Geometrical Measurement of Cultural Differences

Abstract

Differences and similarities between countries, regions, and cultures lie at the core of international business, and they are often measured in the form of a distance index originally proposed by Kogut and Singh. Because research results using this index are ambivalent, critical observers have challenged the concept and proposed partial remedies in the form of a standardized Euclidean or Mahalanobis distance measure. This article suggests a different avenue, construes culture as a weight vector based on Hofstede’s cultural dimensions, and specifies a geometrical difference measurement using the angle of heterogeneity between two such vectors. Its performance is assessed using a mathematical simulation and an empirical example from the field of export marketing, which considers the effect of culture on bilateral export flows.

Keywords

angle of heterogeneity cultural differences Euclidean distance Hofstede dimensions Kogut–Singh index Mahalanobis distance

Mathematical constructs conceptualizing and measuring cultural differences are widely used in international business, where they have been applied to most business administration disciplines—that is, management, marketing, finance, and accounting (Cuypers et al. 2018; Shenkar 2001). While these constructs have become an “international business research workhorse” (Beugelsdijk, Ambos, and Nell 2018, p. 1113), they are continuously and passionately being debated; some of these debates are still unresolved and complex.

After Hofstede (1980) proposed to measure culture and explain differences between cultures through four dimensions—namely, uncertainty avoidance (UAI), power distance (PDI), masculinity/femininity (MAS), and individualism/collectivism (IDV)¹—Kogut and Singh (1988) had the groundbreaking idea that these four dimensions could be used to calculate an index of cultural distance. By treating these dimensions as bases in a Cartesian coordinate system, distances can be arithmetically measured using a derivative of the Euclidean formula. However, the application of the Kogut–Singh index in empirical research leads to mixed and contradictory results (e.g., Berry, Guillén, and Zhou 2010; Kim and Gray 2009; Kirkman, Lowe, and Gibson 2006; Yeganeh 2014). This may be, inter alia, the result of hitherto unresolved methodological problems (Shenkar 2001). For example, many researchers find the use of a composite measure appropriate (e.g., Beugelsdijk, Ambos, and Nell 2018; Cuypers et al. 2018), “whereas a growing number of others reject this outright as evidence of the ‘dark middle ages’ of cross-cultural research” (Tung and Verbeke 2010, p. 1270). The latter group argues that a generalized compound index gives equal weight to each component and does not allow researchers to distinguish the relevance of inputs for different research questions. Perhaps even more importantly, Hofstede’s cultural dimensions are correlated with each other. In other words, they form a nonorthogonal (oblique) feature space. In an oblique coordinate system, however, positions are generally not statistically independent of each other (Templeton 1959), and ignoring correlations between dimensions can thus lead to inaccuracies (Muir and Mallinson 1993). For that reason, various researchers have suggested incremental corrections to the Kogut–Singh index, including the use of a standardized Euclidean or Mahalanobis distance measure (Berry, Guillén, and Zhou 2010; Kandogan 2012; Konara and Mohr 2019). Further strands of literature take a more conceptual standpoint and debate the composition and measurement of cultural dimensions (e.g., McSweeney 2002; Messner 2016), discuss what factors should be included in a cross-national distance index (e.g., Berry, Guillén, and Zhou 2010; Ghemawat 2001), and examine whether cultural difference should be measured at the ecological or individual levels (e.g., Messner 2021a; Muthukrishna et al. 2020).

This article takes an entirely different avenue, completely abandons the arithmetic measurement of cultural distance, and replaces it with a geometrical measurement. To do so, culture is construed as a weight vector in a cultural feature space defined by Hofstede’s cultural dimensions or any other combination of cultural traits (following Desmet, Ortuño-Ortín, and Wacziarg [2017]). The angle between two such weight vectors is geometrically measured. Referred to as the angle of heterogeneity, angular distance, vector angle criterion, or cosine similarity in linear algebra, it is an indication of the cultural difference between two countries. Following established best practice in measurement development (Churchill 1979), the validity of the new geometrical cultural difference measure is empirically assessed in the context of export marketing. Cultural differences are hypothesized to be negatively related to bilateral export flows from India.

Accordingly, this article primarily contributes to the methodological international business literature. First, it sorts through existing measurements of cultural difference, reviewing their known methodological limitations and pinpointing hitherto unidentified problems. Second, and based on this appraisal, the article’s main objective is to develop a better operationalization of cultural difference through adopting a geometrical perspective. It is well-acknowledged that “high-quality research methods are a necessary building block for strong scholarship” (Eden and Nielsen 2020, p. 1609) and “necessary to move international marketing research beyond exploratory, qualitative comparisons” (Steenkamp 2001, p. 31). Third, and in a broader context, it naturally contributes to the use of cultural dimensions in country-level research (Beugelsdijk, Kostova, and Roth 2017; Brewer and Venaik 2012; Steenkamp 2001).

The article proceeds as follows. The subsequent section on the “Arithmetic Distance Measurement” reviews the construction of established arithmetic cultural difference measures. The pertinent literature is reviewed for known measurement issues and suggested improvements. Building on that, further and hitherto unknown conceptual issues are identified. Then, the “Geometrical Difference Measurement” section suggests a fundamentally different way of measuring cultural differences using the angle of heterogeneity between two cultural weight vectors. Drawing parallels from other disciplines, the applicability of this well-established geometrical measurement for cultural differences is discussed. To assess the measure’s validity, the “Effect of Cultural Differences on Exports” section provides an empirical illustration. Finally, in the “Discussion” section, the contribution of this methodological article to the field of international business and marketing is summarized.

Arithmetic Distance Measurement

Kogut–Singh Index

Because culture can be “defined as a vector of traits reflecting norms, values, and attitudes” (Desmet, Ortuño-Ortín, and Wacziarg 2017, p. 2479), a country’s culture can be characterized by its values on Hofstede’s k = 4 dimensions (Hofstede 1980). Accordingly, the cultural weight vector $\overset{⇀}{a} = 〈a_{1}, a_{2}, a_{3}, a_{4}〉$ describes the culture of country A. Let another country, B, be characterized by $\overset{⇀}{b} = 〈b_{1}, b_{2}, b_{3}, b_{4}〉$ . To calculate the cultural distance between A and B, Kogut and Singh (1988, p. 422) present the following index:

K S I (\overset{⇀}{a}, \overset{⇀}{b}) = \sum_{i = 1}^{k} \frac{{(a_{i} - b_{i})}^{2}}{k V_{i}} .

Note that, for consistency purposes, variable names have been changed from Kogut and Singh’s original publication. V_i is the variance of the ith cultural dimension. However, Kogut and Singh do not provide a detailed explanation apart from stating that “this composite index was formed based on the deviation along each of the four cultural dimensions…of each country from [another country]. The deviations were corrected for differences in the variances of each dimension and then arithmetically averaged” (Kogut and Singh 1988, p. 422).

Euclidean Distance Measure

Despite prominent publications referring to the Kogut–Singh index as a Euclidean distance measure (e.g., Beugelsdijk, Ambos, and Nell 2018; Cuypers et al. 2018; Tihanyi, Griffith, and Russell 2005), Konara and Mohr (2019, p. 338) argue that “the use of the arithmetic average of the standardized and squared differences creates a fundamental difference” and suggest that a Euclidean cultural distance measure should be formulated as

E C D (\overset{⇀}{a}, \overset{⇀}{b}) = \sqrt{\sum_{i = 1}^{k} {(a_{i} - b_{i})}^{2}},

or in a standardized form:

E C D_{s t d} (\overset{⇀}{a}, \overset{⇀}{b}) = \sqrt{\sum_{i = 1}^{k} \frac{{(a_{i} - b_{i})}^{2}}{V_{i}}} .

Comparing Equations 1 and 3, Konara and Mohr (2019, p. 338) note that “by failing to take the square root of the sum of the squared differences, the [Kogut–Singh index] creates a second-degree (quadratic) function of distance.” Figure 1, which is based on Konara and Mohr (2019, p. 344), shows the nonlinear relationship $K S I = .25 E C D_{s t d}^{2}$ between them (78 countries, 6,006 country pairs). Accordingly, Lin’s concordance correlation is .815, with limits between [.809, .820], suggesting a poor degree of equivalence (Lin 1989; McBride 2005).² The Bland–Altman test (Bland and Altman 1999) returns a bias of −.636 (SE = .006; SD = .493), for all possible combinations.³ A squared distance measure progressively places greater weights on objects farther apart but does not satisfy the triangular inequality condition of distance measures (Cheney and Kincaid 2012; Konara and Mohr 2019). Conversely, adaptation-level theory (Helson 1964) considers the relationship between a distance measure and perception to be exponential (Plataniotis, Androutsos, and Venetsanopoulos 1998), in support of the Kogut–Singh index.

Figure 1.

Standardized Euclidean distance versus Kogut–Singh index.

Nonindependence of Cultural Dimensions

A substantial part of Hofstede’s work is dedicated to understanding interrelationships between cultural dimensions. For example, “many countries that score high on the power distance index…score low on the individualism index…, and vice versa. In other words, the two dimensions tend to be negatively correlated” (Hofstede and Hofstede 2005, p. 82). The GLOBE project (House et al. 2004), which is an alternative cultural framework outlining nine cultural dimensions and differentiating between societal and organizational values and practices, similarly highlights the interdependence of some dimensions. For example, the “societal collectivism scales are significantly correlated with other GLOBE dimensions. The more a society is characterized by institutional collectivism practices, the more it is characterized by uncertainty avoidance, future orientation, humane orientation, and performance orientation practices, and the less it is characterized by assertiveness and power distance practices” (Gelfand et al. 2004, p. 470).

This raises two issues. First, assuming the independence of cultural dimensions in a feature space is very naive. In addition, the variance-based correction factors in Equations 1 and 3 account for variance within a dimension but not for variance caused by correlations among dimensions (Carroll and Chang 1970). Yet ignoring correlations between coordinates in an oblique coordinate system can lead to inaccuracies in the estimation of standard deviations (Muir and Mallinson 1993). Because the Euclidean distance “neglects the existing correlations among cultural dimensions, [this] plausibly creates some inaccuracy in calculating the national cultural distance” (Yeganeh 2014, p. 442). Second, Hofstede’s cultural dimensions also suffer from different scales. Despite being depicted on a scale of 1 to 100, each dimension has a specific formula designed by Hofstede (e.g., Messner 2016). While Hofstede has “chosen [the] scales such that the distance between the lowest- and the highest-scoring country is about 100 points” (Hofstede and Usunier 2003, p. 141), this potentially affects similarity of the scales; that is, a score of 82 on PDI does not necessarily have the same meaning as a score of 82 on UAI. Positions on the dimensions are therefore not absolute, but relative (Hofstede 2011). If the dimensions were independent, the issue of different scales could potentially be solved by multiplying the scores with appropriate scaling factors (Shugart and Patten 1972). A similar problem persists in the GLOBE study. While all dimensions appear to be on a seven-point Likert scale, the underlying items have multiple different scale anchors (GLOBE 2006).

Because the correlations between Hofstede’s cultural dimensions lead to nonzero covariance, Berry, Guillén, and Zhou (2010), as well as Kandogan (2012) and Yeganeh (2014), suggest using the Mahalanobis distance instead (Mahalanobis, Bose, and Roy 1937):

M D (\overset{⇀}{a}, \overset{⇀}{b}) = \sqrt{{(\overset{⇀}{a} - \overset{⇀}{b})}^{T} \times S^{- 1} \times (\overset{⇀}{a} - \overset{⇀}{b})} .

In this formula, S is the covariance matrix for the four Hofstede dimensions, taking into account the nonorthogonality of the cultural feature space. The Euclidean distance is a special case of the Mahalanobis distance, with all covariances across dimensions being zero. A small correction brings the formula closer to the Kogut–Singh index in magnitude (Kandogan 2012):

M C D (\overset{⇀}{a}, \overset{⇀}{b}) = \frac{1}{k} {(\overset{⇀}{a} - \overset{⇀}{b})}^{T} \times S^{- 1} \times (\overset{⇀}{a} - \overset{⇀}{b}) .

The use of the generalized Mahalanobis distance measure as in Equation 4 is indeed recommended if the axes are of unequal scale and show a mix of high and low correlations (e.g., Berry, Guillén, and Zhou 2010; Brereton and Lloyd 2016; Shugart and Patten 1972). Despite this mathematically correct way out, the next section identifies new methodological problems, which so far have not yet been discussed in the pertinent literature.

