SME efficiency in transforming regional business research and innovation investments into innovative sales output

ABSTRACT Based on data provided by the Regional Innovation Scoreboard on 23 capital and 184 non-capital regions in Europe, slacks-based models of data envelopment analysis (DEA) reveal that the efficiency by which business research and innovation inputs are converted at regional-level aggregated innovative sales output in small and medium-sized enterprises was significantly lower in capital regions in the period 2006–14. In view of efficiency maximization, a majority of the capital regions overinvest in non-research and development innovation activities, are over-specialized in knowledge-intensive industries, and fall behind in converting research and innovation inputs in intermediary intellectual property outcomes.


INTRODUCTION
This paper follows the idea that the regional context is important for innovation (Asheim & Coenen, 2005), and it focuses on the role of capital regions as breeding grounds for innovation in small and medium-sized enterprises (SMEs) in Europe. The central research question is: Compared with other types of regions in Europe, how well do capital regions perform in terms of efficiency in converting their particularly rich research and innovation (R&I) investments (Hollanders & Es-Sadki, 2017) into turnover in SMEs? Dynamic slacks-based data envelopment analysis (DEA) is relied upon to measure the efficiency by which 207 regions in Europe, amongst which 23 capital regions, convert at the regional level aggregated R&I investments in aggregated innovation output in SMEs.
In economic terms, efficiency refers to the maximization of output produced by a unit of input. A situation is called inefficient when a desired output can be achieved with less means, or when the means employed could give rise to more of the desired outputs (Heyne, 1993). Efficiency is relevant from a policy perspective. On the one hand, R&I expenditures are generally accepted as critical components for regional competitive advantage (Lee et al., 1996), and are one of the four priority areas in European regional policy to reduce regional inequalities (e.g., through the European Regional Development Fund -ERDF). On the other hand, appropriate interregional performance comparisons in terms of efficiency are a central criterion in evaluating innovation success considering the invested resources (e.g., Broekel et al., 2018;Han et al., 2016). The particular attention to output efficiency also relates to Europe's significant challenge of converting its perceived failure to translate its abundant scientific advances into marketable innovations, and the role of 'policies able to increase the innovation capability of an area and to enhance local expertise in knowledge production and use, acting on local specificities and on the characteristics, strengths, and weaknesses of already-established innovation patterns in each region' (Camagni & Capello, 2013, p. 357).
The focus on the regional-level aggregated innovation output of SMEs is justified by the fact that SMEs are recognized as generators of employment and economic development (Lukács, 2005). In the EU-28 economy, SMEs represent 99% of all (non-financial) businesses, account for 67% of total employment and generate 57% of gross value added (European Commission, 2019). Regarded as the backbone of regional economies, SMEs are the subject of various policy instruments. The European Commission, complementary to national and regional policies, sustains SMEs through its regional policy to facilitate their creation and operation, as they play an important role in the dynamics of the national and regional economy (Cohendet et al., 2010;Radicic et al., 2016).
Several reasons justify a focus on capital regions. First, capital regions tend to be more urbanized agglomerations, which have proven to be better fits for innovative firms compared with more rural areas (Brouwer et al., 1999;Moseley, 2000; Organisation for Economic Co-operation and Development (OECD), 2011). These urban agglomerations host key players that have an impact on innovative SMEs, including a variety of small and large firms in various industries, and a critical mass of users and potential customers (Iammarino, 2005). Compared with other urban regions, capital regions (cities) 'can be interpreted as the sum of some unique plus some more ubiquitous factors' (Zimmermann, 2010, p. 764). Distinct from most other urban areas, capital regions are characterized by a strong public sector and higher order (central government related) administrative functions (Porter & Stern, 2001;Zimmermann, 2010). The strong presence of the central government public sector has direct effects on employment creation, presence of lobbying firms, positive spillovers to private activities (e.g., spin-offs from the central government), and has a symbolic function and generates a 'special political, cultural and societal environment, which attracts people, enterprises, and other institutions, even if the presence of central government is not essential for their own work' (Zimmermann, 2010, p. 762). Ubiquitous to other urban areas, capital regions have an abundant availability of scientific knowledge related to the presence of universities and broader agglomeration economies related factors (Tödtling & Trippl, 2005;Berkhout et al., 2010).
Second, capital regions are crossroads of knowledge and information flows (Doloreux, 2002). They have a relatively high degree of migration and internationalization (Eurostat, 2021), and the presence of the central government attracts highly educated and innovative young professionals (Zimmermann, 2010). Specific knowledge bases of regions could increase their learning capabilities and facilitate knowledge diffusion between the participating players, facilitating regional growth. In most European countries capital regions have a gross domestic product (GDP) per capita that is superior to the national and European Union (EU) average (Hollanders & Es-Sadki, 2017), and these large urban areas tend to generate agglomeration economies (Segal, 1976). There is evidence that capital regions occupy a specific position in innovation in a national context (e.g., Annoni & Dijkstra, 2019 Cooke (2007) points to the attractiveness for innovative SMEs of being located in regions endowed with knowledge capabilities and a solid knowledge base. In this respect, capital regions are found being of particular relevance for (the location of) SMEs in general (Romero & Martínez-Román, 2012), and in highly innovative knowledge-intensive business services and high-tech manufacturing in particular (Doloreux et al., 2010;Teirlinck, 2018).
