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DISCUSSION PAPER SERIES
Discussion Paper 2009-02 COMPOSITE COMPETITIVENESS INDICATORS WITH ENDOGENOUS VERSUS PREDETERMINED WEIGHTS: AN APPLICATION TO THE WORLD ECONOMIC FORUM’S GLOBAL COMPETITIVENESS INDEX by Harry P. Bowen and Wim Moesen
Contact Information: Harry P. Bowen McColl School of Business Queens University of Charlotte 1900 Selwyn Ave. Charlotte, NC 28210 Tel: +1 704 688 2707 E-mail:
[email protected]
COMPOSITE COMPETITIVENESS INDICATORS WITH ENDOGENOUS VERSUS PREDETERMINED WEIGHTS: AN APPLICATION TO THE WORLD ECONOMIC FORUM’S GLOBAL COMPETITIVENESS INDEX
HARRY P. BOWEN McColl School of Business Queens University of Charlotte 1900 Selwyn Avenue, Charlotte NC 28274 +1 704 688 2707 Email:
[email protected] WIM MOESEN Center for Economic Studies Catholic University Leuven 3000 Leuven, Belgium Email:
[email protected]
September 14, 2008 Revised May 10, 2009
Forthcoming, Competitiveness Review, Special Issue edited by A. Waheeduzzaman
Composite Competitiveness Indicators With Endogenous Versus Predetermined Weights: An Application to the World Economic Forum’s Global Competitiveness Index Abstract In its call for papers, one of the stated aims for this special issue of the Competitiveness Review was research that dealt with “Methodological difficulties in measuring competitiveness” and that would “evaluate the Growth Competitiveness Index (GCI) by the World Economic Forum …”. This is exactly the purpose of this paper. Specially, this paper addresses an important methodological issue concerning the construction of any composite index, and in particular composite indicators of national competitiveness; these indicators often serve as a benchmark for policymakers and others to judge the relative success of their country. Most competitiveness indicators aggregate primitive data using predetermined fixed weight values that are applied uniformly to all countries. The use of fixed and uniform weights may bias inferences of relative performance since it ignores that countries can have different policy priorities or lack inherent capabilities on some dimensions. In addition, since the particular weight values chosen are not likely to be universally accepted, the credibility of any particular index is weakened. To address this issue, this paper proposes a procedure that allows for endogenously determined country specific weights that explicitly take account of a country’s own choices and achievement across primitive dimensions. We then illustrate our procedure by applying it to examine the widely cited Global Competitiveness Index developed by the World Economic Forum. Our resulting Revealed Competitiveness Index uses weights that allow that countries may choose different combinations of the underlying dimensions but still achieve the same level of overall performance. In general, our method will prove useful to those wishing to construct and compare indexes of performance, while minimizing objections about the “importance” of the different component dimensions that often arise when predetermined and uniformly applied weights are used. Keywords: Competitiveness Competitiveness.
Rankings,
Composite
Indicators,
Aggregation,
National
Composite Competitiveness Indicators With Endogenous Versus Predetermined Weights: An Application to the World Economic Forum’s Global Competitiveness Index 1 Each year organizations such as the World Economic Forum (WEF) and the Institute for Management Development (IMD) publish rankings of national competitiveness among countries. These rankings serve as benchmarks for national policy makers and interested parties to judge the relative success of their country in achieving the competitiveness criteria represented by the corresponding competitiveness index. One widely watched composite competitiveness index is the WEF’s Global Competitiveness Index (WEF, 2006).
2
Conceptually, the Global
Competitiveness Index (GCI) is meant to reveal the extent to which a country’s institutions, economic infrastructure, and policies and practices are supportive of the level and growth of GDP per capita.
