An alternative index to the global competitiveness index

This paper reviews the methodology used by the World Economic Forum (WEF) to create the Global Competitiveness Index (WEF-GCI). We propose an alternative competitiveness index that only includes the objective data (hard data) from the WEF-GCI and is created by applying a multivariate statistical procedure (Exploratory Factor Analysis) that allows us to determine the weights from the implicit data structure. The rankings obtained from this index have a high degree of association with those provided by the WEF. The main benefit of this index over the WEF index is that it does not include valuations from opinion surveys given to business executives and/or entrepreneurs of the countries included in the index (soft data). Consequently, the rankings from this alternative index are not affected by political biases or individual interests as it is elaborated only including officially published objective data.


Introduction
The competitiveness of a country or nation, which is the subject of this paper, is a controversial concept that has been under discussion for decades. The scientific literature on the subject offers various definitions that emphasize some of the multiple factors that may be related. Sustained economic growth, political stability, financial and banking infrastructure, the strength of exports, natural resources, the soundness of the government, and the education system, among others, affect a country's competitiveness [1].
In terms of countries, one of the leading, most quoted definitions of competitiveness can be found in the Report of the President's Commission on Competitiveness [2, p. 6], a definition which matches with the Organization for Economic Co-operation and Development (OECD). It is described as ''the degree to which a country can, under free and fair market conditions, produce goods and services which meet the test of international markets, while simultaneously maintaining and expanding the real income of its people over the longer term" [3, p. 237]. This definition refers to the competitiveness of a nation as a whole, in order to be framed within a context of macroeconomic policy, and states that the ultimate goal of a nation's competitiveness is to improve the standard of living and real income of its citizens, which can be achieved by offering goods and services at internationally competitive [4,5]. quantitative indicators in order to exclude the subjectiveness of qualitative indicators. 'The Global Sustainable Competitiveness Report' is published until today. While the WEF-GCI methodology is geared towards the long term and therefore includes a wide variety of social and environmental indicators, which allows for a sustainable perspective of competitiveness in the analyzed countries, the methodology for the index produced by the IMD is oriented towards the short term, which consequently implies more frequent changes in the positions held by the different countries over time [14]. Additionally, the trend from 2012 years is to provide a competitiveness index for geographical clusters of countries: Europe, Latin America, Asia, among others.
There is no doubt that the two most influential and well-known indices out of the aforementioned indices are those developed by the WEF and the IMD. They have both received some criticism in the academic literature, especially the use of subjective data from opinion surveys given to experts in the analyzed countries [15], and the specification of the weights assigned to the basic criteria, which is also subjective [16].
In order to get around these problems, this paper proposes an alternative competitiveness index (CSI) based only on the objective data used by the WEF to create the WEF-GCI. This index, which is computed using a multidimensional statistical technique called Principal Component Analysis (PCA), allows for the objective assignment of weights for the basic criteria as well as the factors and pillars that eventually lead to the creation of said index. As a complement to the aforementioned, we have compared the rankings provided by both indices (CSI and WEF-GCI) and quantified the degree to which the proposed index (CSI) explains the variations of the WEF-GCI in the set of analyzed countries.
Following this introduction, Section 2 briefly describes the methodology used by the WEF to create the Global Competitiveness Index (WEF-GCI). Section 3 describes data and methodology, it explains the proposed synthetic index, including the methodology used to create it and an analysis of the obtained results. Section 4, concerning to the results and discussion, compares the rankings from the proposed index and the WEF-GCI on a global scale, using the scores to analyze the relationship between them in said context. Additionally, by limiting our study to the context of the European Union and to the WEF-GCI belongs to the 2007-08 period, we are able to compare the results obtained from the two aforementioned indices with the results obtained from the European Competitiveness Index (ECI) corresponding to the 2006-07 period (last available period). Developed by the Centre for International Competitiveness, the 2006-07 ECI report is the most recent report and this is the rationale for starting with the WEF-GCI of 2007-2008. Lastly, Sections 5 and 6 present the conclusions of this study and bibliographic references, respectively.