Instability and Weight Effect of the Variance Correction

In some form or another, Equations 1, 3, 4, and 5 all contain the variance of cultural dimensions or between cultural dimensions as a correction factor. Variance calculations, however, depend on the number of countries included in the cultural dimensions. Scholars previously contemplated whether to calculate the distance based on the variance of the full sample for which scores are available or for the subset of countries they include in their study. The prevailing recommendation is to use the variance of the full sample (Beugelsdijk, Ambos, and Nell 2018).

However, a variance correction assumes a normal probability distribution of the scores on each cultural dimension. As a Shapiro–Wilk test shows, only the country scores for PDI and MAS are normally distributed (W(78) = .984, p = .416; W(78) = .981, p = .307, respectively). IDV and UAI do not follow a normal distribution (W(78) = .942, p = .001; W(78) = .952, p = .005 respectively); histograms show that the deviation is not trivial. A Kolmogorov–Smirnov test with the Lilliefors significance correction arrives at an equivalent conclusion (PDI: W(78) = .071, p = .200; IDV: W(78) = .109, p = .023; MAS: W(78) = .081, p = .200; UAI: W(78) = .116, p = .011). From a strict mathematical point of view, a variance correction of cultural scores is thus not appropriate, regardless of whether the Kogut–Singh (Equation 1), the standardized Euclidean distance (Equation 3), or the Mahalanobis distance formula (Equations 4 and 5) is used. In addition, the four original Hofstede dimensions are currently available for no more than 75 countries and 3 regions (Africa East, Africa West, and Arab countries). The GLOBE study is available for only 62 societies, out of the world’s 195 recognized countries. Should additional data be collected from other countries and added to the full Hofstede or GLOBE sample, all variances would have to be recalculated. As a result, the cultural distance between two countries A and B changes every time a new country is added to the database—even though the countries’ positions $\overset{⇀}{a}$ and $\overset{⇀}{b}$ on the cultural dimensions are not revised. For example, the difference between calculating the Kogut–Singh distance based on all 78 versus the first 39 entries in the Hofstede tables is +.218 for Argentina and Austria and −.034 for Argentina and Belgium. The Bland–Altman test returns a bias of .154 (SE = .006; SD = .239) for all possible combinations, and Lin’s concordance correlation is .978 with limits [.976, .980], which overall points to a substantial degree of equivalence (Lin 1989; McBride 2005). And yet, Figure 2 (abscissa: Kogut–Singh index calculated with 39 countries; ordinate: now calculated with all 78 countries) graphically reveals several deviations from the diagonal (gray dashed line). While this can be understood as a form of measurement error pertaining to existing observations, it is problematic because it further undermines the validity of variance-based corrections. Moreover, it could be that the more than 100 countries not included in the Hofstede or GLOBE studies influence the variance correction factor in a substantially different manner.

Figure 2.

Kogut–Singh index with variance correction for 39 versus 78 countries.

With the variance correction factor, the Kogut–Singh formula (Equation 1) attaches a different weight to each of the squared differences. The variance correction factors are 508.129 for UAI, 441.556 for PDI, 346.798 for MAS, and 574.634 for IDV, as calculated for all 78 countries. Thus, Equation 1 effectively becomes

K S I (\overset{⇀}{a}, \overset{⇀}{b}) = \frac{1}{4} \frac{{(a_{U A I} - b_{U A I})}^{2}}{508.129} + \frac{{(a_{P D I} - b_{P D I})}^{2}}{441.556} + \frac{{(a_{M A S} - b_{M A S})}^{2}}{346.798} + \frac{{(a_{I D V} - b_{I D V})}^{2}}{574.634} .

When calculated for the first 39 entries in the Hofstede tables, the variance correction factors are 458.958 for UAI, 422.362 for PDI, 238.780 for MAS, and 656.580 for IDV, and Equation 6 turns into

K S I (\overset{⇀}{a}, \overset{⇀}{b}) = \frac{1}{4} \frac{{(a_{U A I} - b_{U A I})}^{2}}{458.958} + \frac{{(a_{P D I} - b_{P D I})}^{2}}{422.362} + \frac{{(a_{M A S} - b_{M A S})}^{2}}{238.780} + \frac{{(a_{I D V} - b_{I D V})}^{2}}{656.580} .

Lin’s concordance correlation between these two sets of correction factors is .821 with limits [.506, .942], which is considered a poor to moderate agreement. The question arises whether these weights really compensate for different variances, or whether they arbitrarily impose weights on the dimensions. Several reasons speak for the latter. First, and as mentioned previously, Kogut and Singh do not give an explanation for introducing the variance correction factor and even state that this “scaling method imposes weights based on index variance” (Kogut and Singh 1988, p. 422; italics added). Second, these weights give the most importance to MAS and the least importance to IDV. The latter arguably has the most influence on aspects of customer service (Donthu and Yoo 1998; Obal and Kunz 2016; Soares, Farhangmehr, and Shoham 2007). Reducing the number of countries in Equation 7 further amplifies this difference. The issues caused by dynamic variance correction based on measured variance of variables are well-acknowledged in chemical engineering (e.g., Attarwala 2011). In magnetic resonance imagining, the challenge posed by numerical stability of fixed-point noise variance correction formula for separating signal intensity from noise is also well recognized (e.g., Koay and Basser 2006). Scholars in the statistical sciences are also aware of the issue and attempt to advance methods for capturing population variance in successive sampling (e.g., Singh et al. 2011). Third, UAI plays an important role in marketing research (see references in Messner [2016]), but the variance correction factor diminishes the relative influence of UAI as compared with MAS and PDI. More systematically, Yeganeh (2014) uses the Human Development Index (HDI; Roser 2020) to understand the varying importance of cultural dimensions, based on the premise that socioeconomic and cultural factors are strongly correlated (see references in Yeganeh [2014]). Regressing HDI on the cultural dimensions indicates a collective significant effect (R² = .488, F(4, 65) = 15.531, p < .001). But only PDI (−1.403, p = .021) and IDV (2.322, p = .021) are significant predictors in the model, and UAI (.526, p = .225) and MAS (−.284, p = .581) are not significant.⁴ So, the variance correction factors in the Kogut–Singh formula give the least importance to the most important predictor, IDV, and the most importance to MAS, a nonsignificant predictor. And because the IDV scores are not normally distributed across countries (as discussed previously), an IDV variance-correction factor should not have been calculated in the first place. In view of that, it is not surprising that the application of the Kogut–Singh index in empirical research leads to mixed results (for an overview, see Yeganeh [2014]).

Thus, it is now time to move to the core of the research, replace the Euclidean arithmetical distance calculation with its myriad correction attempts, and propose a mathematically correct method.

Geometrical Difference Measurement

Angle of Heterogeneity

Linear algebra distinguishes between arithmetically calculating distances in a coordinate system and geometrically measuring the length and direction of vectors in a feature space. Mathematically, a weight vector (or feature vector, observation vector) is an n-dimensional vector of numerical features that represent some object. The vector space associated with these vectors is called the feature space (e.g., Nagamochi 2009). A cultural feature space, for example, can be defined by Hofstede’s n = 4 dimensions. And a country’s cultural summary on these four dimensions can consequently be understood as a four-dimensional weight vector (Desmet, Ortuño-Ortín, and Wacziarg 2017). Geometrically, the length and direction of a vector are its true identity, not its coordinates, because the length and direction are unaffected by changes in the feature space. The angle $θ$ between two vectors $\overset{⇀}{a}$ and $\overset{⇀}{b}$ is defined as

θ (\overset{⇀}{a}, \overset{⇀}{b}) = {cos}^{- 1} \frac{\overset{⇀}{a} \times \overset{⇀}{b}}{‖\overset{⇀}{a}‖ ‖\overset{⇀}{b}‖} = {cos}^{- 1} (\frac{\sum_{i = 1}^{k} a_{i} b_{i}}{\sqrt{\sum_{i = 1}^{k} a_{i}^{2}} \sqrt{\sum_{i = 1}^{k} b_{i}^{2}}}) .

The Mathematical Appendix explains how this formula is derived from the dot product between two vectors, and Figure 3 illustrates it graphically for two countries (Argentina $\overset{⇀}{a}$ and Austria $\overset{⇀}{b}$ ) and k = 2 cultural dimensions (IDV and PDI). While this is rather intuitive in a two-dimensional space, no attempt should be made to visualize it in more dimensions (Gurney 1997).

Figure 3.

Hofstede-based weight vectors for Argentina (ARG) and Austria (AUT).

Following the property of the cosine function, the definition in Equation 8 provides information about the way two vectors are aligned with each other. The angle $θ (\overset{⇀}{a}, \overset{⇀}{b})$ is called “cosine similarity” (Salton and McGill Michael 1983), “angular distance,” “angle of heterogeneity” (Schnack and Kahn 2016), or “vector angle criterion” (Plataniotis, Androutsos, and Venetsanopoulos 1998, p. 1415). It is a summary statistic for the total difference in a single number; detailed information of the nature of the heterogeneity needs to be obtained by an element-wise comparison of $\overset{⇀}{a}$ and $\overset{⇀}{b}$ (Schnack and Kahn 2016). $θ (\overset{⇀}{a}, \overset{⇀}{b})$ is a symmetrical measure, that is, $θ (\overset{⇀}{a}, \overset{⇀}{b}) = θ (\overset{⇀}{b}, \overset{⇀}{a})$ . While Equation 8 fails to fulfill the triangular inequality condition, the following transformed measure would satisfy triangular inequality (Jiaxing et al. 2019):

θ_{r} (\overset{⇀}{a}, \overset{⇀}{b}) = \sqrt{\frac{π}{2} - θ (\overset{⇀}{a}, \overset{⇀}{b})} .

Application Across Disciplines

In several fields and disciplines, the angle of heterogeneity is used to describe the difference between two weight vectors (e.g., Grzegorczyk, Kurdziel, and Wójcik 2016; Salton and McGill, Michael 1983; Sim et al. 2019). It is “the most widely reported measure of vector similarity” (Ye 2011, p. 91) and applied where common characteristics need to be measured (Xia, Zhang, and Li 2015). For example, in computer graphics, the RGB color model knows red, green, and blue as three primaries, which can produce the color gamut (Salomon 2011). Because color is defined in the RGB color space as relative values in the trichromatic channel and not as triplet values of absolute intensity, a difference measure between two colors must respond to chromaticity (relative intensity) and not luminance (absolute intensity) difference (Plataniotis, Androutsos, and Venetsanopoulos 1998; Trahanias and Venetsanopoulos 1993). The angle of heterogeneity is also used to compare spectral images with a reference image (Deborah, George, and Hardeberg 2014; Kruse and Lefkoff 1994). In image processing, a difficult problem is to accommodate for superficial differences arising from the vagaries of illumination (Viola and Wells 1997). Because the angle of heterogeneity uses only the vector direction and not the vector length, it ensures low sensitiveness to illumination conditions (Lasaponara and Masini 2012). In database applications, it is used for approximate string matching predicates on text attributes (Li and Han 2013; Tata and Patel 2007). In market research, a distance metric based on the angle of heterogeneity can be used to assess the repeatability and reproducibility of consumer preferences (Vanacore et al. 2019). Nautical astronomy, however, uses $θ (\overset{⇀}{a}, \overset{⇀}{b})$ in an entirely different way. Because it typically does not consider linear distances of celestial points or objects (Karttunen et al. 2017, p. 16), it measures the distance between celestial objects based on the angle they make with an observational point on earth. Astronomy refers to this distance as angular distance or angular separation (Young 1882, p. 87).

Application for Measuring Cultural Differences

Similar to color in the RGB model, and as outlined previously, a country’s culture is a combination of positions on the cultural dimensions, referred to as the vector of traits (Desmet, Ortuño-Ortín, and Wacziarg 2017). The angle of heterogeneity $θ (\overset{⇀}{a}, \overset{⇀}{b})$ based on the four original Hofstede dimensions is provided in Table 1 below the diagonal.

Table 1.

Hofstede-Based Cultural Difference Measures: Angle of Heterogeneity θ (Below Diagonal) and Kogut–Singh Index (Above Diagonal).