The GCI is constructed by combining “hard” data on various national
characteristics and “soft” data compiled from the responses to the WEF’s Annual Executive Opinion Survey (WEF, 2006) To aggregate the various hard and soft primitive data into a unified composite indicator, the WEF uses a fixed set of weight values that are then applied uniformly to the underlying data for each country. A natural question that arises is whether the weight values adopted by the WEF, and the uniform application of these weight values to every country, may incorrectly penalize some countries and favor other countries such that the resulting competitiveness index values, and the subsequent ranking of countries, is biased. A major aspect of the present paper is To address the issue of potential bias due to the uniform application across countries of a single
1
We acknowledge that a substantial part of this paper will also appear in a forthcoming CESifo conference volume entitled “The Many Dimensions of Competitiveness,” edited by Paul De Grauwe and published by The MIT Press. 2 The WEF also reports a “Business Competitiveness Index” (BCI) Inspired by Michael Porter. This index focuses on the corporate sector leaving aside the macroeconomic environment and the public sector. The WEF’s newer Global Competitiveness Index incorporates some of the dimensions used in the BCI and is therefore broader in scope than the WEF’s previous index, the Growth Competitiveness Index. 1
set of weight values, we present in this paper a novel procedure that allows for the determination of weights that are specific to each country and that reflect each country’s own relative performance across the different dimensions of competitiveness. Our method therefore recognizes and reflects diversity among countries when attempting to measure and benchmark the relative competitiveness of countries. Benchmarking national competitiveness requires the construction of a unified composite indictor that can be compared across countries. In general, the construction of any composite indicator that collapses information across several primitive data dimensions must address three sets of issues: 1) Scope: what primitive data are to be used to represent the underlying concepts, which the index is intended to summarize? 2) Normalization: on what common scale will the underlying primitive data be measured? 3) Aggregation: what weights are to be given to each primitive data component? Our focus in this paper is the issue of aggregation, that is, how to select the weights to be applied to the primitive sub-indicators (variables) used to form a composite index. A simple and often popular aggregation procedure is to assign equal weights to each sub-indicator. For example, one can take the average of the different sub-indicators, which implies equal weighting. Implicitly, equal weighting reflects a judgment that the different sub-indicators have equal importance within the evaluation process. Unequal weighting is instead desired when the different sub-indicators manifestly do not share the same relative importance. Unequal weights can be derived by informed judgments of external experts, but these opinions are often too divergent to settle upon one set of acceptable weights. Also, the cost to obtain such weights can be high. Our technique meets these objections
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in that it requires less information but nonetheless reveals preferences; the data are allowed to speak for themselves. Endogenous Non-Uniform Weighting Our procedure computes implicit (or ‘shadow’) weights from observed sub-indicator values. The weight accorded to each sub-indicator dimension is therefore endogenously determined, and it reveals the associated relative performance of a country on each dimension being evaluated. Our aggregation methodology selects the most favorable weights for each country, where the most favorable weights are those that give the highest value of a country’s composite index. Good relative performance on a particular dimension can be interpreted as “revealing” that a country sets a higher priority on that dimension. This seems an attractive second best route in the absence of full information about true policy priorities (Melyn and Moesen, 1991). Apart from allowing for the constructive treatment of countries’ diversity, another appealing feature of our endogenous weight method is its flexibility since it still allows for imposing various kinds of additional weight restrictions. Indeed, while it is hardly conceivable that experts will ever agree on ‘point estimates’ for country-specific weights to be accorded to the various sub-dimensions of a given composite index, it seems much more reasonable to assume that they can reach consensus on bounds for the relative policy weights. As is discussed further on, such consensus positions are readily incorporated in our weighting procedure. Our weighting procedure is inspired by data envelopment analysis (DEA) as developed by Charnes, Cooper and Rhodes (1978) in the context of operations research3 (for a textbook
