Technological externalities and wages: new evidence from Italian NUTS 3 regions

Abstract

In this paper, we investigate the relationship between local wages and the internal structure of the regional knowledge base. The purpose is to assess if the workers’ compensations are related to the peculiarities of the knowledge base of the regions in which they supply their labor services. The test of this hypothesis is based on the assessment of the impact of related vis-à-vis unrelated knowledge variety on cross-regional wage differentials. The empirical analysis is carried out by exploiting patent data and a unique employer–employee administrative dataset. First, using OECD-PATREG data on patent filing, we build information entropy indexes proxying the variety of NUTS 3 regions’ knowledge bases, and the decomposition in the related and unrelated component. Second, we assess the impact of these indexes on wages based on administrative data from the Italian National Institute of Social Security. Our results suggest that workers employed in regions with a heterogenous knowledge structure earn positive wage premia, while related variety has a negative effect on compensation levels.

1. Introduction

Economists have long investigated the nexus between labor market dynamics and agglomeration economies. These latter, following the well-established Marshallian tenet, are engendered by three main forces, i.e., thick labor markets, thick markets for intermediate goods, and knowledge spillovers. Indeed, these dynamics are actually an important driver of productivity differentials across local labor markets, and consequently they are deemed to have a significant impact on cross-regional differences in workers’ earnings.

Accordingly, a large stream of empirical literature has investigated the relationship between firms’ location choices and agglomeration (Ellison and Glaeser, 1997; Rosenthal and Strange, 2003). Yet, while this approach can be informative on the existence of some sort of agglomeration incentive, it does not imply the actual existence of agglomeration economies (Moretti, 2011).

Some literature has instead dealt with the empirical appreciation of agglomeration externalities by taking individual wages as a proxy of marginal product of labor, to verify the existence of a premium to agglomeration (Glaeser and Maré, 2001). Extant literature has mainly focused on externalities linked to urban or industrial agglomeration, as proxied respectively by the density of inhabitants and of production plants (De Blasio and Di Addario, 2005; Di Addario and Patacchini, 2008; Moretti, 2011).

However, as recalled above, one of the key arguments put forth by Marshall (1890) points to the role of knowledge spillovers. Technological externalities emerge out of the concentration of technological activities in local contexts and affect the capacity of firms to generate and adopt innovation, which in turn leads to productivity gains. Despite the importance of these dynamics, empirical studies so far have overlooked the direct investigation of the impact of technological externalities on workers’ earnings differentials.

This paper aims at filling this gap, by articulating an empirical framework to investigate the effect of knowledge spillovers on individual wages. In doing so, we extend the scope of the analysis by appreciating the differential impact of Marshall vis-à-vis Jacobs’ externalities. As is well known, the former are associated to the spatial concentration of technological activities in homogenous domains while the latter is associated to the diversification of technological activities of local economies. If knowledge spillovers affect wages because of their impact on innovation and hence on productivity, distinguishing between different kinds of technological externalities is important, as Jacobs’ externalities have proved to be systematically associated to the introduction of more impactful innovation (Castaldi et al., 2015). In addition, when workers have access (or contribute to build up) the knowledge of their firms and exclusive labor contracts are not available, firms may find it rational to compete for strategic labor services by bidding higher wages.¹ In this framework, “flows of workers can be equated with flows of knowledge so that poaching workers is a way for firms to raise their productivity” (Combes and Duranton, 2006). If these wage offers reflect the amount of knowledge that poaching firms are able to seize, we should expect compensations in technologically diversified regions to be relatively higher. Indeed, learning opportunities from poaching are less important when the firms’ knowledge sets are largely overlapping.

In this direction, we graft the recombinant knowledge approach onto the debate on the nexus between agglomeration and wages. More impactful innovation emerges out of the recombination of knowledge across a variety of seemingly unrelated fields. We accordingly posit that in areas featured by higher levels of unrelated technological variety wages are higher than in areas featured by higher levels of related variety, in view of the capacity to foster high-impact innovation yielding higher productivity gains. From the labor market perspective, the wage premium is expected to be positive in areas characterized by high levels of Jacobs’ externalities, where the productivity effect dominates. On the contrary, in areas characterized by a spatial concentration of homogeneous technological activities (i.e., high-related variety), one can expect to observe the counterbalancing supply effect to prevail, pushing wages downwards.

The empirical analysis of the effect of patenting concentration on regional wages is based on the exploitation of a unique employer–employee dataset built using Italian administrative data. Italy has a two-tier bargaining structure where uniform wage floors are set at the sectoral level by industry-wide unions and then adjusted by firm-level organizations (RSU and RSA) that bargain additional mark-ups according to the firms’ relative productivity (Boeri, 2014; Cardullo et al., 2018; Devicienti et al., 2019). In this setting, the link between compensation and productivity is less tight than in purely decentralized regimes (as in Anglo-Saxon countries), but not as tight as in those industrial relation systems where wage bargaining is entirely centralized (as in Scandinavian countries), generating non-negligible variations in workers’ earnings related to productivity differentials emerging at the firm-level.

