Determinants and spatial dependence of innovation in Brazilian regions: evidence from a Spatial Tobit Model

This paper analyses the spatial patterns and spatial interdependencies of innovation and the role that local determinants of innovation play in Brazilian micro-regions. Specifi cally, it evaluates how local fi rms’ R&D, regional academic research, agglomeration level and local industrial specialization or diversifi cation affect regional innovation. To analyse these factors, an empirical model based on the Knowledge Production Function (KPF) is estimated using a Spatial Autoregressive Tobit (SAR-Tobit) with Brazilian patent data. The results indicate that higher levels of regional industrial R&D imply greater innovation and that greater university research at a regional level positively impacts industrial innovation. Moreover, agglomerated and diverse regions present better innovative performance. Regarding spatial dynamics, the proximity of the most innovative microregions positively affects local innovation, which shows the existence of interregional knowledge spillovers that are associated with innovative activities.

Palavras-chave inovação regional, patentes, Brasil, tobit espacial. Códigos JEL O18, O33, R11. Veneziano de Castro Araújo (1) Renato Garcia (2) 1 Introduction The location of innovation and the role of proximity in knowledge fl ows have received increasing attention in the regional science and economic geography literatures. Assessing innovation from a regional perspective assumes that innovative activities are infl uenced by the local context; in certain circumstances, location can enhance or limit fi rms' innovation. This phenomenon occurs because the knowledge and skills necessary for innovation become more easily accessible in locations where more accumulated knowledge are concentrated and a high number of qualifi ed professionals frequently interact.
Geographical proximity among agents can facilitate the assimilation of complex knowledge used in innovative activities. In this way, it is important to analyse the role of local knowledge spillovers and the local context as drivers of regional innovation. Through knowledge spillovers, knowledge created and accumulated due research activities in fi rms and universities may benefi t the innovative activities of nearby fi rms. These interregional spillovers are important determinants of local innovation and can be evaluated with different spatial econometric specifi cations (Greunz, 2003;Fischer and Varga, 2003;Crescenzi et al., 2007;Autant-Bernard and LeSage, 2011).
Innovation activity is not evenly distributed geographically; rather it is concentrated in certain regions. Several empirical studies show that innovation is even more spatially concentrated than manufacturing (Audretsch and Feldman, 1996;Crescenzi et al., 2007;Corsatea and Jayet, 2014) and that denser urban areas are more innovative (Carlino et al., 2007;Carlino and Kerr, 2015). Another point that is often made in the literature and that demands further analysis is how regional sectoral specialization or diversifi cation generates different advantages (Marshallian or Jacobian ones) and how it propagates by the means of spatial spillovers in innovation (Beaudry and Schiffauerova, 2009;De Groot et al., 2016). In spite of the growing concern regarding the relationship between geography and innovation, there is a lack of empirical evidence based on large-scale data for developing countries (Crescenzi et al., 2012).
This paper contributes to the literature by presenting new empirical evidence on this subject and analysing the relation of innovation and agglomeration and regional specialization or diversifi cation. Additionally, it contributes by performing an empirical analysis using data from Brazil, 376 Nova Economia� v.29 n.2 2019 which allows a deeper understanding of the determinants of innovation in the context of developing countries as a way to enable technological latecomers to catch up (Ying, 2008). The empirical model is based on the knowledge production function (KPF) and was estimated by a Spatial Autoregressive Tobit.
The remainder of the paper introduces a literature review about regional determinants of innovation (Sect. 2) and presents an exploratory Spatial Data Analysis that confi rms the spatial concentration of innovation in Brazil -mainly in the South-Southeast regions -which reinforces the relevance of a spatial econometric approach (Sect. 3). Then, the model adopted and its variables are described with several methodological remarks (Sect. 4) and the estimation results are analysed and checked for robustness and alternative specifi cations (Sect. 5). Finally, concluding remarks are presented (Sect. 6).

