The Size of Innovation Space as a Factor of Innovation Activity in Regions

The research objective is to obtain and ground the quantitative characteristics of the impact of science and business on the results of innovation activity of the Russian Federation subjects. Under such results the number of patents issued and new production technologies developed are considered. Hypotheses testing is conducted enabling to establish the relationship between the innovation activity of a region and the number of potential links between the organizations creating new knowledge and innovation active businesses. The totality of these relations is characterized as an innovation space of a region. The results obtained through econometric modelling using the official data from the Rosstat and U. S. Census Bureau, Patent and Trademark Office, National Center for Education Statistics for the period 2009-2013 allow to justify some properties of estimates of the regional innovation space technical efficiency and the estimates of innovation activity results elasticity by the innovation space size for the subjects of the Russian Federation and the states of the USA. An emphasis is made on the role of public authorities in creating a favourable environment for innovation activity enhancement for the Russian Federation subjects through facilitating new research organizations emergence and higher education institutions start-ups.


INTRODUCTION
The current understanding of the innovation system functioning at the national and regional levels is related to the overall efforts of government, business and academia, aimed at creation, dissemination and use of new ideas, knowledge, technologies and products (Itskovits, 2010). In international practice, an important criterion of effectiveness of the innovation system is the R&D (Research and Development) performance. However, the process of emergence of an innovative idea and its further transformation into innovation has been little explored through computer simulation methods and, partly for that reason, we do not have convincing explanations for the effectiveness or failure of a particular innovation system as a whole. The result of the innovation process is largely determined by the ability of regional innovation system subjects to communicate and interact (Butler and Gibson, 2013;Golinchenko and Balycheva, 2012;Ivanov et al., 2012;Larina, 2012;Makoveyeva, 2012;Rumyantsev, 2013;Simachev, 2012). Apart from the direct outcomes, created by such interaction, we might gain positive externalities and synergistic effects (Polterovich, 2010). Obtaining quantitative characteristics of such relationships and interactions is one of the most difficult tasks in the analysis of innovation processes. The key objective of this paper is to obtain and substantiate the quantitative characteristics of the influence of science and business on the results of innovation activity of the Russian Federation subjects. Under such results the number of patents issued and new production technologies are considered, viewed by K. Freeman as the primary outcome of the innovative development of the economy (Freeman, 1987). The research grounds the expediency of estimating the number of potential relationships between the subjects of the Russian regional innovation systems, i.e. organizations, creating new knowledge and innovative ideas, and innovation active businesses using this knowledge to produce innovations. A hypothesis that these relationships is the core driver of production technologies and patents development has been tested.
The paper consists of four sections. The first section presents the hypothesis testing, which confirms the determining impact of a region's scientific and production potential on its innovation activity enhancement. The second section grounds the relationship between the results of innovation activity in the region and the number of potential links between knowledge creating organizations and innovation active enterprises. The totality of these relations is characterized further as innovation space of the region. The third section demonstrates that the parameters of the relationship between the number of patents issued and the size of the innovation space for the Russian Federation subjects are negligibly different from the ones present in the United States federal structure. The fourth, concluding section, describes the elasticity properties of the result of innovation activity in the region by the size of its innovation space and proves the possibility of estimating the region's share in the innovation space used. The role of the state and regional governments in the development of innovation space to support sustainable innovative performance is emphasized.