Country	AFE	AFW	ARA	ARG	AUL	AUT	BAN	BEL	BEF	BEN	BRA	BUL	CAN	CAF	CHL	CHI	COL	COS	CRO	CZE	DEN	ECA	SAL	EST	FIN	FRA
AFE		.137	.427	1.015	2.398	3.132	.339	1.993	1.973	2.136	.396	.561	1.671	1.020	.698	.855	.857	1.396	.448	.869	3.023	.728	.899	.919	1.294	1.423
AFW	.115		.278	1.314	3.160	3.910	.081	2.231	2.123	2.525	.422	.570	2.427	1.540	.852	.577	.644	1.964	.441	1.139	4.361	.355	.882	1.673	2.201	1.688
ARA	.034	.148		.738	2.363	3.311	.175	1.056	.941	1.386	.112	.348	1.917	.993	.871	.973	.526	2.274	.231	.503	4.723	.466	.722	1.529	2.088	.787
ARG	.328	.425	.300		1.532	1.360	1.172	.545	.513	.708	.339	.546	1.282	.751	.906	2.453	.721	1.412	.602	.170	3.991	1.317	.697	.951	1.278	.598
AUL	.594	.698	.564	.466		1.357	3.196	1.456	1.486	1.637	2.132	3.033	.107	.495	3.695	3.366	3.476	4.208	2.839	.922	2.183	3.960	3.865	1.126	1.246	1.503
AUT	.659	.745	.632	.399	.418		3.693	2.559	2.422	2.939	2.697	3.450	1.479	2.070	3.977	4.138	2.754	3.573	3.533	1.559	4.133	3.692	3.656	2.267	2.386	3.011
BAN	.123	.057	.152	.402	.690	.708		2.013	1.826	2.445	.361	.570	2.595	1.677	1.026	.530	.372	2.323	.460	1.027	5.215	.135	.842	2.053	2.662	1.650
BEL	.342	.456	.309	.179	.363	.467	.453		.033	.105	.782	1.076	1.438	.697	1.697	3.562	1.843	2.892	1.041	.365	4.772	2.466	1.506	1.436	1.810	.131
BEF	.311	.424	.278	.152	.364	.449	.418	.047		.252	.735	1.092	1.514	.794	1.816	3.251	1.609	3.114	1.054	.326	5.168	2.190	1.511	1.660	2.092	.233
BEN	.402	.514	.371	.232	.390	.509	.516	.084	.131		.975	1.126	1.515	.715	1.540	4.258	2.319	2.518	1.111	.585	4.274	3.027	1.540	1.186	1.461	.109
BRA	.136	.235	.113	.203	.546	.574	.228	.239	.210	.295		.127	1.669	.798	.485	1.459	.444	1.499	.086	.304	4.204	.619	.380	1.073	1.529	.549
BUL	.210	.271	.203	.254	.649	.647	.271	.306	.291	.335	.125		2.409	1.275	.153	2.076	.558	1.052	.021	.705	4.680	.788	.102	1.281	1.723	.741
CAN	.553	.658	.522	.438	.053	.440	.654	.322	.324	.348	.506	.608		.255	2.865	2.819	3.004	3.250	2.223	.745	1.507	3.381	3.176	.594	.693	1.280
CAF	.404	.514	.372	.327	.235	.498	.518	.172	.180	.202	.350	.443	.184		1.674	2.366	2.119	2.416	1.115	.303	2.014	2.422	1.937	.347	.554	.448
CHL	.315	.357	.312	.321	.731	.712	.362	.372	.368	.379	.236	.113	.689	.521		2.751	1.005	.507	.222	1.230	4.335	1.286	.147	1.231	1.567	1.179
CHI	.342	.290	.361	.600	.720	.784	.279	.625	.585	.700	.461	.540	.695	.617	.638		1.350	4.160	1.819	1.939	5.271	.745	2.614	2.979	3.622	3.137
COL	.258	.259	.265	.318	.716	.604	.213	.448	.412	.508	.242	.246	.687	.565	.312	.437		1.932	.610	.991	6.238	.163	.528	2.404	3.000	1.800
COS	.530	.578	.521	.380	.813	.689	.568	.472	.476	.457	.421	.323	.781	.642	.242	.840	.434		1.236	2.084	3.649	2.517	.843	1.286	1.381	2.330
CRO	.167	.237	.159	.265	.625	.655	.244	.292	.276	.326	.098	.054	.582	.413	.155	.505	.261	.374		.643	4.458	.751	.209	1.203	1.656	.667
CZE	.287	.398	.254	.152	.353	.423	.386	.112	.066	.196	.201	.302	.317	.192	.392	.534	.383	.508	.284		3.464	1.387	1.113	.787	1.140	.354
DEN	.873	.976	.844	.768	.380	.743	.987	.614	.641	.590	.827	.903	.383	.481	.957	1.020	1.043	1.026	.876	.661		6.478	5.516	1.174	.890	3.898
ECA	.237	.176	.259	.429	.769	.709	.130	.525	.487	.588	.296	.311	.737	.612	.383	.327	.145	.549	.306	.453	1.089		.874	2.803	3.481	2.249
SAL	.306	.338	.305	.299	.740	.672	.329	.393	.379	.415	.228	.120	.702	.546	.094	.605	.232	.241	.171	.390	1.000	.321		1.755	2.203	1.217
EST	.445	.559	.413	.295	.311	.504	.563	.126	.167	.094	.356	.415	.268	.137	.467	.713	.574	.550	.398	.218	.498	.645	.503		.044	.951
FIN	.530	.644	.498	.354	.309	.510	.648	.203	.243	.154	.437	.488	.273	.195	.529	.794	.649	.584	.475	.293	.446	.727	.568	.085		1.288
FRA	.326	.437	.294	.236	.396	.543	.444	.077	.106	.090	.236	.293	.349	.174	.355	.621	.468	.482	.272	.161	.610	.530	.392	.130	.211
GER	.488	.591	.457	.283	.219	.254	.569	.262	.245	.314	.413	.509	.217	.248	.590	.651	.538	.645	.499	.219	.576	.618	.577	.285	.311	.328
GBR	.664	.757	.637	.572	.133	.468	.748	.482	.476	.517	.638	.750	.171	.344	.841	.724	.789	.934	.722	.454	.398	.826	.844	.439	.439	.512
GRE	.301	.373	.284	.135	.597	.502	.350	.278	.255	.317	.180	.168	.566	.435	.217	.590	.228	.288	.202	.258	.888	.352	.172	.397	.459	.308
GUA	.329	.296	.347	.476	.877	.851	.307	.541	.525	.564	.333	.237	.834	.665	.210	.568	.299	.389	.253	.530	1.120	.297	.200	.644	.715	.519
HOK	.296	.271	.308	.540	.636	.724	.262	.551	.512	.626	.408	.500	.610	.533	.605	.086	.423	.806	.462	.461	.936	.333	.577	.634	.714	.548
HUN	.469	.568	.439	.272	.251	.241	.543	.274	.250	.334	.398	.498	.249	.271	.583	.620	.507	.641	.488	.214	.616	.586	.563	.314	.347	.341
IND	.246	.292	.240	.454	.483	.665	.301	.404	.374	.471	.330	.438	.447	.354	.545	.280	.459	.750	.390	.334	.751	.414	.544	.462	.539	.389
IDO	.188	.076	.221	.494	.756	.799	.096	.530	.498	.589	.309	.338	.718	.581	.416	.253	.293	.634	.308	.468	1.036	.175	.392	.632	.717	.511
IRA	.160	.275	.127	.214	.455	.544	.273	.186	.153	.254	.103	.219	.413	.258	.323	.451	.323	.498	.183	.134	.737	.362	.327	.291	.376	.181
IRE	.636	.724	.609	.523	.185	.367	.705	.476	.460	.525	.606	.721	.223	.372	.816	.679	.720	.896	.699	.424	.517	.764	.802	.464	.475	.521
ISR	.632	.734	.602	.310	.450	.283	.710	.347	.356	.343	.508	.540	.448	.437	.567	.876	.600	.498	.558	.375	.685	.727	.557	.362	.346	.414
ITA	.419	.526	.386	.246	.225	.329	.509	.193	.173	.254	.346	.447	.203	.176	.532	.604	.499	.613	.431	.147	.570	.571	.526	.226	.271	.253
JAM	.566	.592	.559	.649	.511	.614	.571	.643	.606	.719	.621	.741	.515	.559	.854	.394	.655	1.007	.708	.546	.815	.621	.822	.686	.739	.666
JPN	.380	.448	.360	.213	.490	.312	.404	.348	.306	.420	.313	.391	.479	.429	.474	.524	.299	.529	.397	.258	.853	.397	.418	.453	.509	.409
KOR	.292	.326	.290	.282	.725	.654	.314	.383	.366	.409	.213	.113	.688	.534	.111	.588	.211	.254	.164	.374	.993	.305	.024	.496	.562	.385
LAT	.584	.686	.558	.489	.467	.710	.707	.328	.373	.258	.509	.529	.425	.318	.544	.868	.741	.618	.512	.430	.466	.801	.612	.228	.202	.285
LIT	.485	.593	.456	.355	.420	.604	.605	.201	.247	.125	.393	.418	.377	.243	.443	.783	.618	.516	.406	.309	.527	.689	.499	.123	.130	.168
LUX	.412	.524	.379	.183	.292	.353	.510	.120	.115	.169	.312	.391	.264	.187	.461	.652	.479	.523	.383	.127	.590	.567	.463	.168	.214	.193
MAL	.302	.237	.326	.622	.756	.895	.271	.606	.578	.662	.437	.489	.717	.598	.571	.217	.483	.805	.445	.547	.991	.367	.569	.679	.761	.574
MLT	.353	.459	.323	.127	.455	.473	.451	.108	.119	.121	.224	.252	.418	.279	.298	.661	.404	.366	.258	.169	.700	.502	.315	.206	.263	.146
MEX	.136	.178	.137	.272	.614	.583	.139	.358	.319	.425	.142	.204	.581	.451	.306	.369	.134	.477	.192	.285	.931	.169	.258	.479	.560	.369
MOR	.135	.248	.101	.229	.470	.550	.244	.217	.181	.287	.100	.222	.429	.281	.331	.419	.304	.512	.185	.154	.759	.334	.328	.322	.407	.214
NET	.656	.762	.627	.551	.376	.686	.779	.382	.421	.330	.590	.637	.343	.305	.671	.895	.823	.744	.615	.466	.311	.878	.728	.258	.207	.356
NZL	.661	.766	.629	.478	.116	.339	.751	.406	.406	.429	.597	.693	.160	.317	.769	.790	.743	.815	.678	.396	.416	.813	.770	.360	.343	.454
NOR	.683	.789	.655	.563	.429	.708	.806	.400	.443	.337	.609	.643	.397	.350	.665	.941	.839	.721	.626	.494	.349	.902	.726	.278	.220	.374
PAK	.248	.267	.250	.277	.695	.592	.229	.408	.374	.462	.206	.198	.664	.535	.262	.472	.056	.385	.220	.353	1.012	.185	.182	.533	.607	.426
Country	AFE	AFW	ARA	ARG	AUL	AUT	BAN	BEL	BEF	BEN	BRA	BUL	CAN	CAF	CHL	CHI	COL	COS	CRO	CZE	DEN	ECA	SAL	EST	FIN	FRA