Regional determinants of innovation
Innovation does not occur in the same manner in different locations. Remarkably, it depends on fi rms' local environment because fi rms not only use internal resources to innovate but also employ external local factors to foster innovation. Knowledge creation and diffusion are strongly related to space. Knowledge is embodied in academic and industrial researchers and the tacit dimension of knowledge attests that knowledge exchange occurs with higher effi ciency and lower costs through face-to-face contacts (Storper and Venables, 2004). Furthermore, when a given region possesses a high concentration of highly qualifi ed professionals, a rich and complex local knowledge base is created, which intensifi es local knowledge spillovers and benefi ts fi rm innovation. Innovation is facilitated by interaction, cooperation and a collective learning process (Capello and Lenzi, 2013). Geographical proximity is frequently associated to other types of proximity, such as cultural, social or technological proximity, which strengthen these benefi ts (Paci et al., 2014). Regions with an accumulated knowledge and skill base will perceive advantages in innovation due to better use or access to specifi c and complex knowledge related to industrial or academic research.
Local industrial and academic R&D activities play a crucial role in regional innovation, as the seminal study of Jaffe (1989) has shown. There 377 v.29 n.2 2019 Nova Economia� is an extremely straightforward reasoning for this fi nding: as the resources applied to innovative activities (studies, laboratories, funds, etc.) increase, local innovation increases. A region with a large number of researchers can provide more effi cient assets related to innovation, such as specialized services or skilled professionals, which implies more and better opportunities for technology transfers or R&D cooperation. This environment also affords the attraction of new qualifi ed workers and improves the absorptive capacity of fi rms.
In the case of academic R&D, the new knowledge generated by universities and research centres is utilized by companies for various mechanisms, intentional or not, such as hiring qualifi ed researchers from universities' research groups, generating new spinoff fi rms, or creating formal collaborative contracts.
Geographical proximity plays a crucial role in fostering innovation. Innovative processes in a fi rm in a given location can benefi t from nearby fi rms and university research in the same region due to spatial knowledge spillover mechanisms (Duranton and Puga, 2000;Crescenzi et al., 2007). This physical proximity advantage also extends to neighbouring locations, so regions that are close to highly innovative regions also experience benefi ts. Instead, it is more diffi cult for isolated individual fi rms to benefi t from the innovation of the most geographically distant.
According to this view, being located in a region with a high number of innovative fi rms or near a region with greater innovation allows the fi rm to exploit important benefi ts from spatial intra and interregional knowledge spillovers in its innovative activities. In fact, evidence of both types of spatial spillovers are present in the literature (Autant-Bernard and LeSage, 2011) and several studies show that innovative activities in a certain locality can benefi t the entire neighbouring region and vice versa (Fischer and Varga, 2003;Moreno et al., 2005, Crescenzi et al., 2007. In addition, other studies on regional innovation have evaluated the role of agglomeration in innovation showing that spatial agglomeration presents clear advantages for innovation by allowing external scale economies and more interactions between local agents (Moreno et al., 2005;Carlino et al, 2007;Carlino and Kerr, 2015).
Regarding local sectoral specialization, many studies have found evidence that regions specialized in a given economic activity innovate more (Cabrer-Borrás and Serrano-Domingo, 2007, Henderson 1997. This evidence is theoretically linked to Marshallian externalities that indicate that regional specialization implies a great number of specialized suppliers, a vast pool of skilled workers and a larger stock of industry-specifi c knowledge that fl ows better locally. Specialization reduces transaction costs and facilitates communication-intensifying knowledge spillovers. Together these factors contribute to more innovation among local enterprises in that industry. In contrast, other studies present evidence that the diversifi cation of industrial activities is the most benefi cial for innovation in regions Audretsch, 1999 andSlavtchev, 2007). These activities are closely related to the Jacobian advantage, which posits that knowledge transfers between different sectors allow a greater number of radical innovations through what the author calls 'cross fertilization'. It occurs due to the higher complementarities of fi rms' knowledge bases that generate synergic advantages in innovation. Knowledge creation and learning often depend on a combination of diverse, complementary capabilities among heterogeneous agents (Capello and Lenzi, 2013). This argument is supported by a higher number of new fi rms and industries in more diversifi ed cities (Duranton and Puga, 2001).
Despite the vast number of works related to this topic, the debate on whether specialized or diversifi ed regions are the most important for innovation remains open. Comparing these results is a complex task because of their different specialization-diversifi cation indicators, sector composition or geographical levels of analysis (Beaudry and Shiffareova;.