To allow for different patterns of regional innovativeness, we then distinguish between related and unrelated diversification, that is, between situations where local innovators issue their patents in closely related technological domains (related variety) and situations where they conversely diversify their patenting activity by innovating in a variety of unrelated domains (unrelated variety).² To do so, we first build two different indexes of regional innovativeness, capturing the degrees of related and unrelated variety of a regions’ knowledge base. Then, we regress these indexes against individual wage levels, adding relevant controls that account for various individual and firm characteristics that are likely to have an important role in determining individual salaries. In doing so, we should be able to capture the wage effect of being employed in regions with well-defined innovative characteristics. To rationalize our results, we draw from economic geography and urban economics literature. While these streams of research have extensively analyzed the effect of both sectoral and urban concentration, a key novelty of our approach, as anticipated, is that of considering the agglomeration of innovative activities. We find that workers employed in multi-specialized regions earn positive premia, while the effect of related variety seems to be non-significant or even negative.

The remainder of the paper is organized as follows. Section 2 reviews the literature on agglomeration externalities and presents our working hypotheses. Section 3 presents a simple analytical framework where we disentangle the relationship between technological variety, labor pooling and labor poaching more thoroughly. Section 4 presents the empirical framework and our main results. Section 5 concludes.

2. Theoretical framework

2.1. Wages and agglomeration externalities

A large body of literature has investigated the nexus between agglomeration externalities and wages, building on Alfred Marshall’s seminal contribution (Marshall, 1890). Following the theory, most of the extant literature has focused on the impact of urban agglomeration in this context. The primary channel for such a relationship relates to the differential productivity performances of firms benefiting from external economies compared to those in areas where external economies are not at stake.

According to the established tenet, the positive effect of external economies is due to three core forces, i.e., thick local markets for intermediate inputs, thick local labor markets, and knowledge spillovers. First, the geographical concentration of economic activities favors the reduction of production costs due to scale economies engendered by the sharing of co-localized specialized inputs suppliers. These dynamics also attract the entry of other similar firms that can benefit from the existing network of intermediate inputs suppliers, further reinforcing agglomeration. Second, labor pooling and insurance effects might render the localization in urban areas advantageous for firms and workers. On the one hand, in areas characterized by a high concentration of heterogeneous firms and workers, the likelihood of high-quality matching between labor supply and demand is more considerable. These dynamics, in turn, yield productivity gains for firms in urban areas (Helsley and Strange, 1990).

On the other hand, in thicker labor markets, workers face lower risks of unemployment due to the large number of co-localized firms that might be prospective employers. Similarly, firms in urban areas face lower risks of unfilled vacancies (Duranton and Puga, 2004). Third, geographical proximity favors knowledge spillovers channelled by localized interactions and inter-firm mobility of qualified and specialized human capital. Spillovers, in turn, feed innovation and productivity in firms and clusters.

From a different perspective, Jane Jacobs (1969) elaborated on the sources of agglomeration, stressing the relevance of the structure of economic activities in the cluster rather than of its size and density. While the so-called Marshall–Arrow–Romer (MAR) externalities point to the importance of spatial concentration of activities in a single industry—see Arrow (1962) and Romer (1968)—Jacobs’ externalities stress the relevance of local diversification as a source of increasing returns in urban contexts because of the cross-fertilization of ideas and innovative solutions across different and yet complementary activities.

A further source of agglomeration externalities relates to competition effects. Porter (1990) stresses that rivalry induces firms to allocate resources to innovation to improve their position in the market. In addition, intense competition in local contexts may also directly affect labor market dynamics, as workers face a large choice set concerning alternative employers. The latter, in turn, might want to pay higher wages to reduce the risk of having their specialized employees poached by competitors (Combes and Duranton, 2006).

In sum, spatial concentration, diversification, and competition are key sources of agglomeration externalities that engender local increasing returns in urban contexts and consequently drive, directly and indirectly, urban wage premia (Moretti, 2011). Many studies have empirically tested these hypotheses in the Italian context, mainly focusing on population density or city size measures as proxies of urban agglomeration economies. For example, Di Addario and Patacchini (2008) regress wages against population mass in local labor markets to investigate the impact of urban agglomeration externalities on wages. They found that every additional 100,000 inhabitants in the local labor market raises earnings by 0.1% and that this effect decays rapidly with distance. De Blasio and Di Addario (2005) focus on Italian industrial districts and use population density of local labor markets as focal variable, finding ambiguous results. Belloc et al. (2023) estimate the urban wage premium by using population density as main regressor and find that for employees, the elasticity of nominal wages to urban agglomeration size is very close to zero, while the corresponding elasticity of real wages is negative, while for self-employed the elasticity is positive both in nominal and real terms.

2.2. Recombinant knowledge, technological externalities, and the wage premium

As discussed above, knowledge spillovers are considered as a crucial source of externalities in the MAR, Jacobs, and the Porter frameworks. In particular, as Glaeser et al. (1992) proposed, knowledge spillovers deserve special attention as they drive dynamic externalities, i.e., local increasing returns that trigger innovation-driven growth (Antonelli et al., 2011). Yet, the theoretical and empirical literature has substantially failed to elaborate on their relationship with wages. Traditional wisdom predicts a positive impact of knowledge externalities on wages, but this general statement does not consider the differential effects that specific kinds of knowledge externalities exert on local innovation and productivity and wages dynamics.

Understanding the differential impact of Jacobs’ vis-à-vis MAR externalities also contributes to better qualifying the role of human capital in channelling knowledge flows, hence stressing the differences concerning wage dynamics. Since knowledge is primarily embodied in workers’ human capital, the relationship between spillovers and wages should be particularly tight.³ If poaching workers allows firms to access their competitors’ expertise and increase their productivity, employers in agglomerated areas should be willing to offer higher wages to seize strategic labor services (Combes et al., 2011).