Third, Feldman and Audretsch (1999) found that, given a common knowledge base, the diversity of complementary economic activity which is often prevalent in capital regions promotes innovative output. This idea is expanded on by Frenken et al. (2007) in their discussion on related variety within regions.
Fourth, capital regions are characterized by a highly skilled heterogeneous population (Sassen, 2002). Such qualitatively strong regional research environments are highly conducive to knowledge exchange between innovative actors (Casper, 2013), leading to positive externalities by tapping into knowledge repositories, expertise and skills (Malecki, 2010). These particular characteristics of capital regions enhance regional absorptive capacity which is supposed to contribute to efficiency of knowledge exchange mechanisms (Miguélez & Moreno, 2015), at a level that is hard to reproduce in other regions (Asheim & Isaksen, 2002). Of course, one should not turn a blind eye to potential agglomeration diseconomies such as congestion, crime, commuting costs, land rents, pollution, more intense competition, etc. in densely populated or largely urbanized (capital) regions (e.g., Cooke, 2007;Glaeser, 1998).
This paper adds to the literature in four ways. First, as pointed out by Iammarino et al. (2019), capital regions are in the core of leading (high-income and innovation) regions in Europe, and it can be questioned whether a spatially blind framework focus on efficiency first (in their paper in the form of maximizing agglomeration) can be justified. Unfortunately, limited empirical insights exist regarding differences in efficiency in capital regions compared with other regions. Compared with many other studies that focus at (capital) regions in a national context, (e.g., Broekel et al., 2018;Fritsch & Slavtchev, 2011;Herstad et al., 2011), this study investigates the specificities of capital regions by considering a large number of European regions in a broad set of countries.
Second, the benchmark between capital regions and non-capital regions, whether or not further classified according to the urban-rural typology, provides original insights in how efficientat regional level aggregated -SMEs use the (capital) region's particular available resources. Moreover, our approach allows one to study the specificities of each region individually (in line with the focus in some studies on how firms use one particular regional innovation system's resources; e.g., Avilés-Sacoto et al., 2020). It also complements earlier work on resilience in the EU across the urban-rural divide during and in the aftermath of the 2008 economic and financial crisis (Giannakis & Bruggeman, 2020).
Third, the longitudinal data covering a period of eight years and the slacks-based DEA relied upon allow a more sophisticated methodological approach to deal with the topic of efficiency at regional level, including substantial time lags between inputs and outputs (as recommended by, e.g., Broekel et al., 2018).
Finally, we enrich the literature on innovation efficiency by looking at output efficiency in terms of sales of innovation in SMEs (the overall innovation efficiency; . So far, the variation on the output side for measuring efficiency is relatively small since, due to data availability, patents (referring to the more upstream technological development efficiency -Chen & Guan, 2012) have been the dominant approximation (Broekel et al., 2018).
The remainder of the paper is structured as follows. The next section presents the main insights from the literature regarding specificities of capital regions as breeding places for innovation and innovation efficiency. This is followed by a discussion about the methodological approach and the data. We then turn to the empirical analysis and end up with discussion and conclusions.

Specificities of capital regions
In line with insights from the literature on regional innovation systems (Cooke et al., 1997;Cooke, 2007), Romero and Martínez-Román (2012) argue that territories with high per capita income offer a fertile context for innovation in SMEs. The OECD (2011) outlines that technological innovations are favoured in more urbanized areas, confirming that innovations differ according to the regional context, with innovations based on the development of new patents in products and services, reflecting a strong research and development (R&D) knowledge base which is more widely present in urban contexts (Moseley, 2000). Innovation in SMEs located in less urbanized areas focuses more on exploitation in niche markets (OECD, 2014). Less urbanized contexts in which these SMEs are active are characterized by: lower population density, limited local markets, limited access to providers of technological and financial resources, a shortage of knowledge resources, and a lower R&D intensity and related absorptive capacity (Reidolf, 2016).
Through the ways capital regions position themselves in the national urban hierarchy as information regions, national information brokers or transactional regions (Mayer et al., 2016), they offer a particularly fertile context for innovation in SMEs. These regions are characterized by complex relationships between the private sector, the public sector and government, and often represent national identity (Cochrane, 2006). Capital regions benefit from a strong presence of national and academic research laboratories and technology-mediating organizations as diffusers of knowledge, and knowledge interactions between industry and science actors that are determined by the needs of the public sector (Tödtling & Trippl, 2005). Simmie (2002) highlights that capital regions occupy a particular place in urban hierarchies due to their crossroad function for people and knowledge from other parts of the global economy. Dijkstra et al. (2013) investigate the economic performance of European cities and city-regions from the premise that these areas are important for national economic performance (Glaeser et al., 1992;Krugman, 1991;Porter, 1990). They argue that capital regions tend to play a critical role as global regions exhibiting large concentrations of high-level human capital and skills acting as key conduits for inward and outward knowledge flows which are essential for national competitiveness in the global economy, in other words 'magnets' towards which both international and interregional flows of capital and labour gravitate (Sassen, 2002).