As shown, while the panorama of local innovation is extremely broad and diverse, many questions remain open and require further empirical evidence. Therefore, this paper attempts to conduct a deeper analysis of the role of various factors in local innovation and assess their spatial interregional spillover effects. To accomplish this, a Brazilian regional dataset of patents is used. Additionally, a Spatial Autoregressive Tobit model is used to capture the regional spillover effects on innovation and explicitly control for regions that do not produce any patents.

Regional distribution of innovative activities in Brazil
Innovation in Brazil is concentrated in South and Southeast regions of Brazil (Albuquerque et al., 2009;Gonçalves and Almeida, 2009). The population density, GDP per capita and workforce education levels in these regions are higher than the national average. Although Brazil is a developing country, this scenario is quite similar to that in developed countries such as France (Corsatea and Jayet, 2014) and the United States (Carlino et al., 2007).
Brazilian fi rms belong primarily to low and medium technology industrial sectors (Chaves et al., 2016;Fornari et al., 2014), and many of their innovative activities are supported directly or indirectly by universities that play a fundamental role in fostering innovation in fi rms through formal or informal channels (Suzigan et al., 2009;Fernandes et al., 2010;Chaves et al., 2016).
The number of studies analysing innovation in Brazil from a regional perspective has been increasing. Some of them focus on the regional distribution of innovation in Brazil (Simões et al., 2002;Gonçalves, 2007) or in a specifi c state (Montenegro et al., 2011). Although studies show some evidence of deconcentration (Oliveira et al., 2016), innovation remains strongly concentrated in the South-Southeast regions. Previous studies have also evaluated the innovative potential of these regions (Sobrinho and Azzoni, 2017) or regional differences in technological subdomains (Rodriguez and Gonçalves, 2017).
However, few studies have empirically analysed the determinants of regional innovation in Brazil (Gonçalves and Almeida, 2009, Freitas et al., 2010, Gonçalves and Fajardo, 2011, Oliveira et al. 2016. Using per capita patents in the micro-regions, Gonçalves and Almeida (2009) found that regional structure (local R&D, agglomeration, etc.) and spatial spillover have an important role in regional innovation. Proximity is also a key point in Gonçalves and Fajardo's (2011) study; they found that not only geographic distance but also technological distance (measured by the technological classes of patents) explains a relevant part of knowledge spillovers in Brazilian mesoregions. Finally, Freitas et al. (2010) and Oliveira et al. (2016) evaluated the pace and determinants of convergence in patenting in Brazilian regions.
Given the small number of articles on the subject in Brazil, two points must be better explored and represent the contributions of this article. First, there are several regions with few or no patents. Only two previous studies have highlighted this diffi culty and proposed approaches. Oliveira et al. (2016) opted to exclude regions without patents, while Gonçalves and Fajardo (2011) adopted a more aggregated regional level (mesoregions).
However, these strategies impose limitations to the results, and ignoring the presence of large numbers of zeros naturally leads to the underestimation of the coeffi cients (LeSage and Pace, 2009).
Second, only Gonçalves and Almeida (2009) analysed the effect of relative productive specialization and diversifi cation on innovation in the regions. Therefore, it is still necessary to better evaluate the circumstances surrounding the specialization or diversifi cation of the regional impact on innovation, including a way to better target public policies.
In this sense, this paper seeks to deepen the analysis of the determinants of regional innovation in Brazil with a special focus on the regional productive structure while also dealing more appropriately with the regions without patents. The Spatial Tobit model is adopted as the econometric approach because it more appropriately deals with regions without patents.

Methodology and model specifi cation
The role of geography in innovation was fi rst shown by Jaffe (1989), who applied an adapted version of Griliches' (1979) KPF to geographical units. Later, this set of econometric models was improved with spatial econometrics tools and more specifi c data that were more spatially disaggregated (Acs et al., 1994;Anselin et al., 1997;Crescenzi et al., 2007;Fritsch and Slavtchev, 2007).
Patents granted or patent applications in each location were largely used as a proxy for local innovation output. Patents have advantages as indicators of innovation because they are directly related to the inventive process, depend on objective and stable criteria and are widely available and detailed (Griliches, 1990). However, Nagaoka et al. (2010) recalled that there is no perfect alignment between patents and innovation. This implies some limitations, such as the underestimation of the inventive process, the failure to consider the economic value of the invention, and the fact that a technology can be protected by more than one patent. In this context, the wide prevalence of patents as an indicator of innovation in empirical work testifi es that the benefi ts far outweigh the shortcomings, although it is necessary to adopt controls to guarantee good empirical results, such as the sharing of the manufacturing sector in the region of industries especially prone to patents (Gonçalves andAlmeida, 2009 Gonçalves et al., 2016). Recent studies have also used patents as the standard proxy for innovation (Crescenzi et al., 2007;Slavtchev, 2007, Corsatea andJayet, 2014).