The global competitiveness Index produced by the WEF
Since 1979, the World Economic Forum has published the annual Global Competitiveness Report, whose main objective is to provide knowledge and stimulate debate among all the stakeholders about the best strategies and policies to help countries overcome obstacles to improve competitiveness [17]. The 2011-2012 Report defines competitiveness as "the set of institutions, policies and factors that determine the level of productivity a country." It also specifies that, in turn, the level of productivity establishes the level of prosperity an economy can achieve and also determines the rates of return obtained by investments, which are essential for growth [17]. Accordingly, within the context of this definition, competitiveness involves both static and dynamic components: productivity is identified as the determining factor of a country's capacity to maintain its level of income as well as the investment returns, which is one of the basic factors in the explanation of an economy's growth potential [18].
Since 2005, the WEF has based its analysis of competitiveness on the Global Competitiveness Index (WEF-GCI), which measures the microeconomic and macroeconomic basis of national competitiveness, according to the WEF [17]. Said index is supported by twelve basic pillars that are categorized into three factors or sub-indices: Basic Requirements; Efficiency Enhancers and Innovation and Sophistication (Fig 1 offers a more detailed configuration of WEF-GCI). The exact composition of the WEF-GCI and the technical details of its computation can be reviewed on the WEF website.
Each of the three sub-indices or factors has a different weight, which depends on the stage of development in each country. Accordingly, the criteria for determining the stage of development is unique and exclusively dependent on the GDP per capita, and the limits that determine the different groups of countries are arbitrary, considering their respective stage of development. Similarly, the weights assigned to the different sub-indices in each of ups are also arbitrary (see Table 1).
Moreover, as previously mentioned, the concepts that are implicit in the pillars are not only quantified through statistical data published by internationally recognized official agencies (hard data), such as the United Nations Educational, Scientific and Cultural Organization (UNESCO), the International Monetary Fund (IMF) and the World Health Organization (WHO), but also with data from the annual opinion survey conducted by the WEF with executives from the analyzed countries (soft data). Table 2 shows the total number of indicators used to quantify each pillar for the 2007-08 and 2010-11 periods. The Table 2 also presents the number of objective indicators that form each pillar (hard data) and their percentage share of the total indicators that form each pillar. Considering the data presented in Table 2, it is noteworthy that, for both periods, the characterization of four of the twelve pillars (Institutions, Financial Market Development, Business Sophistication, and Innovation) does not involve indicators considered to be hard data, as established in this paper, and that out of the total indicators used to compute the index, only approximately 25% is hard data, with the high subjectivity this entails.

Data and methodology
The indicators used and their names for reference in future tables are listed in Table 3 and are based on most of the objective, quantitative data (hard data) from the 2007-2008 and 2010-2011 periods, which is available on the WEF website (http://www.weforum.org/). It is shown that some pillars do not consider hard data indicators. Of the total number of countries included in the WEF database, this study only involves 79, which are the countries that have complete data available corresponding to the variables included in Table 3 for the two periods under consideration.
We used the Exploratory Factor Analysis (EFA) multivariate technique to compute the proposed synthetic competitiveness indicator (CSI). This exploratory technique applies to the multidimensional data analysis of a set of elements that are described through a high number of quantitative variables and allows us to synthesize the data regarding said variables in a reduced number of latent variables or factors, which aim to explain the reality of said elements (in this case, the set of analyzed countries) in relation to the complex characteristic being studied (in this case, their competitiveness).
Since the results of the EFA are later used to compute the synthetic competitiveness indicator, which requires the factor scores, we used the Principal Component Analysis extraction method [20], retaining the factors with a higher eigenvalue than the unit [21]. The varimax orthogonal rotation procedure was applied in order to obtain the interpretation of the retained factors) [22]. Finally, we used the scores of the retained factors to create the synthetic competitiveness indicator (CSI) as a weighted average of said scores. These weights are given by the percentage of the total variance explained by each factor identified by the EFA.