More than most other regions, capital regions offer opportunities in terms of interaction between different co-located types of actors (Cooke et al., 1997;Iammarino, 2005), and can be considered as fertile places for a creative class of workers to invent new products or processes which lead to economic growth and wealth (Cohendet et al., 2010; for technology, talent and tolerance, see Florida, 2002). Firms located in capital regions are believed to benefit from 'being there' (Gertler, 1995) and to enjoy significant innovative capacity advantages compared with firms operating in more isolated environments (Baptista & Swann, 1998). Capital regions are advantaged in terms of productivity (McCann & Acs, 2011), knowledge-driven industrial clusters (Porter, 1990), economies of scale and industry diversity (Jacobs, 1969), and enhanced variety of knowledge exchange limiting repetitive information (Fitjar & Rodríguez-Pose, 2011). The abundance of public R&D and of public innovation support systems help SMEs in applying innovative solutions (Virkkala, 2007). With regard to the period under consideration in this paper , Fratesi and Rodríguez-Pose (2016) highlight that, compared with country averages, most capital regions have been able to create more (or lose fewer) jobs during the financial and economic crisis starting in 2008.
However, capital regions, as highly urbanized areas, also face potential agglomeration diseconomies in terms of congestion, cost of land, higher competition due to a concentration of economic activity (e.g., Cooke, 2007;Glaeser, 1998), as well as diseconomies due to competition among firms in the labour market (Lee, 2016). The latter may lead to an increase in the average wage in an industry, restraining further agglomeration of the industry. Lee (2016, p. 340) points out that 'if the weakened agglomeration is absorbed in other cities, the absorption may provide a basis for medium-sized or smaller cities to maintain vitality or thrive'. Moreover, as pointed out by Storper (2010), some economic activities find themselves together in a certain region simply because it has the right factor supply (comparative advantage rather than agglomeration) for that industry (say land, or labour or transport access). In addition, Dijkstra et al. (2013) highlight the advantage in rural and intermediate regions close to cities in terms of quality of life and access to nature, and improved accessibility.
Despite their importance and special characteristics, research on innovation in capital regions is relatively limited (e.g., Campbell, 2000;Mayer et al., 2016). Hollanders and Es-Sadki (2017) have shown that most of the capital regions are high-ranked innovative regions compared with other regions. The reason might be that capital regions have a broader knowledge base since they are an attractive location for creating new products and processes. Romero and Martínez-Román (2012, p. 182), discussing innovation in SMEs, assert that: in highly developed areas with high per capita income, one might expect to find more efficient suppliers of inputs, more and better qualified workers and managers, more public support for selfemployment and entrepreneurship or stronger R&D systems (universities, public and private research centres, etc.).
However, based on a comparison of the Oslo capital region with other Norwegian city-regions, Herstad et al. (2011) illustrate that capital regions are not necessarily high ranked in terms of product and process innovation. Moreover, Herstad et al. claim that the characteristics of the local economy influence innovative outputs. Hence, the relevance of investigating whether the special characteristics of capital regions in terms of a rich knowledge base for innovation and focus on more explorative innovations go at the detriment of efficiency in the innovation process. This question addresses in an empirical way the theoretical reflection made by Iammarino et al. (2019) whether the level of attention paid to efficiency should be in accordance with spatial specificities.

Innovation sales output efficiency of firm level R&I investments
In recent decades, a shift has occurred in the focus of policy, from the promotion of science to technological innovation emphasizing knowledge with commercial potential. Further enhanced by the economic and financial crisis starting in 2008, together with an increasingly generous policy support to R&I investments in a context of severe public budget restrictions, increasing attention is paid to efficiency of R&I investments (OECD, 2019). Liik et al. (2014) highlight the variety of studies analysing the efficiency of R&I investments by using different econometric approaches and different kinds of data. Their overview demonstrates that in the relation between R&I investments and economic performance, various factors come into play, and the straightforward relationship between R&I inputs and economic outputs is an oversimplification. Sales from (new-to-firm or new-to-market) product innovation is commonly used as an indicator for measuring innovation performance, and the share of these sales in overall sales provides a measure of the relative importance of product innovations implemented by companies in the region (e.g., Guan & Chen, 2010;Hall et al., 2013).
Although not necessarily following a linear process, a strong relation exists between outputs in terms of sales from product innovation, R&D and broader (non-R&D) innovation investment inputs, and throughputs in terms of intellectual property (IP). In a dynamic framework (see further below), a throughput refers to an output of a previous period that serves as an input for the following period. IP in the form of patents, trademarks and registered designs refers to ownership rights and can have important consequences (both positive and negative) on efficiency (Stiglitz, 2008). Patents are widely recognized as intermediate outputs that further influence broader economic outputs such as exports (Li et al., 2017), productivity and GDP (Lu et al., 2014). Trademark analysis contributes to capturing relevant aspects of innovation in services and low-tech industries and in SMEs (e.g., Flikkema et al., 2014;Mendonça et al., 2004). Therefore, this form of IP can be seen as a complement to patents as the propensity to patent is lower in SMEs (e.g., Blind et al., 2006). Trademarks and registered designs protect the softer types of innovation, such as marketing and organizational innovation (Flikkema et al., 2014). Flikkema et al. (2014) report that trademarks point to having innovative activities that are close to market introduction. Mendonça et al. (2004) emphasize that innovative firms consistently use more trademarks. Greenhalgh and Rogers (2007) report a positive correlation between trademark registration and product innovation and productivity.