The grafting of the recombinant knowledge approach onto this debate can prove to be fertile in this respect.

The idea that innovation is the outcome of the capacity to combine ideas and technology in new ways dates back to Schumpeter (1942). In the recombinant knowledge theory, growth is triggered by innovation that, in turn, emerges out of the recombination of knowledge inputs that are fragmented and dispersed among innovating agents (Weitzman, 1998; Fleming and Sorenson, 2001; Antonelli et al., 2010).

Evolutionary economics has integrated these insights into models articulating the link between the success of combinatorial efforts and the characteristics of the knowledge landscape, with respect to the diversity of knowledge elements and the complementarity relationships amongst them (Kaufman, 1993; Fleming and Sorenson, 2001). In this framework, knowledge variety is proposed as a fundamental condition for recombinant dynamics, based on the argument that the larger and more diverse the base of potentially combinable elements, the larger the prospects for creative combinations.

In the evolutionary economic geography literature, the debate about agglomeration externalities and knowledge spillovers has been fruitfully combined with the appreciation of the impact of knowledge diversity. In particular, Frenken et al. (2007) have elaborated upon the distinction between related and unrelated variety to qualify knowledge externalities, showing that the impact of (industrial) related variety, i.e., the local presence of activities that are diverse but related to one another, on employment growth is positive. An increase in (industrial) unrelated variety is instead associated with decreasing unemployment growth rates. This evidence suggests that unrelated diversification is more effective in protecting local economies against external asymmetric shocks in demand and thus against rising unemployment.

Subsequent works have focused more explicitly on technological externalities, implementing related and knowledge variety variables by using patent data. The extant literature shows that both related and unrelated knowledge variety are positively associated with regional productivity and the rate of new firm formation in local areas (Quatraro, 2010; Colombelli and Quatraro, 2018).

More recently, a new stream of empirical studies has focused on the determinants of regional innovation capabilities, specifically, on the conditions that enable the development of the capacity to produce breakthrough innovation in local contexts. The rationale for these studies lies in the well-established tenet in evolutionary economics according to which, even if the successful combination of loosely related or cognitively distant pieces of knowledge is more difficult to achieve, it is more likely to produce high-impact innovations (Nightingale, 1998; Saviotti and Frenken, 2008). European evidence indicates that while related technological variety positively impacts innovation in general, unrelated variety is significant when breakthrough or radical innovation is at stake (Castaldi et al., 2015; Miguelez and Moreno, 2018; Martynovich and Taalbi, 2020; Montresor et al., 2023). Similar findings also emerge in studies focusing on the industrial structure, whereby multispecialized clustered regions appear to be better capable of producing breakthrough innovation (De Noni and Belussi, 2021).

Based on these theoretical considerations and empirical studies, the analysis of the relationship between wages and knowledge externalities can be further qualified. In particular, both related and unrelated variety positively affects productivity growth and innovation. Therefore, we expect that both measures drive wage differentials across localities. However, since the diversification across unrelated technological domains proved to yield high-impact innovation in clustered regions, we expect the elasticity of regional wages to local unrelated knowledge variety to be larger than the elasticity to related knowledge variety. Moreover, if firms operate in areas characterized by closely related technological domains, their knowledge sets are largely overlapping, meaning that learning opportunities from poaching are relatively small, and hence the incentive to poaching will also be small.

The differential impact of unrelated vis-à-vis related technological diversification is also rooted in labor supply dynamics. To many studies, human capital mobility is an important channel for knowledge spillovers (Lucas, 1988; Glaser, 1999; Duranton and Puga, 2001). Related technological diversification is expected to attract people with similar skill sets in clusters. These dynamics push the skill supply schedule rightwards, causing a downward shift of wage levels coeteris paribus and mitigating external economies’ positive impact. Unrelated technological diversification requires a labor supply of people endowed with heterogeneous skill sets and the rare capacity to interact and combine rare competencies. These dynamics push wages upwards and reinforce the positive effect of external economies.

Furthermore, previous literature has recognized that unrelated diversification generates a portfolio effect that protects regions from shocks that can be either sector or technology specific (Boschma and Frenken, 2007, 2011). If firms’ productivity is reflected in the workers’ wage, the arrival of adverse shocks should feed through into lower wages, perhaps with some delay due to wage rigidities.⁴

The relationship between the related/unrelated variety framework and the lifecycle theory provides an additional channel supporting our working hypothesis. Accordingly, unrelated variety dominates the early stage of the lifecycle, characterized by the entry of young firms and the introduction of product innovation. In contrast, related variety dominates the maturity stage, characterized by the prevalence of process innovations introduced by incumbent firms (Duranton and Puga, 2001; Capasso et al., 2016; Content and Frenken, 2016). On average, product and process innovations yield different impacts on labor market dynamics. In particular, process innovation is expected to be labor-saving, while product innovation is mostly labor-friendly. In this direction, in areas characterized by the dominance of unrelated variety, the specific nature of innovation can likely foster new job creation, pushing the labor-demand schedule rightwards, and hence driving wages up. The opposite situation is expected to occur in areas featured by the dominance of related variety (Barbieri et al., 2019; Dosi et al. 2021; Goel and Nelson, 2022).