PAN	.246	.199	.269	.449	.821	.815	.211	.508	.486	.543	.280	.218	.779	.615	.240	.470	.252	.447	.217	.481	1.079	.220	.222	.614	.692	.486
PER	.285	.309	.286	.301	.741	.666	.295	.405	.385	.435	.219	.126	.704	.552	.132	.569	.189	.277	.172	.389	1.015	.278	.045	.520	.588	.406
PHI	.225	.189	.244	.517	.654	.759	.198	.518	.483	.585	.354	.433	.620	.513	.532	.141	.394	.749	.390	.441	.932	.297	.515	.601	.684	.502
POL	.259	.368	.228	.101	.423	.446	.354	.125	.084	.199	.148	.236	.388	.253	.324	.538	.329	.441	.226	.073	.721	.410	.318	.250	.325	.168
POR	.357	.408	.349	.298	.721	.680	.408	.361	.360	.361	.258	.147	.681	.520	.063	.682	.331	.186	.194	.389	.946	.421	.108	.453	.508	.352
ROM	.178	.209	.185	.340	.696	.728	.226	.369	.353	.399	.165	.098	.652	.481	.156	.495	.267	.394	.079	.359	.939	.284	.175	.470	.547	.342
RUS	.215	.265	.214	.343	.674	.738	.289	.339	.332	.355	.182	.116	.627	.449	.151	.544	.335	.389	.092	.351	.889	.359	.206	.426	.499	.299
SER	.204	.225	.211	.336	.719	.721	.233	.386	.369	.417	.178	.089	.676	.509	.134	.510	.238	.363	.096	.374	.971	.268	.134	.493	.568	.366
SIN	.497	.444	.515	.780	.802	.955	.457	.762	.730	.828	.626	.703	.776	.712	.796	.221	.645	1.019	.659	.685	1.035	.526	.781	.823	.899	.742
SLK	.306	.320	.307	.483	.540	.624	.302	.493	.452	.573	.389	.499	.519	.464	.610	.185	.423	.792	.462	.394	.860	.369	.580	.571	.647	.502
SLV	.348	.386	.346	.392	.758	.788	.405	.401	.406	.393	.288	.178	.712	.534	.102	.673	.399	.296	.196	.438	.944	.445	.193	.476	.535	.365
SAW	.413	.508	.385	.351	.207	.406	.495	.287	.263	.354	.387	.505	.186	.197	.605	.522	.534	.724	.477	.219	.562	.571	.598	.311	.360	.322
SPA	.304	.408	.275	.138	.478	.511	.404	.118	.120	.142	.176	.204	.438	.284	.259	.622	.372	.363	.205	.166	.724	.461	.280	.226	.293	.133
SUR	.217	.295	.203	.291	.602	.682	.314	.264	.261	.279	.151	.123	.555	.376	.177	.556	.353	.391	.092	.287	.816	.392	.231	.348	.422	.222
SWE	.787	.884	.761	.732	.460	.832	.907	.558	.591	.517	.748	.802	.436	.442	.841	.976	.985	.934	.773	.626	.223	1.020	.903	.438	.397	.526
SWI	.515	.613	.485	.341	.196	.256	.590	.318	.299	.373	.455	.559	.206	.276	.646	.640	.570	.709	.545	.265	.570	.640	.630	.336	.360	.379
SWF	.247	.357	.215	.243	.353	.501	.356	.160	.130	.234	.205	.318	.310	.165	.417	.478	.410	.572	.284	.101	.643	.447	.425	.236	.318	.166
SWG	.584	.680	.554	.392	.211	.218	.655	.379	.362	.427	.521	.622	.236	.336	.705	.695	.623	.750	.611	.332	.570	.697	.686	.386	.398	.442
TAI	.203	.231	.205	.271	.681	.617	.203	.377	.347	.428	.160	.140	.646	.504	.215	.466	.106	.374	.158	.332	.981	.193	.149	.500	.576	.385
THA	.157	.183	.167	.329	.693	.707	.192	.373	.352	.411	.151	.100	.650	.485	.175	.466	.226	.402	.085	.351	.952	.243	.169	.481	.560	.353
TRI	.280	.302	.279	.303	.631	.508	.248	.432	.388	.506	.271	.330	.610	.520	.418	.389	.141	.528	.333	.341	.985	.205	.346	.554	.627	.467
TUR	.209	.294	.191	.181	.577	.576	.288	.237	.218	.275	.083	.077	.537	.379	.170	.538	.253	.339	.086	.228	.844	.334	.169	.353	.427	.236
USA	.603	.703	.573	.497	.044	.447	.696	.392	.391	.422	.565	.671	.074	.252	.757	.709	.733	.848	.644	.376	.375	.778	.765	.342	.343	.420
URU	.324	.397	.309	.212	.633	.599	.392	.275	.273	.282	.203	.129	.595	.439	.123	.654	.317	.227	.170	.303	.871	.417	.143	.374	.432	.277
VEN	.236	.201	.252	.390	.734	.656	.147	.496	.456	.562	.276	.302	.704	.586	.379	.339	.107	.532	.300	.419	1.063	.054	.311	.618	.698	.508
VIE	.246	.187	.270	.562	.711	.829	.214	.555	.524	.616	.382	.443	.673	.555	.532	.180	.424	.760	.399	.490	.967	.315	.523	.636	.719	.530
Country	GER	GBR	GRE	GUA	HOK	HUN	IND	IDO	IRA	IRE	ISR	ITA	JAM	JPN	KOR	LAT	LIT	LUX	MAL	MLT	MEX	MOR	NET	NZL	NOR	PAK
AFE	1.706	2.741	1.355	1.789	.456	3.441	.521	.210	.133	2.206	2.230	2.022	1.541	3.103	.583	1.829	1.180	1.018	.919	1.460	1.176	.407	2.131	2.388	2.171	.337
AFW	2.308	3.536	1.390	1.280	.451	3.768	.510	.034	.415	2.974	3.181	2.409	1.913	3.035	.674	2.731	1.975	1.609	.486	1.780	.820	.454	3.166	3.343	3.291	.427
ARA	1.639	2.936	.746	1.200	.915	2.401	.441	.485	.390	2.674	2.762	1.370	2.345	1.966	.684	2.587	1.866	1.125	.799	.930	.309	.084	2.973	2.832	3.397	.613
ARG	.592	2.267	.218	2.225	1.995	1.254	1.487	1.704	.537	1.884	.832	.593	2.756	1.128	.618	2.117	1.317	.283	2.903	.209	.821	.416	2.379	1.563	2.712	.618
AUL	.350	.150	2.783	6.411	2.597	1.078	1.706	3.585	1.536	.392	1.502	.509	1.905	2.648	3.447	2.215	1.769	.659	4.156	1.739	3.132	1.610	1.638	.206	2.245	2.941
AUT	.523	1.554	2.325	6.697	3.407	1.095	3.312	4.296	2.330	.951	.800	1.124	2.452	1.505	3.219	4.271	3.162	1.093	6.026	2.224	3.189	2.495	3.873	.854	4.143	2.434
BAN	2.207	3.613	1.114	1.157	.568	3.244	.544	.147	.570	3.048	3.308	2.147	2.059	2.334	.720	3.351	2.460	1.669	.544	1.672	.423	.385	3.801	3.485	4.046	.437
BEL	1.055	2.411	.734	2.797	3.178	1.119	1.836	2.802	1.221	2.640	1.841	.490	4.160	1.648	1.630	2.193	1.694	.747	3.405	.195	1.259	.713	2.404	2.062	3.148	1.970
BEF	1.002	2.387	.654	2.733	2.983	.902	1.701	2.670	1.241	2.564	1.985	.402	3.943	1.273	1.646	2.619	2.014	.808	3.208	.268	.996	.642	2.817	2.123	3.597	1.877
BEN	1.321	2.708	.951	2.936	3.666	1.700	2.257	3.133	1.311	2.986	1.693	.834	4.729	2.435	1.649	1.594	1.264	.785	3.904	.183	1.827	.977	1.860	2.157	2.515	2.196
BRA	1.288	2.821	.379	1.170	1.207	2.181	.753	.689	.241	2.485	1.902	1.151	2.540	1.807	.332	2.036	1.332	.705	1.395	.487	.415	.071	2.455	2.399	2.780	.380
BUL	1.973	3.925	.387	.694	1.764	3.079	1.350	.847	.473	3.490	2.133	1.845	3.505	2.461	.120	2.010	1.350	1.084	1.770	.572	.679	.375	2.659	3.220	2.864	.422
CAN	.366	.269	2.479	5.550	1.988	1.531	1.306	2.782	.984	.380	1.231	.668	1.539	2.916	2.717	1.501	1.106	.416	3.449	1.507	2.863	1.245	1.054	.191	1.486	2.281
CAF	.550	.941	1.540	3.661	1.690	1.629	.855	1.912	.458	1.075	1.329	.574	2.017	2.623	1.670	.999	.655	.252	2.460	.728	1.871	.540	.883	.777	1.343	1.582
CHL	2.544	4.660	.770	.835	2.221	4.180	1.989	1.107	.676	4.088	2.106	2.649	4.070	3.530	.104	1.686	1.121	1.370	2.358	.901	1.424	.868	2.444	3.638	2.426	.546
CHI	2.710	3.230	2.794	3.094	.151	3.900	.467	.466	1.261	2.634	4.584	2.882	.996	3.174	2.242	4.699	3.709	2.574	.444	3.391	1.381	1.183	4.774	3.643	5.026	1.341
COL	1.962	4.092	.470	1.150	1.378	2.620	1.423	.806	.922	3.283	2.591	1.929	2.788	1.333	.501	4.036	2.885	1.564	1.784	1.323	.257	.637	4.590	3.540	4.802	.272
COS	2.853	5.122	1.559	2.329	3.193	5.151	3.397	2.208	1.301	4.216	1.435	3.537	4.522	4.588	.592	1.726	1.129	1.627	4.281	1.628	2.965	2.009	2.414	3.538	2.037	.959
CRO	1.919	3.666	.503	.757	1.530	3.037	1.079	.701	.379	3.304	2.266	1.765	3.233	2.529	.207	1.907	1.290	1.055	1.459	.619	.648	.271	2.501	3.100	2.744	.462
CZE	.408	1.499	.568	2.566	1.539	1.003	.839	1.512	.378	1.374	1.199	.291	2.157	1.268	.994	1.879	1.210	.209	2.238	.311	.803	.188	1.965	1.194	2.450	.888
DEN	2.855	2.135	5.789	8.454	3.690	5.909	3.561	4.561	2.543	2.084	2.536	4.014	2.944	7.916	4.636	1.212	1.286	2.279	5.726	4.230	6.827	3.855	.688	1.624	.511	4.261
ECA	2.570	4.412	1.062	1.125	.919	3.396	1.091	.402	1.020	3.610	3.594	2.522	2.487	2.000	.802	4.437	3.308	2.120	1.010	2.004	.352	.737	4.989	4.146	5.192	.441
Country	GER	GBR	GRE	GUA	HOK	HUN	IND	IDO	IRA	IRE	ISR	ITA	JAM	JPN	KOR	LAT	LIT	LUX	MAL	MLT	MEX	MOR	NET	NZL	NOR	PAK