3
The issue of aggregation/weighting in the construction of a single index has also been extensively studied in the literature on productivity indices. See Balk (2002) for discussion. 3
treatment of DEA see Cooper, Seiford and Tone (1999)). DEA was designed to measure the relative efficiency of organizations when multiple outputs are produced with several inputs, and when there is no obvious objective way of aggregating either inputs or outputs into a meaningful index of productive efficiency. In formal terms, out technique consists of solving, for each country i, a linear programming problem in which the unknowns are the weights wij to be given to each of J subindicators (Iij) that are then summed to give a composite index value. The weights are calculated such that they maximize, for country i, the value of an objective function, this being the composite index being considered. Since we will apply this technique to construct a composite index of national competitiveness we will label our index the “Revealed Competitiveness Index” (RCI). Given N countries and J sub-indices (sub-dimensions), the linear programming problem can be written: (1)
J
max RCI i = max ∑ wij I ij wij
i = 1,..., N
j =1
subject to (2)
J
∑w j =1
ij
= 1; wij > 0
i = 1,..., N
Expression (1) states that, for each country i, the value of its RCI is to be maximized by choice of the weights wij. Restriction (2) states that, for each country i, the weights assigned to each sub-component should be positive and sum to one. These restrictions are minimal in that they allow complete flexibility in determining the optimal weights for each country. However, since the objective function is a weighted average of sub-indicators, its value can never be larger than the maximum of the values over all sub-indicators. This means the procedure will always 4
want to assign all weight to the sub-dimension with the highest numerical value. To account for this, and to also recognize that each sub-dimension should contribute to the value of the index, lower and upper bound restrictions on the weights will later be added. For example, we may specify that each weight must be at least 10% and not more than 50%. These restrictions mitigate the problem of “extreme specialization” on one dimension or another. In general, imposing upper and lower bound restrictions for the weights will result in index values lower than what would be obtained without these restrictions. However, this does not materially affect comparison of index values across countries, and in particular it does not affect a ranking of the index values across countries, as will be shown later below. Lastly, a feature of our approach is its generosity in that the researcher takes a position that is sympathetic to each and every country. For each country, the most favorable weights are calculated from among the set of all possible weights, while obeying restrictions (2). In this respect, the procedure may, as in Melyn and Moesen (1991), be labeled “benefit-of-the-doubt” weighting. A similar approach is used in Bowen and Moesen (2007), Cherchye, Moesen and Van Puyenbroeck (2004a and 2004b) and Despotis (2005). Implementation: The Revealed Competitiveness Index Our Revealed Competitiveness Index (RCI) is derived using as data the 2006 values of the three main sub-indices of the WEF’s Global Competitiveness Index. These three main subindices are intended by the WEF to reveal countries’ capabilities and performance on the dimensions of Basic Requirements, Efficiency Enhancers and Innovation Factors, deemed supportive of the level and growth of GDP per capita.
The WEF calculates its Global
Competitiveness Index as a weighted average of the three main sub-indices, which are themselves built up from 9 “pillar” indices as indicated in Table 1. 5
Table 1. Sub-indices and pillars of the Global Competitiveness Index Main Sub-Index
Pillar 1) Institutions
Basic Requirements
2) Infrastructure 3) Macro economy 4) Health and primary education 5) Higher education and training
Efficiency Enhancers
6) Market efficiency 7) Technological readiness
Innovation and Sophistication
8) Business sophistication 9) Innovation
Each pillar is itself constructed from underlying primitive data items, some of which are hard data and some of which are soft data derived from the responses to the WEF’s Executive