It is worth stressing that these effects might be counterbalanced by dynamics working in the opposite direction. The breakthrough innovations associated to relatively greater unrelated variety might not only yield positive impacts because of their higher value, but they could also drive a process of structural change in the local economy, leading to job losses and to the mismatch between extant obsolete skills and those required by the new jobs that are created. Moreover, the local multiplier of emerging high-tech sectors triggered by breakthrough innovations might spread unevenly across the skills distribution, favoring the wage dynamics of high- and mid-skilled workers while pushing the wages of low-skilled workers downwards (Lee and Clarke, 2019).

3. Analytical framework

3.1. Setup

In light of the discussion conducted in the previous section, we now develop a simple analytical framework to assess how the workers’ compensations are related to the peculiarities of the technological space in which they supply their labor services. The channel considered is that of labor poaching. The purpose is to motivate the empirical analysis in a way that is consistent with previous theoretical research on the relationship between agglomeration and wages, not to derive testable predictions.

Consider a model economy composed of a single firm, |${F_1}$|⁠, employing a single worker, |${E_1}$|⁠. Since the local labor market is competitive, |${E_1}$| earns her reservation utility, which we normalize to zero. At this wage, labor supply is assumed to be infinite. While working for |${F_1}$|⁠, |${E_1}$| acquires (or builds up) part of the internal knowledge of the firm. Denoted as |${K_1}$|⁠, the knowledge produced jointly by |${F_1}$| and |${E_1}.$| Since part of this knowledge can be valuable to other firms and exclusive long-term labor contracts are not available, |${E_1}$| may switch employer if offered a higher wage.

Consider the situation where an entrant firm, |${F_2}$|⁠, endowed with an initial knowledge denoted as |${K_2}$| locates in the same local labor market.⁵ To run its business, |${F_2}$| needs employing a single unit of labor. In doing that, it can either draw from the unemployment pool and pay the competitive wage |$w = 0$| to hire a new worker, |${E_2}$|⁠, or try to poach |${E_1}$| from |${F_1}$| to access the expertise they developed together. While we assume that |${F_2}$| would benefit from smuggling the knowledge developed by |${F_1}$|⁠, we leave open the possibility that the two firms may operate in different product markets. The idea that knowledge spillovers may occur between firms producing different goods, in fact, is largely consistent with Jacob’s view of agglomeration economies, and will allow us to remark on the potentially different effects of Marshallian versus Jacob’s externalities on poaching dynamics.

Normalizing |${E_1}$|’s relocation costs to zero, |${F_2}$|’s maximum willingness to pay to poach |${E_1}$| from |${F_1}$| is given by

where |${\pi _2}\left( {{E_i}} \right)$| measures |${F_2}$|’s payoff when it works with employee |$i = 1,2$|⁠, while |$C \gt 0$| measure the recombinant costs that are needed to recombine |${K_1}$| with |${K_2}$|⁠. In what follows, we shall refer to |${\omega ^P}$| as the “poaching wage”. In line with the discussion put forward in section 2.2., we assume that both the benefits and cost of knowledge recombination are increasing in the cognitive distance between the two firms, denoted as |$\left| {{K_1} - {\rm{\,}}{K_2}} \right| \equiv \delta \gt 0$|⁠. On the one hand, the recombination of loosely connected pieces of expertise yields more impactful innovation. On the other hand, recombining distant pieces of expertise may be extremely costly, and largely dependent on the firms’ idiosyncratic ability to do so—for further discussion, see the discussion in the next paragraph.

After observing |${\omega ^P}$|⁠, we assume that |${F_1}$| can raise a counter-offer to retain |${E_1}$|⁠. If this offer is insufficient (and poaching is successful), we assume that |${F_1}$| must draw a new employee, |${E_2}$|⁠, from the unemployment pool, who, as before, is paid the completive wage |$w = 0$|⁠. For this offer to be rational, of course, it must be the case that, when |${E_1}$| leaves, |${F_1}$| incurs in some producticty loss.⁶ Denote this offer as |${\omega ^R}$|⁠. By applying the tie-breaking rule whereby |${E_1}$| remains with |${F_1}$| when indifferent between the two, it is sufficient that |${F_1}$| offers |${\omega ^R} = {\omega ^P}$| to retain |${E_1}$|⁠. This will happen each and every time |${F_1}$|’s willingness to pay to retain |${E_1}$| exceeds |${F_2}$|’s poaching incentive, and also implies that the wage increase obtained by |${E_1}$| is the same, regardless of whether she is poached by |${F_2}$| or retained by |${F_1}$|⁠. Hence, the “retaining wage” that |${F_1}$| is willing to offer is given by:

where |${\pi _2}\left( {{E_i}} \right)$| measures |${F_2}$|’s payoff when it works with employee |$i = 1,2$|⁠. Needless to say, the losses incurred by |${F_1}$| when poaching is successful crucially depends on how strategic |${E_1}$| is for |${F_1}$|’s productivity. If a large share of the firm’s knowledge resides in its organizational rules and routines (“the memory of the organization”, in the parlance of evolutionary economics), the retaining incentive will be less important. Hence, we should expect poaching to occur more frequently and poaching wages to be higher for skilled or talented employees, as well as for those employed in non-routinary tasks, whose efficiency is normally more sensitive to the workers’ human capital.⁷ Similarly, when a large share of the firm’s knowledge is patented, and thus, hard to poach, the retaining incentive will also be less important.