In this paper, the model is based on the KPF, with spatial elements and additional controls. The general specifi cation of the function as follows (Equation 1): where I it is the innovation performance of region i measured by the number of patents fi led in the region; RD it -1 is the R&D expenditure from fi rms and universities in region i in the preceding period; and E it represents the characteristics of the local productive structure (level of agglomeration and specialization of local economy). This time-lag structure allows us to take into account the delay between research and its results are suffi ciently mature in terms of formalization to fi le a patent as adopted in other studies (Corsatea and Jayet, 2014;Paci et al., 2014). Before detailing the model, it is important to note some additional methodological remarks. First, for the geographical level of aggregation, this study adopted the micro-regional level, which is similar to EU NUTS-3. We verifi ed the regional distribution of innovative activities performed with the test of autocorrelation of patents per capita in Brazilian microregions between 2001 and2005. This test rejects the null hypothesis of no spatial autocorrelation (Annex A.1). Additionally, the positive result of the Moran index indicates that more innovative regions are spatially clustered and, consequently, that regions with lower innovation levels are clustered, generating a spatially heterogeneous distribution of innovation in Brazil. The Local Indicator of Spatial Autocorrelation (LISA) map shows a high concentration of highly innovative regions in the southern regions of Brazil, converging to the spatial concentration of manufacturing.
In addition, large geographical gaps can also be noted, because 229 of the 558 micro-regions produced no patents in the 2001-2005 period (Figure 2).
Most of these measurement issues can be mitigated with an appropriated cohort, but Brazil does not have an offi cial statistical selection of targeted industrial and urban centres, such as the Metropolitan Statistical Areas (MSAs) in the United States.
(1)  To address this issue, this study used a Spatial Tobit Model that can address a high proportion of zero-patent regions because it treats patent statistics as a measure censored to zero and modelled by a Spatial Tobit. LeSage and Pace (2009) report that this model deals with observations that result in truncated distributions as the patent statistics that are censored to zero. The latent regression in the spatial model is similar to the case of the Tobit, and the estimation technique consists of producing a latent dependent variable for censored observations using Markovian-Chain Monte Carlo simulation. This model allows the explicit control of regions that do not produce any patents, as reported in previous studies (Autant-Bernard and LeSage, 2011;Kang and Dall'erba, 2015). Regarding spatial dependence, a Spatial Autoregressive (SAR) model was used because it allows the analysis of spatial dynamics and the effects of interregional innovation spillovers in spatial autoregressive terms 1 . The complete model is outlined as follows, and the descriptions of variables are presented in Table 1. Local Innovation (PatPC). The dependent variable is patent applications per capita for each region, a proxy for local innovation (Moreno et al., 2005;Crescenzi et al 2007;Autant-Bernard and LeSage, 2011;Kang and Dall'erba 2014;Corsatea and Jayet, 2014;Paci et al., 2014). Patent grants often take several years to be defi ned, and the number of years may vary considerably between technological classes; thus, the application date is more stable and closer to the time at which knowledge is created (Kang and Dall'erba, 2014). Locational information on patent assignees were obtained and aggregated at the micro-regional level.
Spatially Lagged Local Innovation (WPatPC). The autoregressive term was included in the model in order to evaluate the role of spatial spillovers in innovation to neighbours. A standard spatial weight matrix with a knearest matrix for 15 neighbours was used. Additional estimations were made with another spatial weight matrix as a robustness check.
Industrial R&D Expenditures (R&DInd). The proxy for industrial R&D expenditures at the regional level is related to human capital: the share of workers occupied in R&D. The source is the Brazilian Ministry of Labour. This proxy is used because of the lack of data on R&D expenditures at the fi rm level. Previous studies include either industrial and academic R&D expenditures or just industrial R&D (Crescenzi et. al., 2007). In this paper, the option was to include industrial and academic R&D expenditures separately to measure their individual contributions to local innovation (Fritsch and Slavtchev, 2007;Kang and Dall'Erba, 2015).
