2012

Table 12 Standard matrix for 2013

Table 13 Standard matrix for 2014

Table 14 Standard matrix for 2015

Table 15 Standard matrix for 2016

3.3 Step 3: Computing Compound Distances Among the G20 Economies

Compound distances between the G20 economies are measured by

$$ {D}_{ab}=\sqrt{\sum_{i=1}^n{\left({Z}_{aj}-{Z}_{bj}\right)}^2} $$

(4)

where D_ab is the distance between any two economies “a” and “b.” Thus,

$$ {D}_{aa}=0 $$

$$ {D}_{bb}=0 $$

$$ {D}_{ab\kern0.5em}={D}_{ba} $$

Therefore, as shown in the following tables, the compound distance matrices “D” computed for the G20 countries are symmetric, and their diameter elements are equal to zero. As seen, each element D_ab in the matrices D shows the distance between two countries (a, b), as numbered in Tables 16, 17, 18, 19, 20, 21, and 22.

Table 16 Compound distance matrix for G20 countries in 2010 (“D” matrix)

Table 17 Compound distance matrix for G20 countries in 2011 (“D” matrix)

Table 18 Compound distance matrix for G20 countries in 2012 (“D” matrix)

Table 19 Compound distance matrix for G20 countries in 2013 (“D” matrix)

Table 20 Compound distance matrix for G20 countries in 2014 (“D” matrix)

Table 21 Compound distance matrix for G20 countries in 2015 (“D” matrix)

Table 22 Compound distance matrix for G20 countries in 2016 (“D” matrix)

3.4 Step 4: Assignment of the Shortest Distances

In this step of the methodology, the cells exhibit the gaps between the economies. Every matrix “D” line defines the distances between the economies; i.e., the lowest value in each line is marked to be the shortest distance of that economy in the year of measurement. For instance, there is the most approximation among two economies if “a” and “b” have the shortest distance, that is, economy “b” is a model for economy “a” and economy “a” is named a shade. The shortest distances between the economies in the years 2010–2016 are shown (highlighted in green) in Tables 16, 17, 18, 19, 20, 21, and 22.

3.5 Step 5: Optimum Chart Drawing

In the drawing of the optimum chart, economies which have the most commonalities are connected by designating a vector toward the economy which is considered as the model with the vector length equal to the shortest distance between the economies. For determining homogeneous economies, at first, upper-line distance d(+) and lower-limit distance d(−) were computed, using Eqs. (5) and (6), where d is the shortest distances’ average and S_d is the standard deviation:

$$ d\left(+\right)=d+2{S}_d $$

(5)

$$ d\left(-\right)=d-2{S}_d $$

(6)

It is to be noted that 95.45% of data lie within a band around the mean in a normal (Gaussian) distribution with a width of four standard deviations, i.e., −2S_d to +2S_d(Le Quesne 1969; Phillips 1983).

Furthermore, after calculating d(+) and d(−) for the G20 economies in 2010–2016 from Eqs. (5) and (6), it became evident that the distances among the economies should not be out of upper d(+) and lower d(−) limits range for the years 2010 to 2016; if each economy is out of the range d(−) and d(+), it has to be set aside, and then the other economies pass through this process until the remaining economies are settled within d(−) and d(+) range. This leads to a homogenous group of economies that could be compared with one another. Then the countries are connected by vectors. Consequently, the optimum charts, or “optimum graphs,” for the years 2010–2016 are shown in Figs. 3, 4, 5, 6, 7, 8, and 9.

Fig. 3

Final values of the shortest distances between economies in the optimum graph for 2010. Source: Authors’ own work based on analyzed GII data

Fig. 4

Final values of the shortest distances between economies in the optimum graph for 2011. Source: Authors’ own work based on analyzed GII data

Fig. 5

Final values of the shortest distances between economies in the optimum graph for 2012. Source: Authors’ own work based on analyzed GII data

Fig. 6

Final values of the shortest distance between economies in the optimum graph for 2013. Source: Authors’ own work based on analyzed GII data

Fig. 7

Final values of the shortest distances between economies in the optimum graph for 2014. Source: Authors’ own work based on analyzed GII data