3.2. Discussion

The strategic interaction described in the previous section depicts a situation that may occur each and every time a firm in a local labor market is exposed to a poaching opportunity. Hence, when large numbers of innovative or high-productivity firms cluster in the same area, we should expect labor poaching to be more pervasive, with positive repercussions on local wages. As our simple formalization made clear, however, the relationship between wage growth, poaching dynamics and technological variety is in principle ambiguous, given the ambivalent effect of |$\delta $| on |${\omega ^P}$|⁠. However, since the beneficial effects of unrelated variety should be more pronounced in areas where firms have developed the capability to connect loosely related pieces of expertise, we can draw an additional remark on the relationship between knowledge spillover, poaching, and wages. If recombinant abilities can be purchased in specific labor markets where specialists (such as managers) supply this type of skills, poaching firms will have an extra-incentive to pay for these capabilities, as they will turn out to be crucial in the firms’ recombinant endeavors. Given this, we should explain managerial wages to be higher in areas characterized by high degrees of unrelated variety.

In addition, we have left open the possibility that knowledge spillovers may occur between firms that are not direct competitors in the product market. When this is not the case, however, between-employers competition for strategic labor services will be more intense, thus leading to higher wage for both poached and retained workers. As any oligopoly model would show, in fact, profitability in imperfectly competitive markets depends on the firms’ absolute and relative efficiency, implying that the loss (acquisition) of a strategic resource generates costs (benefits) that are amplified by competition in the product market.

Finally, our model assumes that unemployed workers who cannot leverage on the knowledge acquired in previous occupations receive an exogenously given competitive wage. Since these workers are not affected by between-employer competition for their services, one may draw the conclusion that their wages are independent from the structure of the regional knowledge base. As anticipated in the Section 2.2., however, the differential impact of unrelated vis-à-vis related technological diversification is also rooted in labor supply dynamics. Indeed, related technological variety (RTV) may have a composition effect on the local workforce by attracting in the area large masses of workers with similar skills. When this is the case, the supply schedule for these particular skills shifts rightwards, pushing the competitive, skill-specific wage downwards. This dynamic is likely to be far less pronounced in multispecialized areas. Whether the effect of RTV and unrelated technological variety (UTV) on wages is more sizeable, however, remains an empirical question, to which we shall answer in the following sections.

4. Empirical analysis

4.1. Data and main variables

The analyses concerning the relationship between regional innovation performances and individual wages are developed integrating two different sources of information at the individual and province level. Individual information on wage levels and workers’ characteristics are retrieved from the administrative archive containing information on the employees’ financial conditions provided by the Italian National Institute of Social Security (INPS). The second type of information concerning data on the firms’ patenting activity is taken from the OECD REGPAT archive.

Data from INPS comes from the account statement of the individual contributions paid by each worker to the Fondo pensioni lavoratori dipendenti of the sample of 48 dates, featuring over 2 million observations The dataset makes it possible to retrieve a wide range of information on the demographic profile and contractual conditions, such as age, sex, occupation, duration of contract (fixed-term or open-ended), working hours (part-time or full-time), gross salary, number of weeks worked, industrial sector of employment, firm size, geographical location, etc.

As far as innovation indexes are concerned, the measures calculated from the OECD REGPAT archive are basically three. The first accounts for the overall technological variety (TV = total variety) in each of our geographical units (NUTS 3 Italian regions). The second quantifies how many of this mass of patents belong to the same technological variety (⁠|$RTV = $| related variety). The third captures the degree of technological diversification (⁠|$UTV = $| unrelated variety). To calculate these measures, we used the information entropy index.⁸ Such index was introduced to economic analysis by Theil (1967). Its earlier applications aimed at measuring the diversity degree of industrial activity (or of a sample of firms within an industry) against a uniform distribution of economic activities in all sectors, or among firms (Attaran, 1985; Frenken et al., 2007; Boschma and Iammarino, 2009). Differently from common measures of variety and concentration, the information entropy has some interesting properties (Frenken, 2004). An important feature of the entropy measure is its multidimensional extension. Consider a pair of events (⁠|${X_j},{Y_m}$|⁠), and the probability of co-occurrence of both of them |${p_{jm}}$|⁠. A two-dimensional (total) entropy measure can be expressed as follows (region and time subscripts are omitted for the sake of clarity):

If one considers |${p_{jm}}$| to be the probability that two technological classes j and m co-occur within the same patent, then the measure of multidimensional entropy focuses on the variety of co-occurrences of technological classes within regional patents applications. Moreover, the total index can be decomposed in a “within” and a “between” part anytime the events to be investigated can be aggregated in a smaller number of subsets. Within-entropy measures the average degree of disorder or variety within the subsets, while between-entropy focuses on the subsets measuring the variety across them. It can be easily shown that the decomposition theorem holds also for the multidimensional case. Hence if one allows |$j \in {S_g}$| and |$m \in {S_z}$| (⁠|$g\, = \,1, \ldots ,G;\,z\, = \,1, \ldots ,\,Z$|⁠), we can rewrite |$H\left( {{X_j},{Y_m}} \right)$| as follows:

Where the first term of the right-hand-side is the between-group entropy and the second term is the (weighted) within-group entropy. In particular:

Following Frenken et al. (2007), we can refer to between-group and within-group entropy respectively as UTV and RTV, while total information entropy is referred to as general technological variety (TV). For the purposes of this analysis, the calculation of the three indexes exploits the International Patent Classification, relying on 4-digits technological classes.

