Local knowledge composition and the emergence of entrepreneurial activities across industries: evidence from Italian NUTS-3 regions

Abstract

This paper investigates how the characteristics of the local knowledge bases, stemming from the accumulation and recombination of competences over time, spur the emergence of new entrepreneurial activities across industries at the Italian provincial level. To do so, we exploit information on the number of new firms appearing across diverse industries in each Italian NUTS-3 region (province) from 1997 to 2009 as an indicator of local entrepreneurial activity. To build indicators of both local technological knowledge stocks and local technological knowledge compositions, we collect information on patenting activity at the provincial level. Our findings suggest that the availability of local knowledge spillovers is not sufficient per se to trigger the creation of new firms. Indeed, looking at the properties of local knowledge bases, the rate of new firm formation appears to be higher in contexts featured by knowledge stemming from search activities shaped by the accumulated competences and dispersed across a wide area of the technology landscape. This suggests that, in Italy, entrepreneurship is mostly related to the exploitation of technological knowledge accumulated over time rather than to profiting from radical breakthroughs.

Appendices

Appendix 1. Internal characteristics of the knowledge base

1.1 Knowledge variety

Knowledge variety is measured using the information entropy index.¹⁵ Entropy measures the degree of disorder or randomness of the system; systems characterized by high entropy are characterized by high degrees of uncertainty (Saviotti 1988). Informational entropy is a diversity measure which allows to account for variety, i.e., the number of categories into which system elements are apportioned, and balance, i.e., the distribution of system elements across categories.

Information entropy has some interesting properties (Frenken and Nuvolari 2004), including multidimensionality. Consider a pair of events (X_l, Y_j), and the probability of their co-occurrence p_lj. A two-dimensional total variety (TV) measure can be expressed as follows:

$$ \mathrm{KV}\equiv \mathrm{H}\left(\mathrm{X},\mathrm{Y}\right)=\sum \limits_{\mathrm{l}}\sum \limits_{\mathrm{j}}{\mathrm{p}}_{\mathrm{l}\mathrm{j}}{\log}_2\left(\frac{1}{{\mathrm{p}}_{\mathrm{l}\mathrm{j}}}\right) $$

(10)

Let the events X_l and Y_j be citation in a patent document of technological classes l and j, respectively. Then, p_lj is the probability that two technological classes l and j co-occur within the same patent. The measure of multidimensional entropy, therefore, focuses on the variety of co-occurrences or pairs of technological classes within patent applications.

The total index can be decomposed into “within” and “between” parts whenever the events being investigated can be aggregated into a smaller number of subsets. Within-entropy measures the average degree of disorder or variety within the subsets; between-entropy focuses on the subsets, measuring the variety across them. Let the technologies i and j belong to the subsets g and z of the classification scheme, respectively. If one allows l∈S_g and j∈S_z (g = 1,…,G; z = 1,…, Z), we can write:

$$ {P}_{gz}=\sum \limits_{l\in {S}_g}\sum \limits_{j\in {S}_Z}{p}_{lj} $$

(11)

which is the probability to observe the couple lj in the subsets g and z, while the intra subsets variety can be measured as follows:

$$ {H}_{gz}=\sum \limits_{l\in {S}_g}\sum \limits_{j\in {S}_z}\frac{p_{lj}}{P_{gz}} lo{g}_2\left(\frac{1}{p_{lj}/{P}_{gz}}\right) $$

(12)

The (weighted) within-group entropy can be finally written as follows:

$$ \mathrm{RKV}\equiv \sum \limits_{\mathrm{g}=1}^{\mathrm{G}}\sum \limits_{\mathrm{z}=1}^{\mathrm{Z}}{\mathrm{P}}_{\mathrm{g}\mathrm{z}}{\mathrm{H}}_{\mathrm{g}\mathrm{z}} $$

(13)

Between-group (or unrelated variety) can instead be calculated by using the following equation:

$$ \mathrm{UKV}\equiv {\mathrm{H}}_{\mathrm{Q}}=\sum \limits_{\mathrm{g}=1}^{\mathrm{G}}\sum \limits_{\mathrm{z}=1}^{\mathrm{Z}}{\mathrm{P}}_{\mathrm{g}\mathrm{z}}{\log}_2\frac{1}{{\mathrm{P}}_{\mathrm{g}\mathrm{z}}} $$

(14)

According to the decomposition theorem, we can rewrite the total entropy H(X,Y) as follows:

$$ \mathrm{KV}={\mathrm{H}}_{\mathrm{Q}}+\sum \limits_{\mathrm{g}=1}^{\mathrm{G}}\sum \limits_{\mathrm{z}=1}^{\mathrm{Z}}{\mathrm{P}}_{\mathrm{g}\mathrm{z}}{\mathrm{H}}_{\mathrm{g}\mathrm{z}} $$

(15)

Within-group entropy (or related variety) measures the degree of technological differentiation within the macro-field, while between-group variety (or unrelated variety) measures the degree of technological differentiation across macro-fields. The first term on the right-hand-side of Eq. (A6) is the between-entropy, and the second term is the (weighted) within-entropy.

