(Green) Knowledge spillovers and regional environmental support: do they matter for the entry of new green tech-based firms?

Abstract

This paper studies the role played by the features of the local knowledge base and the regional environmental support in the entry of new green tech-based firms. We compute a set of specific knowledge indicators which capture the recombination of technologies that make up green technologies in French départements (NUTS3 regions) for the period 2003–2013. By using a rich and unique dataset based on firm-level microdata and patents information, we find that the main determinants of the entry of new green tech-based firms are: (i) the combination of high levels of internal coherence with sufficient diversification into unrelated technological categories other than green and (ii) the regional efforts to reduce the environmental impact of economic activities. Indeed, by applying spatial econometrics we found that the impact of knowledge spillovers mainly accrues within the département of entry. These results suggest that more attention should be paid to the context-specific recombination of technologies constituting green technologies and that environmental regulations may have, an indirect, but important impact when it comes to promote green technological entry in regions.

Appendix: The implementation of knowledge spillovers

This section builds on Quatraro (2010) and Colombelli and Quatraro (2019).

1.1 A. Knowledge stock

To measure the local knowledge stock (STOCK_ALL) based on patent applications, we calculate the accumulated stock of past patent applications applying the permanent inventory method as follows:

$$STOCK\_ALL_{it} = h_{it} + \left( {1 - \delta } \right)STOCK_{it - 1}$$

(2)

where ${h}_{it}$ is the flow of patent applications, $\delta$ is the rate of obsolescence of 10%,¹⁰$i$ is the region and $t$ is the time period. This measure has also been calculated for both non-environmental (STOCK_NGREEN) and green technologies (STOCK_GREEN).

1.2 B. Knowledge variety

Our measure of knowledge variety is based on the information entropy index by following a multidimensional approach proposed by (Colombelli and Quatraro 2019).¹¹

Let us consider a pair of events (${X}_{l},{Y}_{j}$) and the probability of their co-occurrence ${p}_{lj}$. A two-dimensional total variety (KV) measure can be expressed as follows:

$${\text{KV}} = H\left( {X,Y} \right) = \mathop \sum \limits_{l} \mathop \sum \limits_{j} p_{lj} {\text{log}}_{2} \left( {\frac{1}{{p_{lj} }}} \right)$$

(3)

where ${p}_{lj}$ is the probability that two technological classes l and j co-occur within the same patent. The measure of multidimensional entropy focuses on the variety of co-occurrences or pairs of technological classes in patent applications and provides an index of how much the creation of new knowledge is focused on a narrower set of possible combinations.

The total index can be decomposed into “within” and “between” parts, whenever the events under study can be aggregated into smaller number of subsets. Within-group entropy measures the average degree of variety within the subsets (at 3-digit level); between-group entropy focuses on the subsets and measures the average degree of variety across them (at 1-digit level).

Let the technologies l and j belong to the subsets g and z of the classification scheme, respectively. If one allows $l\in {S}_{g}$ and $j\in {S}_{z}$, it is possible to write:

$$P_{gz} = \mathop \sum \limits_{{l \in S_{g} }} \mathop \sum \limits_{{j \in S_{z} }} p_{lj}$$

(4)

which is the probability of observing the pair $lj$ in the subsets g and z, while the intra-subsets variety can be measured as follows:

$$H_{gz} = \mathop \sum \limits_{{l \in S_{g} }} \mathop \sum \limits_{{j \in S_{z} }} \frac{{p_{lj} }}{{p_{gz} }}{\text{log}}_{2} \left( {\frac{1}{{p_{lj} /P_{gz} }}} \right)$$

(5)

The weighted within-group entropy or related variety (RKV) can therefore be written as follows:

$${\text{RKV}} = \mathop \sum \limits_{g = 1}^{G} \mathop \sum \limits_{z = 1}^{Z} P_{gz}$$

(6)

The between-group or unrelated variety (UKV) can be calculated using the following equation:

$${\text{UKV}} \equiv H_{Q} = \mathop \sum \limits_{g = 1}^{G} \mathop \sum \limits_{z = 1}^{Z} P_{gz} {\text{log}}_{2} \left( {\frac{1}{{P_{gz} }}} \right)$$

(7)

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

$${\text{KV}} = H_{Q} + \mathop \sum \limits_{g = 1}^{G} \mathop \sum \limits_{z = 1}^{Z} P_{gz} H_{gz}$$

(8)

The first term on the right-hand side of Eq. (8) is the between-entropy and the second term is the weighted within entropy.