Results of the exploratory factor analysis
The determinant values of the correlation matrices for the 2007-08 and 2010-11 periods, (1.02�10 −11 and 1.18�10 −11 , respectively), very close to zero, indicate the existence of linear dependence between the indicators included in this study for both of these periods and the non-existence of redundant indicators; in other words, they are the perfect linear combination of others that are also included in the analysis. Based on these determinants, we have calculated the values of the effective dependence coefficients associated with them, D 07-08 (R) = 0.6366 and D 10-11 (R) = 0.6345, which indicate the existence of a considerable degree of linear dependence between the variables involved in each of the analyzed periods. This coefficient is defined as D(R) = 1-|R|1/(P-1) where |R| is the determinant of the correlations. We know that if one of the variables is the perfect linear combination of others, which are also included in the analysis, the correlation matrix is singular, |R| = 0, and therefore, D(R) = 1. Meanwhile, if the linear correlation between different pairs of variables is null, the correlation matrix coincides with the identity, its determinant is 1 and, therefore, D(R) = 0. The comparison of the dependence coefficient with these extreme cases can give us a good idea of the degree of linear dependence between the indicators used [23].
As a complement to the linear dependence analysis, we calculated the KMO index (Kaiser-Meyer-Olkin). For this analysis, the values of the KMO index are 0.824 and 0.790, respectively. They are both higher than the minimum recommended value for this type of study (0.5) and, therefore, the application of this methodology is considered to be acceptable. According to the factor analysis model, the theoretical correlation coefficients calculated between each pair of unique factors are null by hypothesis. If the partial correlation coefficients approach said theoretical coefficients, they must be close to zero and, therefore, the value of the KMO index should be close to 1. Values of the KMO measurement below 0.5 are not acceptable [24]. Table 4 includes the eigenvalues associated with the retained factors, the percentage of the total explained variance for each of these factors after the varimax rotation and the accumulated percentage. This table shows that competitiveness can be synthesized in seven factors for the two analyzed periods, according to the criteria based on selecting the factors associated with higher eigenvalues than the unit [21]. These factors explain 77% and 76.5% of the total variability, an acceptable percentage considering that the lower limit of acceptability for studies in the social sciences is 60% [25]. Table 5 shows the factor loading matrices after the varimax rotation or rotated component matrices, which are formed by the linear correlation coefficients between the factors and the indicators used to estimate them. In order to facilitate the interpretation of said factors, in terms of the different aspects related to the competitiveness of said factors, the coefficients that have an absolute value greater than 0.4 are shaded in a darker color.
In regard to the interpretation of the retained factors, it should be noted that the only factor that is common to both periods (C5) is the one that includes the variables related to the macroeconomic environment (Pillar 3), with the exception of inflation (Pillar3X3). Said factor explains approximately 7% and can be called "Government budget balance, savings and debt." Meanwhile, other factors related to the 2007-08 period, such as C3, C4, and C6, could be identified in 2010-11 with C2, C3, and C6, respectively, since the variables that have higher correlations with each of these factors are the same for both periods. Accordingly, C3 (2007-08) has high correlations with the variables that quantify inflation (Pillar3X3) and the number  of days and procedures required to start a business (Pillar6X3). The loading for this factor, C3, for the 2007-08 period also includes the variable that quantifies the costs of layoffs (Pillar 7), although it is less significant than those previously mentioned. Therefore, we call this factor  "Inflation and ease of doing business," which is identified with C2 for the 2010-11 period and explains 9.6% (9.7%) of the total variability. Similarly, C4 (2007-08) can be called "Foreign trade," since the higher correlations correspond to the percentage of imports (Pillar6X4) and exports (Pillar10X1) in the GDP. This factor is identified with C3 (2010-11) and explains 8.8% (8.9%) of the total variability. Lastly, the variables that quantify the