Hypothesis 1. The number of organizations, creating new knowledge, and the number of innovation active businesses are the factors determining the result of innovation activity of the Russian Federation subjects.
Testing of the hypothesis is conducted using the methods of econometric modelling based on the official statistics data that characterize the potential of science and business at the regional level.
In (Makarov et al., 2014) the three-factor models of production potential of the Russian Federation regions have been constructed, defining the dependence of GRP on the main production factors: labour, physical and intellectual capitals for the period of 2009-2013. As the characteristics of intellectual capital such indicators as "the number of personnel engaged in research and development" and "the number of higher education institutions" were considered. "The number of personnel engaged in research and development" as the intellectual capital indicator proved to be significant in the models based on the data of 2009 and 2010. In models constructed for 2011-2013 its impact on GRP is being lost, while the importance of "the number of higher education institutions" indicator increases. The research findings allow us to consider the above indicators as characteristics of the scientific potential of regions in assessing the results of their innovation activity.
As an alternative to characterize the number of higher education institutions the indicator of the number of organizations engaged in R&D is applied. The latter to a greater extent takes into account the specific features of scientific research arrangement in the Russian Federation, since it includes the Russian Academy of Sciences institutes, project institutes and design bureaus. The number of higher education institutions is a characteristic of intellectual capital in most developed countries, thus making it convenient for comparative analysis. However, the estimates obtained for the subjects of the Russian Federation on the basis of this indicator, currently can be classified as hypothetical, being valid under the condition that only universities are involved in innovation activities as organizations that create new knowledge, ignoring the participation of other research organizations. Hence, hereinafter the indicator of "the number of organizations engaged in R&D" will be employed as the fundamental characteristics of the scientific potential of the Russian Federation subjects. As a conditional estimate, for comparison purposes, the indicator of "the number of higher education institutions" will be considered.
In (Makarov et al., 2014) it is argued that the significant factor of efficiency in regions production potential models based on 2009-2013 statistical data is the number of innovation active businesses. Further, this indicator is used as the characteristics of business potential at the regional level. For the same purpose fixed assets value is considered.
To test Hypothesis 1 the production functions that determine the dependence of the result of innovation activity in the region on the totality of the above characteristics of science and business for each year in the period 2009-2012 are constructed. Further, we explore power-law production functions 1 , in logarithmic form presented as (1) Here i Q is the result of innovation activity in the region i (two indicators are considered: is applied. This approach to the modelling of residues is consistent with the concept of stochastic frontier (Kumbhakar and Lovell, 2004) and allows to obtain the correct estimates of technical efficiency of production factors.  In the adopted notations the number of innovation active businesses in the region is expressed by the value To test Hypothesis 1 production functions that determine the dependence of the number new production technologies developed (patents issued) on the set of science and business potential characteristics at the regional level are constructed. The factor of results of innovation activity is estimated by the science or business characteristic significant in production functions models constructed for the given period of time. H is rejected for more than 10% of the constructed models, the Hypothesis 1 is rejected. For each year within the period from 2009 to 2012 stochastic production functions (1) are constructed. Their parameters are estimated by maximum likelihood on the basis of information data on 80 subjects of the Russian Federation. The list of regions is presented in column 2 of Table A1 of the Annex. Overall, for this period 16 models (8 for the patents and 8 for production technologies) have been built. Parameter estimates of these models are presented in Tables 2 and 3. The results obtained do not contradict the Hypothesis 1. In all models the characteristics of a region's scientific potential -"the number of organizations engaged in R&D" (the alternative is "the number of higher education institutions") and business capacity -"the number of innovation active businesses" significantly influence both the number of patents granted (Table  2) and the number of production technologies developed (Table 3). The number of organizations creating new knowledge as a characteristic of the scientific potential in a region and the number of innovation active businesses as a characteristic of business affect the result of innovation activity of the Russian Federation subjects. Through testing results for the period 2009-2012 the Hypothesis 1 is accepted. The characteristics of the scientific potential -the number of personnel engaged in R&D" and of business capacity -"the fixed assets value" are insignificant in all models. Model (1) can be transformed to the form (2)

Hypothesis 2. The outcomes of innovation activity in the Russian Federation regions depend on the size of innovation space, which is determined by the number of potential pairwise relationships between organizations, creating new knowledge, and innovation active businesses.
The results of this hypothesis validation allows to prove the possibility of using quantitative estimates of potential pairwise relationships between organizations engaged in R&D (the alternative is higher education institutions) and businesses that use new knowledge for creating innovations, as a factor determining the results of innovation activity at the regional level. The totality of potential links between such organizations and businesses will be referred to as innovation space, and their number as the size of innovation space.

Introduce the notations
,  can be both positive and negative. Then after the transformation of function (2) we get: ( 3) Under the notations , after the transformation we obtain: (4) Testing of Hypothesis 2 is being reduced to the verification of statistical hypothesis (3) or (4). The Hypothesis 2 is accepted for the period in question, when a statistical hypothesis is not rejected for 90% of the total number of the estimated models. If the hypothesis 2 0 H is rejected for more than 10% of the models, the Hypothesis 2 is rejected for the period in question.
Parameter estimates for the eight models of the forms (3) and (4) Table 3. For all models the hypothesis 2 0 H is not rejected. Parameter estimates for the eight models of the forms (3) and (4) for production technologies are presented in Table 4. For 7 out of the 8 models the hypothesis   Table 5. Parameter estimates of models (3) and (4)  The production function of the form (2) can be transformed to the form (5): -is the number of potential pairwise relationships between organizations engaged in R&D (the alternative is higher education institutions) and innovation active businesses. Further value i V will be called the size of innovation space in the region. Thus, model (5) describes the dependence of the result of innovation activity in the region on the size of innovation space. Thereafter, as one of the characteristics of the innovation system of the Russian Federation at the regional level, the  parameter estimate is considered, characterizing the elasticity of innovation activity in the region by the size of innovation space.  Table 6 presents the parameter estimates of the six models of the form (5) for the patents issued with the size of innovation space estimated by the number of organizations engaged in R&D and innovation active businesses for each year of the period from 2008 to 2013. Table 6. Parameter estimates of models (5) Table 7 provides parameter estimates of the 6 models of the form (5) for the patents issued with the size of innovation space, estimated by the number of higher education institutions and innovation active businesses for each year between 2008 and 2013.  Table 8 offers the parameter estimates of five models of the form (5) for new production technologies with the size of innovation space, estimated by the number of organizations engaged in R&D and innovation active enterprises for each year of the period 2008-2012.  Table 9 demonstrates parameter estimates of five models of the form (5) for the production technologies with the innovation space size, estimated by the number of higher education institutions and innovation active businesses for each year of the period 2008-2012. Parameter estimates are significant in all 22 models of the form (5). The size of innovation space can be considered as a factor of the patents issued and production technologies at the regional level.

