Linking innovation, productivity, and competitiveness: implications for policy and practice

Abstract

A country’s competitiveness is a complex concept that has been widely studied from different perspectives. Given that the competitive performance depends on the formation of intellectual capital and society’s capacity to innovate, economic research has identified innovation and productivity as key engines for the increase of competitiveness. There are several alternatives approaches for measuring innovation, productivity, and competitiveness. These approaches lead to different assessments, since there is no universally accepted definition and measuring technique of the aforementioned concepts. Moreover, these definitions appear to have several overlaps and this complicates the analysis of their relations. The aim of this paper is to present a methodological framework for studying the dynamic linkage among innovation, productivity, and competitiveness and explore the implications for policy and practice. For each one of these measures, an overall score is estimated, using a regression-based model that follows the principles of multi-objective mathematical programming. For the purpose of the analysis, a database containing a set of 25 indicators for 19 countries for the period 1998–2008 has been developed. The most important results include a series of contour maps and gap analysis diagrams that illustrate the evolution of the overall innovation, productivity, and competitiveness indices and compare the performance of the examined countries. These results show that, by average, there are no significant gaps among innovation, productivity, and competitiveness, although several variations may be found for particular countries. The motivation for this research from a policy and management perspective, is to explore whether, how and why certain combinations of competitiveness, productivity and innovation levels for a given country as well as across countries reveal any particular set of intrinsic strengths or weaknesses as well as more effective entry points regarding public sector (policy) interventions. A systematic profiling and comparison of competitiveness, productivity and innovation competence levels may reveal guidelines and insights for private sector (management) choices and initiatives as well.

Appendix

1.1 Mathematical model

The applied mathematical model is a regression-based approach that follows the principles of multiobjective mathematical programming. For each year the following mathematical program is formed:

$$ [\hbox{max} ]F_{1} = Corr(X_{s} ,Y_{s} ) + Corr(Y_{s} ,Z_{s} ) $$

(4)

$$ [\hbox{max} ]F_{2} = \sum\limits_{s = 1}^{S} {\left[ {\left( {e_{s}^{ + } + e_{s}^{ - } } \right) + \left( {\varepsilon_{s}^{ + } + \varepsilon_{s}^{ - } } \right) + \left( {\sigma_{s}^{ + } + \sigma_{s}^{ - } } \right)} \right]} $$

(5)

subject to:

$$ X_{s} = \sum\limits_{i = 1}^{n} {a_{i} x_{is} } + e_{s}^{ + } + e_{s}^{ - } \,\quad \forall s = 1,2, \ldots ,S $$

(6)

$$ Y_{s} = \sum\limits_{j = 1}^{m} {b_{j} y_{js} } + \varepsilon_{s}^{ + } + \varepsilon_{s}^{ - } \, \quad \forall s = 1,2, \ldots ,S $$

(7)

$$ Z_{s} = \sum\limits_{k = 1}^{l} {c_{k} z_{ks} } + \sigma_{s}^{ + } + \sigma_{s}^{ - } \, \quad \forall s = 1,2, \ldots ,S $$

(8)

$$ \sum\limits_{i = 1}^{n} {a_{i} } = 1 $$

(9)

$$ \sum\limits_{j = 1}^{m} {b_{j} } = 1 $$

(10)

$$ \sum\limits_{k = 1}^{l} {c_{k} } = 1 $$

(11)

where X _s , Y _s , and Z _s are the aggregated indices for country s of innovation, productivity, and competitiveness, respectively, x _is is the value of innovation indicator i for country s, y _js is the value of productivity indicator j for country s, z _ks is the value of competitiveness indicator k for country s, a _i , b _j , and c _k are the regression coefficients of x _is , y _js , and z _ks , respectively, e ⁺ _s and e ⁻ _s are the overestimation and the underestimation errors, respectively for the innovation regression equation, ɛ ⁺ _s and ɛ ⁻ _s are the overestimation and the underestimation errors, respectively for the productivity regression equation, σ ⁺ _s and σ ⁻ _s are the overestimation and the underestimation errors, respectively for the competitiveness regression equation, S is the total number of countries and

$$ Corr(X_{s} ,Y_{s} ) = \frac{{\sum\limits_{s = 1}^{S} {(X_{s} - \bar{X})(Y_{s} - \bar{Y})} }}{{\sqrt {\sum\limits_{s = 1}^{S} {(X_{s} - \bar{X})^{2} } \sum\limits_{s = 1}^{S} {(Y_{s} - \bar{Y})^{2} } } }} $$

(12)

$$ Corr(Y_{s} ,Z_{s} ) = \frac{{\sum\limits_{s = 1}^{S} {(Y_{s} - \bar{Y})(Z_{s} - \bar{Z})} }}{{\sqrt {\sum\limits_{s = 1}^{S} {(Y_{s} - \bar{Y})^{2} } \sum\limits_{s = 1}^{S} {(Z_{s} - \bar{Z})^{2} } } }} $$

(13)

with $\bar{X}$, $\bar{Y}$, and $\bar{Z}$ being the average values of X _s , Y _s , and Z _s , respectively.

