About One Approach for Comparing Regions of Different Countries According to the Technical Efficiency of Innovation Space

In the work (Aivazyan, etc., 2017) it is presented a parametric description of regional innovation systems of several countries using estimates of innovative space technical efficiency obtained by the national models.


INTRODUCTION
In the paper (Ayvazyan et al., 2017), quantitative characteristics of the influence of science and business on the results of innovative activity of the subjects of the Russian Federation were obtained. In accordance such results, patents, international patent applications and developed new production technologies are considered. As a result of testing a number of hypotheses, it was established that there is a correlation between the result of innovation activity in the region and  The work was supported by the Russian Science Foundation (project 17-18-01080) the number of potential connections between organizations creating new knowledge and innovative active enterprises. The totality of such ties is characterized as the innovative space of the region. It is shown that the dependence of the result of innovation activity on the size of the innovation space is described by the model (1) Here i Q -The result of innovation activity in the region i (Options were considered:  Table 1 for the subjects of the Russian Federation, the US states (2001,2006,2009,2012) and the prefectures of Japan (2001,2006 It was concluded that the set of parameters ( , c , t ), where  and c -The parameters of the model (1), a is the time, can be used for a parametric description of the national innovation system of the Russian Federation when it creates regions of a certain result of innovation activity.
Similarly, using a model of the form (1), a parametric description of other national innovation systems can be obtained. Moreover, it is possible to compare their parametric descriptions. In fig. 1 is a parametric description ( , c , t ) innovation systems of the Russian Federation, the United States and Japan on international patent applications for a number of years of the period 2001-2012. The size of the innovation space of the subjects of the Russian Federation is estimated by the number of organizations performing scientific research and enterprises. The size of the innovative space of US states and prefectures in Japan is estimated by the number of higher education institutions and companies. The abscissa indicates the constant c , on the y-axis -the elasticity estimate  , obtained from a model of the form (1). For each point is the year. Growth in time as a constant c , and elasticity  , testifies to the development of the national innovation system. It is easy to see that in Fig. 1, the points characterizing the innovation systems of Japan and the USA possess the property of Pareto optimality. The points characterizing the parametric description of the innovation system of the Russian Federation are not pareto-optimal. At the same time, it should be noted that the number of international patent applications filed has increased significantly in terms of the size of the innovation space for both the constituent entities of the Russian Federation and the US states. Note. In this table and below, the symbols "*", "**", "***" denote estimates at 10-, 5-, and 1% significance levels, respectively. Table 2 presents estimates of the parameters of a model of the form (1) constructed from the data of 2006. For 80 subjects of the Russian Federation (column 1), 51 states of the USA (column 2), 47 prefectures of Japan (column 3) and a general model for 178 regions (column 4). The size of the innovative space of the subjects of the Russian Federation is estimated by the number of higher educational institutions and enterprises. The size of the innovative space of US states and prefectures in Japan is estimated by the number of higher education institutions and companies.