The distinction between related and unrelated variety is based on the assumption that any pair of entities included in the former generally are more closely related, or more similar to any pair of entities included in the latter. This assumption is reasonable when a given type of entity (patent, industrial sector, trade categories, etc.) is organized according to a hierarchical classification. In this case, each class at a given level of aggregation contains “smaller” classes, which, in turn contain yet “smaller” classes. Here, small refers to a low level of aggregation.

Finally, to relate the information on individual workers and the measures of regional innovativeness we have just discussed, we have used the NUTS 3 geographic identification codes.

4.2. Estimation strategy

Our empirical strategy follows a very well-established two-stage approach first introduced by Combes et al. (2008) and widely used in urban economics (see for instance, De la Roca and Puga, 2017; Loschiavo, 2021; Belloc et al., 2023). This approach allows one to separately identify the effects of worker’s characteristics from the effects of area’s characteristics and, hence, to properly estimate in our setting, the wage elasticity to innovation externalities, while accounting for observed and unobserved individual and firm specific heterogeneity. Moreover, the two-stage setting seems to be the most suitable method since yields standard errors that account for the grouped structure of the data (individual and province).⁹

More formally, in the first stage, following the notation proposed by Combes et al. (2011), we regress the following Mincer-type wage equation on individual- and firm-specific factors (Heckman et al., 2003):

where |$\log \left( {{W_{it}}} \right)\,$|is the logarithm of the real wage (adjusted for part time) of individual |$i$|⁠, employed in firm j at time |$t$|⁠, over the period 2005–2018. As for explanatory variables, the parameter |${\alpha _{a\left( {it} \right)t}}$| formalizes the province (a)-year (t) fixed effects and |${X_{it}}$| is the vector of workers characteristics: gender, having a part-time contract, having a fixed-term contract, occupation dummies like blue collar, white collar, executives, other, age groups dummies. The vector |${Z_{jit}}$| includes a number of firm-level controls: firm size in classes, two-digit sector of activities, and a dummy variable indicating how many times a person changes firm, thus capturing skill transferability. Furthermore, in order to account for unobservable workers’ time invariant heterogeneity, we also include individual fixed effects, |${\gamma _i}$| (see for instance Glaeser and D.c, 2001; Combes et al., 2008), while the parameter |$\psi_{j\left( {it} \right)}$| formalizes the firm fixed effects in explaining wage differentials. Finally, |${\varepsilon _{ijt}}$| is an idiosyncratic error term with zero mean and finite variance.

We estimate model (3) by pooled OLS, one-way fixed effects, and AKM models with residuals clustered at the local (province-year) level. In the second stage, we take into account our province-level variables of regional innovativeness, respectively capturing the degree of total variety (TV), related variety (RTV), and unrelated variety (UTV) of a province’ knowledge base (see description provided in Section 3.1). These indices are in turn regressed against province-year effects estimated in the first stage (3), in which individual wage levels are explained with a number of relevant controls that account for a variety of individual and firm characteristics that are likely to have an important role in determining individual payments. In doing so, we should be able to capture the wage effect of being employed in provinces with well-defined innovative characteristic (see Aarstad et al., 2016).

More in detail, in the second stage, the province-year effects estimated in the first stage, |${\alpha _{a\left( {it} \right)t}}$|⁠, are regressed on the lagged province-level indicators, TV, UTV, and RTV. We first estimate a model including total variety TV only (see eq. (4)), RTV only (see eq. (5)), then UTV (see eq. (6)). In a final specification, we further disentangle the total variety into the separate contribution of RTV and UTV (see eq. (7)). Each specification also adds |${\tau _t}$| year fixed effects to control for business cycle—as in Combes et al. (2008)—and |${\varsigma _{at}}$| two relevant province-level controls: |$Kcap\_rati{o_{at}}$|⁠, the ratio between knowledge capital and the total labor force and its square term, which controls for traditional technological externalities (size effects), and the logarithm of population density per square kilometer of province |$a$| at time |$t$| to account for urban agglomeration effects (Frenken et al., 2007).

The inclusion of population density along with related and unrelated varieties will be able to capture their potential effects on wages and innovation (see Frenken et al., 2007). In this way, unrelated and related varieties will be constant for individuals residing within a particular province and will vary between provinces. All second stage models in |$\left( 4 \right)$|–|$\left( 7 \right)$| are estimated with OLS and will therefore produce different sets of elasticities of predicted wages with respect to each of the variety’s indicators.

However, we reckon that endogeneity bias could still occur if there are omitted variables causing the error term to be correlated with our indicators of social interactions. Typically, this may be an outcome of sorting into geographical areas where hiring firms compete on value added, innovation and social inclusion rather than labor cost minimization (Venables, 2011).