Combining the above insights, we will look at sales of innovations by SMEs as a result of R&D expenditures in the private sector and non-R&D innovation spending by SMEs in the region. As the composition of the industry is an important determinant for explaining (differences) in R&I investments between regions (e.g., European Commission, 2019), account is taken of the structure of the economy by including employment in medium-and high-tech manufacturing and knowledge-intensive services. We consider IP (patents, trademarks and registered designs) as throughputs between R&I investment inputs and innovation sales. This approach is in line with Lu et al. (2014) and Li et al. (2017), and considers insights from other studies relying on the DEA technique (see further below). For example, Edquist et al. (2018) select public R&D expenditure, non-R&D innovation expenditure, business R&D expenditure, and venture capital to explain sales of new-to-market and new-to-firm innovations. Li et al. (2017) measure the efficiency of 26 high-tech regions in China from 1998 to 2011. The inputs are R&D expenditure, employment and fixed assets' capital stock. The outputs include gross output value and total export value. They also use the number of patents as a throughput. Chen et al. (2018) measure the R&D efficiency of 29 Chinese regions during the period 2006-11. They select R&D expenditure and R&D personnel as inputs: papers in journals listed in the Science Citation Index (the world's leading journals of science and technology), domestic granted patents as outputs and R&D capital stock as throughput.

RESEARCH METHOD
Regions in the regional innovation scoreboard The basis for the evaluation of output efficiency of business R&I investments are the 220 regions in 22 EU member states covered in the regional innovation scoreboard 2017 (RIS) (Hollanders & Es-Sadki, 2017). We extend this by the information available in the RIS for seven regions in Norway. A large majority of the regions, 200, are defined at NUTS (Nomenclature of Territorial Units for Statistics)-2 level, which is the basic regional dimension for the application of EU Structural Funds and cohesion policies. Because of a lack of data at the NUTS-2 level, NUTS-1 level (major socio-economic regions) data are included in the RIS for 27 regions in five countries (Belgiumthe capital region is the same at NUTS-1 and -2 levels, Bulgaria, Francethe capital region is the same at NUTS-1 and -2 levels, Austria and the UK). Cyprus, Estonia, Latvia, Lithuania, Luxembourg and Malta are excluded from the analysis because the data for these countries are exclusively available at the national level and the indicators for these countries are calculated based on a country comparison ranking and not on a region-based comparison (Hollanders & Es-Sadki, 2017). As explained above, for policymaking reasons our focus is on the NUTS-2 level. This does not disregard that the NUTS levels are not always defined in a homogenous way for capital (and other) regions. For example, some capital regions such as Rome (Lazio -ITI4 -NUTS-2) and Paris (Île-de-France -FR10 -NUTS-2) include their commuting belt, whereas others such as Brussels (Région de Bruxelles-Capitale -BE10 -NUTS-2) and Prague (CZ01 -NUTS-2) do not (for more insights in these differences, see, e.g., Annoni & Dijkstra, 2019).
In the literature review arguments are made in terms of economies of agglomeration, which a simple comparison between capital and non-capital regions might overlook. To address this issue, the OECD and Eurostat classification of urban-rural regions is considered to further refine the group of non-capital regions (Eurostat, 2018). Based on the shares of a region's rural and urban population, the urban-rural typology classifies NUTS-3 regions in predominantly urban (rural population counts < 20% of the total population), intermediate (rural population between 20% and 50%) and predominantly rural (over 50%) regions. By considering the presence of urban centres that can turn regions in a higher (urban) level category (Eurostat, 2018), the urban-regional taxonomy in a creative way can be used at higher NUTS levels that resonate the policy level of the RIS (e.g., by Giannakis and Bruggeman, 2020, to investigate linkages between NUTS-3 and -2 levels). We follow this approach and identify regions having within ('presence of') a large urban area/city versus others (Capello et al., 2015). So, to define the degree of urbanization at NUTS-2 (and in a limited number of regions NUTS-1) level we start from the classification of the underlying NUTS-3 levels and complete this classification by considering the size of the urban centres in the region. A predominantly rural region containing an urban centre of more than 200,000 inhabitants making up at least 25% of the regional population becomes intermediate. An intermediate region that contains an urban centre of more than 500,000 inhabitants making up at least 25% of the regional population becomes predominantly urban.
This approach leads to a group of 23 capital regions, 79 regions (excluding 21 capital regions that were also in this classification) that are 'predominantly urban'; 91 'intermediate' regions (excluding two capital regions in this class); and 14 'predominantly rural' regions.

Inputs, throughputs and output
The inputs and throughputs are selected from the RIS 2017, the outputs are selected from the RIS 2019 (Table  1). In particular, with regard to innovation, the RIS focuses entirely on SMEs, and the IP-related throughputs refer to registration in Europe, which is coherent with the focus on innovation output in SMEs. The RIS ranks the regions' performance based on the average of the indicators in such a way that the higher the average of the indicators, the higher the performance of the region. The resulting data are indexes of each indicator. These indexes are calculated in the RIS by applying a square root to the data since the distribution of the data is not normal and the skewness of the data is > 1 (Hollanders & Es-Sadki, 2017). Further, the max-min technique (applied on a yearly basis) is used to normalize the data by dividing them by the difference between the maximum and the minimum value of each index. All data required for the empirical analysis are available for 207 regions (out of the target population of 227 regions) in 23 countries.
Dynamic slacks-based DEA Given the existence of multiple inputs, through-and outputs, a multiple factors technique called data envelopment analysis (DEA) is applied. DEA is a non-parametric technique enabling simultaneous evaluation of the relative efficiency of multiple inputs (resources) and multiple outputs (products) of a group of decision-making units (DMUs)here the DMUs are the regionsby applying a linear programming technique (Charnes et al., 1978). DEA allows the efficient regions to form a 'best practice' or 'efficient frontier' as a benchmark for less efficient regions, without guarantee that the efficiency of regions at the frontier is at the optimum level (Cook et al., 2014).