SAL	2.448	4.876	.358	.564	2.305	3.577	2.054	1.159	.856	4.227	2.242	2.385	4.217	2.581	.061	2.571	1.789	1.470	2.403	.790	.857	.781	3.377	3.892	3.472	.435
EST	.982	1.622	1.811	3.727	1.975	2.858	1.522	1.994	.463	1.473	.854	1.432	2.334	3.746	1.360	.375	.102	.338	3.113	.991	2.678	1.008	.385	.965	.479	1.386
FIN	1.180	1.733	2.274	4.425	2.457	3.253	2.020	2.539	.773	1.590	.818	1.759	2.645	4.343	1.748	.306	.103	.506	3.813	1.298	3.371	1.466	.261	.967	.291	1.793
FRA	1.222	2.419	.838	2.348	2.660	1.777	1.439	2.187	.807	2.637	1.862	.779	3.817	2.350	1.270	1.420	1.068	.658	2.726	.205	1.322	.506	1.687	2.062	2.298	1.670
GER		.653	1.460	4.799	2.080	.633	1.535	2.699	.993	.477	.734	.223	1.731	1.361	2.121	2.394	1.641	.232	3.722	1.011	1.942	1.012	2.099	.330	2.547	1.645
GBR	.310		3.760	7.594	2.475	1.539	1.814	3.866	1.967	.188	2.108	1.000	1.385	3.214	4.303	2.931	2.429	1.167	4.304	2.732	3.806	2.156	2.149	.282	2.719	3.461
GRE	.415	.700		1.350	2.560	1.844	2.009	1.793	.986	3.279	1.657	1.217	3.946	1.145	.470	3.012	2.099	.977	2.992	.340	.524	.625	3.575	2.940	3.940	.684
GUA	.736	.969	.359		3.201	5.743	2.866	1.480	2.082	6.969	5.024	4.324	6.137	4.091	.842	4.423	3.628	3.489	2.201	2.157	1.226	1.677	5.600	6.835	5.786	1.441
HOK	.574	.644	.546	.564		3.665	.336	.374	.752	1.892	3.481	2.478	.598	3.297	1.834	3.437	2.594	1.839	.640	2.865	1.592	.954	3.442	2.664	3.565	1.011
HUN	.045	.330	.400	.719	.546		2.596	4.315	2.463	1.602	2.123	.274	3.363	.624	3.519	4.722	3.757	1.306	5.002	1.557	2.041	1.809	4.398	1.511	5.297	3.053
IND	.459	.510	.492	.567	.199	.444		.607	.525	1.686	3.220	1.498	1.077	2.728	1.760	2.680	2.051	1.307	.544	1.904	1.140	.422	2.661	2.174	3.100	1.246
IDO	.653	.806	.438	.320	.257	.628	.322		.610	3.212	3.625	2.890	1.840	3.455	.899	3.116	2.322	1.988	.419	2.289	1.067	.714	3.551	3.718	3.610	.549
IRA	.348	.543	.251	.426	.383	.338	.263	.347		1.609	1.470	1.221	1.589	2.505	.577	1.318	.735	.435	1.392	.828	1.100	.204	1.512	1.573	1.677	.417
IRE	.252	.130	.649	.935	.603	.258	.501	.770	.522		1.598	1.080	.820	2.757	3.592	3.040	2.328	.961	4.011	2.645	3.374	1.947	2.362	.224	2.711	2.613
ISR	.299	.560	.406	.754	.809	.315	.702	.803	.493	.515		1.385	3.271	2.700	1.869	1.856	1.183	.494	5.629	1.168	3.218	1.976	1.819	.909	1.851	1.761
ITA	.083	.327	.375	.675	.525	.097	.394	.590	.273	.291	.331		2.504	.993	2.262	2.789	2.072	.469	3.540	.744	1.490	.850	2.587	.884	3.304	1.987
JAM	.511	.448	.719	.874	.351	.486	.378	.598	.556	.390	.798	.507		3.663	3.476	4.158	3.258	2.038	2.280	3.950	3.112	2.026	3.648	1.705	3.771	2.161
JPN	.284	.555	.266	.565	.474	.246	.453	.497	.316	.464	.392	.285	.522		2.646	6.053	4.689	1.894	4.375	1.745	1.061	1.700	6.126	2.950	6.854	2.144
KOR	.560	.827	.154	.210	.560	.544	.529	.382	.312	.783	.547	.510	.800	.395		2.208	1.436	1.192	2.202	.846	.966	.681	2.901	3.334	2.903	.219
LAT	.505	.583	.557	.720	.792	.538	.605	.756	.459	.646	.517	.451	.870	.673	.613		.120	1.288	4.188	1.711	4.244	2.041	.131	2.137	.180	2.669
LIT	.403	.547	.428	.628	.708	.432	.534	.666	.349	.583	.414	.346	.797	.543	.498	.134		.707	3.514	1.149	3.197	1.367	.272	1.606	.302	1.721
LUX	.150	.411	.315	.627	.576	.167	.441	.594	.256	.386	.270	.103	.602	.297	.449	.393	.274		3.110	.484	1.674	.603	1.253	.604	1.550	1.048
MAL	.713	.780	.599	.489	.221	.693	.274	.202	.430	.769	.917	.646	.547	.623	.559	.778	.716	.671		3.348	1.513	1.194	4.521	4.796	4.868	1.778
MLT	.318	.576	.198	.485	.596	.324	.473	.533	.220	.556	.316	.265	.715	.335	.306	.370	.237	.174	.642		1.165	.596	2.070	2.003	2.535	1.221
MEX	.462	.686	.224	.325	.333	.435	.332	.235	.203	.632	.577	.410	.571	.280	.237	.648	.530	.400	.395	.341		.461	4.729	3.638	5.263	.825
MOR	.360	.552	.257	.418	.352	.347	.243	.319	.033	.526	.515	.287	.537	.309	.312	.491	.382	.279	.404	.248	.178		2.290	1.974	2.710	.581
NET	.478	.477	.646	.843	.813	.517	.618	.830	.519	.561	.533	.438	.823	.702	.726	.155	.234	.408	.827	.451	.719	.548		1.549	.111	3.135
NZL	.207	.180	.613	.926	.709	.241	.573	.825	.516	.181	.392	.252	.559	.485	.754	.522	.468	.309	.846	.479	.658	.532	.433		1.892	2.718
NOR	.512	.535	.652	.845	.860	.552	.667	.859	.547	.614	.529	.474	.883	.727	.726	.131	.228	.432	.866	.455	.742	.577	.067	.475		3.111
PAK	.517	.777	.176	.280	.450	.489	.462	.312	.295	.713	.563	.475	.678	.294	.160	.695	.571	.445	.499	.356	.130	.280	.781	.722	.795
PAN	.688	.903	.346	.099	.466	.668	.478	.222	.366	.868	.747	.625	.781	.518	.222	.709	.615	.590	.397	.468	.253	.352	.820	.876	.829	.243
PER	.575	.839	.172	.191	.545	.557	.525	.360	.321	.793	.571	.525	.794	.398	.032	.639	.524	.470	.543	.332	.225	.318	.751	.772	.752	.142
PHI	.591	.679	.508	.483	.105	.567	.182	.177	.338	.652	.804	.530	.443	.492	.500	.739	.659	.564	.140	.556	.296	.309	.777	.734	.819	.413
POL	.274	.526	.187	.467	.471	.265	.362	.440	.120	.491	.376	.211	.594	.248	.302	.447	.319	.166	.544	.131	.242	.140	.504	.459	.524	.292
POR	.573	.836	.197	.263	.646	.567	.580	.469	.341	.808	.519	.520	.874	.463	.123	.532	.427	.441	.627	.273	.334	.352	.660	.750	.649	.278
ROM	.575	.789	.260	.186	.463	.562	.414	.270	.247	.766	.633	.506	.742	.456	.173	.564	.468	.462	.415	.335	.215	.243	.674	.753	.683	.234
RUS	.569	.774	.280	.234	.505	.563	.425	.328	.245	.763	.618	.496	.770	.488	.209	.497	.408	.444	.446	.308	.272	.250	.613	.735	.619	.296
SER	.584	.813	.239	.158	.482	.570	.446	.282	.271	.783	.627	.520	.760	.445	.133	.593	.491	.473	.444	.340	.210	.266	.704	.770	.712	.202
SIN	.793	.782	.780	.714	.251	.770	.363	.402	.597	.768	1.047	.742	.447	.724	.768	.939	.884	.797	.241	.817	.564	.570	.949	.890	1.001	.674
SLK	.477	.544	.514	.606	.111	.447	.176	.328	.346	.496	.727	.435	.272	.400	.560	.749	.660	.498	.316	.546	.326	.318	.755	.607	.805	.445
SLV	.643	.870	.309	.230	.639	.641	.563	.442	.359	.860	.625	.578	.900	.560	.210	.509	.429	.505	.571	.341	.375	.370	.647	.807	.638	.353
SAW	.179	.259	.464	.716	.440	.176	.306	.561	.296	.230	.468	.142	.382	.340	.580	.514	.429	.237	.576	.376	.427	.300	.478	.273	.529	.522
SPA	.347	.595	.182	.438	.559	.350	.439	.484	.180	.576	.370	.286	.704	.341	.271	.379	.250	.207	.593	.055	.303	.208	.467	.512	.474	.324
SUR	.502	.706	.256	.305	.506	.500	.401	.366	.193	.699	.556	.428	.739	.453	.231	.431	.336	.373	.470	.241	.274	.207	.542	.662	.550	.310
SWE	.621	.516	.829	.994	.895	.660	.697	.943	.666	.630	.714	.585	.870	.863	.900	.321	.422	.580	.895	.638	.869	.692	.197	.528	.227	.948
SWI	.068	.262	.469	.781	.563	.072	.455	.670	.384	.188	.354	.127	.460	.308	.611	.550	.457	.214	.716	.381	.492	.392	.508	.183	.548	.555
SWF	.275	.440	.324	.530	.400	.272	.246	.424	.105	.428	.469	.195	.505	.327	.410	.424	.322	.204	.471	.240	.289	.120	.453	.423	.490	.385
SWG	.119	.258	.521	.844	.621	.125	.521	.736	.454	.170	.353	.193	.483	.344	.667	.593	.505	.267	.782	.435	.553	.462	.539	.159	.578	.609
TAI	.516	.767	.169	.242	.440	.493	.433	.284	.256	.714	.568	.466	.684	.324	.128	.649	.529	.431	.467	.328	.115	.244	.741	.717	.754	.064
THA	.563	.782	.245	.187	.437	.547	.401	.245	.239	.752	.629	.497	.716	.426	.163	.591	.489	.458	.403	.339	.177	.231	.695	.747	.707	.196
Country	GER	GBR	GRE	GUA	HOK	HUN	IND	IDO	IRA	IRE	ISR	ITA	JAM	JPN	KOR	LAT	LIT	LUX	MAL	MLT	MEX	MOR	NET	NZL	NOR	PAK

