Linking National Competitiveness, Productivity, And Innovation

8/20/2019 Linking National Competitiveness, Productivity, And Innovation

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Using multiobjective mathematical programming to link

national competitiveness, productivity, and innovation

Elias G. Carayannis1 · Evangelos Grigoroudis2

© Springer Science+Business Media New York 2015

Abstract Innovation-driven competitiveness is critical for a country’s long run economic

performance in today’s knowledge-based global economy. Although several alternative mea-

sures of innovation, productivity, and competitiveness have been proposed, these concepts are

inherently linked and this justifies the necessity of studying them in an integrated way, giving

emphasis on their potential interrelations. This paper proposes a methodological measure-

ment framework based on multiobjective mathematical programming in order to study the

linkage among national innovation, productivity, and competitiveness and discover potentialperformance patterns. The model is applied in a set of European countries for the period 1998–

2008. The empirical results reveal important gaps and show that innovativeness, income, and

geographic area significantly affect national performances.

Keywords Innovation · Productivity · Competitiveness · Multiobjective mathematical

programming

1 Introduction

The concepts of innovation, productivity, and competitiveness have received much attention

among managers and policy-makers as a result of their importance to economic development.

Although these concepts have been widely studied from different perspectives, they appear

rather complex and vague, and thus no agreed definitions may be found. In fact, the alterna-

B Evangelos [email protected]

Elias G. [email protected]

1 School of Business, The George Washington University, 2201 G Street, NW, Duquès Hall,Washington, DC 20052, USA

2 School of Production Engineering and Management, Technical University of Crete,University Campus, 73100 Kounoupidiana, Chania, Greece

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tive measurement approaches may serve also as definitions of the aforementioned concepts,

leading to different assessments.

While the notion of productivity is clear at the firm or the country level, since it may be

generally defined as the value of the output produced by a unit of labor or capital, national

competitiveness differs according to the examined level or perspective (Kaoetal.2008). Thus,competitiveness at the firm level focuses on market share, while national competitiveness may

be considered as the capability of national economies to achieve sustained economic growth,

by efficiently allocating available resources (e.g., human and natural resources, capital) and

having the appropriate structures, institutions, and policies. In this context, competitiveness

of nations is defined as “how nations create and maintain an environment which sustains the

competitiveness of its enterprises” (IMD 2003) while numerous other alternative definitions

may be found in the literature (see for example Krugman 1994; Carayannis and Provance

2008; WEF 2012). On the other hand, innovation appears as an economic or social term,

focusing on product or process changes. For example, Drucker (1985) considers innovation

as change that creates a new dimension of performance, or as “changing the yield of resources

and as changing the value and satisfaction obtained from resources by the consumer” .

The literature shows that there are several alternative measures of innovation, productiv-

ity, and competitiveness, depending on the level and the purpose of the analysis. In several

cases, significant overlaps may be observed, mainly because these concepts are inherently

linked (Carayannis and Sagi 2001, 2002; Shane 2004; Carayannis and Grigoroudis 2012)

and thus, researchers focus on studying their drivers and outcomes, e.g., in a cause-and-

effect way (see for example Jansen 2006). The previous limitations justify the necessity of

studying innovation, productivity, and competitiveness in an integrated framework, giving

emphasis on their potential interrelations, since innovation-driven competitiveness is criticalfor a country’s long run economic performance in today’s knowledge-based global econ-

omy.

The main aim of the paper is to propose a methodological measurement framework based

on multiobjective mathematical programming in order to study the linkage among national

innovation, productivity, and competitiveness and discover potential performance patterns.

The proposed approach is a regression-based MONLP that extends the work of Carayannis

and Grigoroudis (2012), estimating aggregated national innovation, productivity, and compet-

itiveness (IPC) indices, based on a set of relevant indicators that describe the various aspects

of these concepts. The main characteristic of the model is that, due to its multiple objective

nature, it both minimizes the estimation errors and maximizes the correlation between theaggregated IPC indices. Moreover, the proposed model is a nonparametric approach, and

thus no assumptions for the statistical properties of the examined variables are posed. Also,

the weights of the aggregation formula do not follow an arbitrary equal weighting scheme,

but they are estimated based on the previous multiple objectives. Other important advantages

include the flexibility of the model to consider additional desired properties for the exam-

ined variables and its ability to perform a dynamic analysis based on complete time series

data.

2 Background

2.1 Measuring innovation, productivity, and competitiveness

Alternative methods for measuring innovation include approaches based on both single (e.g.,

R&D expenditures, number of patents) and composite indicators. Since a single indicator

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can provide only a limited view of such a broad concept, the role of composite indicators has

been significantly increased in recent decades (Paas and Poltimäe 2010). In this context, the

relevant literature reveals two major approaches:

• Evaluation of national performance and ranking of countries;

• Analysis of national innovation systems.

The first approach mainly focuses on a comparative analysis of different aggregated inno-

vation measures, while the second approach characterizes only a particular counter and puts

emphasis on the factors that may impact innovation performance.

The most widely used composite innovation index is provided by the European Innovation

Scoreboard (EIS), which has been introduced as part of the Lisbon strategy and aims to

measure, on a yearly basis, the innovation performance of member countries (Hollanders and

van Cruysen 2008). The EIS consists of three main blocks, 7 dimensions, and 29 indicators.

The first block (enablers) refers to the main drivers of innovation that are external to the firmand includes the dimensions of human resources (availability of high-skilled and educated

people) and finance and support (availability of finance for innovation projects and support of

governments for innovation activities). The second block (firm activities) captures innovation

efforts at the firm level, including firm investments (investments firms make in order to

generate innovation), linkages and entrepreneurship (entrepreneurial collaboration efforts),

and throughputs (Intellectual Property Rights and Technology Balance of Payments flows).