We rely on the slacks-based dynamic DEA model, which is able to consider the lagged effects (called carryovers, and referring to the IP throughputs in our model) and compute efficiency over a multiple time period (Tone & Tsutsui, 2010). Dynamic DEA, which measures dynamic efficiencies over multi-periods, is more accurate and proper than traditional DEA models which measure a single time period and static performance. Dynamic DEA models have the advantage over standard DEA models that they are unit invariant and stable over changing the input and output slacks (Tone & Tsutsui, 2010).
The dynamic DEA needed for our research is an 'output-oriented' technique since the focus lies on maximizing the production of outputs given fixed inputs, thereby reflecting the logic of maximizing the outputs of restrained R&I budgets. In line with expected increasing returns to scale for R&I investments (Romer, 1990;Scherer, 1982), we focus on the variable returns to scale (VRS) technique, because in this case a proportional change (increase or decrease) in inputs does not lead to the same proportional change (increase or decrease) in outputs (Cooper et al., 2007). If the proportionate variation of outputs is larger than proportionate changes of inputs, then the return to scale is increasing.
The slacks-based DEA model not only determines the efficient regions but also allows for identifying the extent to which each region has allocated inputs above the optimum amount (excess) and produced output below the optimum amount (shortfall). As such, the slacks-based efficiency measure is a scalar measure that allows measuring the excess of inputs and the shortfalls in outputs by region. This technique considers a region as 'efficient' if the efficiency score is equal to 1 and the region does not encounter any excess and/or shortfall (none of the inputs and outputs can be improved by diminishing the input excess and/or compensating the output shortfalls). For further information on the DEA method and the DEA model relied upon in this paper, see Appendix A in the supplemental data online. Table 2 summarizes the methodological framework. Efficiency is calculated for three subperiods (2006-10, 2008-12 and 2010-14), referred to as term efficiency, and for the entire period . This approach is largely similar to that by Chen and Guan (2012) who applied network DEA and considered three time periods (1995-99, 1999-2003 and 2003-07) for studying the efficiency of China's regional innovation systems. Potential endogeneity due to a simultaneous causal relationship between the input and the output variables is reduced by including a time lag between inputs and outputs. With respect to the time lag between the inputs, throughputs and the output, different authors allow for three to five years Lee & Park, 2005;Wang & Huang, 2007). Belderbos et al. (2004) select a two-year time lag. We have selected a four-year time lag for the inputs and a two-to three-year lag for the throughputs, conditional on the availability of data in the RIS. Sales of new-to-market and new-to-firm innovations as a percentage of total turnover of SMEs Note: In the regional innovation scoreboard 2017 (RIS) the variables are classified in 'firm level investment', 'innovation activities' and 'impact' variables (Hollanders & Es-Sadki, 2017). The 'inputs' here refer to firm-level investments in research and innovation (R&I), the 'throughputs' refer to 'innovation activities' (with focus on intellectual assets), and the 'output' refers to impacts with a focus on small and medium-sized enterprises (SMEs). This classification is in line with that commonly used in the analysis of the RIS (Hollanders & Es-Sadki, 2017). We apply one difference compared with the RIS classification, that is, we control for the sector structure of the economy by including the share of employment in medium-and high-tech manufacturing and in knowledge-intensive services as an input indicator since the sector structure largely determines R&I behaviour (European Commission, 2019).  Table 3 first presents the normalized scores for the inputs, throughputs and output for each of the 23 capital regions, averaged for the entire period. At the bottom of Table 3 a comparison is made between capital and non-capital regions, and between capital regions and non-capital regions further divided by urban-rural classification. Based on t-tests comparing capital regions with the entire group of non-capital regions, we note significant higher inputs in terms of R&D expenditures in the business sector in capital regions, as well as higher employment in medium-and high-tech manufacturing and knowledgeintensive services. Expenditure on non-R&D innovation in SMEs is significantly lower in capital regions. For the throughputs there is a stronger trademark application base in capital regions. No significant differences are found for sales of innovations. If we subdivide the noncapital regions by urban-rural classification, significant differences are found for all inputs, throughputs and the output variable. These results are confirmed if we rely on non-parametric rank tests (rank tests are useful since DEA efficiency scores display relative performances for which it is useful to compare ranks, e.g., . For the single dimensions of the inputs, throughputs and output, despite some differences, we see relatively similar scores between 'capital regions' and 'predominantly urban regions' (especially in comparison with 'intermediate and predominantly rural regions'). This makes sense since both types of regions share some important similarities with regard to agglomeration economies (Zimmermann, 2010). Furthermore, between the capital regions we see a relatively large variation in terms of R&D expenditure in business and in terms of patent applications and design registrations.

Specificities for capital regions
The results of the slacks-based DEA for the sales efficiency for the 23 capital regions are presented in Table 3 (DEA VRS (M1)). The efficiency scores are based on an analysis including all 207 regions. The difference in efficiency score between capital regions (average score of 0.34) and non-capital regions (0.49) is significant (independent sample t-test). A similar finding of lower efficiency of the capital region at national level was found, for example, by Chen and Guan (2012). The multivariate compare means test also indicates significant differences in efficiency score if we further classify the non-capital regions according to the urban-rural classification. These findings are confirmed by non-parametric rank tests.