COMPARATIVE ANALYSIS OF INNOVATION SPACE IMPACT ON THE NUMBER OF PATENTS ISSUED TO THE SUBJECTS OF THE RUSSIAN FEDERATION AND THE USA
Hypothesis 3: The parameters of the function (5) describing the dependence of the number of patents issued on the size of innovation space of the Russian Federation subjects, estimated by the number of organizations engaged in R&D and innovation active businesses do not differ significantly from the parameters of the function (5) representing the dependence of the number of patents issued on the size of innovation space across the US states, estimated by the number of higher education institutions and high-tech companies.
While testing Hypothesis 3 for the subjects of the Russian Federation, the data presented in Table 1 were used, for the US states -the data described in Table 10, respectively.     Table 11). Series 2 in Fig. 2 reflects the dynamics of the elasticity values by the size of innovation space of the Russian Federation subjects, calculated subject to the number of organizations engaged in R&D and innovation active businesses (see the  parameter estimates in Table 6 Table 12. Control variables are not significant in each of the three models (M2). To compare the technical efficiency of the subjects of the Russian Federation and the US states, models of the form M1, built for the totality of 131 regions, can be used.        Thus, the elasticity estimates demonstrate weak dependence on the method of innovation space evaluation. Their dynamics is consistent with different estimation methods. It should be noted that the method of evaluating the innovation space affects the constant of the model, which scales the x-axis.

Property 2. For most regions of the Russian Federation the technical efficiency in the use of innovation space estimated by the number of organizations engaged in R&D and innovation active businesses is close to technical efficiency in the use of innovation space of the US states, estimated by the number of higher education institutions and high-tech companies.
The estimated parameters 2 2 , u v   enable to estimate mathematical expectation According to the stochastic frontier concept (Kumbhakar, Lovell, 2004), the value i TE characterizes the technical efficiency of innovation space use in the region. Technical efficiency estimates i TE are relative characteristics of regional efficiency. Their values can vary from year to year. However, the regions ranks determined by the technical efficiency estimates, are the sustainable characteristics of their innovation activity. Table 14 provides the values of Spearman's rank correlation coefficients of efficiency estimates obtained by model M1 (see Table 15) for 2008, 2009 and 2010 for the totality of 131 subjects of the Russian Federation and the US states that demonstrate their high dependence over time. In (Aivazyan, Afanasyev, 2015) it has been argued that the value  / c e w  assumes being interpreted as the expected share of the size of innovation space used by the region, effectively creating 2 discrete results of innovation activity. As an estimate i w of the share of innovation space used by the region when creating the innovations of a specific type the value The verification of Hypothesis 3 testing evidences that the dependence of the innovation activity results on the size of the innovation space for the subjects of the Russian Federation 2 Estimate i TE for a region, whose technical efficiency in the use of innovation space equals one and the US states is described by a generic model M1 (see Table 12). In Fig. 7a across the xaxis to the vertical line 80 subjects of the Russian Federation are distributed according to the classification adopted by the Rosstat (see, for example, Razrabotannyye..., 2013). After the vertical lines 51 states of the USA in alphabetical order are displayed (see, for example, Number of Patents..., 2014). The axis of ordinates on a logarithmic scale shows the values of the innovation space size in these regions. Among the 6 regions with the largest size of the innovation space from the total number of subjects of the Russian Federation and states of the USA by the 2010 data are the two subjects of the Russian Federation, i.e. Moscow and Saint Petersburg. At that, the innovation space size of Moscow exceeds the size of the innovation space of any of the US state. In Fig. 7b across the x-axis the subjects of the Russian Federation (before the vertical line) and the US states (after the vertical line) are arrayed in the same way as in Fig. 7a. Y-axis for each region displays the number of patents issued using a logarithmic scale. The maximum number of patents issued is in the state of California. The second biggest region in the number of patents issued is Moscow. Among the 15 regions the next highest in the number of patents issued is Saint Petersburg. The size of the innovation space of the US states on the average significantly exceeds the one of the RF subjects (Fig. 7a). The number of patents issued in the United States significantly exceeds the number of patents granted to the RF subjects (Fig. 7b). However, the estimates of technical efficiency in the use of innovation space by the majority of the Russian Federation subjects are comparable to respective estimates of the US states. In Fig. 7b across the x-axis the subjects of the Russian Federation (before the vertical line) and the US states (after the vertical line) are arrayed in the same way as in Fig. 7a If under evaluation of the parameters of model (5) for the totality of 131 regions we use the underestimation of the size of innovation space of Russian Federation subjects, among the 13 most efficient regions are the 7 subjects of the Russian Federation (Ivanovo, Kursk, Ulyanovsk, Penza, Kaluga, Saratov and Tomsk oblasts) and 6 US states (Idaho, Vermont, Washington, Connecticut, Rhode Island and Oregon). However, when comparing the technical efficiency estimates we should take into account that patent regulations of the Russian Federation and the United States are different. Moreover, patenting activity in the US exhibits a wider range of participants, apart from high-tech companies. Therefore, the estimates of the size of innovation space of the US states are too low, and the estimates of innovation space technical efficiency are inflated, respectively. Yet, these estimates were obtained using the official statistics information, and thus can serve as a basis for identifying the factors of innovation space technical efficiency.  variance in the innovation activity result. For such innovation activity outcomes as the number of patents issued and the number of new production technologies the elasticity estimates exceed 0.5 and range from 0.5 to 0.65. Therefore, the increase in the number of research organizations in a region by 1% and the number of innovation active businesses by 1% should be accompanied by the regional innovation activity growth by more than 1%.

