How does accessibility to knowledge sources affect the innovativeness of corporations?—evidence from Sweden

Abstract

This paper studies the innovative performance of 130 Swedish corporations during 1993–1994. The number of patents per corporation is explained as a function of the accessibility to internal and external knowledge sources of each corporation. A coherent way of handling accessibility measures, within and between corporations located across regions, is introduced. We examine the relative importance of intra- and interregional knowledge sources from 1) the own corporation, 2) other corporations, and 3) universities. The results show that there is a positive relationship between the innovativeness of a corporation and its accessibility to university researchers within regions where own research groups are located. Good accessibility among the corporation's research units does not have any significant effects on the likelihood of generation of patents. Instead the size of the R&D staff of the corporation seems to be the most important internal factor. There is no indication that intraregional accessibility to other corporations' research is important for a corporation's innovativeness. However, there is some indication of reduced likelihood for own corporate patenting when other corporate R&D is located in nearby regions. This may reflect a negative effect from competition for R&D labor.

Appendices

Appendix A: details on the construction of accessibility variables

These sections describe the construction of the accessibility variables used in the empirical estimations.

1.1 Internal corporate group knowledge accessibility

Internal accessibility to R&D plants within each group can be calculated by matrix algebra in the following way. First, we define an 81 × 81 symmetrical matrix, T, displaying mean time distance from one local labor market region to another. Since we did not have actual values for 1994, we took the average of time distances from 1990 and 1998.

$$T = {\left[ {\begin{array}{*{20}c} {{\tau _{{1,1}} }} & { \cdots } & {{\tau _{{1,81}} }} \\ { \vdots } & { \ddots } & { \vdots } \\ {{\tau _{{81,1}} }} & { \cdots } & {{\tau _{{81,81}} }} \\ \end{array} } \right]},\;{\text{where}}\;\tau _{{i,j}} = e^{{ - \lambda t_{{i,j}} }} $$

(A.17)

We define a matrix R describing the distribution of each group's R&D personnel across space. This matrix is 81×130 so that:

$$R = {\left[ {\begin{array}{*{20}c} {{R_{{1,1}} }} & { \cdots } & {{R_{{1,130}} }} \\ { \vdots } & { \ddots } & { \vdots } \\ {{R_{{81,1}} }} & { \cdots } & {{R_{{81,130}} }} \\ \end{array} } \right]}$$

(A.18)

where for example R _39,53 denotes the research activity of group 53 in region 39. R denotes the number of research personnel. Also, a dummy matrix is defined so that

$$D = {\left[ {\begin{array}{*{20}c} {{D_{{1,1}} }} & { \cdots } & {{D_{{1,130}} }} \\ { \vdots } & { \ddots } & { \vdots } \\ {{D_{{81,1}} }} & { \cdots } & {{D_{{81,130}} }} \\ \end{array} } \right]}$$

(A.19)

Each value D _r,k has a value of 1 if group k has research activity in region r and 0 otherwise. This matrix is constructed to ensure that if a group is not present in a region, it will not have access to other research within the group from that region. Then we define

$$TRD = {\left( {TR} \right)}. * D$$

(A.20)

where .* denotes the Hadamard (elementwise) matrix multiplication (./ will later denote Hadamard, elementwise, matrix division). To sum over the columns in the matrix TRD and account for the number of regions in which a group is present we form an 1 × 81 row vector i ₈₁ of ones and premultiply TRD by this. The result is a 1 × 130 row vector, showing the sum of a group's accessibility of all locations in which it is present.

$$TRD_{{sum}} = i_{{81}} TRD$$

(A.21)

Next, we premultiply the D matrix by the same row vector i. The resulting 1 × 130 row vector, N, shows for each element the number of locations in which a group has research activities.

$$N = i_{{81}} D$$

(A.22)

Finally, we divide each element of TRD _sum by the corresponding element of N and take the transpose, so that internal accessibility shows up as a 130 × 1 column vector:

$$A_{{int}} = {\left( {TRD_{{sum}} ./N} \right)}\prime $$

(A.23)

1.2 Knowledge accessibility between groups

We want to separate external accessibility to other groups' knowledge into knowledge access within a region where the group has own research, and access to research staff outside regions of own research personnel. We wish to obtain a matrix 81×130 showing first total external accessibility to other groups' R&D. To accomplish this, we must first remove own research. We sum a region's research amount by post multiplying R with an identity column vector i ₁₃₀. The result is an 81×1 column vector where each element shows the total amount of research in region r. Then we multiply the result with i ₁₃₀. The end result is a 81×130 matrix, $\widetilde{R}$, where an element from row r shows the sum of research within region r so that $\widetilde{R}_{{r,1}} = \widetilde{R}_{{r,k}}$. Then we deduct research from the own company so that only external research is left.

$$R^{e} \widetilde{R} - R = \begin{array}{*{20}l} {{R^{e}_{{1,1}} } \hfill} & { \cdots \hfill} & {{R^{e}_{{1,130}} } \hfill} \\ { \vdots \hfill} & { \ddots \hfill} & { \vdots \hfill} \\ {{R^{e}_{{81,1}} } \hfill} & { \cdots \hfill} & {{R^{e}_{{81,130}} } \hfill} \\ \end{array} $$