number of the country's inhabitants and income (both ancillary, Anc3 and Anc2, GDP per capita as a proxy of citizen's income) are included in C6 for both periods. This factor, C6, which we call "Overall country size," explains 6.1% (6.4%) of the total variability. Note it presents a weak, negative correlation with the normalized variable that quantifies the total tax rate (Pillar6X1) for the 2007-08 period, while it appears to be correlated with the Gross National Savings for the 2010-11 period (Pillar3X2). Theoretically, we cannot establish as clear of a correspondence for the remaining factors in the 2007-08 period and the 2010-11 period as those described in the previous paragraph. However, C1 presents intense correlations with the variables related to infrastructure (Pillar 2), innovation (Pillar 9), education (Pillars 4 and 5), per capita income (Anc2) and some health-related variables (infant mortality, Pillar4X4, and life expectancy, Pillar4X5) for both periods. This factor also appears to be associated with other health variables, cases of malaria (Pillar4X1) and tuberculosis (Pillar4X2) for the 2010-11 period. It presents a weak correlation with the women's participation in the labor market (Pillar7X2) for the 2007-08 period and the number of procedures required to start a business (Pillar6X2). According to the structure of said factor (which is common to both periods), a possible name could be "Human development and ease of communication." This factor explains 28.4% (31.5%) of the total variability.

Eingen values Extraction Sums of Squares Loadings Rotation Sums of Squares Loadings
Meanwhile, the C2 factor (12% of the total variability) for the 2007-08 period unites all of the variables that quantify health-related aspects, even those that appear to be accounted for in Factor C1. However, this factor is not exclusive of health for the 2010-11 period, but some of the variables included in this factor (such as life expectancy and cases of tuberculosis and HIV) are correlated with C4 (8.2% of total variability). It is surprising that said component presents a high negative correlation with the variable that quantifies women's participation in the labor market (Pillar7X2). According to the above, Factor C2 (2007-08) could be called "Health," but we cannot find an appropriate name or clear interpretation for Factor C4 (2010-11).
The last component (C7) appears to be associated with the labor market (Pillar 7) for the 2007-08 period, both in terms of the cost of layoffs (Pillar7X1) and women's participation in the labor market (Pillar7X2). The name ("Labor market") is clear and explains 5.4% of the total variability. For the 2010-11 period, this component presents moderate, positive levels of correlation with the variables that quantify the cost of layoffs, the total tax rate (Pillars6X1) and the number of procedures required to start a business (Pillars6X2), as well as a moderate, negative correlation with the participation in primary education (Pillar5X1). This factor could complement the data on "ease of doing business" provided by Factor C2 for the same period, but the negative correlation that said factor has with participation in primary education makes its interpretation more complicated. Table 6 presents a summary of the names of the factors identified in the two periods under consideration, their identification with the corresponding component, and the pillars that encompass the variables that allow for their interpretation.
The data provided by the scores of the retained factors have been synthesized in a sole index, the synthetic competitiveness index (CSI), which summarizes the situation of each of the analyzed countries in terms of competitiveness. Said indicator was obtained as a weighted average of the scores for the seven retained factors, using the percentage of the total variance explained by each factor as the weight of the score for each factor.
It should bear in mind other relevant factors not considered in this WEF indicators, so, these missed relevant factor are given 0% of the total explained variance. Be aware, there is not included hard data into the following pillars: the Pillar 1 -Institutions-, the Pillar 2 -Financial market development-, the Pillar 11 -Business sophistication-and the Pillar 12-Innovation-.
The following section presents an analysis of the results of said indicator for the two analyzed periods.

Rankings and geographic distributions: WEF-GCI versus CSI
This section presents a comparison of the rankings provided by the proposed index (CSI) and the WEF-GCI, on a global scale. Table 7 shows the rankings from the CSI and WEF-GCI for the analyzed countries and periods.