PROBLEMS OF COMPARISON OF INNOVATIVE ACTIVITY OF REGIONS DIFFERENT COUNTRIES
With the estimated parameters 2 2 , u v   Models (1) can be calculated (Battese, Coelli, 1988) mathematical expectation In accordance with the concept of the stochastic boundary (Kumbhakar, Lovell, 2004), the value characterizes the expected value of the technical efficiency of the innovation space of the region as a ratio of the actual result of innovation activity in the region } ln exp{ Set of four parameters (  , c , t , i TE ) Can be used to describe a regional innovation system. The latter parameter is of particular interest, since the evaluation of technical efficiency can be considered as a characteristic of the quality of management of a regional innovation system. At the same time, a direct comparison of different regional innovation systems functioning within the framework of a common national innovation system for a fixed time is allowed, since in this case the technical efficiency estimates obtained on the basis of one model are comparable.
For a parametric description of regional innovation systems of different countries, it is appropriate to use different models of the form (1). Each such model allows to obtain estimates of the parameters of the national innovation system and comparable estimated of the technical efficiency of innovation space in different regions of the same country. These economic entities have the property of homogeneity in the sense that they create innovative products in the general institutional environment formed by the state. Estimates of technical efficiency of regions of different countries, obtained using different models of the form (1), are not comparable, since they are relative. Therefore, comparing the estimates obtained for different models of the form (1), each of which characterizes the set of regions of a particular national innovation system, is generally not permissible.
In column 6 of Table A1 of the appendix, it is presented the technical efficiency estimates obtained for the model of form (1)    In total, column 6 of Table P1 contains 178 (80 + 51 + 47) technical efficiency ratings. They are taught in three different models of the form (1) and their direct comparison is not correlated. Looking at Fig. 2 we can assume that the technical efficiency of the innovation space of any US state is higher than that of any prefecture in Japan and any region of the Russian Federation, but this is not true, since estimates obtained by different models are not comparable.
Another mistake may be the assumption that all US states are equally effective. However, an analysis of estimates with a higher level of accuracy of their values, as shown in Fig. 3, allows you to rank the regions in terms of efficiency level. In the works of the authors (Aivazyan et al., 2016, Aivazyan, Afanasyev, 2015, 2016 it was shown that the specification of model (1) and residual distribution functions can have a significant effect on the values of technical efficiency estimates. In this case, the ranks of these estimates have the property of resistance to the specification of the mode. It is quite natural to be able to compare the regions of different countries on the basis of technical efficiency estimates obtained from a common model for the whole region of the model  Obtained by "national" models. The grades of these grades differ, moreover, the difference in ranks can be significant. In Table 3, for each country, Spearman's rank correlation coefficients of the regional technical efficiency estimates are presented for the general and "national" model. For Japan prefectures, grades of assessments vary slightly, for US states, changes in grades are significant. It can be concluded that the transition from "national" models of the form (1) to the general model 0 M allows to ensure comparability of estimates, but leads to a distortion of their ranks. The task is to ensure comparability of technical efficiency estimates for regions of different countries in such a way that the ranks of these estimates are equal to the ranks of the estimates obtained from the "national" models. To solve this problem, the method of adjusting the technical efficiency estimates obtained from the general model described in the next section can be used.

METHOD OF ADJUSTING THE TECHNICAL EFFICIENCY ESTIMATES TO COM-PARABLE FORM.
In this section, it is presented a description of the method which is capable to bring the estimates of the technical efficiency of the innovative space of regions from several countries to a comparable type. We proceed from the premise that a "national" model can be built for each country separately, which makes it possible to obtain estimates of the technical efficiency of the innovation space of the regions from given country. However, the efficiency estimates obtained by the "national" models are not comparable. We get the comparable efficiency estimates from the mod-el, which is common to the whole set of considered regions from different countries. The method described below makes it possible to adjust these comparable estimates so that the inferred ratings of regions from each country coincides with the rating of regions constructed according to the "national" model.

THE PROPERTY OF THE ADJUSTED TECHNICAL EFFICIENCY ESTIMATES.
For each country s we order the estimates  the Spearman's coefficient differs from its maximal value 0.908224 by less than one percent. Therefore, taking eps as sufficiently small value, we get the ranks of the estimates, obtained from the model x M , for which the Spearman's correlation with the estimates from the model 0 M , as closely as necessary to the maximum value.

CONCLUSION
In this paper it is presented a method for obtaining comparable estimates of the technical efficiency of the innovation space in the regions from several countries. These estimates are obtained as a result of adjusting the technical efficiency estimates obtained on the basis of a model common to the whole set of regions, which determines the dependence of the innovation activity result of the region on the size of its innovation space. The construction of a general model for obtaining comparable estimates of technical efficiency is entirely natural. However, the ranks of the estimates of the regions of a particular country obtained by it do not necessarily correspond to the ranks of the estimates obtained from the "national" model used to compare the regions of that country separately. In addition, the general model, as a rule, does not have a satisfactory economic interpretation, since the innovative activity of the regions of different countries is conditioned by different institutional conditions. These drawbacks of the estimates obtained by the general model require their correction.
The proposed method of adjusting allows, solving the problem This approach can be used in a wide variety of problems of assessing technical efficiency and constructing ratings of economic entities operating under different institutional conditions. On its basis it is possible to rank objects belonging to different groups of generality in the case when theoretically justified comparison of them can be performed only within each group. To rank the entire set of objects, we need estimates obtained from a common model for all objects. These estimates, like the general model, do not need to have a rigorous theoretical justification. However, they must conform to the general principle of comparison used for objects within groups. When ranking the entire set of objects using the proposed optimization problem with a quadratic objective function and linear constraints, corrections are made to estimates obtained by the general model to ensure that their ranks correspond to the ranking results of objects obtained from group models.