Finally, the last block (outputs) focuses on the outputs of firm activities and includes the

dimensions of innovators (number of firms that have introduced innovations onto the market

or within their organizations, covering technological and non-technological innovations),

and economic effects (economic success of innovation in employment, exports and sales). Adetailed presentation of these metrics can be found in Pro Inno Europe (2010).

It is important to note that the EIS framework has been significantly modified over years

and it has been recently transformed into the Innovation Union Scoreboard (IUS) in order to

monitor the implementation of the Europe 2020 Innovation Union flagship (Pro Inno Europe

2011). For example, the first version of 2000 was based on 16 indicators and covered 17

countries, while the version of 2008 had been extended to 29 indicators and 37 countries.

These revisions try to overcome the major criticism of the EIS methodology, including

mostly the choice of dimensions and indicators. In addition, the updated framework captures

new forms of innovation (e.g., services, open innovation) and is able to provide an overall

innovation performance for each country (see Hollanders 2009 for an overview of the changes

in the EIS over time). In any case, these revisions show the ongoing debate on defining

innovation and justify the lack of a universally accepted constant framework for measuring

it.

Historically, the measurement of productivity was initially based on a production function

context and linked with economic growth, while current research integrates the theory of the

firm, the index number theory, and available national accounts (OECD 2001). Alternative

productivity measures may be found in the relevant literature (see for example Diewert

and Nakamura 2007). These different productivity measures are classified according to the

following criteria:

• Number of factors: This categorization includes single factor productivity, which relates

a measure of output to a single measure of input, and multifactor productivity, where a

bundle of inputs is considered.

• Type of output measure: The alternative categories refer either to gross output or value

added.

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It should be noted that besides labor and capital, additional intermediate inputs may also

be considered. Many scholars argue that labor productivity is the most useful productivity

measure because it is related with the most important factor of production, it can be easily

measured, and it is a key determinant of living standards (OECD 2001). However, it captures

only partially the different aspects of this concept, and thus multifactor productivity is usuallyconsidered. As noted by Diewert and Nakamura (2007), although it is impossible to measure

all inputs at a national level, estimations and approximations may be considered.

The concepts of productivity and competitiveness seem inherently related, given that

competitiveness is considered as the capability of national economies to achieve sustained

economic growth, by efficiently allocating available resources (e.g., human and natural

resources, capital). In addition, WEF (2012) defines competitiveness as “the set of insti-

tutions, policies, and factors that determine the level of productivity of a country”. Thus, in

several cases, productivity is considered as the only meaningful concept of national compet-

itiveness (Porter 1990), and as a result the Gross National Product (GNP) per capita may be

used as a reliable performance index, only when a single measure should be considered.The most important efforts for developing a competiveness measurement framework refer

to the Global Competitiveness Index (GCI) developed by the World Economic Forum (WEF)

and the World Competitiveness Yearbook (WCY) provided by the International Institute for

Management Development (IMD).

The CGI consists of three subindices that cover the basic requirements (institutions,

infrastructure, macroeconomic environment, health and primary education), the efficiency

enhancers (higher education and training, goods and labor market efficiency, financial mar-

ket environment, technological readiness, market size), and the innovation and sophistication

factors (business sophistication, innovation). It also includes many components that measuredifferent aspects of competitiveness. These are grouped into 12 pillars of competitiveness

that contain a total of 111 detailed indicators, and the GCI is estimated based on a weighted

average formula.

The previous subindices are able to assess the most important factors for different types

of economies, according on the economic theory of stages of development. In particular, the

CGI adopts different weighting schemes depending on the development stage of a national

economy (i.e., factor-driven, efficiency-driven, or innovation-driven).

Similarly, the WCY estimates an overall national competitiveness ranking of countries

based on four main factors that include economic performance, government efficiency,

business efficiency, and infrastructure (IMD 2010). These factors are divided in into 20sub-factors, which in turn comprise more than 300 competitiveness criteria. The main

characteristic of the WCY is the emphasis given to the firm level, since the considered

factors and criteria are oriented to a national environment that enhances the ability of

firms to compete domestically or internationally (IMD 2010). It is important to note that

besides statistical data, IMD uses survey data drawn from annual executive opinion sur-

veys.

The aforementioned frameworks show that, in most cases, the measurement techniques

adopted by the major IPC barometers are mainly based on simple estimation techniques,

since a weighted average formula is usually adopted. Different aggregation methods mayalso be found in the relevant literature, but they appear to have important limitations (see

for example Nardo et al. 2005; Hollanders and Arundel 2007; Grupp and Schubert 2010).

However, composite indicators are still the best tool available for analyzing such complex

concepts (Paas and Poltimäe 2010). In addition, the interrelations among these concepts are

rather strong. All these justify the necessity of developing new measurement frameworks

that are able to study together IPC composite indices.

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2.2 Linking innovation, productivity, and competitiveness

As discussed in Sect. 2.1, the concepts of national IPC appear to have overlaps and/or

significant interrelations. The relevant literature shows that, usually, these concepts are

jointly studied in a firm, industry, or country level. In addition, several studies includealso other related aspects, like creativity and entrepreneurship (see for example Carayan-

nis and Gonzalez 2003) that increase the difficulty of analyzing the linkages among

IPC.

The linkage between innovation and productivity/competitiveness is relatively strong, as

emphasized by numerous studies (see for example Chakrabarti 1990; Clark and Guy 1998;

Carayannis and Sagi 2001). Technology appears as a key factor which, through innovation,

may influence the economies of scale, the timing of processes and the introduction of new

methods, and thus affect the competitive advantage of firms. Discussing these interrelations,

Carayannis and Sagi (2001) emphasize that innovation and competitiveness are intrinsically

unified; although one does not cause the other, both are necessary for competitiveness andfor each other.