We therefore also perform IV regression by relying on synthetic variables, typically used when working with spatial data series. The point of departure is the use of eigenvector analysis of the usual spatial weight matrix used in spatial statistics. Eigenvectors obtained from a transformed weights matrix are known to represent latent map patterns. Our proposal is to use these patterns to obtain synthetic variables for use as instruments in IV estimation. By their very nature, instruments based on synthetic variables are exogenous. Furthermore, they can provide relatively high levels of correlation with the endogenous variable (Le Gallo and Páez, 2013). Following Doran and Fingleton (2015), we produce a synthetic instrument for each endogenous variable, TV, UTV, and RTV. We first define a contiguity matrix and obtain the eigenvectors of this matrix. Then each eigenvector is regressed on the endogenous variable and the significant eigenvectors are retained and summed to create an exogenous instrument (each significant eigenvector is weighted according to the regression coefficient obtained by regressing the eigenvector on the endogenous variable). For a full explanation of the approach, see Le Gallo and Páez (2013).

4.3. Results

Tables 1 and 2 report the Spearman rank correlations and some descriptive statistics for our provincial-level variables, respectively. Table 3 shows descriptive statistics for our individual- and firm-level variables of the INPS database instead. The output of our first-stage estimates (equation 1) for the whole sample of Italian private sector employees aged 18–64, is thereby reported in Table 4. We can observe that the Mincerian variables are always highly significant (at 1% level) in all the specifications. In line with the predictions of the human capital literature, female, part-time fixed-term and dummy for changing firm, are all negatively correlated with wages. Higher wage premia are associated with higher qualifications as well as larger firms.

In Tables 5, 6, and 7 we report the output of our second-stage regressions of models from 4 to 7. Table 5 starts by showing the output of the second stage obtained by estimating OLS in the first stage (equation 3). Specifications of models (4)–(7) are reported in order from the first to the fourth column, where our focal regressors are in turn: TV, RTV, UTV, and both RTV and UTV. As already discussed, all specifications add knowledge capital in a quadratic form and the logarithm of population density.

As described in Section 3.2, since both our dependent and independent variables are expressed in logs and estimates of the second stage are performed by OLS, each of the coefficients can be interpreted as wages’ elasticities to each variety indicator.

Total variety as well as related and unrelated variates (columns 1–3), all show a positive and statistically significant elasticity to wages in provinces with same population density and knowledge capital. However, the elasticity of wages to unrelated variety emerges as the highest (0.0153). When we assess the joint impact of related and unrelated variety on wages (column 4), we observe that only the elasticity of wages to unrelated variety remains statistically significant at 10% level.

Table 6 shows the output of the second stage (equations 4–7 from column 1 to 4) based on fixed effects estimates of the first stage. As we can clearly see, compared with Table 4, all elasticities show a reduction. This suggests that part of the observed impact of innovation externalities to wages is driven by unobserved individual-specific heterogeneity. The sign of the correlations remains positive and the elasticity to wages of RTV is still the highest. In the specification presented in column (4), where both related (RTV) and unrelated variety (UTV) are included along with the other provincial level controls, RTV and UTV show no significant impact on individual wages.

Finally, Table 7 reports the second-stage output obtained by performing AKM estimates in the first stage, thus accounting for both individual- and firm-specific time invariant characteristics. By comparing these estimates with that of Tables 5 and 6, we can clearly observe that part of the elasticities of wages to technological varieties can also be explained by unobserved firm-specific factors. In fact, each of the coefficients of TV, RTV, and UTV (Table 6) shows an additional drop in the magnitude compared with those estimated accounting for individual fixed effects only (Table 5). The impact of each indicator on wages remains significant (see columns 1, 2, and 3 of Table 5) with the elasticity to wages of UTV emerging amongst the other varieties’ elasticities (column 3 of Table 5).

As far as the last specification is concerned, results are in line with those presented in Table 4, where the elasticity to wage of RTV is not statistically different from zero, but the elasticity of wages to UTV is positive and significant.

Estimates presented so far, still remain highly correlational, as we are in no position to use the latter to infer a clear causal effect linking regional innovativeness to the local wage level.

Therefore, in Tables 8 and 9, we show a series of results based on the IV synthetic variables approach discussed in Section 3.2. More specifically, Table 8 reports the outcome of our 2SLS regressions where the dependent variable has been computed using only workers’ fixed effect in the first stage. Table 9 instead refers to AKM specifications of the first stage. The key difference between these results and those obtained in the previous estimations (OLS, FE, and AKM in the first stage) is interesting. First of all, we find no causal impact of either TV or RTV on wages, while the positive elasticity of UTV on wages is confirmed when accounting for endogeneity issues (see columns 1, 2, and 3 of both Tables 8 and 9).

Moreover, when considering the joint impact of RTV and UTV on wages (column 4 of Tables 8 and 9), the story is very different from that emerging with OLS, FE, and AKM estimates (column 4 of Tables 4–7). In each of the latter models, the elasticity to wages of RTV was always positive but non-significant, while that of UTV was always positive and significant in all specifications, but in the fixed effect model (Table 5). When dealing with endogeneity issues, the impact of UTV on wages is confirmed positive and statistically significant. This is consistent with the already anticipated idea according to which workers in multispecialized regions are likely to command higher wages. The causal impact of related variety, RTV, on wages, turns out to be negative and statistically significant. These results are also confirmed in Table 9 with the IV–AKM estimates. While supporting our hypotheses on the differential impact of UTV on wage dynamics, these results call for some additional discussion concerning the effect of RTV. In particular, as stressed in Sections 2 and 3, while RTV is generally positively associated to innovation, this latter tends to be of low quality and weak economic impact. Moreover, the concentration in geographical areas of similar technological activities pushes wages downwards in the labor market for almost homogeneous skills. The IV setting evidently allows for better account for these effects, which clearly emerge from endogenous dynamics.