Indeed, as we argued in Sect. 3, we adapt the entropy index to capture the recombination of technological classes associated with green technologies.

1.3 C. Knowledge coherence

The degree of complementarity among the technological classes composing the local patent’s portfolio has been calculated in different steps for the 96 metropolitan départements of France (Nesta and Saviotti 2006; Nesta 2008; Quatraro 2010).

Following Teece et al. (1994), the weighted average relatedness (${\mathrm{WAR}}_{l}$) is defined as the degree to which technology $l$ is related to all other technologies $j\ne l$ in the regions’ patent portfolio, weighted by patent count ${P}_{jt}$.

$${\text{WAR}}_{lt} = \frac{{\mathop \sum \nolimits_{j \ne l} \tau_{lj} P_{jt} }}{{\mathop \sum \nolimits_{j \ne l} P_{jt} }}$$

(9)

Finally, the coherence of the region’s knowledge base at time $t$ is defined as the weighted average of the ${\mathrm{WAR}}_{lt}$ measure:

$${\text{COH}}_{t} = \mathop \sum \limits_{l} {\text{WAR}}_{lt} \times \frac{{P_{lt} }}{{\mathop \sum \nolimits_{l} P_{lt} }}$$

(10)

The technological relatedness measure ${\tau }_{lj}$ indicates that the utilisation of technology $l$ also implies the use of technology $j$, in order to perform specific functions that are not reducible to their independent use.

To set the $\tau$ parameter first, we built a relatedness matrix as follows (Nesta, 2008). Let the technological universe consist of $k$ patent applications. Let${P}_{jk}=1$, if the patent $k$ is assigned to technology $j$ [$j=1,\dots , n$] and 0 otherwise. The total number of patents assigned to technology $j$ is ${O}_{j}={\sum }_{k}{P}_{jk}$. Similarly, the total number of patents assigned to technology $m$ is ${O}_{m}={\sum }_{m}{P}_{mk}$. Since two technologies may be present within the same patent, ${O}_{j}\cap {O}_{m}\ne \varnothing$, the number of observed co-occurrences of technologies $j$ and $m$ is${J}_{jm}={\sum }_{k}{P}_{jk}{P}_{mk}$. By applying this relationship to all the possible pairs, we obtain a square matrix $\Omega (n \times n)$ where the generic cell is the observed number of co-occurrences:

$$\Omega = \left( {\begin{array}{*{20}c} {J_{11} } & \ldots & {J_{n1} } \\ \vdots & \ddots & \vdots \\ {J_{1n} } & \ldots & {J_{nn} } \\ \end{array} } \right)$$

(11)

We can assume that the number ${x}_{jm}$ of patents assigned to both the $j$ and $m$ technologies is a hypergeometric random mean and variance variable:

$$\mu_{jm} = E\left( {X_{jm} = x} \right) = \frac{{O_{j} O_{m} }}{K}$$

(12)

$$\sigma_{jm}^{2} = \mu_{jm} \left( {\frac{{K - O_{j} }}{K}} \right)\left( {\frac{{K - O_{m} }}{K - 1}} \right)$$

(13)

If the observed number of co-occurrences ${J}_{jm}$ is larger than the expected number of random co-occurrences ${\mu }_{jm}$, then the two technologies are closely related: the fact that the two technologies occur together in the number of patents ${x}_{jm}$ is not random. Thus, the measure of relatedness is given by the difference between the observed and the expected number of co-occurrences, weighted by their standard deviation:

$$\tau_{jm} = \frac{{J_{jm} - { }\mu_{jm} }}{{\sigma_{jm} }}$$

(14)

It should be noted that this measure of relatedness has lower and upper bounds: ${\tau }_{jm} \in (-\infty , +\infty )$. Moreover, the index shows a similar distribution to a t-student distribution; so, if ${\tau }_{jm}\in (-1.96, +1.96)$, one can assume the null hypothesis of non-relatedness of the technologies. Therefore, the technological relatedness matrix $\Omega$ can be considered a weighting scheme to evaluate the technological portfolio of regions.