University R&D Expenditures (R&DUniv). Data on the academic expenditures of R&D are not available in Brazil. Thus, to measure academic R&D, two different proxies are chosen. The fi rst is the share of full-time university professors at the regional level, and the second is the number of graduate students applying to master's, doctoral and post-doctoral degrees. However, both proxies are imperfect because university professors may be dedicated only to teaching activities and graduate students may be employed in other activities not directly related to research. To limit these imperfections, these two variables were combined using principal component analysis, generating a new variable corresponding to the fi rst component, labelled R&DUniv. This single component corployment: , b) the share of the same industry employment of all other regions and; c) the absolute values of the difference between these shares, added over all industries: .
v.29 n.2 2019 Nova Economia� responds to more than 80% of the explanatory power of both variables (Appendix A2).

Indicator of specialization and diversifi cation -Krugman Index (KI).
In order to assess whether more specialized or diversifi ed regions are more innovative, the Krugman index was used as a measure for the region's industrial structure (Crescenzi et al., 2007). The Krugman index varies from 0 to 2: most specialized regions assume values near 2 and the most diversifi ed regions close to 0. The index uses the number of employees in the manufacturing industry (at 2-digit level).
Agglomeration (Agglom). Previous studies show that local innovation is frequently related to agglomerative advantages (Moreno et al., 2005). Therefore, denser regions tend to demonstrate higher innovative performance. In this way, an additional variable for the population density using the population census was introduced to the model.
Controls. Four controls were included: fi rst, the share of employment in manufacturing and mining or the share of the active population (ShrInd) (Carlino et al., 2007;Gonçalves and Almeida, 2009); second, the presence of certain industries is more prone to patents (Sec); third, dummies for the North, Northeast and Centre-West regions (N); and fourth, dummies for Brazilian metropolitan regions (Metro).

Results
Three versions of the model were estimated using 2 years of pooled data (2004 and 2005) with a total sample size of 1,116 observations (558 microregions x 2 years). The fi rst version is an OLS (model 1) that includes all the variables but without spatial factors. The second estimated model is an SAR model (2) that includes the autoregressive term for patents. Finally, the third model is the SAR-Tobit model (3, Table 2). The results were mainly the same.
Both Industrial (R&DInd) and University (R&DUniv) R&D exhibit signifi cant and positive coeffi cients, as expected, which means that patents at the local level grow when local companies' and universities' R&D increase. Previous empirical studies that use similar specifi cations found that both local industrial and academic R&D are local determinants of innovation (Fritsch and Slavtchev, 2010;Kang and Dall'erba, 2015).  Notes: *** p < 0.1%; ** p < 1%; * p < 5%; t-stat in brackets.
Regarding the local industrial structure, the Krugman index (KI) coeffi cient is negative and signifi cant. KI takes higher values in specialized regions; therefore, as regions become more diversifi ed, their innovative performance improves. This evidence shows the importance of local benefi ts of diversifi cation for local innovation, in line with previous studies (Greunz, 2003, Fritsch andSlavtchev, 2007;Corsatea and Jayet, 2014). Additionally, population density is positively correlated with innovation, indicating that denser cities are more innovative. This result also confi rms previous studies on the U.S. (Carlino et al., 2007;Carlino & Kerr, 2015), Europe (Moreno et al., 2005) and Brazil (Goncalves and Almeida, 2009). From a spatial perspective, the positive and highly signifi cant parameter of the spatially lagged dependent variable (WPatPC) suggests that knowledge fl ows between spatially proximate regions are important sources of innovation. Therefore, more innovative neighbours implies more innova-tion in the region, probably through spatially mediated spillovers. The positive and signifi cant coeffi cient of the spatial lagged dependent variable confi rms Gonçalves and Almeida's (2009) previous results but better deals with the reality that some regions present zero patents in some years with correction of the potential downward bias in samples censored to zero (LeSage and Pace, 2009).
All controls present the expected sign and are signifi cant. Metropolitan regions, with higher shares of industrial activities and specifi c sectors with greater propensities to patent, present higher levels of patents per inhabitant -similar to previous studies (Moreno et al., 2005;Carlino et al., 2007;Gonçalves and Almeida, 2009). Finally, micro-regions not located in the South and Southeast present lower levels of patents per capita confi rming the importance of the regional heterogeneity of innovation in Brazil with a lower innovation pattern outside the main industrial areas.