Opinion Survey (WEF, 2006). Prior to 2005, the key index used by the WEF to rank countries was its Growth Competitiveness Index whose underlying “pillars” were a subset of the pillars underlying the newer Global Competitiveness Index. Since this paper is concerned with the issue of choosing the weights to construct a composite index, it is useful to digress briefly on the development of the WEF’s competitiveness indicators. Like its newer Global Competitiveness Index, the WEF’s original Growth
Competitiveness Index identified three main sub-indices intended to reveal the extent to which a nation’s technological capabilities, public institutions, and macroeconomic environment support growth in GDP per capita. Prior to 2003, the WEF assigned the following weights to these three main sub-indices: Technology: 50%; Institutions: 25%; and Macroeconomic Environment: 25%. Starting in 2003, the WEF expanded its list of countries to include many low-income countries 6
and, since many of these countries are constrained in terms of their ability to devote significant resources toward technology related activities, the WEF chose adopt a different set of weights for such “non-core innovators” when calculating their Growth Competitiveness Index value. Specifically, for “non-core innovators,” the WEF assigned equal weight (33%) to the three main sub-indices. For “core innovator” countries (mainly high GDP per capita countries), the weights used by WEF remained Technology: 50%; Institutions: 25%; and Macroeconomic Environment: 25%. This illustrates how analysts may wish to choose different weights for different (groupings of) countries in order to reduce potential biases that would arise from important differences among countries. In 2005, the WEF introduced its new Global Competitiveness Index. This index is both broader scope than the Growth Competitiveness Index and it uses a different weighting scheme. Instead of differentiating countries solely on the basis of their technological capability, countries are instead grouped according to their “stage of development” as reflected by their level of GDP per capita. Three such stages are identified: Factor Driven, Efficiency Driven, and Innovation Driven (WEF, 2006). Each stage of development is then matched to one of the three main subindices, since the latter are meant to gauge a nation’s capabilities/performance on the dimensions deemed most important for “competitive success” in each stage. Hence, for Stage 1 (Factor Driven) countries, the Basic Requirements sub-index is assigned the highest weight (50%) while the Innovation sub-index receives the lowest weight (10%). For Stage 2 (Efficiency Driven) countries, the Efficiency Enhancers sub-index receives the highest weight (50%) and the Innovation sub-index again receives the lowest weight (10%). However, for Stage 3 (Innovation Driven) countries, the WEF oddly deviates from the weight values used for Stage 1 and 2 countries; specifically, the WEF assigns equal weight to the
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Innovation and Basic Requirements sub-indexes (30% each) and assigns the highest weight (40%) to the Efficiency Enhancers sub-index. This choice of weights seems odd for two reasons. First, the three weight values are not 50%, 40% and 10% as for Stage 1 and Stage 2 countries and second, the highest weight (40%) is not assigned to the Innovation sub-index, despite the WEF’s statement that its weight pattern is in each case intended to place “more weight on those pillars that are most important at a given stage of a country’s development” (WEF, 2006: p.12). Hence, following the WEF’s logic for Stage 1 and Stage 2 countries, the “consistent weights” for Stage 3 countries should be: Basic Requirements: 10%; Efficiency Enhancers: 40%; and Innovation: 50% In subsequent analysis we will investigate the implications of computing the WEF’s Global
Competitiveness Index using these “consistent weights” for Stage 3 countries. Aside from the an apparent inconsistency regarding the weights for Stage 3 countries, the above summary of the development of the various WEF competitiveness indexes indicates the desire to adjust both the values and the pattern of weights to recognize differences among countries. Our endogenous weight procedure takes this recognition that countries may differ in both capabilities and policy priorities a step further by allowing the assignment of weight values to vary country by country. In what follows, we focus mainly on Stage 3 (Innovation Driven) countries in order to parsimoniously illustrate our weighting methodology. In particular, we limit our attention to 21 (mostly OECD) countries identified as being in Stage 3.