The first three constraints (6), (7), and (8) refer to the regression equations for the innovation, productivity, and competitiveness indices. Each one of these regression equations assumes that the evaluated aggregated measure is a weighted sum of selected indicators (see Table 3). On the other hand, the last three constraints (9), (10), and (11) refer to the normalization of regression coefficients. Since x _is , y _js , z _ks  ∈ [0, 1] it is easy to see that X _s , Y _s , Z _s  ∈ [0, 1].

Having two separate error terms (overestimation and underestimation error) for each regression equation gives the ability to assume that all variables are nonnegative. It is easy to see that e ⁺ _s  · e ⁻ _s  = 0, ɛ ⁺ _s  · ɛ ⁻ _s  = 0, σ ⁺ _s  · σ ⁻ _s  = 0 ∀s, and thus the aforementioned model adopts the principles of goal programming.

The first objective function (F ₁) refers to the correlation between X _s and Y _s and between Y _s and Z _s , while the second objective function (F ₂) refers to the sum of regression error terms.

The proposed approach adopts the principles of linear regression analysis and canonical correlation analysis (Hair et al. 1995; Tabachnick and Fidell 1996). Thus, the main aim of the model is to estimate a set of aggregated innovation, productivity, and competitiveness indices for each country, maximizing the correlation between these indices and minimizing at the same time the sum of absolute estimation errors. This estimation takes into account the values of individual innovation, productivity, and competitiveness indicators for each country. Because of (4) the proposed approach is a nonlinear mathematical programming model, having two optimality criteria.

Moreover, the objective function (4) assures the interrelation among innovation, productivity, and competitiveness. It should be emphasized that Y _s serves as a mediator, while there is no order in in these relations. As noted by Carayannis and Sagi (2001) innovation and competitiveness are intrinsically unified; although one does not cause the other, both are necessary for competitiveness and for each other. This explained by the fact that innovation may improve national productivity, which in turn gives the ability to compete on the global marketplace. This competition may produce knowledge, which along with the profitability resulting from productivity, enables research and development investments (funds and/or resources), and thus leads to an increase in innovation (Carayannis and Sagi 2001).

Since this is a multiobjective mathematical model, it is not always possible to find a solution that optimizes both objective functions. For this reason, the following heuristic approach is adopted:

• 1. In the first step the following three linear programming models (LPs) are solved:

$$ \left\{ \begin{gathered} [\hbox{min} ]F_{21} = \sum\limits_{s = 1}^{S} {\left( {e_{s}^{ + } + e_{s}^{ - } } \right)} \hfill \\ {\text{subject to}} \hfill \\ {\text{constraints (5) and (8)}} \hfill \\ a_{i} ,X_{s} ,e_{s}^{ + } ,e_{s}^{ - } \ge 0 \hfill \\ \end{gathered} \right. $$

(14)

$$ \left\{ \begin{array}{l} [\hbox{min} ]F_{22} = \sum\limits_{s = 1}^{S} {\left( {\varepsilon_{s}^{ + } + \varepsilon_{s}^{ - } } \right)} \hfill \\ {\text{subject to}} \hfill \\ {\text{constraints (6) and (9)}} \hfill \\ b_{j} ,Y_{s} ,\varepsilon_{s}^{ + } ,\varepsilon_{s}^{ - } \ge 0 \hfill \\ \end{array} \right. $$

(15)

$$ \left\{ \begin{array}{l} [\hbox{min} ]F_{23} = \sum\limits_{s = 1}^{S} {\left( {\sigma_{s}^{ + } + \sigma_{s}^{ - } } \right)} \hfill \\ {\text{subject to}} \hfill \\ {\text{constraints (7) and (10)}} \hfill \\ c_{k} ,Z_{s} ,\sigma_{s}^{ + } ,\sigma_{s}^{ - } \ge 0 \hfill \\ \end{array} \right. $$

(16)

• 2. In the second step the following nonlinear mathematical model is solved:

$$ \left\{ \begin{array}{l} [\hbox{max} ]F_{1} = Corr(X_{s} ,Y_{s} ) + Corr(Y_{s} ,Z_{s} ) \hfill \\ {\text{subject to}} \hfill \\ F_{21} \le (1 + \rho )F_{21}^{*} \hfill \\ F_{22} \le (1 + \rho )F_{22}^{*} \hfill \\ F_{23} \le (1 + \rho )F_{23}^{*} \hfill \\ {\text{all constraints of LPs (13) - 15)}} \hfill \\ \end{array} \right. $$

(17)

where F ^*₂₁ , F ^*₂₂ , and F ^*₂₃ are the optimum values of F ₂₁, F ₂₂, and F ₂₃, respectively, as found during the first step, and ρ is a small number (e.g. 0.01, 0.05) referring to the trade-off of F ₂ optimum value.

This heuristic approach is similar to a lexicographic optimization process and it is adopted in several previous research efforts (see for example Jacquet-Lagrèze and Siskos 1982; Siskos 1985; Siskos et al. 1998; Grigoroudis and Siskos 2002; 2010).