TRI	.452	.688	.272	.432	.364	.415	.408	.333	.312	.606	.564	.426	.534	.198	.323	.751	.625	.432	.488	.412	.154	.290	.805	.652	.831	.169
TUR	.432	.680	.127	.312	.488	.422	.411	.367	.165	.649	.474	.371	.696	.332	.157	.492	.372	.315	.507	.186	.193	.174	.588	.618	.598	.205
USA	.250	.098	.625	.895	.625	.278	.473	.758	.470	.172	.493	.254	.486	.512	.750	.490	.449	.327	.746	.487	.628	.483	.394	.145	.450	.715
URU	.482	.748	.135	.321	.608	.478	.527	.466	.274	.719	.444	.430	.807	.392	.144	.482	.364	.351	.614	.185	.298	.289	.596	.660	.591	.261
VEN	.574	.792	.318	.322	.337	.541	.410	.213	.340	.725	.681	.532	.599	.344	.293	.785	.668	.529	.398	.471	.140	.314	.858	.772	.882	.153
VIE	.654	.739	.541	.462	.171	.632	.231	.159	.375	.720	.856	.589	.510	.556	.511	.752	.680	.615	.068	.590	.333	.348	.800	.795	.839	.441
Country	PAN	PER	PHI	POL	POR	ROM	RUS	SER	SIN	SLK	SLV	SAW	SPA	SUR	SWE	SWI	SWF	SWG	TAI	THA	TRI	TUR	USA	URU	VEN	VIE
AFE	1.231	.656	.933	1.691	1.159	1.098	1.467	1.066	1.066	3.516	1.014	1.109	.848	1.222	2.653	1.865	.984	2.286	.218	.127	.429	.593	2.444	1.088	1.283	.281
AFW	.725	.650	.509	1.724	1.291	.788	1.201	.774	1.049	2.852	1.136	1.546	1.160	1.122	3.849	2.472	1.100	3.006	.320	.249	.621	.668	3.184	1.255	.801	.337
ARA	.662	.620	.497	.687	1.038	.410	.663	.449	1.951	2.046	1.129	1.111	.620	.517	4.242	1.847	.371	2.400	.513	.554	.928	.300	2.424	.811	.615	1.030
ARG	1.835	.661	2.146	.360	.802	1.212	1.446	1.107	3.687	3.487	1.420	.866	.188	1.012	3.929	.865	.519	1.157	.641	1.009	.870	.287	1.740	.429	1.340	2.271
AUL	5.366	3.663	3.270	1.775	3.863	4.106	4.247	4.203	3.897	3.901	4.289	.345	1.729	3.297	2.684	.302	1.058	.373	2.889	3.123	2.443	2.419	.016	3.036	4.105	3.246
AUT	5.846	3.381	4.625	2.273	3.947	4.989	5.559	4.749	5.364	4.984	5.134	1.263	2.318	4.638	5.112	.502	2.324	.344	2.713	3.601	1.824	2.798	1.532	3.170	3.622	4.387
BAN	.582	.632	.358	1.372	1.349	.665	1.116	.639	1.386	2.172	1.387	1.531	1.172	1.069	4.766	2.365	.955	2.912	.390	.471	.642	.616	3.231	1.235	.388	.662
BEL	2.395	1.643	2.583	.176	1.398	1.347	1.242	1.427	5.027	3.359	1.924	1.243	.422	.778	4.471	1.388	.362	1.821	1.857	2.048	2.458	.727	1.645	.863	2.291	3.487
BEF	2.271	1.621	2.302	.075	1.514	1.305	1.274	1.374	4.863	2.812	2.114	1.164	.506	.837	4.930	1.298	.296	1.733	1.808	2.083	2.304	.727	1.660	.945	1.941	3.423
BEN	2.668	1.727	3.237	.494	1.240	1.503	1.279	1.588	5.474	4.538	1.643	1.577	.386	.782	3.847	1.730	.652	2.162	2.013	2.063	2.813	.819	1.863	.786	2.987	3.724
BRA	.767	.320	1.036	.516	.567	.409	.626	.389	2.431	2.812	.775	1.044	.240	.410	3.774	1.562	.371	2.043	.296	.388	.760	.057	2.263	.363	.791	1.241
BUL	.523	.111	1.570	.841	.186	.242	.395	.186	3.016	3.884	.327	1.802	.291	.284	4.018	2.369	.847	2.910	.299	.307	1.061	.048	3.226	.148	1.034	1.532
CAN	4.603	2.956	2.827	1.750	3.146	3.500	3.654	3.578	3.059	4.113	3.374	.242	1.332	2.787	1.842	.360	.920	.468	2.183	2.280	1.868	1.926	.127	2.488	3.714	2.374
CAF	2.957	1.835	2.023	.981	1.856	1.987	2.025	2.089	2.785	3.610	1.957	.335	.555	1.388	1.927	.690	.351	.984	1.413	1.374	1.575	.953	.557	1.369	2.723	1.828
CHL	.827	.164	2.381	1.568	.097	.583	.707	.481	3.354	5.481	.104	2.435	.503	.601	3.562	3.015	1.534	3.534	.380	.269	1.288	.299	3.932	.219	1.745	1.678
CHI	2.054	2.166	.273	2.733	3.410	2.287	2.980	2.304	.492	1.722	3.315	1.609	2.676	2.829	5.174	2.598	1.732	3.054	1.344	1.452	.977	2.043	3.237	3.156	1.105	.544
COL	.752	.382	1.207	1.045	1.057	.823	1.353	.656	2.784	2.626	1.586	1.833	1.051	1.283	5.986	2.197	1.212	2.646	.373	.801	.564	.524	3.631	.897	.178	1.672
COS	2.427	.795	4.297	2.855	.662	2.136	2.357	1.883	4.391	8.089	.801	3.144	1.156	2.063	3.156	3.339	2.851	3.632	.859	.847	1.542	1.170	4.526	.854	3.200	2.508
CRO	.514	.199	1.303	.830	.308	.220	.364	.201	2.671	3.579	.367	1.626	.306	.244	3.790	2.281	.706	2.836	.316	.271	1.050	.065	2.998	.248	1.021	1.309
CZE	1.971	1.041	1.547	.283	1.233	1.246	1.426	1.251	2.993	2.656	1.666	.391	.254	.944	3.402	.591	.120	.918	.848	1.087	1.002	.401	1.041	.763	1.433	1.885
DEN	7.602	5.164	5.916	5.572	5.112	6.473	6.557	6.531	3.893	9.490	4.637	2.504	3.531	5.519	.205	2.865	3.933	2.844	3.967	3.527	3.715	4.398	2.185	4.792	7.644	3.239
ECA	.605	.654	.657	1.566	1.526	.870	1.457	.758	1.947	2.229	1.797	2.049	1.550	1.484	6.113	2.738	1.423	3.268	.497	.784	.661	.840	4.032	1.428	.124	1.154
SAL	.547	.033	2.163	1.149	.104	.390	.599	.251	3.722	4.633	.378	2.462	.526	.554	4.832	2.911	1.407	3.442	.363	.471	1.190	.199	4.121	.151	1.093	2.025
EST	3.231	1.631	2.951	1.813	1.522	2.354	2.411	2.357	2.915	5.638	1.491	.901	.635	1.759	1.022	1.204	1.131	1.426	1.190	1.042	1.447	1.083	1.253	1.257	3.413	1.721
FIN	3.945	2.075	3.676	2.307	1.879	2.971	2.999	2.963	3.385	6.573	1.830	1.183	.932	2.265	.791	1.408	1.573	1.573	1.584	1.407	1.818	1.503	1.386	1.613	4.171	2.135
FRA	1.980	1.326	2.230	.395	1.043	1.014	.875	1.122	4.163	3.682	1.265	1.182	.243	.458	3.415	1.570	.312	2.050	1.470	1.437	2.201	.509	1.665	.650	2.308	2.683
GER	3.968	2.261	2.724	1.026	2.592	3.031	3.337	2.980	3.654	3.420	3.283	.245	1.018	2.554	3.336	.037	.756	.113	1.713	2.176	1.308	1.450	.454	1.902	2.609	2.745
GBR	6.314	4.540	3.427	2.640	5.015	5.131	5.412	5.234	3.525	3.947	5.381	.464	2.597	4.388	2.850	.464	1.614	.463	3.442	3.699	2.643	3.268	.087	4.123	4.640	3.265
GRE	1.162	.411	2.237	.368	.521	.732	.954	.599	4.432	3.546	1.208	1.766	.375	.736	5.469	1.846	.866	2.272	.720	1.126	1.250	.237	3.044	.263	.948	2.774
GUA	.117	.665	2.255	2.219	.798	.314	.481	.247	4.407	4.883	.801	4.381	1.787	.806	7.238	5.351	2.521	6.173	1.288	1.205	2.576	1.024	6.637	1.047	1.299	2.721
HOK	2.218	1.862	.550	2.584	2.914	2.278	2.900	2.277	.307	2.468	2.760	1.123	2.123	2.615	3.645	1.995	1.492	2.362	.975	1.004	.618	1.712	2.499	2.683	1.441	.222
HUN	4.834	3.503	3.433	.923	3.870	3.741	4.014	3.731	5.858	2.569	5.026	1.089	1.968	3.259	6.511	.661	1.157	.796	3.224	4.011	2.790	2.368	1.198	2.898	2.885	4.884
IND	1.924	1.769	.329	1.537	2.466	1.608	1.957	1.728	.896	1.762	2.333	.645	1.413	1.627	3.363	1.522	.585	1.975	1.123	1.069	1.069	1.205	1.623	2.096	1.419	.603
IDO	.881	.873	.527	2.207	1.643	1.072	1.558	1.048	.815	3.009	1.414	1.817	1.567	1.512	4.054	2.829	1.466	3.366	.448	.356	.674	.986	3.584	1.650	.918	.237
IRA	1.526	.679	1.198	1.100	.990	1.106	1.368	1.091	1.635	3.425	1.010	.634	.403	.990	2.288	1.169	.533	1.532	.303	.283	.510	.379	1.614	.782	1.456	.694
IRE	5.751	3.820	3.146	2.616	4.500	4.848	5.320	4.835	2.933	3.940	4.964	.375	2.400	4.361	2.884	.285	1.689	.231	2.682	3.069	1.742	2.903	.359	3.721	3.899	2.664
ISR	4.630	2.137	4.807	2.008	2.077	3.665	3.905	3.454	5.232	6.755	2.811	1.475	1.130	3.088	2.911	.977	2.030	.952	1.816	2.240	1.703	1.727	1.773	1.646	3.885	3.657
ITA	3.531	2.313	2.437	.480	2.520	2.502	2.673	2.533	4.248	2.598	3.252	.421	.924	1.987	4.302	.315	.405	.528	2.019	2.469	1.872	1.306	.614	1.763	2.333	3.236
JAM	4.794	3.616	1.865	3.652	4.872	4.586	5.351	4.558	.934	3.235	4.944	.959	3.253	4.697	3.544	1.434	2.296	1.517	2.231	2.474	1.172	3.183	1.752	4.352	3.022	1.218
JPN	3.377	2.485	2.817	.890	3.180	2.872	3.396	2.721	5.585	2.059	4.492	1.819	2.059	2.970	8.363	1.456	1.511	1.693	2.437	3.419	2.080	1.943	2.818	2.431	1.391	4.511
KOR	.733	.019	2.017	1.286	.183	.591	.864	.440	3.088	4.660	.397	2.082	.486	.747	4.074	2.522	1.348	2.985	.155	.246	.800	.203	3.675	.225	1.139	1.547
LAT	4.130	2.564	4.402	2.993	1.995	3.038	2.807	3.127	4.182	7.957	1.597	2.224	1.298	2.161	.676	2.753	2.153	3.069	2.285	1.765	3.036	1.920	2.368	1.876	5.275	2.699
Country	PAN	PER	PHI	POL	POR	ROM	RUS	SER	SIN	SLK	SLV	SAW	SPA	SUR	SWE	SWI	SWF	SWG	TAI	THA	TRI	TUR	USA	URU	VEN	VIE

LIT	3.302	1.736	3.549	2.228	1.396	2.385	2.316	2.403	3.481	6.759	1.210	1.560	.761	1.713	.900	1.963	1.560	2.245	1.445	1.133	2.002	1.240	1.931	1.251	4.025	2.061
LUX	2.909	1.357	2.466	.845	1.447	2.050	2.231	2.004	3.245	4.046	1.870	.396	.371	1.580	2.385	.407	.563	.592	1.006	1.224	1.027	.742	.805	.990	2.353	2.065
MAL	1.368	2.103	.209	2.822	2.989	1.544	1.955	1.690	.787	2.207	2.500	2.339	2.595	1.984	5.060	3.760	1.753	4.451	1.588	1.320	1.858	1.906	4.029	2.900	1.458	.615
MLT	1.919	.899	2.673	.295	.662	1.056	1.037	1.032	4.656	4.139	1.170	1.315	.096	.619	3.897	1.401	.542	1.791	1.131	1.324	1.765	.330	1.983	.305	1.999	2.951
MEX	.726	.787	.826	.565	1.370	.603	.985	.562	3.083	1.581	1.880	1.674	1.051	.922	6.482	2.163	.730	2.713	.871	1.250	1.186	.568	3.244	1.061	.170	2.049
MOR	1.105	.677	.782	.482	1.007	.663	.888	.692	2.092	2.260	1.188	.656	.353	.596	3.542	1.202	.161	1.657	.494	.583	.792	.233	1.687	.694	.891	1.126
NET	5.095	3.299	4.620	3.273	2.825	3.857	3.661	3.975	4.130	7.851	2.459	1.905	1.671	2.854	.405	2.345	2.229	2.564	2.772	2.297	3.225	2.445	1.740	2.553	5.828	2.894
NZL	5.844	3.620	3.934	2.334	3.884	4.674	4.940	4.660	3.945	5.035	4.381	.516	1.893	3.920	2.295	.278	1.619	.218	2.725	3.039	2.098	2.623	.262	3.135	4.445	3.230
NOR	5.355	3.346	5.121	3.981	2.910	4.253	4.129	4.306	4.113	8.923	2.471	2.372	1.995	3.336	.225	2.808	2.871	2.985	2.754	2.245	3.182	2.729	2.366	2.766	6.207	2.841
PAK	1.062	.236	1.476	1.418	.784	1.048	1.538	.870	2.114	3.755	1.071	1.491	.770	1.343	4.026	1.878	1.261	2.238	.028	.264	.195	.427	3.094	.720	.784	1.002
PAN		.558	1.349	1.770	.896	.182	.429	.150	3.290	3.609	.890	3.400	1.517	.673	6.580	4.393	1.843	5.167	.934	.890	1.929	.771	5.518	1.023	.767	1.944
PER	.200		1.880	1.218	.211	.472	.764	.322	3.160	4.360	.462	2.200	.561	.698	4.575	2.665	1.349	3.161	.187	.313	.852	.203	3.889	.250	.923	1.629
PHI	.385	.485		1.905	2.828	1.401	1.867	1.509	1.111	1.153	2.723	1.633	2.149	1.803	5.529	2.724	1.130	3.331	1.399	1.418	1.448	1.542	3.170	2.546	.832	.900
POL	.425	.318	.442		1.291	1.019	1.113	1.035	4.456	2.410	1.951	1.169	.477	.763	5.352	1.311	.295	1.754	1.405	1.768	1.828	.524	1.952	.778	1.299	3.066
POR	.297	.151	.578	.319		.544	.598	.429	4.372	5.613	.200	2.707	.441	.498	4.320	3.131	1.563	3.664	.642	.631	1.676	.286	4.156	.073	1.813	2.450
ROM	.147	.171	.382	.304	.213		.079	.023	3.523	3.441	.592	2.630	.816	.160	5.520	3.473	1.111	4.198	.877	.805	1.919	.366	4.275	.535	.976	2.044
RUS	.213	.217	.420	.300	.203	.077		.153	4.189	4.007	.569	2.957	.862	.069	5.458	3.844	1.228	4.616	1.295	1.109	2.564	.522	4.435	.591	1.563	2.547
SER	.131	.126	.406	.313	.190	.048	.112		3.582	3.597	.552	2.669	.789	.237	5.627	3.430	1.207	4.124	.735	.729	1.732	.316	4.394	.442	.862	2.054
SIN	.619	.751	.274	.701	.846	.641	.675	.666		3.687	3.781	2.224	3.601	3.944	3.728	3.487	2.815	3.898	1.986	1.741	1.579	3.086	3.699	4.264	2.781	.293
SLK	.511	.550	.186	.417	.641	.483	.519	.501	.333		6.151	2.535	4.075	3.826	9.597	3.251	2.021	3.804	3.872	4.403	3.434	3.502	3.753	4.830	1.734	3.767
SLV	.267	.226	.554	.379	.140	.180	.139	.179	.805	.652		3.046	.745	.526	3.602	3.824	1.852	4.443	.804	.495	2.011	.549	4.527	.401	2.327	1.995
SAW	.648	.590	.461	.290	.607	.542	.538	.563	.634	.343	.643		1.113	2.272	2.821	.206	.485	.389	1.479	1.725	1.083	1.376	.345	2.079	2.233	1.690
SPA	.418	.296	.512	.116	.243	.282	.255	.290	.776	.517	.299	.380		.487	3.142	1.376	.480	1.777	.652	.730	1.247	.138	1.935	.189	1.730	2.060
SUR	.280	.246	.429	.240	.210	.134	.077	.165	.687	.504	.174	.477	.187		4.593	3.018	.809	3.702	1.111	.959	2.227	.318	3.480	.397	1.602	2.342
SWE	.962	.923	.864	.673	.838	.823	.761	.860	.981	.843	.805	.586	.649	.696		3.469	3.734	3.611	3.622	2.957	3.819	3.893	2.704	4.170	7.350	2.876
SWI	.726	.624	.591	.324	.632	.619	.616	.630	.773	.460	.699	.160	.407	.551	.634		.915	.042	1.968	2.464	1.380	1.807	.368	2.384	2.781	2.771
SWF	.470	.421	.374	.146	.427	.349	.338	.375	.606	.341	.446	.201	.219	.276	.592	.305		1.345	1.165	1.296	1.413	.559	1.122	1.061	1.425	1.863
SWG	.791	.681	.655	.388	.687	.685	.683	.694	.827	.514	.761	.223	.465	.618	.658	.072	.376		2.365	2.935	1.614	2.291	.443	2.869	3.324	3.211
TAI	.200	.112	.390	.270	.240	.170	.232	.142	.657	.440	.298	.510	.289	.250	.905	.557	.355	.615		.124	.287	.336	3.034	.611	.900	.852
THA	.134	.155	.360	.295	.227	.043	.117	.047	.623	.456	.215	.530	.287	.162	.845	.604	.344	.670	.133		.626	.432	3.244	.697	1.359	.615
TRI	.370	.309	.369	.308	.430	.360	.418	.344	.606	.335	.503	.443	.390	.415	.959	.471	.369	.519	.210	.320		.961	2.526	1.483	1.041	.848
TUR	.284	.173	.432	.160	.181	.161	.166	.161	.705	.470	.234	.437	.138	.134	.758	.483	.257	.546	.158	.157	.306		2.608	.133	1.004	1.641
USA	.835	.765	.647	.448	.750	.713	.692	.738	.780	.530	.782	.209	.507	.622	.460	.220	.366	.234	.701	.709	.645	.601		3.311	4.197	3.178
URU	.332	.175	.549	.234	.091	.221	.207	.207	.821	.589	.194	.522	.157	.183	.778	.542	.351	.597	.226	.229	.389	.120	.662		1.598	2.435
VEN	.250	.268	.312	.377	.411	.292	.364	.274	.547	.356	.451	.537	.434	.389	1.005	.596	.422	.652	.173	.249	.152	.314	.744	.398		1.922
VIE	.366	.495	.078	.486	.584	.377	.413	.403	.265	.262	.542	.523	.542	.433	.881	.658	.419	.724	.412	.360	.422	.455	.703	.566	.340