However, for completeness, an
Appendix presents the calculations for the full set of 125 countries covered by the WEF in 2006. In addition, we will use the results for the full set of countries to examine for statistical differences between the values of our Revealed Competitiveness Indication and the WEF’s
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Global Competitiveness indicator in terms of both their values and the rankings based on these values. As mentioned in the previous section, upper and lower bound restrictions on the weights are needed to insure that each sub-index contributes at least something to the value of the RCI, and that no one sub-index completely dominates in its contribution to the value of the RCI. The WEF assigns a maximum weight of 40% when computing its GCI for Stage 3 countries and a minimum weight of 30%. We instead choose 50% as an upper bound for our weights, and we further specify that each sub-index should contribute at least 10% to the value of the RCI.4 Our choice of maximum and minimum weight values matches those used by the WEF for Stage 1 and Stage 2 countries, and will facilitate also comparison with a “consistently weighted” Global
Competitiveness Index computed for Stage 3 countries. Analytically, our endogenous weight methodology first assigns, for each country, the maximum weight value (50%) to the sub-index with the highest numerical value and it assigns the minimum weight value (10%) to the sub-index with the lowest numerical value; the remaining 40% is then distributed among the remaining sub-indices. In the present exercise, only three sub-indices are used to construct the RCI. Therefore, the automatic assignment of minimum and maximum weight values will fully determine the weight value (40%) for the remaining (third) sub-index. Hence, for each country, the weight values that result from our procedure will always be 50%, 40% and 10% However, unlike the WEF, in our procedure the weight assigned to any particular sub-dimension can vary country by country.
4
Formally, our upper and lower bound restriction can be written (for country i): 0.1 ≤ wij ≤ 0.5 (j = 1,…, J). Implementation of this restriction is made by including it along with restrictions (2) when determining the weights that maximize the value of a country’s RCI. 9
As previously discussed, the WEF’s weighting for Stage 3 countries appears inconsistent with that used for Stage 1 and Stage 2 countries. We will therefore present two versions of the WEF’s Global Competitiveness Index (GCI). The first, which we label GCI-1, is that produced by the WEF. The second, which we label GCI-2, instead aggregates the three main sub-indices using a fixed but “consistent” weight pattern for Stage 3 countries (i.e., Basic Requirements: 10%; Efficiency Enhancers: 40%; and Innovation: 50%).
We remark that our computation of
GCI-2 values is also done for the purpose of comparison since the weight values used for GCI-2 (i.e., 50%, 40% and 10%) are same weight values that arise from our endogenous weight procedure. As a final remark, we emphasize that our weight values follow closely those used by the WEF.
In particular, our analysis in no way specifies which underlying competitiveness
dimensions are the ones that “best” determine a nation’s competitiveness, or even if a given subdimension is relevant. As noted in the first section of this paper, it is not our intent in this paper to address the question of the appropriate scope of a composite competitiveness indicator. Instead, our analysis deals only with the issue of assigning weight values to whatever underlying dimensions are thought to influence national competitiveness. Competitiveness Score Results Table 2 presents the results of our exercise with respect to 21 countries in terms of index values.
The countries are listed in descending order of their value on the WEF’s Global
Competitiveness Index, as given in column (1) under the heading “GCI-1.”
The country
“Utopia” is of course fictitious, but serves as an absolute benchmark. For Utopia, its value on each sub-index is the maximum value observed in the sample of 21 countries. In this regard, Utopia in comprised of Demark (highest score on Basic Requirements), the United States 10
(highest score on Efficiency Enhancers), and Japan (highest score on Innovation).