In order to ensure the accuracy of the main results, other model specifi cations were tested. To ensure that the weight matrix specifi cations are appropriate and the results are not particularly sensitive to the form adopted in the weight matrix, the original model was estimated again with alternative spatial weight matrices 3 . The results, presented in the Annex, remain the same, even in terms of the coeffi cients (original signal and signifi cance level) and the magnitude of the coeffi cients is quite similar (LeSage and Pace, 2014).
Alternative specifi cations were also tested with changes in the dependent variable (models I and II). First, following Ying (2008), we used a more restrictive proxy for innovation. The Brazilian Patent Offi ce categorizes patents as invention patents or design/utility models. We replaced total patents per capita by the number of invention patents per capita because this nomenclature represents higher-quality intellectual property. Second, a model with total patents excluding university patents. Although the total number of university patents is of little signifi cance, it is important to check that the positive impact of R&D University on the total level of patent remains after this exclusion (the new variables are listed in Table  A.4 in the Annex).
Regressions with alternative specifi cations that use only invention patents (PatInvPC -Model I) and without university patents (PatnUnivPC -Model II) present the same results as the original model, showing that the empirical results are robust to more specifi c innovation types and when university patents are removed. Two other variables were also changed (models III and IV). In model III, the KI was replaced by the Herfi ndahl-Hirschman index (HH) as the proxy for the industrial specialization of the regions. It intended to assess whether the effects found for the specialization or the diversifi cation of regions with the KI remain with an alternative specialization index. In model IV, the proxy for University R&D was replaced by the number of full-time 389 v.29 n.2 2019 Nova Economia� professors per inhabitant to verify the robustness of the results. Again, the results remained the same. Finally, two additional regressions were estimated: one only for South and Southeast regions (model V) and another for all Brazilian micro-regions but for a longer period of time (model VI). The South and Southeast cohort is supported by the extensive innovation gaps in the northern portion of Brazil, which are evident in the previous LISA analysis and in the heterogeneity of the spatial dimensions of the regions. Finally, model VI includes fi ve years of patents (2001)(2002)(2003)(2004)(2005) and allows a guarantee that the results are not restricted to specifi c factors or to the short time frame of two years (2004)(2005) but rather remain over a longer period. However, to accomplish this estimation, it is necessary to have another independent variable for the level of Industrial R&D because the original proxy is not available for periods before 2003. Therefore, although it is a weaker proxy, the share of engineers in the total employees at the regional level was used because data are available for the whole period.
Overall, results from these models confi rm former results: positive and signifi cant coeffi cients for industrial and academic R&D; a signifi cant and positive autoregressive term (WPatPC); and a negative and signifi cant specialization index. Signs and signifi cance of the controls remained the same; the only exception was the level of agglomeration (Agglom) which was not signifi cant in two models (III and V).

Agglomeration and diversifi cation
It is important to take a specifi c look at the results on the industrial structure of the regions. First, the main results show that diversifi ed regions are more innovative than specialized ones. Second, agglomerated regions are positively related to innovation, which shows the role of the agglomeration of resources in the urban areas in fostering innovation.
Previous studies indicate that the degree of diversifi cation is closely associated to agglomeration (Duranton and Puga, 2000). Therefore, it is relevant to consider in detail the cases in which diversifi cation and agglomeration occur simultaneously, which can be accomplished by including a simple interaction between the variables in the model. Thus, the interaction would distinguish the effect of diversifi cation and agglomera-tion together and the sole effect of both diversifi cation and agglomeration. In order to link diversifi cation and agglomeration, the specialization index was built in the opposite direction, by inverting the KI and multiplying it by -1. Thus, this new indicator,"-KI", ranges from -2 to 0, which means that the most specialized regions take the value closest to -2 and the most diverse closest to 0. The estimation is presented in Table 4. Notes: *** p < 0.1%; ** p < 1%; * p < 5%; t-stat in brackets.
Obviously, the inversion of KI causes a reversal of the sign of the specialization index, and other coeffi cients remain similar to the original model. However, the inclusion of the interaction term (-KI * Agglom) changes the results. The diversifi cation and agglomeration per se are not signifi cant, although they maintain their initial signs, and the interaction term is positive and signifi cant, suggesting that the density of the regions and diversifi cation have signifi cant and positive effects on innovation only when they occur at the same time.