The efficiency scores by capital region reveal strong heterogeneity among the capital regions, with two capital regions (London (NUTS-1) and Madrid (NUTS-2)) being fully efficient, and half the capital regions presenting an efficiency score < 0.20. The Copenhagen (NUTS-2) capital region, with an efficiency score of 0.84, is the third-ranking efficient capital region on the SME innovation sales frontier. An efficiency-based ranking of the regions (data not presented) reveals that six capital regions are in the upper quartile of the rankings, and eight (i.e., more than one out of three) are in the lowest ranked quadrant in terms of innovation sales in SMEs.
These findings confirm specificities of capital regions (even compared with the group of 'predominantly urban regions') in terms of attention given to efficiency by whichat a regional level aggregated -firm-level R&I investments are converted into outputs in terms of at regional-level aggregated innovation sales in SMEs.
Before going into more detail for these findings, as indicated above and commonly applied in DEA (e.g., Edquist et al., 2018), we follow a constant returns to scale (CRS) approach as an alternative (robustness check) for the variable returns to scale (VRS) approach. The CRS approach reflects the fact that the inputs' proportional change contributes to the same outputs' proportional change (Charnes et al., 1978), while the VRS assumption assumes the inputs' proportional change may not yield the same outputs' proportional change (Banker et al., 1984). The efficiency scores and ranks based on the CRS technique (Table 3, DEA CRS (M1)) confirm the findings using the VRS technique that capital regions present lower output efficiency in terms of innovation sales in SMEs, both in terms of average efficiency score as in terms of ranking. On the SME innovation sales frontier, no efficient capital region is identified. Even though the London (NUTS-1) and Madrid (NUTS-2) capital regions were positioned on the efficient frontier based on the VRS Table 2. Methodological framework.

Inputs Throughputs Output
. R&D expenditure in business sector (2006-2008-2010) . Non-R&D innovation expenditure SMEs (2006-2008-2010) . Employment in medium/high-tech manufacturing and knowledge-intensive services (2009 a -2009-2011) . EPO patent applications (2007-2009-2011) . Trademark applications (EUIPO) (2008-2010-2012) . Design applications (EUIPO) (2008-2010-2012) . Sales of new-to-market and new-tofirm innovations by SMEs (2010-2012-2014) Note: a No harmonized data are available for 2007, so they are replaced by data for 2009. As the economic structure changes little in a two-year time span, this can be supposed to have little influence on the outcomes of the model.  SME efficiency in transforming regional business research and innovation investments into innovative sales output technique, they do not outperform other regions when they are being evaluated based on the CRS technique. As additional robustness checks to these findings, we consider a shorter time lag between R&D inputs, throughputs and outputs. In line with Belderbos et al. (2004) we consider a two-year time lag. First, we test this for the same period and on the same data as for 'DEA VRS (M1)', but by considering the output with a two-year time lag instead of four years. The results ('DEA VRS (M2)') demonstrate that the differences in efficiency between capital and non-capital regions persist, but they are no longer significant at the 5% level. In addition, we consider this same two-year time lag model for a more recent period of the RIS (shifting all inputs, throughputs and the outputs with two years compared with the 'DEA VRS (M2)' model). The results ('DEA VRS (M3)') are based on the RIS 2019 and reveal no significant differences between capital and non-capital regions. The less or non-significant differences found in the models with a two-year time lag reveal both the importance of the time lag chosen and a potential influence of the time period under consideration. However, they still confirm that capital regions are not more efficient than non-capital regions in turning their particularly rich knowledge base into innovation sales in SMEs.

Output efficiency gap in innovation sales in SMEs
The descriptive statistics in Table 3 demonstrated significant differences in terms of firm-level R&I inputs, as well as in terms of the sector structure of capital regions. To gain deeper insights into the reasons for lower attention to output efficiency in terms of innovation sales in SMEs in capital regions, Table 4 provides more details on the VRS efficiency scores presented in model 1 ('DEA VRS (M1)') in Table 3. More specifically, 'term' efficiency, that is, the efficiency score in each of the three consecutive periods under consideration, is added (t 1 : 2006-10; t 2 : 2008-12; t 3 : 2010-14), as well as insights into the excess use of inputs (business R&D expenditure, non-R&D innovation expenditure excess, employment in medium-and high-tech manufacturing, and knowledge-intensive services excess), sales of innovations output shortfall, and throughputs' shortfall in terms of patent, trademark and design applications.
For example, the overall efficiency of 0.66 for the Brussels Capital Region (NUTS-2) can be traced back to a period efficiency of 0.55 in 2006-10 (t 1 ), an efficiency of 0.57 in the second period , and a fully efficient performance in period 3 (2010-14). The Brussels Capital Region (NUTS-2) could have been fully efficient in term 1 by decreasing (with 0.05 units) R&D expenditures in the business enterprise sector, increasing IP throughput (for all forms of IP considered: patent, trademark and design applications), and increasing innovation sales (0.09). The lack of full overall efficiency in period 2 can be explained by a shortfall in sales output of 0.18. Based on the strong increase of business R&D expenditure in this region during the period 2006-10, 1 we notice an initial decrease in efficiency, but a gradual shift to full efficiency in terms of innovation sales of SMEs, compared with the benchmark group at the efficient frontier. With regard to the generous policy actions giving clear incentives to enhance IP outputs during the period under consideration, 2 the shortfalls in terms of IP applications disappeared in periods 2 and 3. An opposite evolution can be seen, for example, in the Copenhagen (NUTS-2) capital region. In periods 1 and 2 this region was fully efficient, whereas in period 3 the region was characterized by excess inputs in business R&D, shortfall in patent and trademark applications, and shortfall in innovation sales output.
