Firm Size and Sustainable Innovation: A Theoretical and Empirical Analysis

: This paper explores the relationship between ﬁrm size and sustainable innovation in large international ﬁrms. To this end, we develop a labor demand framework. The contribution to the literature is to explore external knowledge in determining the employment impact of sustainable innovation. Our investigation is based on ﬁrms in three economic areas: Europe, Japan, and the United States. In this way, we will appreciate the extent to which the technological spillovers are important from a geographical perspective. The ﬁndings provide evidence of the signiﬁcance of spillover e ﬀ ects on a ﬁrm’s size; however, these e ﬀ ects depend on the spillover stock type.


Introduction
The analysis concerning the impact of sustainable innovation on a firm's size in terms of employment is subject to present economic debate [1][2][3]. Indeed, technological progress represents a quest to reduce labor costs, which is a key sustainable goal in a world of finite natural resources.
There exist many definitions of sustainable innovation in the literature. The idea used in this analysis is in line with the concept introduced by Pezzey [4]: Innovation is sustainable in the sense that the innovation process, contributing to sustainable development, assures that the consumption of the current generation is less than or equal to the maximum consumption of future generations, on the basis of the production opportunities available at present.
Thus, the investigation concerning the impact of sustainable innovations on firms' size is important with regard to increasing production opportunities. The main contribution of our analysis is that we explore the role of external knowledge in the context of sustainable innovation. Indeed, the literature lacks a comprehensive explanation of how the firms adapt their strategies after the innovations, as discussed in Cozzolino et al. [5]. Our analysis attempts to provide this by paying attention to the knowledge diffusion process.
In particular, there are studies that provide evidence of the importance of robotics on firms' size quality, as discussed in Brynjolfsson and McAfee [6,7]. We demonstrate that a reduction of the number of employees to achieve the same production level can result after sustainable innovation (destruction effect), and an increase in the number of employees produced by the new competitive context could derive from sustainable innovation (compensation effect). The effect of sustainable innovation on firm size depends also on the product or process innovation, the elasticity of the market demand of the product with respect to its price, the market power, and wage negotiation. Since theoretical and empirical work in the literature has focused on the internal firm size impact of innovation, this paper deals with the important role of international, national, inter-industry, and intra-industry spillovers in affecting firms' sizes in Europe, Japan, and the USA [8][9][10][11][12].

Theoretical Framework
In this section, we follow the approach in Garcia et al. [36], where a firm competes in the differentiated product market and minimizes costs. The choice of this approach is opportune for sustainability context, because the resources are finite and firms must obtain the production at the lowest cost as possible. In this way, the firms, through the sustainable innovation process, allow the use of resources by future generations [4].
We define the accumulated knowledge capital as k, and w and c are the vector inputs prices and the marginal cost, respectively. Thus, we get c = c(w, k) and we denote with y the production, l the firms' sizes in terms of employment, p the output price, µ the mark-up, d e a measure of the market dynamics, and finally, with p R , k R the rival output prices and firms' accumulated knowledge capital, which represent the knowledge spillovers: where w R , c R , µ R denote the inputs prices, marginal cost, and mark-up, respectively. For the other firms, c L measures the derivative of the marginal cost with respect to employment. Once simple computations are made, Equation (4) becomes: From this equation, we can see that the short run impact of innovation on firms' sizes is: The first term is the displacement effect, while the second is the compensation effect. If we consider that wages are w and decided by unions, and denote with z and z R other potential changes we can get: Hence, Equation (6) can be written as: Equations (6), (7) and (13) allow us to identify the role of the knowledge diffusion process on firms' sizes, through the impact of external sustainable innovations (knowledge spillovers).
In the subsequent paragraph, we analyze the impact of R&D spillovers on firms' sizes in terms of employment.

Data
In our dataset, the information comes from all R&D investment scoreboards [37]. We combine the most recent scoreboard to avoid multiple counting of the same observations.
We select sales (y), the firms' sizes (l), the capital expenditures (c), R&D activity (k), and profit (op). The Industrial Classification Benchmark (ICB) measures industrial fields. The data regarding patents are selected from the OECD, REGPAT database [38] (See Maraut, Dernis, Webb, Spiezia and Guellec [39] for the methodology used for the construction of REGPAT database and please contact Helene.DERNIS@oecd.org to download it). We implement the same matching procedure as that described in Aldieri and Vinci [10]. At the final stage, we use an unbalanced panel of 879 firms from 2002 to 2010.
To compute the spillovers components (k R in theoretical model), we follow Jaffe [40]'s technological index: The sum of R&D weighted on the correlation index between the distribution vectors of patents relative to domestic firms represents the "national spillovers" (ns); the sum of R&D weighted on the correlation index between the distribution vectors of patents relative to firms located in different countries is defined as "international spillovers" (is); the weighted sum of R&D relative to firms operating in the same technological sector is identified as "intra-industry stock of spillovers" (intra-s); and the weighted sum of R&D relative to firms in other technological fields is associated with "inter-industry stock of spillovers" (inter-s).
Because there are no available data on wages, we introduce operating profit and capital expenditures as proxies, as discussed in Bogliacino [41]. Table 1 shows the statistical features of our variables. We estimate the following equation: l = (y, c, op, k, ns, is, intra-s, inter-s)