A similar linkage regarding competitiveness and productivity is also discussed in the

literature. In fact several researchers emphasize that national productivity is the only

meaningful concept of competitiveness (see for example Porter 1990). On the other

hand, innovation without productivity is insufficient to produce wealth and increase

national competitiveness. Thus, productivity appears inherently related with innovation

and competitiveness in a country level, since it is the root cause of national capital

income.

Consequently, although the strength of linkages among IPC may vary depending onthe level of analysis, these interrelations are adopted by numerous studies. In the OR/MS

literature these concepts are usually studied in a cause-and-effect way, adopting a Data

Envelopment Analysis (DEA) approach (see for example Guan et al. 2006). A characteris-

tic holistic approach is given by Carayannis and Sagi (2001, 2002), who argue that these

linkages may be observed both horizontally and vertically, sharing factors and resources

such as funding, knowledge and signals. Figure 1 presents the CPI model proposed by the

authors, where national productivity results not only from national innovation programs,

but also from industrial productivity, university structures, government policies, and so

forth.

Based on the previous discussion, the present work assumes that innovation may improvenational productivity, which in turn gives the ability to compete on the global marketplace.

3 Proposed approach

3.1 Multiobjective programming model

The proposed model adopts the modeling approach of the main IPC barometers presented in

Sect. 2.1. In this context, the model assumes that national IPC are aggregated measures overa set of relevant performance indicators, and thus they can be considered as latent variables.

In addition, the proposed model assumes that these aggregated measures are interrelated, as

discussed in Sect. 2.2.

Taken into account the previous two research objectives, the following multiobjective

optimization problem may be formulated:

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D e f i n e s p o l i c y ,

p r o g r a m s

Competitiveness Productivity Innovation

SOL GDP/Capita/Industry %GDP

I n f l u

e n c e

s

Government

Competitors


Sales Sales/Employee %GDP

Buyers Suppliers

Industry

S u p p o r t s

D e f i n e s


stnetaPIOR selaS

S u p p o r t s

D e f i n e s

S u p p o r t s

D e f i n e s

S u p p o r t s

D e f i n e s

Value chain

R e s u l t s K

n o w l e

d g e

Firm

A t t r a c t s

Internal R&D,

Development Labs

Consortia,Universities, Applied

Research Labs

Programs, High Risk,Uncertainty, Basic &

Applied Research,

Defense R&D

M e m b e r s h i p

Influences by policies,

exchange rates, WTO

membership

Trades and

competes

Knowledge creation

Knowledge diffusion

Marketability

Fig. 1 The CPI model (Carayannis and Sagi 2001)

[max] F 1 = ϕ( I , P, C )

[min] F 2 = ψ(γ, δ,ε)

subject to I = f 1(i j ) + γ j = 1, . . . , J

P = f 2( pk ) + δ k = 1, . . . , K

C = f 3(cm) + ε m = 1, . . . , M

(1)

where I , P , and C are the aggregated measures of innovation, productivity, and competitive-

ness, respectively, i j is the of innovation indicator j, pk is the productivity indicator k , cmis the competitiveness indicator m, γ , δ, and ε are error terms, f i and ψ are aggregation

functions, and ϕ is a measure of interrelation.

The optimization problem (1) estimates the overall performance indices (i.e., aggregatedmeasures) of innovation, productivity, and competitiveness ( I , P , and C ), based on the sets

of relevant indicators i j , pk , and cm with the maximum interrelation among I , P , and C and

the minimum estimation errors ψ . It should be noted that although i j , pk , and cm appear as

independent variables in f i , they are interrelated through ϕ .

In order to further develop the optimization problem (1), the functions ϕ,ψ, f i should be

determined. In particular, the correlation function may serve as a measure of interrelation ϕ ,

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(Mirkin 2011), while ψ may be modeled using a simple aggregation form. Regarding f i , a

linear function may be adopted, since the aggregation of i j , pk , and cm into I , P , and C is

not known in detail. However, linear aggregation forms may also be adopted by the major

IPC barometers, as presented in Sect. 2.1. In addition, γ , δ, and ε may be modeled using a set

of double error variables (i.e., overestimation and underestimation error) in order to adopt agoal programming approach. In this case, the complexity of the optimization problem may

be reduced, since error variables are nonnegative.

Finally, in order to apply a linear form in f i and have a comparable set of indicators,

i j , pk , and cm should be normalized. A min-max normalization formula is used in this case,

which is the most common normalization approach (Myatt 2007). For increasing indicators

(larger-the-better), the following normalization formula is used:

x s = X s − X min

X max − X min(2)

where X s is the value of a particular indicator for country s, x s is the normalized value of X s, X min = min

s{ X s } and X max = max

s{ X s }. In the case of a decreasing indicator (smaller-

the-better), the previous normalization formula should be written as:

x s = X max − X s

X max − X min(3)

Assuming that data from S countries are available and taking into account the aforementioned

principles and assumptions, the optimization problem (1) may be formulated through the

following multiobjective mathematical problem:

[max] F 1 = Corr ( I s, Ps) + Corr (Ps, C s)

[min] F 2 =S

s=1

γ +s + γ

−s

+

S s=1

δ+s + δ

−s

+

S s=1

ε+s + ε

−s

(4)subject to

I s = J

j =1

a j i j s − γ +

s + γ −

s

Ps =K

k =1bk pks − δ

+s + δ

−s

C s =

M m=1

d m cms − ε+s + ε−s

∀s = 1, 2, . . . , S (5)

where I s, Ps , and C s are the aggregated indices of IPC for country s, i js is the value of

innovation indicator j for country s, pks is the value of productivity indicator k for coun-

try s, cms is the value of competitiveness indicator m for country s, a j , bk , and d m are the

regression coefficients, γ +s and γ −

s are the overestimation and the underestimation errors,

respectively, for the innovation regression equation, δ+s and δ−s are the overestimation and

the underestimation errors, respectively, for the productivity regression equation, ε+s and ε+s

are the overestimation and the underestimation errors, respectively, for the competitiveness

regression equation, S

is the total number of countries, and Corr

is the Pearson correlationcoefficient.