We use the scores to analyze the geographic distribution of the indices within said context and the relationship between the two. Additionally, limiting our study to countries in the European Union, we have compared the results obtained for the 2007-08 period for the two aforementioned indices with those from the European Competitiveness Index (ECI) for the 2006-07 period.
Considering the classification presented in Table 7, according to the CSI, we can see that the most competitive countries for the two analyzed periods are Singapore and Norway. Similarly, although it may seem obvious, the two indices provide different rankings, both in terms of the majority of the countries that are classified as the most competitive according to the WEF-GCI (the first 20 countries) and the majority of the countries that are classified as the least competitive (the last 20 countries), which remain in the same group according to the alternative index CSI.
Meanwhile, based on the rankings shown in Table 7, the correlation coefficients have been calculated according to Spearman's rank correlation corresponding to the rankings provided by both indices in Table 8. This coefficient quantifies the degree of association between the two rankings and indicates their direction, as well as the association between the WEF-GCI for the countries analyzed in this study, which is statistically significant, positive and high.   Table 9 presents a summary of the countries that are among the least competitive (first quintile) and the most competitive (last quintile), respectively, for the two analyzed periods, according to both indices. In turn, the country distribution considering their scores in the GCI and CSI for the two analyzed periods is shown in Figs 2, 3, 4, and 5. The geographic representation is based on the quintiles (values that divide the corresponding distribution into five types, each with the same number of countries, approximately).
In summary, and in terms of the evolution of the countries positioned in the first and fifth quintiles, it is noteworthy that for both periods, the majority of the least competitive countries are located in Africa, except for Cambodia, while the most competitive countries are located in Australia (Oceania), United States (America), Singapore (Asia), and others in Central and Northern Europe (Denmark, Finland, Holland, Norway, Sweden, and Switzerland). According to Loo (2012), Singapore was ranked 1st in the rank using an average between IMD-WCY and WEF-GCI. Moreover, the 2012 GSCI report [13] indicates that countries in northern Europe are the leading countries: Denmark-rank 1-, Sweden-rank 2-Norway-rank 3-have the highest rakings, although this index is proposed from a sustainable perspective.
Furthermore, in terms of the evolution of the WEF-GCI over time (see Figs 2 and 4), it should be noted that the composition of the first quintile for the two time periods is very similar and over 50% of the countries classified in this quintile are on the African continent. Similarly, all of the countries classified in the last quintile for the 2007-08 period, except for Israel,   Finally, the CSI shows a very similar evolution as mentioned in the previous paragraph (see Figs 3 and 5). Accordingly, the majority of the least competitive countries maintain their position in the two analyzed periods and are generally African countries. Meanwhile, the most competitive countries for both periods belong to Oceania (Australia), America (United States), Central and Northern Europe (Denmark, Finland, Holland, Norway, Sweden, and  Switzerland), and Asia (Singapore). Furthermore, there is a group of countries that, relatively speaking, experienced a decline in the 2010-11 period as compared to the 2007-08 period: Canada (America), Ireland, Iceland (Europe), and Taiwan (Asia). At the same time, other countries' relative competitiveness improved from one period to the next: Austria, Germany, Estonia (Europe), and Oman (Asia).

Competitiveness in Europe: WEF-GCI, CICUW-ECI and CSI
In terms of the competitiveness of European countries for the 2007-08 period, as previously mentioned, this section compares the results obtained for the two aforementioned indicators with those corresponding to the European Competitiveness Index (ECI) for the 2006-07 period. This comparison is based on the data in common among 22 countries: Germany, Austria, Belgium, Denmark, Spain, Estonia, Finland, France, Greece, Holland, Hungary, Ireland, Italy, Latvia, Lithuania, Norway, Poland, Portugal, United Kingdom, Czech Republic, Sweden, Switzerland. The association between the rankings based on the scores of said indices, measured by Spearman's correlation coefficient, is considered to be statistically significant, positive, and high for the different pairs considered in this study, as shown in Table 10.