In order to test whether selection into the labor market might partially drive our results, we exclude from the sample female workers and estimates of all our models for the subsample of male workers only. Results are all consistent and are provided in  Appendix A.

5. Conclusions

In this paper, we have developed an empirical framework to investigate the relationship between technological agglomeration and wage premia. Using PATSTAT information on the innovative activity of Italian firms, we have built a set of entropy indexes to qualify the knowledge structure of our geographical units to assess the extent to which the workers’ compensations are related to the peculiarities of the knowledge base of the regions in which they supply their labor services. By distinguishing between RTV and UTV, we have investigated if knowledge diversification strategies positively affect local wage dynamics. To do so, we applied the empirical approach proposed by Combes et al. (2008) using rich administrative data on Italian workers and firms. We have found that workers in diversified regions earn positive premia, while the effect of related variety is ambiguous. These results are consistent with the idea that technological diversification spurs more impactful innovation generating learning dynamics that intensify between employer and competition for valuable labor services. Once again, this is consistent with the already established evidence that poor diversification may cause long-term lock-in effects, affecting both productivity and wages.

Our results offer new insights into the factors affecting cross-regional wage differentials, particularly the role played by agglomeration economies. The existing literature has mainly focused on two out of the three main channels indicated by Marshall, i.e., thick capital and labor markets in areas characterized by spatial concentration of economic activities in single industry (Duranton and Puga, 2004). This study explicitly focuses on the third channel mentioned by Marshall, i.e., knowledge spillovers, which deserve special attention due to their impact on innovation-driven local growth dynamics (Glaeser et al., 1992). To the best of the authors’ knowledge, empirical studies have largely neglected the direct assessment of these dynamics.

In addition, in developing an explicit focus on the impact of knowledge spillovers, our work connects with the established literature in the evolutionary economic geography framework, which stresses the differential impact of related vis-à-vis unrelated variety on growth. This literature associates the two types of variety with two different typologies of agglomeration externalities, i.e., Jacobs’ vis-à-vis Marshallian externalities. Jacobs’ knowledge externalities are captured by unrelated knowledge variety, while related knowledge variety is an indicator of Marshallian externalities (Quatraro, 2010; Frenken et al., 2007). The emphasis on such difference also allows for appreciating the link between wage dynamics and product lifecycle theory, providing further support to the literature establishing a relationship between product and process innovations on the one hand, and employment and new job creation on the other hand (Barbieri et al., 2020; Dosi et al., 2021).

Our results also pave the way to interesting avenues for further research. First, refining the dataset would be useful to assess the persistence of our evidence when local labor systems instead of NUTS 3 regions are taken as a geographical unit. Second, it would be useful to investigate the direct relationship between recombinant novelty dynamics and cross-regional wage differentials. Third, it would be worth studying whether the relationship between wage structure and recombinant dynamics may differ according the differential technological specializations of geographical units. Finally, as discussed in Section 2, some dynamics might offset the hypothesized positive effect of diversification on wage differentials. It would be useful to develop a closer look at these potential negative effects, by investigating the impact of knowledge externalities on within-region income inequalities and job displacement.

As with any study, this work has a few caveats, including the well-known limitations of using patent statistics as indicators of technological activity. Yet, prior research proves that patents represent a reliable measure of innovation (Acs and Audretsch, 1989; Archibugi and Pianta, 1996) and are particularly useful in the context of regional innovation patterns (see e.g., Acs et al., 2002). Finally, it is fair to stress that our results are based on Italian data. Since the institutional setting behind labor market dynamics in general, and wage setting, shows significant variations across countries, the validity of our results with respect to other contexts may be limited.

Yet, this study offers remarkable insights into the regional development policy discourse. The existing literature has primarily documented the positive impact of knowledge spillovers on regional innovation and productivity growth. Our results suggest that generic technology policies promoting innovation might be ineffective for improving regional average income. Regional innovation policies should instead target the direction rather than the rate of technological change and should be based on the careful assessment of the local domains of specialization to ensure the introduction of sufficient levels of technological variety. This would increase the likelihood of creating novelty and opening new trajectories in local economies, which would engender virtuous dynamics in employment and wages. However, these policies should be coordinated and consider the need to shape the local skills supply to fit the new structural conditions.

Acknowledgments

The authors would like to thank all participants at the 6th GeoInno conference held at Bocconi University in 2022, all participants at the 63rd SIE conference held at the University of Turin in 2022, all participants at the 39th EBES Conference held at the Sapienza University of Rome in 2022, all participants at the 2nd LABORatorio Revelli biannual workshop held at Collegio Carlo Alberto (Turin) in 2002, all participants at the workshop on “Technology, Employment and Industrial Dynamics: Theory and Empirical Evidence” held at Scuola Superiore Sant’Anna in 2022. All mistakes remain ours, as all the ideas expressed here remain ours and do not reflect those of the Italian National Institute for Public Policy Analysis.

Funding

This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

Footnotes

References

Appendix A Robustness (only male workers)

In this Appendix, we replicate estimates on the subsample of male workers only. The output from the first stage is displayed in Table A1, while Tables A2–A6, present the output of the second stage.