The optimization problem (4), (5) is a multiobjective nonlinear program (MONLP), having

as constraints the regression equations for the competitiveness, productivity, and innovation.

Each one of these regression equations assumes that the evaluated aggregated measure is a

weighted sum of relevant performance indicators. In particular, for the regression coefficients,

the following normalization properties are assumed:

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J j =1

a j = 1,

K k =1

bk = 1,

M m=1

d m = 1 (6)

Equation (6) gives the ability to estimate normalized aggregated measures; as already men-

tioned, i j s, pks , and cms are normalized in [0, 1] and thus, I s, Ps, C s ∈ [0, 1]. In addition,given Eq. (6), the estimated regression coefficients a j , bk , and d m represent the relative con-

tribution of i j s, pks , and cms in I s, Ps , and C s , respectively. Consequently, the MONLP takes

the following final form:

[min] F 1 = −Corr ( I s, Ps) − Corr (Ps ,C s)

[min] F 2 =S

s=1

γ +s + γ

−s

+

S s=1

δ+s + δ

−s

+

S s=1

ε+s + ε

−s

(7)subject to

Constraints (5) and (6)a j , bk , d m ≥ eγ +s , γ

−s , δ

+s , δ

−s , ε

+s , ε

−s ≥ 0

(8)

where e is a small positive number assuring that i j s, pks , and cms have a positive impact on

I s , Ps , and C s , respectively.

The proposed model is a mathematical programming approach to canonical correlation

analysis (CCA), which is a statistical tool for identifying and measuring the associations

between two multidimensional variables (Hair et al. 1995; Tabachnick and Fidell 1996).

In particular, the proposed approach is a MONLP is similar to two-stage CCA, since it

considers three regression equations and two optimality criteria. The first objective function(F 1) maximizes the overall interrelation among IPC, where Ps serves as a mediator and

there is no order in these relations. The second objective (F 2) minimizes the overall sum

of absolute estimation errors, and since a goal programming approach is adopted, we have

γ +s · γ −

s = 0, δ+s · δ

−s = 0, ε

+s · ε

−s = 0 ∀s.

Mathematical programming approaches have been proposed for modeling CCA problems

(see for example Tofallis 1999), emphasizing the flexibility that constrained optimization

models may offer (e.g., addition of constraints for fitted coefficients). This flexibility is the

main advantage of the proposed approach, since it may consider additional desired properties

for the examined variables (see for example constraints (6)). Another important advantage is

that the MONLP (8) is a nonparametric approach, given that no assumptions for the statisticalproperties of the examined variables are posed.

Although several multiobjective methods may be applied for solving MONLP (7), (8), in

this study a compromise programming approach is adopted. The main aim of compromise

programming, introduced by Zeleny (1974, 1982) and Yu (1973, 1985), is to determine a set

of efficient solutions with the nearest distance to an ideal solution (i.e., solution where all

objectives are optimized). Usually, the following p-metrics are used as a distance function:

min L p = n

i =1

wi F ∗i − F i

F ∗

i − F i ∗

p

1/ p

(9)

where F i is the i -th objective function, F ∗

i and F i ∗ are the ideal (i.e., the optimum value of F iwithout considering the other objective functions) and the anti-ideal solution (i.e., the worst

value of F i when the other objective functions are optimized) of the i -th objective function,

respectively, wi is the weight of the i -th objective function, p is the topological metric, and

n is the number of objective functions.

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Based on the aforementioned modeling approach, the final optimization problem consid-

ered in this study has the following form:

min L1

= 0.5 F ∗1 −F 1F

∗1 −F 1∗

+ 0.5 F ∗2 − F 2F

∗2 −F 2∗

subject to

Constraints (8)

(10)

The optimization problem (10) considers the L1-norm (Manhattan norm) and assumes that

the relative importance of the two objective functions is equal (w1 = w2 = 0.5). Thus,

the applied compromise programming approach is similar to the global criterion method

in multiobjective optimization. A detailed review of alternative multicriteria optimization

approaches may be found in Ehrgott (2005) and Ehrgott and Wiecek (2005).

3.2 Data and indicators

The main aim of the model proposed in the previous section is to estimate a set of aggregated

competitiveness, productivity, and innovation measures for each country, maximizing the

correlation between these measures and minimizing at the same time the sum of absolute

estimation errors. This estimation takes into account the national performance in a set of

measurement indicators for each one of the aforementioned latent variables.

The selection of these indicators is mainly based on the previous research efforts (see

for example Carayannis and Grigoroudis 2012), and particularly the major IPC barometers

(Sect. 2.1). Although this set of indicators is limited by data unavailability, it is able to coverdifferent measurement dimensions of the examined latent variables. In order to have a reliable

set of indicators, only international sources have been used. Moreover, an effort has been

made so that the selected set of indicators has some basic properties, like independence,

measurability, relevancy, and non-redundancy. A detailed discussion about the properties of

a set of measurement indicators may be found in the multicriteria decision analysis literature

(Keeney and Raiffa 1976; Keeney 1992; Kirkwood 1997).