CONCLUSIONS
The number of organizations creating new knowledge, as a characteristic of the region's research potential and the number of innovation active enterprises as a characteristic of business success affect the overall result of innovation activity of the Russian Federation subjects, i.e. the number of production technologies developed and the number of patents issued.
The results of innovation activity in the regions of the Russian Federation depend on the size of the innovation space, which is determined by the number of potential pairwise relationships between organizations, creating new knowledge, and innovation active businesses.
The parameters of the function describing the dependence of the number of patents issued on the size of innovation space used by the Russian Federation subjects, estimated by the number of organizations engaged in R&D and innovation active businesses do not differ significantly from the parameters of the function governing the relationships between the number of patents issued and the size of innovation space of the US states, measured by the number of higher education institutions and high-tech companies.
For the majority of the Russian Federation subjects the results of innovation activity to the same extent correlate to the size of innovation space as of for the US states. For such subjects of the Russian Federation the estimates of innovation space technical efficiency are close to the respective technical efficiency estimates of the US states.
A method of estimating the size of the innovation space for the subjects of the Russian Federation (subject to the number of higher education institutions, or the number of organizations engaged in R&D) and for the US states (with regard to the number of high-tech companies, or the total number of firms) has no significant effect on the estimates of the elasticity of innovation activity results by the size of innovation space and their dynamics.
The elasticity of innovation activity result by the size of innovation space reflects the possibility of enhancement of innovation system at the regional level through extensive development of business, education and science.
The current reform of the education system of the Russian Federation is aimed at consolidation of higher education institutions and is carried out through universities mergers. The reform of the Russian Academy of Sciences also suggests incorporation or alliance of academic institutions. In conditions of economic crisis it is hardly likely this reduction would be offset by an increase in the number of innovation active businesses. Therefore, one can expect a reduction in the size of innovation space at the regional level and, as a consequence, a decline in innovation activity results.
The limitation of this research is that the above models do not account for specific features and the intensity of interaction between individual research organizations and businesses. Under the innovation space reduction the results of innovation activity can still show a growth trend by enhancing the intensity of interaction between particular actors. However, such variant of innovation system development can be defined as optimistic. Given the above research findings a more realistic option is the one when the reduction in innovation space would apparently affect the decline in innovation activity of the Russian Federation subjects.
Implementation of the strategy of development against the background of reduction of the innovation space might challenge targeted investments that exceed the cost of maintenance of the achieved size of innovation space if the current number of research organizations and higher education institutions is retained. Based on the results obtained it can be concluded that the increase in innovation activity of the Russian Federation subjects assumes that state and regional governments would create the environment facilitating the expansion of regional innovation space through new research organizations and higher education institutions start-ups, increase of overall innovation activity of businesses.