This work aims to construct the best regression model in which small business density is the indicator of the level of the population's entrepreneurial activity. The regressors are the volume of investments into the xed capital of small businesses, the rate on insurance contributions for individual entrepreneurs to extra-budgetary funds of the Russian Federation, and the loan rate for small business. The pooled model, the unrelated model, the xed e ects model, the random e ects model are constructed, and their statistical characteristics are calculated. We verify statistical hypotheses about the choice of the most preferred model according to the criteria of Wald test, Breusch { Pagan LM-test, and Housman test. We select the best model. Based on obtained results we propose a classi cation of the regions of the Russian Federation by the type of the dependence of their entrepreneurial activity on the regressors. We analyze all regions and construct the best regression model for each of them. The unrelated regression model is found to be the best for each group of regions. The authors suggest that strong di erences between the regions can be attributed to qualitative factors, such as registration procedures of small businesses, the rate of regional taxes, etc. The results of the study can be used in state and municipal programs of small business development to improve forecasting of economic development of each region of the Russian Federation. Also, we point out that to boost entrepreneurial activity in di erent groups of regions, di erent adjustments are required, such as reduction of the rate on insurance contributions for individual entrepreneurs, improvement of the investment climate, or loan rates for small businesses.
level of development of small business is an indicator of the well-being of the
economy as a whole. Small and medium entrepreneurship research has been
intensively developing since the late 1980s. An overview of di erent areas of the
research can be found in the works of A. Yu. Chepurenko [17, 18]. Dynamics
of entrepreneurship development in countries worldwide is evaluated through
two global monitoring programs: \Panel study of dynamics of entrepreneurship"
(PSED) and \Global entrepreneurship monitor" (GEM) [
The entrepreneurial activity of the population is one of the small business
development indicators. Entrepreneurial activity is a qualitative dynamic
indicator of entrepreneurial capacity in current business climate [
At the moment there is a very limited body of works devoted to statistical
analysis of the factors in uencing entrepreneurial activity and econometric
business modeling in Russia. In particular, Pin'koveckaja Ju. S. [
Unlike the above works [
SB { Small Business { the number of small businesses in the Russian Federation;
EAP { Economically Active Population { the number of economically active population of the Russian Federation, in thousands;
SB SBD = EAP { Small Business Density;
I { Investments { the volume of investments into xed capital of small businesses, thousand rubles;
IC { Insurance Contributions { the tax rate on insurance contributions for individual entrepreneurs to extra-budgetary funds of the Russian Federation (before 2010 { the uni ed social tax);
LR { Loan Rate { the average rate for small business loans; t { year (t = 2000; 2014); n { region index number (n = 1; 79).
The regions (Federation subjects) of Russia are the objects of the study. We
collected panel data of listed statistical economic indicators in all regions from
2000 to 2014 [
In [
SBD = a0 + aII + aICIC + aLRLR: (1)
In this paper, we formulate the task to identify regional di erences that in uence the level of entrepreneurial activity of the population by panel data analysis method and carry out the grouping of regions according to the degree of regional di erences.
The calculations are performed using the Microsoft Excel add-in \data Analysis". The level of signi cance is 0.05.
In accordance with the theory [
Statistical characteristics of the constructed models are presented in Table 1.
For the constructed models at a signi cance level of 0.05 we tested the following base hypotheses: 1. about absence of individual di erences (Wald test on the insigni cance of individual coe cients, OR-model preferable to FE-model); 2. about absence of relationship between regions (Wald test on the insigni cance of the coe cients on the regressors in the FE-model, UR-model preferable to FE-model); 3. about absence of relationship between regions (Wald test on the insigni cance of the coe cients on the regressors in the RE-model, UR-model preferable to RE-model); 4. about the absence of random individual di erences (Breusch { Pagan LMtest); 5. about random individual di erences preferable to xed e ects (Housman test, we used the evaluation in the form of the auxiliary regression equation SBD ( ) = X ( ) +ZW +", matrix X ( ) = (I ( ) ; IC ( ) ; LR ( )) is constructed according to the adjusted data for the RE-model, = 1 q ~v2+~Tv2 ~u2 , ~v2 is the estimation of residual variance of the OR-model, ~u2 is the estimate of the variance of random e ects, T = 79; matrix ZW = (IW ; ICW ; LRW ) is constructed according to the adjusted data for the FE-model, base hypotheses: = 0).