By
construction, the GCI-1 value for Utopia (5.92) therefore measures the highest GCI-1 score that could be achieved among these 21 countries based on the observed data. How close each country is to Utopia in terms of the GCI-1 is indicated in column (2), which lists each country’s
GCI-1 value relative to the GCI-1 value for Utopia. For example, Switzerland’s GCI-1 value is 98.2% of Utopia’s value. These relative scores give perhaps a better indication of a country’s relative competitiveness than does a ranking of the values. The implication of our calculations for the ranking of countries is examined later in this section. -----------------------------------[Insert Table 2 about here] -----------------------------------In Table 2, columns (3) and (4) list the values of our Revealed Competitiveness Index (RCI) calculated using our endogenous weighting procedure. As expected, a country’s RCI value is never lower than its Global Competitiveness Index (GCI-1) value based on fixed weights. As indicated in the last row of Table 2, the use of best weights reduces the variation in competitiveness index values by about 8.9%, as measured by the percentage reduction in the coefficient of variation of index values in moving from the GCI-1 to the RCI. Hence, adopting weights that reflect a country’s individual performance on each sub-index reduces the measured differences in competitiveness scores among countries. Although a country’s RCI value will always exceed its GCI-1 value, when the values on each index are measured relative to Utopia’s value, this relative value can rise or fall in moving from the GCI-1 to the RCI. Such changes in relative values are indicated in column (5) of Table 2 which reports the percentage increase or decrease in a country’s performance relative to Utopia when moving from the GCI-1 to the RCI. Those showing a decline in their relative performance 11
are Austria, Belgium, Canada, Finland, Ireland, Italy, Netherlands, Sweden, Switzerland, the United Kingdom and the United States. Those showing an increase in their relative performance are Australia, Denmark, France, Germany, Greece, Japan, New Zealand, Norway, Portugal, and Spain. In general, countries showing a relative performance decline are those for whom the WEF’s fixed and uniform weighting was a better “fit” (i.e., Austria, Belgium, Canada, Finland, Ireland, Italy, the Netherlands, Sweden, Switzerland, the United Kingdom and the United States) while those showing an increase in their performance relative to Utopia are instead penalized by the WEF’s fixed weight scheme. For further comparison, columns (6) and (7) in Table 2 report the “consistently weighted”
Global Competitiveness Index scores, i.e., when the index is calculated using the fixed weights: Basic Requirements: 10%; Efficiency Enhancers: 40%; and Innovation: 50% As previously noted, these weight values are the same as those that arise from our endogenous weight procedure, and it is therefore interesting to observe how this fixed weighting compares to our endogenous weighting. Generally, by assigning the highest weight (50%) to Innovation and the lowest weight (10%) to Basic Requirements, countries that score well on the Innovation dimension would be expected to do better on the GCI-2 relative to GCI-1 (which assigns a 30% weight to Innovation). In fact, only 3 countries show a higher score on GCI-2 compared to their
GCI-1 score: Germany, Japan and the United States. As will be noted below, these are the only countries among the 21 examined that show their highest internal performance on Innovation. Column (8) in Table 2 shows the relative change in performance (relative to Utopia) in moving from the GCI-2 to the RCI. Only six countries evidence a relative performance decline (Austria, Japan, Sweden, Switzerland, the U.K. and the U.S.); this compares with a total of 10 countries that evidenced a decline in relative performance in moving from the GCI-1 to the RCI.
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That a smaller number of countries show a relative decline in moving from the GCI-2 to the RCI partly reflects that the weight values used for the GCI-2 match those of the RCI (i.e., 50%, 40%, 10%). Finally, columns (9) to (11) in Table 2 show the pattern of “best” weights for each country as revealed by our endogenous weight procedure. As discussed above, our weight values are always 50%, 40% and 10%. These columns therefore report for each country the “weight priority” that our method assigns to each of the three sub-components. For example, for Switzerland, Basic Requirements has weight priority “1.” This means that, for Switzerland, the Basic Requirements index was assigned the maximum weight value of 50%; conversely, Efficiency Enhancers has weight priority level “3” so, for Switzerland, this component was assigned the minimum weight value of 10%. A useful benchmark for examining the pattern of revealed weight priority levels for each country is the weight priority levels of Utopia. For Utopia, Basic Requirements ranks first, Innovation second and Efficiency Enhancers last. Countries having the same weight pattern as Utopia are generally also the top ranked countries (Switzerland, Finland, Sweden, Denmark), but some lesser ranked countries (Austria, France and Belgium) also have Utopia’s weight pattern. All but three countries (Japan, Germany and the U.S.) show their highest internal performance on Basic Requirements. These same three countries are also the only countries that show their highest internal performance on Innovation. The pattern of weight priority levels suggests that the fixed weight scheme used by the WEF to compute GCI-1 tends to favor countries with higher scores on Basic Requirements and Innovation, despite that these two dimensions are each given the intermediate weight value of 30%. In this regard, the United States is unique among the 21 countries for having its lowest weight priority on Basic Requirements, and for having a weight