An element R _r,k ^e shows the potential amount of external knowledge available for group k coming from region r. Finally, we have to adjust for time distance to external knowledge and for a company's own research in the region, in a fashion similar to the above.

$$TRD^{e} = {\left( {T\operatorname{R} ^{e} } \right)}. * D$$

(A.24)

We use the same procedure as outlined above to arrive at the column vector A _ext:

$$A_{{ext}} = {\left( {i_{{81}} TRD^{e} ./N} \right)}\prime $$

(A.25)

This leaves us with a 130×1 column vector of external accessibilities to other groups' research available for each group. Now we divide this effect into intra-and interregional accessibilities to external knowledge. First, we calculate only those effects which are internal to the region and subtract this from (A.25). We construct a matrix $\widetilde{T}$ with dimensions 81×130. This matrix consists of 130 identical column vectors. Each element of the vectors shows the internal time distance of the corresponding row (e.g. any element on row 80 shows the internal time distance in region 80):

$$\widetilde{T} = {\left[ {\begin{array}{*{20}l} {{\tau _{{1,1}} } \hfill} & {{\tau _{{1,1}} } \hfill} & { \cdots \hfill} & { \cdots \hfill} & {{\tau _{{1,1}} } \hfill} \\ {{\tau _{{2,2}} } \hfill} & {{\tau _{{2,2}} } \hfill} & { \cdots \hfill} & { \cdots \hfill} & {{\tau _{{2,2}} } \hfill} \\ { \vdots \hfill} & {{} \hfill} & { \ddots \hfill} & {{} \hfill} & { \vdots \hfill} \\ { \vdots \hfill} & {{} \hfill} & {{} \hfill} & { \ddots \hfill} & { \vdots \hfill} \\ {{\tau _{{81,81}} } \hfill} & {{\tau _{{81,81}} } \hfill} & { \cdots \hfill} & { \cdots \hfill} & {{\tau _{{81,81}} } \hfill} \\ \end{array} } \right]}$$

We multiply R ^e elementwise with $\widetilde{T}$ to form intraregional but external knowledge accessibility, AR _ext,1 for each group again similar to what has been done before:

$$\widetilde{{TRD}}^{e} = {\left( {\widetilde{{T.}} * \operatorname{R} ^{e} } \right)}. * D$$

(A.26)

$$A_{{ext,1}} = {\left( {i_{{81}} \widetilde{{TRD}}^{e} ./N} \right)}\prime $$

(A.27)

The dummy D again plays the role of only taking into account effects when the group conducts research in the region. Then, to calculate external knowledge from other groups in other regions, we simply subtract A _ext,1 from A _">ext :

$$A_{{ext,2}} = A_{{ext}} - A_{{ext,1}} $$

(A.28)

1.3 Accessibility to university research staff

We now turn to accessibility to research in universities (and other higher education). We start out with an 81×1 column vector, u, each element showing the amount of university research personnel in a region. This is premultiplied with the mean time distance matrix T (A.17) to form:

$$TU = \begin{array}{*{20}c} {{Tu_{1} }} \\ { \vdots } \\ {{Tu_{{81}} }} \\ \end{array} $$

(A.29)

where Tu _r shows region r's total accessibility to university research. Next, we form a matrix $\widetilde{{Tu}}$ which we get by postmultiplying by a column identity row-vector i ₁₃₀. This results in an 81×130 matrix, $\widetilde{{Tu}}$. We then proceed with the same method as above,

$$AU = {\left( {i_{{81}} {\left( {\widetilde{{TU}}. * D} \right)}./N} \right)}\prime $$

(A.30)

which results in a 130×1 vector in which each element represents a group's average accessibility to university research. To separate between intra- and interregional accessibility, exactly the same method is applied as for knowledge accessibility between groups. We label intraregional university research AU ₁ and interregional accessibility AU ₂.

Appendix B: results of the Negative Binomial and the Zero-Inflated Negative Binomial models

Table A presents the results of the Negative Binomial model and the Zero-Inflated Negative Binomial model not included in the main text.

Table A Estimates of the Negative Binomial (Neg. bin.) and the Zero-Inflated Negative Binomial (ZINB) models

Appendix C: prediction graphs of the presented models

Figures A and B show the predicted values plotted on the Y-axis against actual values on the X-axis, for the various models in use. Perfect predictions would result in straight 45° lines from the origo.

Fig. A

Predicted values for the Poisson, Zero-Inflated Poisson and the Zero-Inflated Negative Binomial model. One outlier is not shown for the ZINB model, 75.44 corresponding to actual value 37

Fig. B

Predicted values for the Negative Binomial model. Note: there are some extraordinary outlier predictions outside the range shown. 139,000,000,000, 2,080.196 and 280.6752 corresponding to actual patent values 37, 0 and 11