We can label between- and within-entropy respectively as unrelated technological variety (UKV) and related technological variety (RKV), while total information entropy is referred to as general technological variety (Frenken et al. 2007; Boschma and Iammarino 2009). This means that we consider variety not only as a global entity but also as a new combination of existing bits of knowledge versus variety as a combination of new bits of knowledge. When variety is high (respectively low), this means that the search process has been extensive (respectively partial). When unrelated variety is high compared to related variety, the search process is based essentially on the combination of novel bits of knowledge rather than new combinations of existing bits of knowledge.

1.2 Knowledge coherence

We calculate the coherence of the regional (NUTS-3) knowledge bases, defined as the average relatedness or complementarity of a technology chosen randomly within the firm’s patent portfolio with respect to any other technology (Nesta and Saviotti 2006; Nesta 2008; Quatraro 2010).

Obtaining the knowledge coherence index requires a number of steps. First of all, we need to calculate the weighted average relatedness WAR_l of technology l with respect to all other technologies in the regional patent portfolio. This measure builds on the measure of technological relatedness amongst any pair of technologies i and j, τ_lj.

Following Teece et al. (1994), the weighted average relatedness, WAR_l is defined as the degree to which technology l is related to all other technologies j∈l in the region’s patent portfolio, weighted by patent count P_jt:

$$ WA{R}_{lt}=\frac{\sum_{j\ne l}{\tau}_{lj}{P}_{jt}}{\sum_{j\ne l}{P}_{jt}} $$

(16)

Finally, the coherence of the region’s knowledge base at time t is defined as the weighted average of the WAR_lt measure:

$$ CO{H}_t=\sum \limits_l WA{R}_{lt}\times \frac{P_{lt}}{\sum_l{P}_{lt}} $$

(17)

Note that this index implemented by analyzing the co-occurrence of technological classes within patent applications measures the degree to which the services rendered by the co-occurring technologies are complementary and is based on how frequently technological classes are combined in use. The relatedness measure τ_lj indicates that utilization of technology l implies use also of technology j in order to perform specific functions that are not reducible to their independent use.

1.3 Cognitive Distance

A useful index of distance can be derived from technological proximity proposed by Jaffe (1986, 1989), who investigated the proximity of firms’ technological portfolios. Breschi et al. (2003) adapted this index to measure the proximity between two technologies.

Let P_lk = 1 if the patent k is assigned the technology l [l = 1, …, n], and 0 otherwise. The total number of patents assigned to technology l is O_l = ∑_kP_lk. Similarly, the total number of patents assigned to technology j is O_j = ∑_kP_jk. The number of patents that are classified in both technological fields l and j is ${V}_{lj}=\sum \limits_k{P}_{lk}{P}_{jk}$. By applying this count of joint occurrences to all possible pairs of classification codes, we obtain a square symmetrical matrix of co-occurrences whose generic cell V_lj reports the number of patent documents classified in both of the technological fields l and j.

Technological proximity is proxied by the cosine index, which is calculated for a pair of technologies l and j as the angular separation or uncentered correlation of the vectors V_lm and V_jm. The similarity of technologies l and j can then be defined as follows:

$$ {S}_{\mathrm{lj}}=\frac{\sum_{m=1}^n{V}_{\mathrm{lm}}{V}_{\mathrm{jm}}}{\sqrt{\sum_{m=1}^n{V}_{\mathrm{lm}}^2}\sqrt{\sum_{m=1}^n{V}_{\mathrm{jm}}^2}} $$

(18)

The cosine index provides a measure of the similarity between two technological fields in terms of their mutual relationships with all the other fields. The greater the S_lj, the more two technologies l and j co-occur with the same technologies. It is equal to one for pairs of technological fields with identical distribution of co-occurrences with all the other technological fields, while it goes to zero if vectors V_lm and V_jm are orthogonal (Breschi et al. 2003).¹⁶ Similarity between technological classes is thus calculated on the basis of their relative position in the technology space. The closer technologies are in the technology space, the higher is S_lj and the lower their cognitive distance (Engelsman and van Raan 1994; Jaffe 1986; Breschi et al. 2003).

The cognitive distance between j and l can be therefore measured as the complement of their index of technological proximity:

$$ {d}_{lj}=1-{S}_{lj} $$

(19)

Having calculated the index for all possible pairs, it needs to be aggregated at the regional level to obtain a synthetic index of distance amongst the technologies in the firm’s patent portfolio. This is done in two steps. First, we compute the weighted average distance (WAD) of technology l, i.e., the average distance of l from all other technologies.

$$ WA{D}_{lt}=\frac{\sum_{j\ne l}{d}_{lj}{P}_{jt}}{\sum_{j\ne l}{P}_{jt}} $$

(20)

where P_j is the number of patents in which the technology j is observed. The average cognitive distance at time t is obtained as follows:

$$ C{D}_t={\sum}_l WA{D}_{lt}\times \frac{P_{lt}}{\sum_l{P}_{lt}} $$

(21)

The cognitive distance index measures the inverse of the similarity degree amongst technologies. When cognitive distance is high, it signals the combination of core technologies with unfamiliar technologies.

Appendix 2. Further results

Table 8 Econometric results (full sample)

Table 9 Econometric results (SB – no controls)

Table 10 Econometric results (SS – no controls)

Table 11 Econometric results (SI – no controls)

Table 12 Econometric results (SD – no controls)