The set of innovation indicators adopts the structure of the EIS (Pro Inno Europe 2010)

and covers four main measurement dimensions and 13 indices. The first dimension refers

to “Human Resources and Research Systems” and is considered as an important innova-

tion enabler. It consists of the following indices: (1) Graduates in mathematics, science andtechnology (per 1000 population, aged 20–29), (2) Participation in life-long learning (% of

25–64 aged population), (3) Researchers in science and technology (per 1000 employed),

(4) Scientific and technical journal articles (per capita). The second dimension that serves

also as an innovation enabler is related to “Finance”, and consists of the following indices:

(5) Venture capital investment, early stage (% of GDP), (6) Public R&D expenditures (%

of GDP), (7) Business expenditures on R&D (% of GDP). The third dimension refers to

“Exports and Patents” and captures the innovation results (output). The indices included in

this dimension are as follows: (8) High technology exports (% of manufactured exports), (9)

EPO patents applications (per million population), (10) USPTO patents (per million popu-lation), (11) Trademark applications (per million population). The last dimension is related

to “Employment” and is considered also as an innovation result. It consists of the following

indices: (12) Employment in high-tech services (% of total workforce), (13) Employment in

medium-high and high-tech manufacturing (% of total workforce).

Regarding the set of productivity indicators, two major measurement dimensions are

considered: workforce productivity and value added in a national economy ( OECD 2001).

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These dimensions are measured through the following indices: (14) Labor productivity (GDP

in purchasing power standards), (15) Gross value added at factor cost (per capita).

The set of competitiveness indicators, following the GCI framework (WEF 2012) con-

sists of three main performance dimensions and 10 indices. The first dimension considers

infrastructure, which is a basic competitiveness requirement, and consists of the followingindices: (16) Internet users (per 100 population), (17) Mobile Cellular subscriptions (per

100 population), (18) Telephone lines (per 100 population). The second dimension takes

into account economic variables and consists of the following indices: (19) GDP per capita

(PPP, current international $), (20) GDP growth (annual %), (21) Inflation rate (consumer

prices, annual %). The third dimension refers to the national macroeconomic environment

and serves also as a basic competitiveness requirement. It consists of the following indices:

(22) Balance of trade (exports-imports), (23) Interest rate spread (lending rate minus deposit

rate), (24) Central government debt (% of GDP), (25) Unit labor cost, total economy (annual

%).

Based on this set of 25 IPC indicators, a database containing data of 19 countries forthe period 1998–2008 has been developed. The countries examined in this study include:

Austria, Belgium, Czech Republic, Denmark, Finland, France, Germany, Greece, Hungary,

Italy, Norway, Poland, Portugal, Ireland, Slovakia, Spain, Sweden, Switzerland, and United

Kingdom. All but the indicators referring to inflation rate, interest rate spread, government

debt, and labor cost are larger-the-better. It should be emphasized that all these indicators are

measured in a relative scale (e.g., as % of GDP or population), and thus it is valid to apply

the normalization Eqs. (2) and (3) in order to develop a fully comparable set of measurement

indicators.

4 Results

4.1 Overall results

Based on the assessed set of performance indicators, the proposed multiobjectice mathemat-

ical program is applied on the aforementioned set of 19 countries. The NLP (10) is solved

for each year of the examined period 1998–2008, and thus a set of overall IPC indices is

estimated for each country and each year.

The fitting of the model may be measured using the objectives functions considered,i.e., the absolute estimation errors and the correlation coefficients among IPC. According to

the estimated results, the fitting of the model is relatively high: the average absolute error

for the IPC regression equation (γ +s , γ −

s , δ+s , δ

−s , ε

+s , ε

+s ) is 0.0331, 0.0073, and 0.0012,

respectively (average over all countries and years). Moreover, the average correlation between

the aggregated innovation and productivity indices Corr ( I s, Ps) is 0.961 (average over all

countries and years), while the average correlation between the aggregated competitiveness

and productivity indices Corr (Ps, C s) is 0.984. As a result, the average correlation between

the aggregated competitiveness and innovation indices Corr ( I s , C s) is 0.950 (average over

all countries and years).The performance map presented in Fig. 2 provides an overview of the estimated aggregated

IPC indices. This performance map is based on the average values for 1998–2008 and presents

the relative ICP scores in order to standardize the graph and avoid comparability problems

(see details in Grigoroudis and Siskos 2002, 2010). Thus, each country score is compared

to the scores of the other countries. Since three series of aggregated indices are available,

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P r o d u c t i v i t y

Innovation HighLow

H i g h

L o w

AT BE

CZ

DK

FI

FR

DE

GR

HU

IT

NO

PL

PO

IE

SK

ES

SE

CH

UK

Fig. 2 Relative performance map (average for 1998–2008)

Fig. 2 has the form of a bubble chart, where the horizontal and the vertical axes refer to the

average overall innovation and productivity scores, respectively, and the size of bubbles is

proportional to the average overall competitiveness score.

As expected, Fig. 2 shows that high (low) innovation scores correspond to high (low)

productivity and competitiveness performance, since all countries are located in the upper

right or the lower left quadrant, while the size of bubbles (competitiveness) increases as bothinnovation and productivity performances increase. These findings show that there are no

significant gaps among IPC and are justified by the main assumption of the model, i.e., the

interrelation among these latent variables. In addition, these results are supported by the major

innovation and competitiveness barometers; Finland, Norway, Sweden, and Switzerland are

ranked among the top countries in the EIS and the GCI, while the performance of Greece,

Slovakia, Portugal, and Poland is below of the European average (Pro Inno Europe 2010,

2011; WEF 2012).

However, important differences among the examined European countries may be found.