We made the following conclusions based on Table 2: 1. Wald test on the insigni cance of individual coe cients of the FE-model showed that individual di erences between regions are signi cant, i.e., the FE-model was preferable to the OR-model; 2. Wald test on the insigni cance of the coe cients on the regressors in the FEmodel showed that the factor coe cients are insigni cant; i.e., the individual xed di erences of regions such that the regions can not be combined in the FE-model; 3. Wald test on the insigni cance of the coe cients on the regressors in the REmodel showed that the factor coe cients are insigni cant; i.e., the individual random di erences of regions such that the regions can not be combined in the RE-model; 4. Breusch { Pagan LM-test showed that the RE-model was preferable to the
OR-model; 5. Housman test showed that RE-model was preferable to the FE-model.
Based on 1{5 we can put the studied models in the ascending order of preference: OR-model, FE-model, RE-model, UR-model. In other words, with a probability of 0.95, the individual di erences of the regions are random but so signi cant that the UR-model is the best to construct the dependence of SBD on I, IC, and LR.
We then analyze the signi cance of the coe cients of the regressors for each equation of the UR-model, perform the correlation analysis of the factors for each region's data, and classify the regions according to the type of dependence of SBD on I, IC, and LR. The classi cation results are presented in Table 3.
We drew the following conclusions from Table 3 (signi cance level of 0.05). 1. There is no Russian region for which all three regressors of equation (1) are signi cant. 2. The most numerous group consists of the regions where the small business density is determined by the volume of investments into xed capital of small enterprises (the regression equation has the form SBD = a0 + aII, group No 3). 1 SBD = a0 + aII + aLRLR 2 SBD = a0 + aII + aICIC
SBD = a0 + aII
SBD = aICIC 5 SBD = a0 + aLRLR 6 No signi cant coe cients of regressors in the
equation (1) 3. There is a group of regions in which the SBD does not depend on any of the regressors (group No 6). 4. In groups 1{3, the regression equation contains the volume of investments into xed capital of small enterprises. Therefore, there is a possibility to manage small business growth by attracting investments in these regions. 5. Control at the Federal level a ects the development of small businesses in groups 1 and 4, and group 4 { only at the Federal level. 6. Control of small business development can be realized through improvement of credit conditions in the regions that fall into groups 1 and 5. For a single region in group 5, such control is possible only via improving credit conditions.
We supplement this research with an analysis of partial panels formed by groups 1{4. We identi ed regional di erences within each group and analyzed the nature of these di erences ( xed or random). The results of this analysis are presented in Tables 4 and 5.
Thus, we found that the UR-model was the best model in each group of regions. We can explain this fact by the presence of local qualitative factors in uencing the level of regional entrepreneurial activity. Those factors might include procedures of registration of small businesses, rates of regional taxes, etc. 4
In this paper, we developed a regression model of entrepreneurial activity level (i.e., small business density) of Russian population using panel data analysis. Explanatory variables were the volume of investments into xed capital of small businesses, the rate of contributions to extra-budgetary funds of the Russian Federation for small businesses, and the average interest rate on loans to small businesses. We classi ed the regions based on the explanatory variables in uence degree on the small business density. We studied each region group separately and found that UR-model was the most suitable. It can be explained by the presence of local qualitative factors in uencing the level of regional entrepreneurial activity, including business regulations.
Previously the authors determined the presence of a direct positive linear
correlation between 1) the density of small businesses and employment
(including self-employment) of the population, and 2) between the density of small
businesses and a gross regional product [
Foresight-Russia 9(2), 44{57 (2015) 18. Tchepurenko, A.: Entrepreneurship as a sphere of social studies Russia and international experience. Sociological Studies 9, 32{42 (2013)