While $θ$ can mathematically assume values in $[- π / 2; π / 2]$ , in the context of culture, $θ$ has values in the interval between 0 (no difference) to $π / 2$ (totally different). Because Hofstede’s cultural dimensions are defined only within positive numbers, the weight vectors exist only in the nonnegative orthant, and are undefined with negative coordinates. If values in the range of 0 (no difference) to 1 (totally difference) are desired, $θ$ can be normalized:

\tilde{θ} (a, b) = \frac{θ (a, b)}{π / 2} .

The country weight vectors $\overset{⇀}{a}$ and $\overset{⇀}{b}$ are not standardized for several reasons. First, in computing similarity between data sets, the angular distance typically outperforms the Euclidean distance measure on nonstandardized data; however, there is no clear performance difference between the measures for standardized data (Nkweteyim 2018). Second, Kogut and Singh (1988) do not provide a detailed explanation of the reason for the variance correction in their index (Konara and Mohr 2019). Third, and as discussed previously, standardization is not desirable for cultural dimensions because the country scores do not follow a normal distribution and the variance factor is dependent on the number of countries.

Evaluation of Construct Validity

To contrast the overall quality of the geometrical measurement with the Kogut–Singh index, multidimensional scaling (MDS) is deployed on both difference measures. MDS is a technique used to determine coordinates for a set of objects in a n-dimensional space, strictly using matrices of pairwise differences between these objects (Giguère 2006). The geometrical measurement has lower stress levels and higher levels of variance explained than the arithmetical measurement ( $θ$ : stress = .101, R² = .953; KSI: stress = .182, R² = .843); that is, the amount of conflict present in the data is less for the angle of heterogeneity than for the Kogut–Singh index (Hout, Papesh, and Goldinger 2013).

Figure 4 compares the angle of heterogeneity with the Kogut–Singh index for all 6,006 country pairs. Lin’s concordance correlation is poor at .117 with limits [.113, .121]; the Bland–Altman test shows a mean difference of .862 (SE = .008, SD = .683),⁵ and the second-order polynomial trendline through the origin is $K S I = 3.250 θ^{2} + 2.700 θ$ , R² = .779. The Kogut–Singh index progressively places greater weight on the differences as they increase, but even more importantly, as differences between countries increase, both indices seem to be fanning out and showing less agreement. Similarly, Figure 5 compares the angle of heterogeneity with the standardized Euclidean distance. Lin’s concordance correlation is again poor at .066 with limits [.063; .068]; the Bland-Altman test shows a mean difference of .225 (SE = .007, SD = .594),⁶ and the trendline is $E C D_{s t d} = - 2.881 θ^{2} + 7.404 θ$ , R² = .823. As opposed to the Kogut–Singh index, the standardized Euclidean distance progressively places lesser weight on the differences as they increase. Again, as differences between countries increase, the indices show less agreement.

Figure 4.

Angle of heterogeneity θ versus Kogut–Singh index.

Figure 5.

Angle of heterogeneity θ versus standardized Euclidean distance.

These effects of convergent and discriminant validity (Churchill 1979) can be pointed out with a mathematical simulation. Let two countries A and B be characterized by vectors $\overset{⇀}{a} = \overset{⇀}{b} = 〈55, 55, 55, 55〉$ , wherein 55 is the rounded average of all Hofstede country scores across the four dimensions. Now let $a_{1}$ change stepwise from 55 to 100, keeping all other scores constant, calculate $θ$ at each step using Equation 8, and compare it with the standardized Euclidean distance (Equation 3) and the Kogut–Singh index (Equation 1).⁷ Figure 6 shows that the angle of heterogeneity is strictly concave on the interval; that is, it has a nonincreasing slope. The slope of the standardized Euclidean distance is linear, and the Kogut–Singh index is strictly convex with an increasing slope. Thus, the Kogut–Singh index forgives small changes in one dimension and only starts paying more importance to it as the change becomes more pronounced. The angle of heterogeneity, in contrast, first emphasizes a small deviation in one dimension and, as the deviation increases, reduces its emphasis on it.

Figure 6.

Simulating the performance of difference measures.

These effects owe to the fact that the $θ$ -formula (Equation 8) mathematically does not take the length of the weight vectors into account. As discussed previously, this is a desired feature when comparing colors or images, because differences in illumination need to be filtered out. But what does a focus on the vector direction imply for comparing cultures? It is best to start the discussion with considering an example. Let country A score 20 on all four Hofstede dimensions, and country B score 80 on all dimensions. Because the weight vectors of both these countries are linearly dependent, the angle of heterogeneity does not detect a difference—even though any Euclidean measure would indicate a difference. This seeming idiosyncrasy deserves some explanations. First and probably most importantly, a constellation with weight vectors of two countries being perfectly linearly dependent is purely theoretical. As a matter of fact, across all 78 countries or regions covered by Hofstede, the tolerance statistic of the cultural dimensions is well above the threshold of .2 (UAI: .937, PDI: .592, MAS: .935, IDV: .616). That is, multicollinearity is not an issue (Mansfield and Helms 1982). Second, a country’s culture is represented as a combination of relative (but not absolute) positions on the Hofstede cultural dimensions. As explained before, the scales have been stretched so that the difference between the lowest- and highest-scoring countries is about 100 (Hofstede 2011; Hofstede and Usunier 2003). Desmet, Ortuño-Ortín, and Wacziarg (2017) refer to this combination as the vector of traits, which unveils a striking similarity to the RGB color vector. When comparing colors, images, or cultures, filtering out superficial differences of illumination or intensity is actually a desired effect. And indeed, prior research has shown that cultural or linguistic response style differences can lead to a systematic cross-cultural bias in country averages (e.g., Harzing 2006; Harzing et al. 2012). Thus, it would be possible that a country systematically scores lower or higher across all dimensions, and that weights might be smaller or larger without meaning anything different. Because the angle of heterogeneity disregards the length of the weight vector, this improves, in point of fact, the quality of the difference measure by filtering out potential response style differences.

In addition, and related to this discussion, at least a two-dimensional feature space is required for calculating the angle of heterogeneity. Vectors do not exist in a one-dimensional feature space, and so Equation 8 returns 0 whenever k = 1.

Effect of Cultural Differences on Exports

The construct validity of the angle of heterogeneity as a new geometrical cultural difference measure is next illustrated with an empirical example and an exemplary research hypothesis. This follows suggestions for best practices in measurement development (Churchill 1979) and prior literature on developing and comparing cultural difference measures (e.g., Berry, Guillén, and Zhou 2010; Kim and Gray 2009) as well as other measurement tools (e.g., concordance correlation [Lin 1989], necessary condition analysis [Messner 2021b], outlier detection [Mullen, Milne, and Doney 1995], cosine similarity [Tata and Patel 2007]).

Research Hypothesis

Prior studies on export marketing have consistently found that cultural differences are negatively related to bilateral export flows (e.g., Cyrus 2012; Shoham and Albaum 1995; Slangen, Beugelsdijk, and Hennart 2011; Sousa and Tan 2015; Tadesse and White 2010). Export flows from India are a good case study because typical confounding factors in export marketing, such as the existence of land borders, do not play a major role for India. Most of the country’s exports go through sea- and airports, rather than land border crossings. There is no trade between India and China via the land route, trade between India and Pakistan through the land route is very limited, and trade volumes with Myanmar and Bhutan are also relatively low. While trade with Bangladesh is mainly carried out by road, it is also supplemented with coastal shipping. Note that, until 2015, Indian vehicles were not even allowed to enter Bangladesh, Bhutan, and Nepal (Sinate, Fanai, and Joy 2018). More formally, the following hypothesis is tested:

H₁: India’s bilateral export volume is negatively associated with cultural differences to its partner economies.

Research Model and Data

The dependent variable in the research model is the average export volume to India’s 194 partner economies from 2014 to 2018 (WTO 2019). The main independent variable is cultural difference, separately operationalized with the angle of heterogeneity (Model A), the Kogut–Singh index (Model B), Euclidean distance (Model C), and Mahalanobis distance (Model D). The Hofstede dimensions are directly available for 68 of the 194 partner countries; no substitutions for neighboring countries are made, and the general Hofstede scores for Africa West, Africa East, and Arab countries are not used. Three additional variables are introduced into the model: First, gross domestic product (GDP) measures the size of the partner economy. Second, GDP per capita in purchasing power parity (PPP) approximates the national income. Both are calculated as a ten-year average from 2010 to 2019 (World Bank 2020a, b), and a positive association with export volume from India is expected. Third, the physical distance to a partner economy is calculated as the air distance between New Delhi and the partner economy’s capital city (https://www.timeanddate.com/worldclock/distance.html); a negative association with export volume is expected (e.g., Frankel, Stein, and Wei 1997; Ghemawat 2001; Sheng and Mullen 2011).

Results

The four models using different cultural difference measures are estimated separately with a linear regression in SPSS 27. Cook’s D, an influence statistic measuring the impact of an observation on all regression coefficients (Everitt and Skrondal 2010), identifies the United States and China as outliers. Depending on the model, Cook’s D for the United States is between 9.882 and 10.848. For China, the angle of heterogeneity in Model A produces the lowest (D = 1.266) and Model C the highest (D = 1.542) statistic. All other countries are inconspicuous. With a share of 16.02% and 5.08%, respectively, the United States and China are India’s largest and third-largest trading partners, which justifies them being considered outliers. Thus, the models are estimated again without the United States and China; the results are shown in Table 2.