Table 1 presents the aggregated IPC indices for different country categorizations. The first

categorization refers to the innovation performance according to the EIS (2010, 2011), andincludes the innovation leaders (Finland, Sweden, and Switzerland), the next best performers

(Austria, Belgium, Denmark, France, Germany Norway, Ireland, and United Kingdom), the

followers (Czech Republic, Hungary, Italy, and Spain), and the lagging countries (Greece,

Poland, Portugal, Slovakia). Other alternative categorizations presented in Table 1 are based

on geographic or income criteria (high income $40,000–$53,000 GDP per capita; upper

medium income $35,000–$38,000 GDP per capita; lower medium income $26,000–$30,000

GDP per capita; low income $19,000–$23,000 GDP per capita).

The main finding of Table 1 is that innovation performance, as well as income, signif-

icantly affects all three aggregated IPC indices. In addition, the geographic categorizationclearly shows a Europe of two speeds. Northern and Western European countries appear to

have higher performance in all three IPC indices, while the performance of the Northern

and Eastern European countries is significantly weaker, particularly regarding the aggre-

gated productivity and innovation indices. According to WEF (2013), although all European

countries have been improved in terms of aggregated prosperity since the 1980s, the path

of Northern and Southern European countries has been diverging up until 2008–2009. This

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Table 1 Overall aggregated indices based on several categorizations (average for 1998–2008)

Country groups Innovation index Productivity index Competitiveness index

Innovation leaders 0.567 0.710 0.681

Next best performers 0.464 0.653 0.625Followers 0.222 0.224 0.349

Lagging 0.150 0.110 0.248

Northern Europe 0.513 0.700 0.671

Western Europe 0.467 0.631 0.602

Southern Europe 0.220 0.301 0.393

Eastern Europe 0.151 0.033 0.204

High income 0.534 0.764 0.711

Upper medium income 0.457 0.589 0.581

Lower medium income 0.223 0.274 0.384Low income 0.148 0.060 0.213

P e r f o r m a n

c e

Importance

L o w

Low High

H i g h Employment

Economy

Infrastructure

Macroeconomic

EnvironmentLabor productivity

Gross value added

Finance

Exports & Patents

Human Resources &Research Systems

Fig. 3 Relative importance/performance map (average over all countries and years)

divergence looks similar to the EU–US gap and has been widening after the recent financial

crisis (WEF 2012, 2013). Since this study examined the period between 1998 and 2008, the

observed inability of some countries to innovate and compete internationally is consistent

with the ongoing sovereign debt crisis in Northern Europe and Ireland.

In order to identify the strong and the weak points of IPC, an importance/performance

diagram is developed, as shown in Fig. 3. This map presents the importance of the IPC

components, as measured by the regression coefficients, in the horizontal axis, while thevertical axis refers to the performance value of the IPC components. It is important to note

that, similarly to Fig. 3, all values have been standardized in order to have fully comparable

results. Thus, this importance/performance map shows the relative strong and weak points

of the examined components. Moreover, the presented importance is not related to the “true

significance” of the IPC components, but it rather refers to their contribution in the aggregated

IPC indices, so as to maximize the overall interrelation among IPC.

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The results of Fig. 3 show that there is a significant gap in all IPC components during the

examined period. Although the contribution of “Exports & Patents” and “Human Resources &

Research Systems” is high, their performance appears relatively low. In addition, “Finance”

also has a relative low performance, and thus the observed gap is mainly focused on the

components referring to innovation enablers. This is rather unfavorable, since the enablersare the main drivers of innovation and may affect the performance of other components, due to

the assumed IPC interrelations. This result is consistent with recent findings underlining that

the EU underperforms against other advanced economies, particularly in terms of innovation

capacity and higher education and training (WEF 2013). A similar gap is also observed for the

productivity components. While “Labor Productivity” is located in the upper-left quadrant

(low importance/high performance), “Gross Value Added” appears as a weakness (high

importance/low performance) and justifies the recent efforts of EU policymakers to develop

a long-term and visionary strategy for the European economy. As noted in WEF (2013),

many emerging-market economies (e.g., BRIC economies) have managed to improve their

competitiveness, increase their pressure on value added activities in Europe, and sometimesovertake some of theEuropean economies. Finally, the gap in thecompetitiveness components

reveals that “Economy” is a weakness, while “Macroeconomic Environment” has a relatively

higher performance, since it is located in the upper-left quadrant. Indeed, the recent results

emphasize that the macroeconomic environment is the only pillar of the CGI methodology

with a performance higher in the EU27 than in the US (WEF 2013).

The aforementioned gaps may also be observed in the examined countries, particularly if

the different innovation performance country groups are considered. As noted by Pro Inno

Europe (2011), innovation leaders share a number of strengths in their national research

and innovation systems with a key role of business activity and public-private collaboration.The most important finding from all these studies is that an overall higher performance is

usually a result of a balanced performance in the examined components. Regardless of the

distinctive characteristics of each country, this means that the variability of drivers/results,

enables/outcomes or lead/lag indicators should be relatively low.

4.2 Dynamic analysis

The results presented in the previous section are able to give an overall average view for the

whole examined period, but cannot provide a dynamic analysis of the IPC measures. The

relative evolution of the aggregated IPC indices between 1998 and 2008 is shown in Fig. 4for different country groups. Since the main aim of the analysis is not to develop a prediction

model and provide absolute CPI measures, the dynamic analysis is based on a series of 100 %

stacked area charts. Thus, Fig. 4 shows the relative evolution of the aggregated performance

indices, aiming to identify potential patterns in the dynamics of the IPC measures.

As shown in Fig. 4 and pinpointed in the previous section, countries with higher innovation

performance according to the EIS appear to have more balanced performance in all IPC

measure. Additional results show that similar performance can be observed regarding the

Northern and Western European counties or the countries with higher income versus the

southern and eastern countries or those with lower income. This is somehow expected, since

geography, income, and innovation performance give similar categorizations.