This fi nding reduces the importance of diversifi cation and agglomeration per se and reinforces the perception that Jacobian advantages are especially linked to major agglomerated and diversifi ed centres (Storper and Venables, 2004). Thus, the occurrence of diversifi cation and agglomeration in a region creates these special local conditions, which provide greater innovation performance.

Conclusions
Innovation depends on a wide range of factors. Several elements that can benefi t from the innovation results must be considered when analysing this phenomenon from the regional point of view. For this reason, many studies have sought to explore how and why different local factors can allow better innovative performance.
To assess this topic, the empirical analysis in this paper involved estimating a model based on the Jaffe-Griliches KPF using a Spatial Autoregressive Tobit (SAR-Tobit) estimation. The adoption of a Spatial Tobit is justifi ed by the large number of Brazilian micro-regions that did not register any patents in this period because it allows us to adequately address the observations of regions without patents. In this way, it is possible to obtain the estimated results without the potential downward bias that would occur with a sample censored to zero and to assess the spatial dynamics and the effects of interregional innovation spillovers.
The empirical results show that the local R&D level is positively related to innovation in the region which points to the importance of local fi rms' research as a main component of regional innovation. Additionally, there is a positive association between university research and the number of patents per capita which corroborates several studies that report academic research as an important factor of local patenting.
With regard to local characteristics, the estimation results show that agglomeration and diversifi cation imply a higher innovation corroborating the advantages of agglomeration are also important in the Brazilian case. Additionally, diverse regions tend to have higher numbers of patents, which is evidence of Jacobian advantages for innovation in Brazil.
An alternative estimation with an interaction term between density and diversity indicated that urban agglomeration and diversifi cation are ben-efi cial for innovation only when they occur at the same time. Therefore, agglomeration and diversifi cation per se do not generate benefi ts for companies to innovate, but the combination of these two factors does. This result indicates that large, diversifi ed urban centres generate signifi cant benefi ts for innovation, supporting Storper and Venables's (2004) view that companies in locations with these characteristics have largely favourable conditions for innovation.
Regarding spatial effects, the autoregressive term indicated a positive effect of the proximity of particularly innovative regions. This fi nding points to the occurrence of interregional spillovers of innovative activity, indicating that companies in a particular region can benefi t from effects of proximity to the innovations of a neighbouring locality.
In short, two main contributions derive from this work. First, spatial interregional spillovers are important drivers of regional innovation in Brazil reaffi rming benefi ts for fi rms in locations near innovative regional poles. Second, this study corroborates the evidence that Jacobian externalities are benefi cial for innovation since local industrial diversifi cation and agglomeration are benefi cial for local innovation.
Our results have some policy implications. First, they show the importance of private R&D levels not only for local innovation but also for the generation of spillovers towards neighbouring regions. Policies designed to foster the increase in private R&D expenditures can reinforce the positive regional effects of innovation. In addition, diverse and dense regions present a particularly positive dynamic for innovation, which suggests the opportunity for policy measures tailored to this industrial confi guration. This result confi rms the need to move away from a "one size-fi ts-all" policy approach to innovation.
Nevertheless, policy makers can develop measures to take advantage of the more favourable conditions for innovation offered by large diversifi ed centres. The results show that local characteristics can play an important role in fostering regional innovation, namely, agglomeration and diversifi cation. In this way, policies should comprise measures that strengthen the role of local characteristics by stimulating fi rms to benefi t from the geographical concentration of innovative inputs. This implication is particularly important for developing countries, since their industrial R&D expenditures are weaker and scarcer than those in developed countries. Policies that aim to strengthen local factors could mobilize a set of local 393 v.29 n.2 2019 Nova Economia� innovation efforts, such as local university research, to support private inhouse innovation efforts. At the same time, less specialized and densely populated regions need a different schedule of policy imbalance because these locations do not have the same favourable terms of densifi cation and diversifi cation for innovation; therefore, they depend on the formation of local skills and capabilities geared towards innovation.
Finally, for research agendas, this paper points to the relevance of further studies that deeply address the relation between agglomeration and diversifi cation not only for innovation but also for productivity and economic growth.