The three dimensions of relatedness

is tacit or non-codified knowledge, studies like Patel and Pavitt 1997 have shown that other measures that embody tacit knowledge such as RD expenditure, or judgement of technological peers give results that are very similar to those obtained using US patenting. Sectoral and geographical characteristics of firms constituting our sample are reported in Table 1. The comparison with the relevant characteristics of the Fortune 500 firms also reported in Table 1 allows to assess the balance of the sample.

4. The three dimensions of relatedness

In order to investigate firms’ diversification patterns in the period considered, and particularly whether they moved into related or unrelated areas of activity, we developed a survivor measure of relatedness. According with Teece et al. 1994, this measure is based on the principle that economic competition will lead to the Table 1 Sectoral and geographical characteristics of the sample considered vs. Fortune 500 firms Industry Sample Fortune 500 1993 No. firms No. firms 47 5.9 9.4 15 Food 18 3.6 10 Drink 4.0 Tobacco 1.0 5 1.6 4 53 9.1 10.6 23 Chemicals 5.2 23 9.1 26 Pharmaceuticals 25 9.9 Metals 53 10.6 Mechanical engineering 15 5.9 26 5.2 18 8.8 44 Electrical equipment 7.1 3.6 Office equipment 18 5.1 13 6.3 16 43 Motor vehicles 8.6 3.0 14 5.5 15 Aircraft 9 1.8 3.6 Textiles and clothing 9 13 Paper products 4.6 23 5.1 12 3.6 9 Printing and publishing 2.4 11 2.4 2.2 Rubber and plastic products 6 4.3 23 11 4.6 Non-metallic mineral products 16 6.3 56 11.2 Coal and petroleum 2.0 8 3.2 10 Professional and scientific instruments Total 248 100.0 492 98.4 Geographical area 86 31.0 Europe 155 34.0 159 31.8 109 United States 43.1 20.9 53 Japan 27.0 135 449 100.0 248 Total 89.8 disappearance of relatively inefficient organisational forms Stigler, 1961. There- fore, the underlying assumption is that the activities in sectors which are more related will be more frequently combined within the same firm. Thus, if corpora- tions which engage activity in sector i almost always engage activity also in sector j, then these two sectors are likely to be related. Accordingly, considering the universe as constituted by K firms = 1,..., k,..., K, it is possible to define: C ik = 1 if firm k is active in sector i, and 0 otherwise; m k = i C ik = the number of activities 3 of firm k; n i = k C ik = the number of firms active in sector i Therefore: J ij = k C ik C jk = the number of firms which are active in both sector i and sector j; m ij = Ex ij = the expected number of firms active in both sector i and sector j, under the hypothesis that diversification is random. In order to operationalise the random hypothesis, we consider the number x ij of firms active both in sector i and j as a hypergeometric random variable. Therefore, with population K, and specific participants n i and n j , random diversification would imply 4 : m ij = Ex ij = n i n j K s 2 ij = m ij [K − n i K][K − n j K − 1] If the actual number J ij of linkages observed between sector i and sector j greatly exceeds the expected number m ij , then the two sectors are highly related. Therefore, the measure of relatedness between sector i and sector j is: RELAT ij = J ij − m ij s ij which, by analogy with a t-statistic, measures the degree to which the observed linkage between the two sectors exceeds that which could be expected if the assignments of activities were simply random. In order to avoid subjectivity problems, the data employed to evaluate related- ness between industries refer to the data obtained from the 1985 Trinet Large Establishment data set 5 . The values of RELAT ij range from a minimum of − 18.85 3 Following the notation adopted in Teece et al. 1994, activity has been defined as the operation of a firm in a sector. 4 It is perhaps worth reminding that the hypergeomentric distribution is derived from a sampling without replacement, which is the most appropriate for the case under study. Indeed, it can be associated to an experiment in which we are interested in the probability of drawing a firm k active in sector i after drawing the same firm k active in sector j from the universe of pairs firm, sector. 5 The Trinet data set provides information on every establishment in the United States with over 20 employees; each of the approximately 400,000 records constituting the data set describes an establish- ment, recording its name, address, telephone number, employee count, activities in each four-digit SIC sector, estimated value of shipments, and corporate company, if any. In order to apply such a relatedness measure to our sample of firms, we aggregated the four-digit SIC sectors into the 42 sectors considered. between Holding services and Distribution services to a maximum of 46.22 between Holding services and Financial services. The average relatedness is 3.20 and the standard deviation is 6.47. The hypothesis developed in this paper is that relatedness between sectors is only partially explained by industry-specific i.e. vertical integration between sequential phases in the production chain, and market similarity and technology-specific technological spillovers characteristics. In fact, the remaining unexplained vari- ance has mostly to do with firm-specific characteristics, that is with individual firms’ capabilities and competencies. In order to test the multi-dimensional character of relatedness, we develop an econometric model. According whith previous theoretical and empirical studies, the variables considered as proxy for the different dimensions are the followings. The industry-specific aspects of relatedness have been proxied by vertical integra- tion and market similarity. Specifically, as far as vertical integration is concerned, we evaluated the linkages between sectors as obtained from inputoutput tables 6 Eurostat, 1980. Accordingly, the variable VERT ij is a dummy which assumes the value 1 if the two sectors i and j are sequential in the productive chain, and 0 otherwise. The market similarity has been proxied by the variable MKT ij , which is a dummy equals to 1 if two sectors i and j are both oriented to the industrial market, and 0 otherwise. The technology-based inter-sectoral linkages or spillovers have been proxied by an input – output measure of the interlinkages in terms of RD flows Scherer, 1982. Such a measure is consistent with a two-way interaction between sectors Laursen and Meliciani, 1999. Thus, the variable TECH –LINK ij is a dummy which assumes the value 1 if the two sectors i and j have high technological linkages in terms of RD flows 7 . The firm-specific aspect has been proxied by the affinity or proximity in the underlying technological competencies 8 . The firm’s idea is that firms require spe- 6 We considered as the critical value a share of 5. Other studies e.g. Orecchia, 1998 consider a critical value of 3, but the results obtained are very similar in both cases. 