It should be noted that in case of unbalanced performance, the evolution of the aggregated

productivity index shows a relatively lower contribution, compared to the other IPC indices.

In addition, due to potential influences from external factors, the variability of the overall

productivity is higher. These results reveal the higher vulnerability of the national economies

of followers and lagging countries.

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0%

20%

40%

60%

80%

100%

1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008

Innovation Leaders

Innovation Productivity Competitiveness Innovation Productivity Competitiveness

Innovation Productivity Competitiveness Innovation Productivity Competitiveness

0%

20%

40%

60%

80%

100%

1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008

Next Best Performers

0%

20%

40%

60%

80%

100%

1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008

Followers

0%

20%

40%

60%

80%

100%

1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008

Lagging

Fig. 4 Relative evolution of aggregated indices (innovation performance groups)

The evolution of IPC performance in the examined period may be studied through a series

of dynamic performance maps, as shown in Fig. 5 (see also Carayannis and Grigoroudis 2012).

Similarly to Fig. 2, these maps present the average overall innovation and productivity scores

in the horizontal and the vertical axis, respectively, while the size of bubbles is proportional

to the average overall competitiveness score. The IPC scores are also standardized (i.e., the

score of each year is compared to the scores of the other years).

Figure 5 presents the relative performance of the different country groups according totheir geographic area categorization. The main aim of this analysis is to discover potential

performance patterns in the examined period. The main findings of Fig. 5 may be summarized

as follows:

• The Northern European countries seem to follow a clockwise path, starting from the

lower-left quadrant (low innovation/low productivity) and ending at the lower-right quad-

rant (high innovation/low productivity). In addition, their competitiveness performance

appears relatively constant in the examined years. These results show that the North-

ern European countries managed to improve their relative innovation performance andsustain their competitiveness levels during this period.

• Regarding the Western European countries, generally, the observed path starts mainly

from the upper-left quadrant (low innovation/high productivity) and ends at the lower-

right quadrant (high innovation/low productivity). Moreover, their competitiveness

performance appears relatively constant between 1998 and 2008. Overall, it seems that

the Western European countries managed to improve their innovation performance, sus-

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Innovation HighLow

H i g h

L o w

1998

1999

2000

2001

2002

2003

2004

2005

20062007

2008

Northern Europe


Innovation HighLow

H i g h

L o w

19981999

2000

2001

2002

2003

2004

2005

2006

20072008

Western Europe


Innovation HighLow

H i g h

L o w

19981999

20002001

2002

20032004

2005

20062007

2008

Southern Europe


Innovation HighLow

H i g h

L o w

19981999

2000

20012002

2003

2004

20052006

2007

2008

Eastern Europe

Fig. 5 Relative dynamic performance diagram (geographic area groups)

tain their competitiveness levels, while their productivity received pressure during this

period.

• In the case of Southern European countries, a counterclockwise path may be observed,

starting from the upper-right quadrant (high innovation/high productivity) and ending at

the lower-right quadrant (high/innovation/low productivity). Also, their competitiveness

seems to decrease during the last years, particularly after 2005. As an overall result,

it seems that although these countries managed to sustain their innovation levels, their

productivity and competitiveness performance have been weakened.

• Compared to Western Europe, the opposite path may be observed for the Eastern Euro-

pean countries: lower-left quadrant (low innovation/low productivity) → upper-left

quadrant (high innovation/high productivity). This result may be justified by the signif-

icant improvement margins in their innovation and productivity performance. However,

the competitiveness of this particular country group seems to vary during this period.

The previous findings show that some European countries were able to follow a more “sus-

tainable” path during the examined period. This means that these countries are able to improve

or at least hold their position in a global competitive environment. Given the financial crisisof 2008, which leads to the 2008–2012 global recession and the recent European sovereign

debt crisis, this result is very important. As already mentioned, the diverging IPC perfor-

mance within Europe reveals the significant difficulties faced by several European countries,

particularly in Southern Europe, to lift their economies onto a soundly positive growth path

(WEF 2013). The previous dynamic performance maps are able to justify a Europe of two

speeds based on geography, income, and innovation performance.

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4.3 Performance and progress analysis

The dynamic maps presented in the previous section are mainly focused on the relative IPC

performance of particular country groups, and thus they are not able to provide a comparative

analysis among different country groups. In addition, besides performance, in several casesit is important to study the progress made during the examined period.

Table 2 presents the most recent IPC performance of different country groups, together

with the progress made, as measured by the average annual growth of the aggregated IPC

indices between 1998 and 2008. In several cases, the country groups with the lowest IPC

indices show a relatively higher growth, since improvement margins in all of the examined

aggregated indices are larger. However, no particular trend may be identified, given that the

observed progress depends on the alternative country categorizations.

Figure 6 presents analytically the current innovation performance and the average cor-

responding growth between 1998 and 2008 for all the examined countries. All values have

been standardized, and thus both performance and progress are measured in a relatively way.Similarly, Figs. 7 and 8 present the relative productivity and competiveness progress maps.

The most important results of these diagrams are the following:

• The Northern and Western European countries are located in the “moving further” quad-

rant in the innovation progress diagram. In addition, these countries appear close to the

horizontal axis in the productivity and competitiveness progress diagrams, thus it is dif-

ficult to categorize them. The same results can also be observed for countries with higher

income or innovation performance. This is consistent with the performance gaps men-

tioned in the previous sections. From the total set of the examined countries, Norway and

Switzerland appear to have the highest relative performance scores in all ICP measuresand a positive growth in their innovation scores.

• The group of next best performers, which mainly refers to the Western European countries

and the largest economies, is mainly located in the right quadrants, but rather close to

the axes origin. Thus, in several cases, it is difficult to categorize these countries in the

four distinct quadrants. Nevertheless, the progress diagrams show that these particular

countries are able to perform relatively high in all IPC indices, without worsening their

position.

