APPLYING SOCIAL NETWORK ANALYSIS TO INPUT–OUTPUT BASED INNOVATION MATRICES: AN ILLUSTRATIVE APPLICATION TO SIX OECD TECHNOLOGICAL SYSTEMS FOR THE MIDDLE 1990s

Abstract

The paper discusses, illustrates and possibly contributes to overcoming two methodological problems that emerge in applying Social Network Analysis (SNA) to the study of IO-based innovation flows matrices. The first has to do with the scale-effects these matrices suffer from. The second refers to the need of dichotomising the matrices. Through an illustrative application to six OECD countries in the mid-1990s, the paper shows that, as for the former problem, different relativisation procedures can be, and have been, used, which either tend to alter the actual meaning of standard SNA indicators, or do not properly take into account the actual composition of countries' final demand. As for the latter problem, the paper shows that the choice of discrete cut-offs is extremely sensitive, as comparative results actually change along the continuum of the matrices values. In order to overcome the scale problem, a new relativisation procedure is put forward that measures innovation flows embodied in a unit value basket of final demand and thus properly retains all the information provided by the original matrix of intersectoral innovation (embodied) flows. In addressing the problem of dichotomisation, the paper suggests, as a second best, to work with density distributions that can make the choice of discrete cut-off values less arbitrary.

Keywords:

• Technological systems
• Embodied innovation flows
• Input–Output analysis
• Network analysis

Acknowledgements

Although the authors contributed equally in the development of this article, and share the attribution of Sections 2 and 3, Sections 1 and 5 could be attributed to Sandro Montresor, whereas Section 4 could be attributed to Guiseppe Vittucci Marzetti. The authors would like to thank Maria Semitiel Garcia and the other participants to the 2007 Input–Output Conference (Istanbul, 26 July 2007), for their useful comments. The authors are particularly indebted to an anonymous referee for his suggestions on an earlier version of the article. Guiseppe Vittucci Marzetti also gratefully acknowledges support for this research from the Provincia Autonoma di Trento, post-doctoral scholarship (PAT) 2006. The usual disclaimers apply.

Notes

¹ More in general, the same issue is relevant whenever two or more countries are compared on the basis of a certain intersectoral matrix, which distributes the sectoral values of a certain variable along their subsystem structure. The comparative analysis of deindustrialisation and tertiarisation processes is thus another potential field of application for it (Montresor and Vittucci Marzetti, 2007).

² The B operator was first proposed by Siniscalco (1982). Each row of it adds up to 1 and shows ‘the shares of output of each sector which contribute to the different subsystems’. Thus, B can be used to reclassify any physical or value magnitude from sectors into subsystems. As noted by Rampa (1982), it is relative price invariant and depends not only on strict technological factors, but also on the structure of final demand.

³ As Montresor and Vittucci Marzetti (2008) show, the same kind of analysis can be fruitfully employed to detect and investigate different forms of innovation clusters within the TSs.

⁴ Although Chang and Shih (2005) convert all values in US dollars, this does not prove strictly necessary. Indeed, denoting with E the nominal exchange rate of the home currency to the US dollar, we have that the matrix obtained by using E () is equivalent to that without (R ^unit ):

⁵ It is also worth noting that such a method tends to underestimate the weight of the R&D efforts of the less developed countries, unless a PPP correction is introduced.

⁶ It is worth noting that, given the way R is defined, dividing its cells by the sum by row simply returns the operator B; in formal terms:

⁷ Recent empirical applications of this complex weighted-network analysis are Fagiolo et al. (2008) and De Montis et al. (2007).

⁸ Although matrix inversions have been carried out for each country at the maximum level of disaggregation in order to reduce the distortions introduced by sectoral aggregation, the blanks in the series of the ANBERD dataset have forced us to limit our empirical application to 16 sectors only (see Appendix A for details).

⁹ As we have said, the Z elements of t _Z are obtained by ordering the cells of all the six relativised matrices, so that .

¹⁰ For the delicate issue of R&D data on PPP see also Dougherty et al., 2007.

¹¹ Intersectoral embodied flows are quite low compared with the intrasectoral ones, amounting on average for the six countries to 18% of the total flows, with a coefficient of variation of 32.6%.

¹² However, it is worth noting that, assuming normality – not rejected at the 10% significance level (5% for Netherlands) by the Kolmogorov–Smirnov test – and variance homogeneity across the different groups – not rejected by the Levene statistic (F(5,90) = 0.244, p-value = 0.942) – the ANOVA test does not reject the null hypothesis of mean equality of these weights across the different TSs (F(5,90) = 0.354, p-value = 0.88). This result does not change if non-parametric statistics are used (Kruskal Wallis test p-value = 0.794).

¹³ In this respect, Chang and Shih (2005) are right when they point out that this relativisation procedure is ‘unable to produce a comparable base for displaying the differences between […] countries’ Chang and Shih, 2005, p. 157), although it has to be stressed that, as seen before, such a remark can be equally applied to their method too.

¹⁴ Given the way it is defined, the degree of centralisation, inward or outward, tends to 0 when the density of the correspondent network tends to 1 or 0.

¹⁵ It has to be stressed that the situation would be different if one instead had to compare two or more subsystems within the same TS in order to infer their relative position in it.