Fig. 8

Final values of the shortest distances between economies in the optimum graph for 2015. Source: Authors’ own work based on analyzed GII data

Fig. 9

Final values of the shortest distances between economies in the optimum graph for 2016. Source: Authors’ own work based on analyzed GII data

3.6 Step 6: Ranking of the Economies in Terms of Improvement and Development

According to step 5, if the G20 economies are not settled in homogeneous groups, then the new data matrix could be formed for homogenous group of economies, and again the standard matrix can be computed. In the standard matrix, the largest value in each column can be found and named the “ideal amount.” It is noteworthy that for development being a positive function of the indicators, the largest value is the “ideal amount,” and the lowest value is the shortest distance between two economies.

In this chapter, the twenty reviewed economies do not all settle in an equally seamlessly space. Hence, the computation process was followed to achieve a homogeneous group, by calculations in a process of eight steps, for every year from 2010 to 2016 with the outranging data. Thus, an acceptable seamlessly space of distinct economies was obtained (with similar economic features) which could be measured and compared to distinguish the degree of development in economies in order to present a benchmark pattern for development. The calculation processes are shown in Tables 23, 24, 25, 26, 27, 28, and 29.

Table 23 The eighth round of the homogenization process for the year 2010 (the shortest distances between economies highlighted in blue)

Table 24 The fifth round of the homogenization process for the year 2011 (the shortest distances between economies highlighted in blue)

Table 25 The sixth round of the homogenization process for the year 2012 (the shortest distances between economies highlighted in blue)

Table 26 The fourth round of homogenization process for the year 2013 (the shortest distances between economies highlighted in blue)

Table 27 The fourth round of homogenization process for the year 2014 (the shortest distances between economies highlighted in blue)

Table 28 The second round of homogenization process for the year 2015 (the shortest distances between economies highlighted in blue)

Table 29 The third round of homogenization process for the year 2016 (the shortest distances between economies highlighted in blue)

For instance, the results of the homogenization process for the year 2010 suggested elimination of China and the United States and then India, the European Union, Japan, Brazil, Indonesia, and Russia, in successive steps of the homogenization process calculations. These results are illustrated in Table 23, and Fig. 3 demonstrates the compound distances between homogenous economies.

Similarly, the results for the year 2011, again, suggested elimination of China and the United States and then India, the European Union, Japan, and Indonesia in consecutive steps of homogenization process calculations. The corresponding results are presented in Table 22 and Fig. 4.

Moreover, based on the results for the year 2012, China, the United States, India, the European Union, Japan, Indonesia, and South Korea were omitted in continued steps of homogenization process calculations. These results are depicted in Table 25 and Fig. 5. It is observed that within the G20 economies, only thirteen economies remained in the homogenization process after six rounds of computations.

Subsequently, for the year 2013, in the fourth round, the results lead to omission of China, the United States, India, the European Union, and Indonesia in the consecutive steps of homogenization process calculations. The results are shown in Table 26 with Fig. 6.

Furthermore, for the year 2014, China, the United States, India, the European Union, and Indonesia were eliminated in the successive steps of homogenization process calculations. The results are rendered in Table 27 and Fig. 7.

Nevertheless, in the year 2015, the second round leads to deletion of China, India, the United States, and the European Union in the consecutive steps of homogenization process calculations. This process is demonstrated in Table 28 and Fig. 8.

Finally, in 2016, the third round leads to omission of China, the United States, India, and the European Union in the consecutive steps of homogenization process calculations. Table 29 with Fig. 9 presents the corresponding results.

3.7 Step 7: Calculation of the Economies’ Development Degrees

To find development degrees (fi) for the economies within the G20 group, Co, i.e., the upper limit of the development pattern should be measured for substitution in the following relationship:

$$ \mathrm{fi}=\left(\mathrm{Cio}/\mathrm{Co}\right) $$

where Cio is development pattern over the upper limit of the development pattern and Co is obtained from Eq. (7):

$$ \mathrm{Co}=\overline{\mathrm{Cio}}+2\ \mathrm{Sio}, $$

(7)

where $\overline{\mathrm{Cio}}$ and Sio are the average and standard deviation of the development pattern corresponding to fi (Le Quesne 1969; Phillips 1983).