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priority pattern that matches the pattern used for computing GCI-2. Since the U.S.’s GCI-2 and
RCI score values are therefore the same, the U.S. undergoes a large decline in its relative performance in moving from the GCI-2 to the RCI (since Utopia’s score rises when moving from the GCI-2 to the RCI index). Table 3 summarizes the pattern, or distribution, of weight priority levels across the 21 countries (excluding Utopia). Only three countries (Germany, Japan and the U.S.) perform best on Innovation across the three sub-indices, and hence this dimension is assigned the highest weight priority for these counties. For no country is Efficiency Enhancers assigned the highest
RCI weight value of 50%. This indicates that, for each country, the value of the Efficiency Enhancers sub-index always lies between the values obtained on the Innovation and Basic Requirements sub-indices. The Basic Requirements dimension is first priority for 18 countries and second priority for 2 countries, and third priority for only one country (the United States). Since most countries show their best performance on Basic Requirements and their worst performance on Innovation, the WEF’s weight pattern for its Global Competitiveness Index (GCI-1) appears to favor countries with high relative performance on Basic Requirements and Innovation, as least among Stage 3 countries. This would seem to run counter the WEF’s claim that its fixed weight values are meant to capture the dimensions deemed most important at different stages of development which, for Stage 3 counties, are Efficiency Enhancers and Innovation. -----------------------------------[Insert Table 3 about here] -----------------------------------Figure 1 gives an indication of the countries that benefit most from allowing the weights attached to each sub-index to deviate from the fixed weight pattern adopted by the WEF. Each 14
bar in Figure 1 indicates the percentage increase in the “competitiveness” that a country achieves when such competitiveness is measured by the RCI rather than the GCI-1. For example, Sweden, the U.K. and the U.S. show limited gains from the use of best weights. The countries that show the largest gain from using best weights are those whose performance differs most across the three sub-indicators. For example, Greece, Spain and Portugal perform poorly on Innovation. By assigning a weight of only 10% to this dimension, rather than a weight of 30% as done by the WEF, the relative competitiveness score of these countries improves. More generally, our endogenous weighting procedure, unlike the use of uniform weights, does not penalize countries that show greater diversity in their relative performance across the three sub-indices. This indicates the sympathetic nature of the endogenous weighting procedure. -----------------------------------[Insert Figure 1 about here] -----------------------------------Competitiveness Rankings Relative competitiveness is normally gauged not by the numerical value of a country’s competitiveness index but by the ranking of these values across countries. Columns (1) to (3) in Table 4 indicate the rank each country obtains on, respectively, GCI-1, RCI and GCI-2. Columns (4) to (6) in Table 4 give the change in a country’s rank that arises when moving from, respectively, GCI-1 to RCI, GCI-2 to RCI, and GCI-1 to GCI-2. The last line in columns (4) to (6) indicates the number of countries whose rank either increased or decreased in moving from one index to another. -----------------------------------[Insert Table 4 about here] ------------------------------------
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Column (4) in Table 4 indicates that nine countries change rank in moving from the GCI-
1 to the RCI; four countries increase their rank while five countries decrease their rank. One can further examine these rank changes to identify countries that particularly benefit (lose) from the use of endogenous weights (RCI) compared to the uniform fixed weights adopted by the WEF (GCI-1). In this respect, a notable loser from the use of endogenous weights is the United States whose rank falls two places (from 5th to 7th); notable winners are Australia and Germany who move up 3 and 2 places, respectively, in the ranking. In general, those losing rank do so because, although endogenous weights give them the highest possible value of their RCI, they generally performed poorly on each dimension relative to other countries. In this sense, these countries do not represent “best practice,” despite being given their preferred weighting on each of the three sub-dimensions. Comparing the rankings based on GCI-2 and RCI, Column (5) in Table 4 indicates that 16 countries undergo a change in rank in moving from the GCI-2 to the RCI, with seven countries improving their position and nine countries losing rank. This reflects that, while the weight values of the GCI-2 are the same as those used for the RCI (50%, 40% and 10%), the RCI allows flexibility in assigning weight values across the 3 main sub-indices. Finally, Column (6) in Table 4 indicates that using fixed but “consistent” weights to compute the GCI-2 rather than the actual weights used to compute the GCI-1 would cause 13 countries to undergo a change of rank, with 8 of showing an improved ranking. By assigning a higher weight to the Innovation sub-index and a lower weight to the Basic Requirements subindex, the resulting GCI-2 would improve the ranking of Austria, Belgium, France, Germany, Ireland, Japan, the United Kingdom and the United States, but lower the rank of Australia, Denmark, Finland, the Netherlands and Norway.