7 The cut-off point considered, in accordance with a sensitivity analysis run for different values, is US15 millions in Scherer’s table. Our choice of RD flows as indicators for technological spillovers obviously implies that we take a limited perspective on the issue. Spillovers are much broader than what is captured by our indicator. Griliches 1979 distinguishes between two types of spillovers, i.e. rent spillovers and pure knowledge spillovers. Like all the studies considering RD as a neasure of spillovers, we are within the interpretation of rent spillovers Coe and Helpman, 1995; Laursen and Meliciani, 1999. 8 Other approaches have been suggested. Among the most recent, Engelsman and van Raan 1994 based their approach on co-classification maps built through patents; Verspagen 1997 suggested a method which is based upon the distinction between the main or primary classification code assigned to a patent document, and the supplementary or secondary classification codes. cialised technological competence in order to produce attractive products by efficient methods in their respective industries. The firm’s competencies con- struction activity proceeds purposively Markides, 1995, 1996 through an evolu- tionary learning process, based on trial and error which is gradual and path- dependent. Therefore, the affinity between the technological profiles of sectors determines firms’ diversification into them. Consequently, it helps explain their relatedness. According to the survivor principle, innovative activities and therefore, compe- tencies in related technological fields would be more frequently combined within the same firm. In order to build a proxy for this dimension of relatedness, the analytical framework used in Teece et al. 1994 has been applied to the firms’ technological competencies. By measuring the firms’ technological competencies through their patenting activity in the relevant technological fields, it is possible to define 9 : P ik = 1 if firm k has been granted at least one patent in technological field i, and 0 otherwise; r k = i P ik = the number of technological fields in which the firm k patents; s i = k P ik = the number of firms patenting in technological field i Therefore: Y ij = k P ik P jk = the number of firms patenting in both technological field i and j; n ij = Ex ij = the expected number of firms patenting in both technological field i and j, under the hypothesis that technological diversification is random. Considering the number x ij of firms which patent in both technological field i and j as a hypergeometric random variable, it will be: g ij = Ex ij = n i n j K s 2 ij = m ij [K − n i K][K − n j K − 1] Therefore, if the actual number Y ij of linkages observed between technological field i and j greatly exceeds the expected number n ij , the two technological fields are highly related. The measure of the technological competence-based relatedness between fields i and j, is: COMPET ij = Y ij − g ij s ij The values of COMPET ij range from a minimum of − 2.53 between field 40, i.e. motor vehicles and components, and fields 20, food products, and 21, tobacco products to a maximum of 27.57 between food products and tobacco products. The average value is 6.06 and the standard deviation is 3.94. 9 Again, in order to limit subjectivity problems, the data refer to the whole data set on patents developed at the University of Reading. In order to respect homogeneity with the data employed for product diversification and, particularly, for the calculation of the relatedness between sectors, the data considered refer to 1985. Table 2 Correlation matrix VERT MKT TECH –LINK RELAT COMPET RELAT 1 COMPET 0.456 1 VERT 0.403 0.188 1 TECH –LINK 0.139 0.149 0.124 1 0.276 0.093 MKT 0.398 1 0.230 Table 3 Results of the econometric models dependent variable = RELAT a Model c 1 Model c 2 − 0.804 −1.484 Constant − 0.853 −1.560 0.574 7.582 COMPET 0.568 7.436 0.523 0.707 TECH –LINK 5.254 5.696 5.311 5.785 VERT 3.236 5.123 3.253 5.157 MKT Model statistics 324 No. observations 324 61.490 Regression, F 46.171 0.358 Adjusted R 2 0.359 a Notes: the t-statistics are reported in parentheses all are two-tail tests. Significant at PB0.01. 4 . 1 . The econometric model In order to investigate whether the relatedness between two sectors i and j depends on industry-, technology- and firm-specific dimensions, we modelled the dependent variable RELAT ij as a function of the variables described in the previous section 10 . Such a model has been estimated by OLS. Before running the regression, we performed a correlation analysis in order to detect if any problem of multicollinearity amongst the variables existed see Table 2. RELAT shows a noteworthy correlation with COMPET r = 0.456, but also with VERT r = 0.403 and MKT r = 0.398. The independent variables do not show any multicollinearity problems, as the highest simple correlation is that between MKT and VERT r = 0.276. The results of the regression are reported in Table 3. In particular, Model 1 illustrates the regression in which all the independent variables are jointly tested, 10 It is worth observing that i and j concern here only industrial activities i.e. the 26 sectors described in Appendix B. Accordingly, we adopted a higher level of aggregation for the original 56 technological fields see Appendix C into 26 fields see Appendix D. The author wish to thank Bart Verspagen and an anonymous Referee for the stimuli which led to clarify this delicate point. while Model 2 represents the best specification obtained. The econometric results support the hypothesis that relatedness among sectors depends on: “ industry-specific factors. The proximity in the productive chain, VERT, shows a positive coefficient significantly different from zero at P B 0.01 in both the models. Likewise, the proxy for the market similarity, MKT, is always significant at P B 0.01; “ the firm-specific dimension. The variable COMPET is always significant at P B 0.01 in both the models. Interestingly, the technology-specific dimension proxied by TECH –LINK does not seem to influence the dependent variable significantly. Nonetheless, that might well reflect shortcomings in the measurement of technological specificity.

5. Coherence in technological and product diversification