The development degree is between “0” and “1,” that is, when “fi” values get near to “0,” the economy is more developed than the case “fi” approaches to “1”; namely, the economy gets close to less developed characteristics. By measuring Cio and fi, the economies were ranked based on the development degrees. In this step, results obtained for the G20 economies lead to the development degree (fi) for each of the economies, as presented in Tables 30, 31, 32, 33, 34, 35, and 36.

Table 30 Development degrees for 2010

Table 31 Development degrees for 2011

Table 32 Development degrees for 2012

Table 33 Development degrees for 2013

Table 34 Development degrees for 2014

Table 35 Development degrees for 2015

Table 36 Development degrees for 2016

4 Conclusion

In this chapter, population and GDP, together with seven indicators, extracted from the Global Innovation Index (GII), were used in the measurement of the “development degree” for G20 countries. It was remarkable not only to find out the indicators most effective on the development degrees but also to rank the G20 economies on this basis, as shown in Tables 30, 31, 32, 33, 34, 35, and 36 for the period 2010–2016.

Scrutinizing the selected indicators measuring the development degrees leads to significant remarks. The United States and China having the largest GDP among these countries during 2010 to 2016 underwent elimination from the group in the first round of iterations for homogeneity (leading to a homogenous group of economies that could be compared with one another). In Tables 16, 17, 18, 19, 20, 21, and 22, compound distance matrices were rendered for the first round of iterations during 2010–2016. Computations for similar homogenous economic groups finally lead to country performance rankings (based on the economic development degrees in consecutive years) presented in Tables 23, 24, 25, 26, 27, 28, and 29.

From the 20 economies within the G20, in 2010, 12 economies formed the homogenous category. Similarly, 14, 13, 15, 16, and 16 economies formed the homogenous categories, corresponding to the years 2011, 2012, 2013, 2014, 2015, and 2016, respectively. Nonetheless, throughout the entire homogenization iterative processes, the United States, China, the European Union (EU), and India were set aside to achieve homogeneity, with the employed GII data. These countries have highest populations (China, India, and EU) or largest GDPs (the United States, China, and EU) compared to others. It is also noted that the EU encompasses 28 countries (some of them members of G20). Hence, the data for the European Union were prorated; i.e., for GDP and the other indicators, the average values over 28 countries and, for population, the sum of populations of the 28 member countries were calculated and used in each year.

Subsequently, the development degrees “fi” for every year were computed and shown on the left side of Tables 30, 31, 32, 33, 34, 35, and 36. The right side of each table also ranks the countries based on their development degrees. It was noted that the development degrees were between “0” and “1,” that is, when “fi” values get near to “0,” the economy is more developed than the case “fi” approaches to “1”; namely, the economy gets closer to less developed characteristics. For instance, in 2010, Germany with a development degree of 0.369 (fi = 0.369) is observed to be the most developed, and Argentina with a development degree of 0.91 (fi = 0.91) is marked as the least developed. Thenceforth, the United Kingdom and Japan appear to alternate as the most developed, while Argentina remains (alternating with Turkey only in 2012) the least developed in the years 2011 to 2016. Moreover, based on the GII data used in this research (setting aside the United States, China, EU, and India for homogenous grouping), it was explored that Germany, the United Kingdom, and Japan made the most progress in development during 2010–2016. However, as outlined in Tables 1, 2, 3, 4, 5, 6, and 7, the latter three are countries with higher GDPs and other indicators such as institutions, market sophistication, etc., contributing to innovation and prosperity.

Nevertheless, in the course of development degrees computations, shortest distances between the G20 economies were also generated. The results were yielded in Tables 23, 24, 25, 26, 27, 28, and 29 and Figs. 3, 4, 5, 6, 7, 8, and 9, which can be useful for benchmarking within the Group of Twenty.

Finally, for future research, use of the following indicators may be suggested:

• Human Development Index (HDI)—which includes GDP, education, and health

• Gini coefficient as a measure of inequality in society

• Environmental sustainability, including factors such as pollution, climate change, deforestation, etc.

• The United Nations’ Sustainable Development Goals

• Inclusion of the following forms of capital (as defined by the United Nations): human capital, social capital, and natural capital