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Predicting Competitiveness and Statistical Evaluation In this section we compare the relative merits of our Revealed Competitiveness Index and the WEF’s Global Competitiveness Indicator as predictors of national competitiveness. We also assess statistically the extent to which these two indicators differ with respect to the distribution of their values and the ranking of nations based on the values of the two indices. For this analysis we make use of the full set of results for the 125 countries as presented in Appendix Table A2. As previously indicated, the WEF’s Global Competiveness Index is meant to provide an indicator of the extent to which a country’s institutions, economic infrastructure, and policies and practices are supportive of a high level of income per capita and growth in GDP. It is therefore of interest to observe the relationship between the values of WEF’s GCI and the values of our Revealed Competitiveness Index (RCI) in relation to the level of income per capita and output growth across nations. To this end, Figure 2 is a scatter plot between the 2007 values of Gross National Income (GNI) per capita (World Bank, 2008) and the values of the WEF’s GCI (GCI-1) and our RCI measure (where each index is for 2006). As Figure 2 indicates, the scatter of the values for each index in relation to GNI per capita evidences a nonlinear relationship which is indicated by the appearance of the quadratic trend line fitted to each scatter of data points. The suggested nonlinear relationship between GNI per capita and the values for each index is statistically validated by the results reported in Table 5, which reports the results of regressing the level of GNI per capita on the level and square of the value for each index. As shown in Table 5, for each regression, both the level and square of the value of the competitiveness index value is significant. Based on the R-square values, our RCI measure provides for a slightly
17
better “fit” of the GNI per capita data compared to the WEF’s GCI. However, the relative improvement in R-square is not dramatic. ------------------------------------------------------[Insert Figure 2 and then Table 5 about here] -------------------------------------------------------Figure 3 shows a scatter plot between the growth rate of GDP averaged over the years 2005, 2006 and 2007 (World Bank, 2008) and the values of the WEF’s GCI (GCI-1) and our RCI measure (where each index is for 2006) while Table 6 reports the results from regressing the average growth rate of GDP between 2005 and 2007 on the value of each competitiveness index. Figure 3 indicates a generally negative relationship between the growth rate of GDP and the values of each given competitiveness index; this negative relationship is confirmed by the regression results in Table 6; we note that for our RCI measure that this negative relationship evidences a higher level of significance (p < .01) than for the WEF’s GCI. Further, like for GNI per capita, our RCI measure does incrementally better in explaining the variation in the rate of growth of GDP across the sample of countries in terms of R-square. ----------------------------------------------------[Insert Figure 3 and then Table 6 about here] ------------------------------------------------------We now turn to examine statistically for differences in the two measures. For this purpose we employ the Wilcoxon matched-pairs signed-ranks test to statistically assess if the distribution of score values on each index are statistically different. hypothesis is that the distribution of score values is the same.
Formally, the null
Performing the needed
calculations on all 125 observations resulted in a z-statistic value of -8.226 with corresponding pvalue