Table 2.

Empirical Illustration: Export Volume From India.

A: Model Using the Angle of Heterogeneity θ
Variable	B	SE	β	t	p	VIF
	4,988,700	1,100,138		4.535	<.001
GDP	1.20E−06	2.96E−07	.402	4.051	<.001	1.051
GDP per capita PPP	28.141	15.850	.193	1.776	.081	1.258
Geographic distance	−129.688	65.661	−.207	−1.975	.053	1.164
Angle of heterogeneity	−7,393,704	2,300,806	−.338	−3.214	.002	1.176
R² = .427; adjusted R² = .389
B: Model Using the Kogut–Singh Index
Variable	B	SE	β	t	p	VIF
	3,975,172	861,467		4.614	<.001
GDP	1.27E−06	2.86E−07	.425	4.435	<.001	1.042
GDP per capita PPP	27.895	15.103	.191	1.847	.070	1.215
Geographic distance	−142.549	62.305	−.227	−2.288	.026	1.116
Kogut–Singh index	−1,344,456	348,104	−.382	−3.862	<.001	1.110
R² = .461; adjusted R² = .426
C: Model Using the Euclidean Distance Proximity
Variable	B	SE	β	T	p	VIF
	6,209,775	1,201,456		5.169	<.001
GDP	1.31E−06	2.85E−07	.439	4.598	<.001	1.042
GDP per capita PPP	27.984	15.009	.192	1.864	.067	1.212
Geographic distance	−116.025	63.525	−.185	−1.826	.073	1.172
Euclidean distance	−86,585	21,869	−.397	−3.959	<.001	1.148
R² = .467; adjusted R² = .432
D: Model Using the Mahalanobis Distance
Variable	B	SE	β	t	P	VIF
	5,360,450	1,142,258		4.693	<.001
GDP	1.30E−06	2.92E−07	.436	4.447	<.001	1.042
GDP per capita PPP	22.858	15.186	.157	1.505	.137	1.175
Geographic distance	−131.176	64.752	−.209	−2.026	.047	1.152
Mahalanobis distance	−1,318,262	387,406	−.344	−3.403	.001	1.105
R² = .437; adjusted R² = .400

Cultural differences negatively and significantly influence the export volume in all four models, which confirms H₁. In addition, the partner economy’s GDP exerts a positive and significant effect. The effect of GDP per capital PPP, however, is not significant. The physical distance of the partner economy from India is negatively associated with the export volume, but the effect is significant for only Models B (−142.549, p = .026) and D (−131.176, p = .047); it is not significant for Models A (−129.688, p = .053) and C (−116.025, p = .073).

As a robustness test, the necessary impact of a potentially unobserved confound for invalidating the inference that cultural difference is associated with India’s export volume is examined (following Frank [2000], Frank et al. [2013], and Rosenberg, Xu, and Frank [2018]). In Model A, such a confounding variable would have to be correlated with the angle of heterogeneity and the export volume at .423. In addition, the robustness with respect to external validity is examined by determining that 37.775% (or 25 countries) would have to be replaced with unobserved cases for which the null hypothesis is true to invalidate the inference. This thought experiment helps defend a potential concern that the 66 countries for which the Hofstede dimensions are available may not be representative for all 194 partner economies.

Model Comparison

The negative influence of cultural differences on export volume is confirmed in all four models with high statistical significance, albeit with some notable differences. At first glance, the angle of heterogeneity in Model A has a lesser statistical significance (−7.393, p = .002) than the Kogut–Singh index (Model B; −1.344, p < .001), Euclidean distance (Model C; −.086, p < .001), and Mahalanobis distance (Model D; −1.318, p = .001). Generally, multicollinearity is not an issue in any of the models; the variable inflation factor never exceeds 1.258. The collinearity diagnostics tables, however, show lower condition indices and associated variance proportions for Models A and D. However, there is a slight multicollinearity effect in Models B and C, which seems to marginally increase the significance of coefficients in these models.

Next, a comparison of the absolute values of the standardized regression coefficients provides a rough indication of the importance of the variables in the models (Siegel 2017). Potential concerns about comparing coefficients directly between models can be alleviated by very similar overall model fits; the R² values fall within a range from .427 (Model A) to .467 (Model C). In Model A, the importance of the angle of heterogeneity is 45.799%, calculated as .338/(.402 + .193 + .207 + .338). However, in Models B, C, and D, the importance of the cultural distance measure is only 31.118%, 32.728%, and 30.001%, respectively. Across the models, the angle of heterogeneity attracts the highest importance.

In the four models, the choice of cultural difference measure also influences the statistical significance of the regression coefficient for geographical distance. A stream of literature finds that developing countries often face higher costs to export, and that within-country infrastructure to transport increases border costs (Van Leemput 2016; e.g., Limão and Venables 2001). For example, each day in transit adds costs up to an ad valorem tariff of 2.3% (Hummels and Schaur 2013). India is notorious for its dismal transport infrastructure and long customs clearing time at its ports (Mackie and Greer 2012). This arguably reduces the influence of intercountry transportation costs to overall logistics costs. In addition, shipping rates are influenced by not only geographical distance but also competition, overall trade volume, direction, and season.⁸ Thus, models with a negative but statistically nonsignificant coefficient might be the more accurate ones for developing economies, which further supports the choice of the angle of heterogeneity as a cultural difference measure.

Taken together, this illustrative empirical analysis reveals that the angle of heterogeneity is indeed a different construct from the Kogut–Singh index, Euclidean distance, and Mahalanobis distance (discriminant validity; Churchill 1979) and might be better suited for examining international business research questions.

Discussion

This research does not propose a new approach to conceptualizing or examining the influence of cross-national cultural difference. Instead, it reviews and highlights why the Kogut–Singh index, the (standardized) Euclidean distance measure, and the Mahalanobis distance are unsuitable mathematical tools when applied to cultural dimensions. The use of deficient measures—that is, measures that do not fully capture the construct or are not sufficiently reliable—has been identified as the most frequent challenge in international business research (Aguinis, Ramani, and Cascio 2020; Eden and Nielsen 2020). Because the concept of cultural difference continues to play a central role in international business research and managerial practice, the use of a mathematically correct measure is paramount (Konara and Mohr 2019).

In this vein, this article first identifies the methodological shortcomings of arithmetic distance measurement with respect to cultural dimensions. First, cultural dimensions are undoubtedly interrelated and therefore a nonorthogonal feature space. Second, due to the design of Hofstede’s dimensions, a country’s position on a cultural dimension is a relative position, but not an absolute position. Third, country scores on cultural dimensions are not normally distributed, which makes a variance correction unsuitable from a mathematical point of view. Fourth, country scores are only available for less than half of the world’s countries; for that reason, variance and covariance correction factors are instable and should not be used. In addition, variance correction factors introduce counterintuitive weights contradicting much of extant international business research. The adverse influence of the weight effects is demonstrated in this article.

As a contribution to the international business methodology literature, the article then offers a geometrical measurement of cultural differences based on the angle of heterogeneity between two cultural weight vectors. This metric measures common characteristics (Xia, Zhang, and Li 2015) and thus expresses how related (or different) two countries are. It does not necessitate independence of the cultural dimensions, does not call for the dimensions to have equivalent measurement scales, and produces identical results independent of the number of countries the dimensions are based on. The MDS technique shows that there is less conflict present in the geometrical difference measurement than in the Kogut–Singh index. An empirical example using export volumes as a dependent variable illustrates that the angle of heterogeneity has noteworthy and appropriate effects in a linear regression model as compared with other arithmetical measures. The angle of heterogeneity reduces multicollinearity between the independent variables and emphasizes the relative importance of cultural differences as compared with other variables. Future research should certainly investigate these effects in other business administration disciplines.

Setting aside these advantages, two limitations of the angle of heterogeneity should be noted. First, geometrical measurement does not detect a difference between two countries if their weight vectors are multiples of each other. While such a constellation is purely theoretical, this article shows that this feature actually reduces cultural differences in survey response styles. Second, because geometric measurement works on vectors defined in a multidimensional feature space, at least two dimensions are required. It is therefore not possible to calculate separate angles of heterogeneity for UAI, PDI, MAS, or IDV; the angle of heterogeneity is a composite measure (Schnack and Kahn 2016) requiring at least two dimensions. Commentators disagree on how many dimensions should be aggregated into a measure of cultural difference. One view recommends calculating the measure separately for multiple dimensions, as called for by theoretical and domain considerations (Shenkar 2001). The angle of heterogeneity does not support this view. While a Euclidean distance measure could theoretically be used, the extant international business literature has not yet evaluated different forms of single-dimension difference measures. This opens up promising avenues for future methodological research. In contrast, other commentators argue that an overall measure integrating as many dimensions as possible, even from competing frameworks, picks up more variation in cultural differences (Beugelsdijk, Ambos, and Nell 2018; Beugelsdijk, Kostova, and Roth 2017; Steenkamp 2001). Geometric measurement is much better equipped to support this view than arithmetic formulas because it does not require the dimensions to have comparable scales and scale anchors. Using dimensions from several frameworks with the angle of heterogeneity would further reduce the already unlikely occurrence of linear dependence between two countries. Further research could attempt to portray these effects.

Although measuring the angle of heterogeneity between two vectors is well established in linear algebra and regularly used in applied fields such as computer image processing, it has not yet been exploited by international business researchers. Equation 8 is easy to compute with a spreadsheet or in any statistical program. It is therefore my hope that the proposed geometrical measurement of cultural difference using the angle of heterogeneity between two cultural weight vectors will help resolve some of the inconsistencies reported in the international business and marketing literature concerning the effects of arithmetic distance indices, such as the Kogut–Singh index, the (standardized) Euclidean distance index, and the Mahalanobis distance.

Footnotes

Mathematical Appendix

The Mathematical Appendix explains how the formula for the angle of heterogeneity (Equation 8) is derived from the dot product between two vectors.

The arithmetic calculation is the dot product (or inner product or scalar product) between two weight vectors. It is a “dimension-reducing operation” (Farouki 2007, p. 82) resulting in a scalar value:

When the dot product is zero, the two vectors have an angle of $π / 2$ between them (i.e., they are orthogonal).

The norm (or length or magnitude) of a vector is defined as

Let M be the (hyper)plane spanned by two vectors $\overset{⇀}{a}$ and $\overset{⇀}{b}$ . The two vectors generate a triangle with sides of length $‖\overset{⇀}{a}‖$ , $‖\overset{⇀}{b}‖$ , and $‖\overset{⇀}{a} - \overset{⇀}{b}‖$ . If $θ$ is the angle between $\overset{⇀}{a}$ and $\overset{⇀}{b}$ in M, then the cosine rule gives the following expression (proof in, e.g., Cheney and Kincaid 2012, p. 415; Galbis and Maestre 2012, p. 4):

Equation MA.3 is generally used to define the cosine of the angle between two vectors:

Equation MA.4 is commonly referred to as cosine similarity (e.g., Ye 2011). The effect of the denominator in Equation MA.5 is to length-normalize the vectors $\overset{⇀}{a}$ and $\overset{⇀}{b}$ to unit vectors (Manning, Raghavan, and Schütze 2008). The equivalence of the arithmetic and geometric definition of the dot product is a general result holding up for any vectors (Gurney 1997). Substituting Equations MA.1 and MA.2 into Equation MA.5 leads to

As the angle approaches $π / 2$ , the cosine diminishes and eventually reaches zero. The dot product $\overset{⇀}{a} \times \overset{⇀}{b}$ follows in agreement with this, and when the two vectors are at right angles, they are said to be orthogonal with $\overset{⇀}{a} \times \overset{⇀}{b} = 0$ . When $\overset{⇀}{a}$ and $\overset{⇀}{b}$ are well aligned, they point in roughly the same direction, with $\overset{⇀}{a} \times \overset{⇀}{b}$ being close to its largest positive value of $‖\overset{⇀}{a}‖ ‖\overset{⇀}{b}‖$ .

List of Abbreviations and Mathematical Symbols

Associate Editor

Babu John Mariadoss

Acknowledgments

The author is very grateful for insights, suggestions, and constructive guidance offered by the JIM review team, which led to substantial changes and improvements in this article. Any errors remaining are the responsibility of the author.

Declaration of Conflicting Interests

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

Funding

The author’s research work is partly funded through the Center for International Business Education and Research (CIBER) at the University of South Carolina.

ORCID iD

Wolfgang Messner

Notes

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