• On the other hand, the Eastern and Southern European countries are mainly located in

the left quadrants in all progress diagrams, and this can also be observed for countrieswith lower income or innovation performance. However, some of these countries are able

to show a relatively higher progress in certain aggregated indices. Generally, progress

appears higher when improvement margins are larger.

• Extending the previous result, it seems that the Eastern European and the Southern

European countries are generally located in the “catching up” and the “falling further

behind” quadrant, while this cannot be clearly observed for the followers or the lagging

countries.

It is important to note that the majority of countries show a zero progress regarding produc-

tivity and competitiveness. In general, there are no countries clearly located in the “fallingfurther behind” or the “losing momentum” quadrants in the corresponding diagrams. This

reveals that the gap among the European countries is more clearly increased in the case of

innovation, compared to productivity and competitiveness. This is rather important, since

short-term policies and fiscal improvements may affect more easily the latter, while inno-

vation requires a long-term commitment. As reported by several studies, closing these gaps

among the European countries is considered as the most important and critical long-term

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T a b l e 2

P e r f o r m a n c e a n d p r o g r e s s b a s e d o n s e v e r a l c a t e g o r i z a t i o n s

C o u n t r y g r o u p s

I n n o v a t i o n


C o m p e t i t i v e n e s s

P e r f o r m a n c e a

P r o g r e s s

b


P r o g r e s s b


P r o g r e s s

b

I n n o v a t i o n l e a d e r s

0 . 5

6 7

0 .

0 2 5

0 . 7

1 0

− 0

.

0 0 9

0 . 6

8 1

− 0

.

0 1 2

N e x t b e s t p e r f o r m e r s

0 . 4

6 4

0 .

0 1 3

0 . 6

5 3

− 0

.

0 0 4

0 . 6

2 5

− 0

.

0 1 2

F o l l o w e r s

0 . 2

2 2

− 0

.

0 0 6

0 . 2

2 4

− 0

.

0 1 7

0 . 3

4 9

0 .

0 2 4

L a g g i n g

0 . 1

5 0

0 .

0 0 9

0 . 1

1 0

0 .

0 0 5

0 . 2

4 8

0 .

1 3 1

N o r t h e r n E u r o p e

0 . 5

1 3

0 .

0 2 8

0 . 7

0 0

0 .

0 0 4

0 . 6

7 1

− 0

.

0 0 9

W e s t e r n E u r o p e

0 . 4

6 7

0 .

0 0 3

0 . 6

3 1

− 0

.

0 1 8

0 . 6

0 2

− 0

.

0 1 6

S o u t h e r n E u r o p e

0 . 2

2 0

− 0

.

0 0 9

0 . 3

0 1

− 0

.

0 2 0

0 . 3

9 3

− 0

.

0 0 2

E a s t e r n E u r o p e

0 . 1

5 1

0 .

0 1 2

0 . 0

3 3

0 .

1 1 5

0 . 2

0 4

0 .

5 0 5

H i g h i n c o m e

0 . 5

3 4

0 .

0 2 5

0 . 7

6 4

0 .

0 0 3

0 . 7

1 1

− 0

.

0 0 6

U p p e r m e d i u m i n c o m

e

0 . 4

5 7

0 .

0 1 0

0 . 5

8 9

− 0

.

0 1 5

0 . 5

8 1

− 0

.

0 1 9

L o w e r m e d i u m i n c o m

e

0 . 2

2 3

− 0

.

0 1 1

0 . 2

7 4

− 0

.

0 1 5

0 . 3

8 4

0 .

0 0 9

L o w i n c o m e

0 . 1

4 8

0 .

0 1 4

0 . 0

6 0

0 .

0 1 4

0 . 2

1 3

0 .

3 0 4

a A v e r a g e o f c a t e g o r y

f o r 2 0 0 8

b A v e r a g e o f a n n u a l g

r o w t h ( 1 9 9 8 – 2 0 0 8 )

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I n n o v a t i o n p e r f o r m a n c e p

r o g r e s s

Current innovation performance HighLow

H i g h

L o w

AT

BE

CZ DK

FI

FR

DEGR

HU

IT

NO

PL

PO

IE

SK ES

SE

CHUK

Catching up Moving further ahead

Losing momentumFalling further behind

Fig. 6 Relative innovation progress diagram

P r o d u c t i v i t y p e r f o r m

a n c e p r o g r e s s

Current productivity performance HighLow

H i g h

L o w

AT

BECZ

DK FI FR

DEGR

HU

IT

NO

PL

PO IE

SK

ES SE CHUK

Catching up Moving further ahead

Losing momentumFalling further behind

Fig. 7 Relative productivity progress diagram

challenge for improving or sustaining growth (see for example WEF 2013; Pro Inno Europe

2011; European Union 2012).

5 Concluding remarks

National innovation, productivity, and competitiveness are complex concepts having different

measurement layers and aspects. Although there are several approaches that study theseconcepts, there is no universally accepted definition and in many cases several overlaps may

be observed (Carayannis and Grigoroudis 2012). Thus, the existing measurement approaches

serve also as definitions of these terms and lead to different assessments. The main aim of

this paper is to propose a methodological measurement framework based on multiobjective

mathematical programming in order to study the linkage among national IPC and discover

potential performance patterns.

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Finally, it is important to note that the main aim of developing national benchmarks or

scoreboards based on composite indices is not only to obtain country rankings and similar

results, but also to help policy-makers in identifying strengths and weaknesses, tracking

changes over time, and, in some cases, develop early warning systems.

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Linking National Competitiveness, Productivity, And Innovation

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