If we focus on the use of inputs, an excess in business R&D expenditure occurs in over one out of three capital regions, and an excess in non-R&D innovation expenditure appears in close to half the regions. The excess in non-R&D innovation expenditure contrasts with the significantly lower overall efforts in this field in capital regions compared with non-capital regions ( Table 3). The latter indicates that even the lower endowment with this type of firm-level investments in capital regions compared with other regions is not an incentive to focus more on efficiency of amounts invested. A total of 20 out of the 23 capital regions demonstrate an excess input in employment in medium-and high-tech manufacturing or knowledge-intensive services. Most capital regions also present a shortfall in terms of all forms of IP, that is, these regions generate IP outputs at a lower rate than the regions at the efficient frontier. This finding confirms the assertion that most capital regions allocate the inputs in excess of their efficient amount (in view of IP throughputs).

DISCUSSION AND CONCLUSIONS
Differences in output efficiency of business R&I investment cannot be seen independently of regional specificities (Iammarino et al., 2019). The central research question in this paper was whether business R&I investment in capital regions is as efficiently converted into innovation sales of SMEs as in non-capital regions. Capital regions are characterized by geographical concentration and easy access to (high-skilled educated) labour, allowing knowledge to diffuse more rapidly and broadly (Gertler, 1995). They offer specific conditions for innovation in SMEs in terms of factors internal to SMEs, external environment characteristics, and regulation and public support measures (Romero & Martínez-Román, 2012). Capital regions have unique characteristics as crossroads for international talent and in terms of a strong presence of central government (Zimmermann, 2010) and institutions (Mayer et al., 2016). They share strong agglomeration effects with predominantly urban areas (Simmie, 2002).
Based on dynamic slacks-based DEA, a comparison was undertaken between 23 capital and 184 non-capital regions in Europe during the period 2006-14. The application of a non-parametric technique for evaluating R&I investment output efficiency at the regional level makes it possible to include a set of inputs and throughputs, and to assess the excess or shortfall of each of these in their contribution to sales efficiency. The application of  the DEA technique to investigate efficiency, whereby firm level inputs are converted into innovation outputs, extends the use of the RIS which has hitherto been used as a popular source for monitoring and policy purposes (Hollanders & Es-Sadki, 2017). Our analysis revealed that capital regions in Europe, compared with non-capital regions (whether or not further subdivided by degree of urbanization), demonstrate significant lower efficiency in converting at the region level aggregated firm-level investments in R&I into innovation sales of SMEs. The significant lower performance in innovation sales of SMEs in capital regions supports the literature emphasizing the particularities and types of regional innovation systems (e.g., Cooke, 2007;Capello & Lenzi, 2013). It indicates that these places that are central to the location of (SMEs in) highly innovative knowledgeintensive services (Doloreux et al., 2010;Teirlinck, 2018) or SMEs more generally (Romero & Martínez-Román, 2012), and perceived as places which reflect, shape and change the cultural, social and political characteristics of a country, and as regulators of capital flows which are implemented according to the setting and institutions of these areas (Mayer et al., 2016), innovate with less focus on efficiency.
A detailed analysis of the excess and shortfall contributions of the different R&I inputs and IP throughputs showed thatin view of an efficient conversion of business R&I investment inputs in innovation sales outputs in SMEsexcess in expenditure is more often the case for non-R&D expenditure compared with R&D expenditure. Also, it is rather common for capital regions that at regional-level strong business R&I investments are not fully efficiently translated (there is a shortfall) in IP in terms of patents, trademarks and registered designs, from a viewpoint on efficient implementation of innovation sales in SMEs. Moreover, to be fully efficient, a large majority of capital regions overspecialize in medium-and high-tech manufacturing and knowledge-intensive services. Furthermore, marked differences exist between capital regions, implying that capital regions are among the most dynamic in terms of income and employment creation, and forming a rather homogeneous group of high-income leading regions in Europe (Iammarino et al., 2019), are heterogeneous in their focus on efficiency. Our findings also confirm that in terms of efficiency of turning R&I inputs into innovation outputs, capital regions in Europe evolved differently during and in the aftermath of the economic crisis of 2008 (Dijkstra et al., 2015). One of the reasons for this could be that policy decisions influence the output efficiency of firm-level investments in R&I, as demonstrated for one of the capital regions, thereby confirming Romero and Martínez-Román (2012).