Methodology and Empirical Results
The number of employees is a discrete variable, and there are some large values that contribute substantially to the overdispersion. This feature makes it difficult to specify a model with a conditional mean and variance that captures the main characteristics of the data. For this reason, we estimate Equation (14) using Poisson and Negative Binomial models. In Table 2, we run the fixed-effect-Poisson (FE-POISS) estimates based on national versus international spillovers for all samples, while in Table 3 we show the fixed-effect Negative Binomial (FE-NBREG) for all samples. Akaike's information criterion (AIC) and Bayesian information criterion (BIC) procedures are used, see Table 4, to choose the best model. Because of the lower AIC and BIC, the FE-NBREG model is preferred. In this way, we can take into account the overdispersion in the data in a more opportune way. In particular, we include time and industry dummies in the estimation methods to control the impact of shocks and sector heterogeneity for the firms.    Hence, the other estimates are relative to the FE-NBREG model. In particular, Table 5 presents the findings by geographical perspective, and Table 6 shows the results using an intra/inter-industry perspective. We can observe that the output represents the most relevant determinant of firms' sizes with a significant positive effect, as expected. The effect of operating profit is negative; this leads to higher wages, and to lower firm sizes, as suggested in the empirical literature [41].
From the empirical findings, we observe that the compensation effect can be higher than the destruction one: Indeed, R&D activity produces a positive impact on firms' sizes. As far as the knowledge spillovers are concerned, international components have a negative effect on firms' sizes for American firms and a positive effect for European ones, while national spillover components produce a positive impact on firms' sizes in Japan. These findings could be explained by the higher absorptive capacity of American firms to improved productivity and finally, to the decrease in firms' sizes. The reverse idea could be applied to Japan and Europe which have lower absorptive capacities.    Moreover, in the same vein, inter-industry externalities have a negative effect on firms' sizes for American firms, and intra-industry spillovers have a positive impact in Europe.
The results demonstrate the key role that competitive firms have with regard to the potential to help the economies to sustain firms' sizes in terms of employment in crucial periods of time, such as during a worldwide economic crisis. The novelty of this analysis for policymakers' industrial strategy is to outline not only the relevant impact of their own innovation [31], but also the existence of a complex structure for the transmission of external innovation through knowledge spillovers. We cannot distinguish between process and product innovation because of the lack of available data. Thus, future research could examine, in depth, this important aspect of firms' industrial organization.

Conclusions and Policy Implications
The paper explores the interaction between R&D activity, spillovers, and firms' sizes in terms of employment. The analysis is based on 879 firms from 2002 to 2010 in Europe, Japan, and the USA. The findings outline the significant role of spillover effects on firms' sizes.
This paper confirms both the impact of the internal effects of innovation on firms' sizes, and the external effects due to technological spillovers. For this reason, industrial policy that favors these industrial mechanisms should be supported.
Indeed, adequate policy responses could become important instruments to sustain the effects of innovation on firms' sizes. Firstly, skill levels are closely related to inequality because technological change increases the demand for skilled employment, so it seems essential to invest in education [42].
Secondly, fiscal measures should encourage investments in R&D to obtain the competencies relevant for full competitiveness in the long-run, as discussed in Peneder [43].
Finally, policymakers are likely to face some challenges due to the development of labor markets and the increasing flexible work structure, as requested by the markets.
These industrial strategies towards innovation are important in terms of sustainability, because on the one hand, firms can minimize the costs in such a way that the production is as efficient as possible, and on the other hand, the sustainable innovation allows them to achieve more production opportunities for future generations.
However, the research should be further analyzed. Indeed, we cannot distinguish between process and product innovation impact on firms' sizes. Thus, we could not analyze the extent to which our results are robust with respect to previous technological taxonomy. Moreover, with a wider scope, we could analyze what happens after crises.