Discussion
Depending on what indicators are used to measure competitiveness, the outcome will be different. The eternal question: What is the best index? Depend on the economic and political interest of countries: from the USA's point of view, from Switzerland's point of view or Singapore's perspective, among other countries. These rankings are guides for relevant decisions such as the investment in countries as usually is going to be directly related to the more competitive countries instead of to the less competitive ones.
Regarding the countries, different sizes, geographical location, populations, political situations, or climate are other characteristics to take into account in order to elaborate an index. The elaboration of the competitiveness index for geographical areas by WEF in last recent years has filled a gap in the need to consider the geographical location, which in our opinion is more reasonable than producing a unique world ranking.
Moreover, in any elaboration of an index, there is subjectivity as humans are involved in the process. However, it is not questionable that inside the subjectivity, our proposed index is less manipulable for humans as no survey opinions are included. Some results are supported by literature as in the case of Singapore. According to Loo [26], Singapore was ranked 3rd using an average between IMD-WCY and WEF-GCI during the period 2007-2011, and in the period 2009-2011 was ranking the first one. Moreover, Loo states there is still a controversial opinion concerning the different rankings provided by WEF and IMD, both Switzerland-based institutions. Nevertheless, these two indices keep being the most authoritative sources in global competitiveness. In 2012, Loo states the need for a third organization to measure competitiveness in order to conciliate both results WEF and IMD. One year later, in 2013, the first report of SolAbility-GSCI [13] only using quantitative indicators was published by this South Korean company and maintains the publication currently but from the perspective of sustainability. It could be questioned the importance in using the WEF-GCI but the transparency of the information (freely available online) and continuation in yearly published since 1979 are relevant advantages of using this index.

Conclusions
Based on a review of the methodology used by the WEF to compute the global competitiveness index, we can conclude that there is a very high percentage of qualitative data in the total data used (approximately 75%), which results in the subjectivity of the index. This subjectivity is accentuated by the arbitrary selection of weights, both for those that quantify the percentage of the different indicators in the corresponding pillar and those that indicate the importance of each pillar in the total, where the latter are also almost exclusively dependent on the country's income level.
Additionally, the rankings provided by the WEF for the two analyzed periods include the countries for which there is no data for certain quantitative indicators (hard data) in the database the WEF provides as a basic instrument to analyze global competitiveness with the GCI. This suggests that this agency has performed some sort of data treatment to account for the missing values, either through estimation or substitution; nevertheless, the treated values are not included in said database.
This paper proposes an objective global competitiveness index that exclusively uses the data provided by the WEF and quantifies to what degree the resulting rankings are associated with those corresponding to the GCI. This index only encompasses quantitative indicators (hard data) used by the WEF and is computed by applying the multivariate exploratory technique of factor analysis, which ensures the elimination of qualitative data and, consequently, the subjectivity of the weighting.
The rankings provided by the proposed index (CSI) present a high degree of association with the rankings from the Global Competitiveness Index (GCI) for the two analyzed periods. Similarly, when limited to the European context, the association between the CSI index and the European Competitiveness Index (ECI) is not only maintained, but rather increases.
In regard to the WEF's methodology, we lean toward a competitiveness index based on official, quantitative data that is computed using statistical and/or mathematical procedures, which considers weights that can be implicitly determined by the inherent structure of the data. We believe that this is the only way to eliminate any political biases or individual interests.
Nevertheless, this study presents some limitations such as the existence of key indicators (hard data) not considered during the analyzed period in the elaboration of WEF-GCI and therefore in the CSI; the no representation of some pillars as these pillars do not include hard data indicators.
Moreover, in any elaboration of an index, there is subjectivity as humans are involved in the process. However, as we mentioned previously it is not questionable that inside the subjectivity, our proposed index is less manipulable for humans as no survey opinions are included.
Finally, the relevant advantages of using this index are the transparency of the information of WEF-GCI (freely available online) and continuation in yearly published since 1979. It is a guide for governments, enterprises, investors, citizens among others, to manage to progress in prosperity or to achieve high living of standards.