From the literature, several arguments help explain these results. First, diseconomies of agglomeration (Cooke, 2007;Lee, 2016) could make capital regions less output efficient in terms of product innovation sales in SMEs. These effects weaken the expected localized agglomeration advantages of capital regions in terms of: enhanced knowledge spillovers which may be more prominent in capital regions; the concentration of people and economic activities; spatial concentration, which helps SMEs find specialized skills and lower transport costs; enhanced knowledge transfers and mutual learning; and culture and creativity (Montalto et al., 2018). However, we would also expect these diseconomies of agglomeration for 'predominantly urban regions', whereas the latter regions are the second most efficient type of region in the analysis. This renders the argument of diseconomies of agglomeration to explain the relatively low output efficiency in capital regions less obvious. Therefore, lower efficiency in capital regions could be more due to rather unique characteristics of capital regions in terms of setting and institutions (Mayer et al., 2016;Zimmermann, 2010) giving rise to policy failures (e.g., Edler & Fagerberg, 2017;Grashof, 2021) and/or create an abundance of opportunities through an extensive provision of inputs that firms do not need to care so much about efficiency of R&I investments. A second argument for moderate efficiency in capital regions is provided by Zabala-Iturriagagoitia et al. (2007) who state that less wealthy regions (in terms of GDP per capita), which non-capital regions generally are, target to absorb and adopt innovation from other regions, which requires lower investment and lower risk. Guan and Chen (2012) arrive at similar conclusions and point out that regions that invest modestly in innovation still enjoy significant innovation outputs, and therefore reach high output efficiency. This is confirmed at the EU country level by Edquist et al. (2018). Furthermore, while the aim of 'leading' innovative regions is a radical innovation that brings uncertainty, high-risk and failure, less R&D-intensive regions may be more efficient because these regionsrelatively more than capital regionstarget short-term and innovation objectives of a more applied nature. Consequently, they invest fewer inputs and contribute to more marketable output during a shortperiod time lag which is not enough for leading regions to follow radical innovation (Iammarino et al., 2019). From a policymaking perspective, besides effectiveness of R&I investments, efficiency by which scarce regionallevel business R&I investment inputs are converted in regional-level innovation sales outputs in SMEs increasingly gained attention (Broekel et al., 2018;Han et al., 2016). SMEs are a focal point of regional, national and European policy alike. At the European level, the monitoring of innovative SMEs in regions in the RIS is a way for countries to support all policy levels in their efforts to grow and to hasten the renewal of their economies by stimulating the innovativeness of their SMEs. However, public resources to stimulate private R&I investments are limited and there is increasing 'value for money' pressure expressed in a huge range of evaluation studies tackling both effectiveness and efficiency of public support (OECD, 2019). Our finding of lower efficiency in capital regions implies that a blind focus in policymaking on efficiency in all types of regions should be avoided (confirming the stream of literature that focuses on classifications of types of regions according to variance in terms of innovation, technology and knowledge; e.g., Camagni & Capello, 2013;Capello & Lenzi, 2013). On the one hand, it may be that innovative ideas generated in capital regions are commercialized outside these regions. If the abundant R&I knowledge base in capital regions in Europe is commercialized elsewhere in Europe (i.e., in non-capital regions), our findings have other policy implications than if it turns out that innovation sales largely take place outside the EU ('leakage' of the outputs of the R&I knowledge base towards other parts of the world). The latter may be facilitated by the position of capital regions as crossroads of international talent and given their role as places which offer the strategic combination of patents, industrial design, and trademarks that supports technological innovation, in particular in services industries, including SMEs in knowledge-intensive business services (Doloreux et al., 2010). Iammarino et al. (2019) refer to a mechanism of interpersonal and interregional compensation acting from spatially concentrated economic growth through the diffusion of knowledge (i.e., spatial knowledge spillovers). Similarly, agglomeration diseconomies affecting the labour market condition of a capital (or highly urbanized) region may affect employment growth in other regions (Lee, 2016). On the other hand, if the moderate output efficiency results from a systematic weakness of at regional level aggregated SME innovation in capital regions, more attention is needed to provide a framework for the conditions for SMEs to innovate in capital regions. As Iammarino et al. (2019) point out, highincome regions are challenged to maintain their specialization in high-wage activities as in the face of a changing wider landscape of comparative advantages these activities may become progressively more widespread, and because innovative sectors when maturing spread out geographically. The challenge for the richest regions therefore is to maintain prosperity through replacing old activities with new ones on the technological frontier and by continuously pushing the edge of innovation.
Further research could pay attention to potential differences between (capital and other) regions in terms of economic evolution and the reasons behind them (Annoni & Dijkstra, 2019;Fratesi & Rodríguez-Pose, 2016;McCann & Acs, 2011), including the influence of the use of EU funds in regions across time (Dijkstra et al., 2013), and institutional quality since institutions play a key role in determining the regional development potential (Iammarino et al., 2019). The analysis presented also allows further comparison between the more finegrained urban-rural classification and other types or classifications of regions, and to extend the RIS as a tool for regional benchmarking analysis for R&I efficiency. Another aspect is that the focus on SMEs should not disregard the role of multinational firms in the R&I knowledge base of many regions. Differences in the degree of knowledge spillovers from these firms to SMEs within the region may be an important factor for explaining differences in efficiency by which a region's aggregated firm level investments in R&I are converted in innovation sales in SMEs. In this respect, a more systematic uptake in the RIS of SME and non-SME inputs and throughputs, would be recommended, as for now some of these indicators are measured at the level of the entire business enterprise sectors, whereas others are measured at SME level. Doing so would allow more profound insights in knowledge spillovers between SMEs and other parts of the business enterprise sector, and eventually also of the public sector (Fritsch & Slavtchev, 2011). In addition, even in the limited time span for which harmonized data are available , our analysis revealed differences in efficiency according to the time lag considered between inputs and outputs, and to the period under consideration (in line with Fratesi and Perucca (2018) who found heterogeneous influence of the 2008 economic and financial crisis on regions). Availability of indicators that are comparable over a longer time period would allow more detailed analysis in this respect. Finally, the for-policy reasons that used the NUTS-2 level in this and in many other papers do not fully consider differences in functional diversity in these territorial areas in terms of degree of inclusion of commuter areas (e.g., Annoni & Dijkstra, 2019). This as well is an area for further improvement.