Keywords

1 Introduction

To date, agriculture in Russia has received significant development. Currently, it is among the top four countries that have the largest areas of arable land. According to some estimates, about 9% of the world’s farmland is located in Russia [17]. The solution of managerial tasks in the Russian economy requires an understanding of the factors that affect the volume of agricultural production. In Russia, there is currently an urgent need for accelerated development of agriculture. The efficiency of agricultural production, as one of the directions of increasing the productivity and competitiveness of this branch of the economy, is directly related to the use of resources, with the degree of their involvement in the production process. To a large extent, efficiency depends on the quantitative and qualitative ratio of resources among themselves, on their balance. Determining the cost structure that ensures an increase in output per unit of resource becomes an urgent task of the management system. The justification of the resources mandatory for the successful operating of agriculture can be relying on regression models.

Scientific publications conducted in the twenty-first century have demonstrated the possibility of economic analysis of the activities of farmers who specialize in crop production and animal husbandry using regression models. These mathematical models describe the dependence of agricultural output volumes on factors describing capital and labor costs [4, 15, 16]. Most scientific publications considered data for a number of years (the so-called time series). For example, in the article [8], according to the agricultural sector of India, the efficiency of farms was evaluated using the Cobb-Douglas production function. Evaluation of agricultural production in China was described in the article [1]. While data were analyzed in 12 prefectures during the period from 2009 to 2019. In contrast to the above articles, the study [10] developed models using spatial data for 25 provinces of Cambodia. Four models were built corresponding to the information for each of the four years from 2012 to 2015. Capital and labor costs were used as factors influencing agricultural production volumes in most previously performed scientific studies [3, 14, 19, 20].

The purpose of our research was to develop economic and mathematical models to assess the impact of indicators characterizing the use of resources on agricultural production in the regions of Russia. Our study responds to the calls for taking into account the regional characteristics of agricultural production, formulated in publications [12, 23].

Our article makes a certain contribution to the knowledge about the regional peculiarities of the development of agriculture in Russia. The theoretical contribution is related to the methodology proposed by the authors, which makes it possible to assess the dependence of agricultural production volumes on factors such as fixed assets, wages of employees, ratio volume of crop production to livestock production, arable land area discussed on the development of economic and mathematical models representing regression models. Based on empirical data in the course of the study, new knowledge was obtained about the impact of each factor on the volume of agriculture production. In addition, regions were identified in which high and low values of resource efficiency were noted.

The structure of this article is given below. The following section provides an overview of scientific publications characterizing the production volumes of the agricultural sector in Russia and its regions. The third section presents the methodology and design of the study. The results of empirical data modeling are given in section four. The fifth section is devoted to the discussion of the developed regression models. The sixth section contains conclusions, followed by bibliographic references.

2 Literature Review

Regression models describing the activities of enterprises, organizations and farmers in the agricultural sector of Russia and its regions aroused some interest among researchers. The most interesting of such studies carried out in recent years are presented in Table 1.

Table 1. Characteristics of Russian studies.
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The data in Table 1 show that in most cases the objects of research are agricultural sectors in specific regions (five cases). The other three publications discuss production functions for Russia as a whole. The initial data in seven studies were time series, only one publication used spatial data for one year. In most studies (seven cases), the number of employees was used as labor costs. In two publications, the values of working time costs were considered. Data on fixed assets of agricultural enterprises were used as capital factors in six publications. In two cases, the costs of production assets were considered, and in one case, the costs of purchasing products from the machine-tool, fuel and chemical sectors. In addition, in one of the articles [24], the area of arable land was used as a factor of the production function. Thus, previous Russian scientific publications did not pay sufficient attention to the comprehensive assessment of regional characteristics of agricultural production in Russia.

3 Methodology and Design

The objects of our research were agricultural complexes and individual farmers who were engaged in crop production and animal husbandry, as well as related activities in each region of Russia. The development of regression models using time series (data for fifteen years or more) does not seem appropriate, since there is a large inflation in Russia. Taking this into account, a methodological approach was used based on the study of data on a large number of regions in one year. Since agriculture in Russia has been widely developed in sixty-five regions, the amount of empirical data was significant and met the requirements for the development of high-quality regression models. It should be noted that the advantage of using spatial data in evaluating such models compared to data for a number of years was demonstrated in the article [2].

As the factors that have the greatest impact on the total output of agricultural products, the following were considered in our study: the total cost of all capital assets in the agricultural sector of each region (factor 1), the total labor costs of agricultural workers in each of the regions (factor 2), the ratio volume of crop production to livestock production in each of the regions (factor 3), arable land area in each of the regions (factor 4). This conclusion followed from the correlation analysis of the influence of these factors on the resulting indicator, that is, the output of agricultural products. At the same time, there was no collinearity between the factors and the resulting indicator. It is essential that the use of these factors and the resulting indicator, as shown in the article [6], provides a good approximation of the initial data, since they all have the same dimension. The empirical data in our study were official statistical data for sixty-five regions of Russia for 2017 and 2018 [5]. In our study, three hypotheses were tested:

  • the first hypothesis is that regression models can be used to model the production volumes of the agricultural sector in the regions.

  • the second hypothesis is that regression models demonstrate the presence of stable dependence of agricultural production volumes on factors such as fixed assets, wages, ratio volume of crop production to livestock production, arable land area.

  • the third hypothesis is that the factors of the total value of fixed assets of agricultural enterprises, as well as the volume of arable land available to them in both regression models affect turnover to a greater extent than the other two factors.

In the course of the study, two regression models were developed, reflecting the dependence of agricultural production volumes on the total cost of all capital assets in the agricultural sector and the total labor costs of agricultural workers in each of the regions, ratio volume of crop production to livestock production, arable land area.

4 Results

Below are the first and second regression models designed on the base of data for 2017 and 2018:

$${y}_{1}\left({x}_{1},{x}_{2},{x}_{3},{x}_{4}\right)=2.056\times {x}_{1}^{0.286}\times {x}_{2}^{0.150}\times {x}_{3}^{0.035}\times {x}_{4}^{0.324}$$
(1)
$${y}_{2}\left({x}_{5},{x}_{6},{x}_{7},{x}_{8}\right)=2.238\times {x}_{5}^{0.303}\times {x}_{6}^{0.173}\times {x}_{7}^{0.023}\times {x}_{8}^{0.292}$$
(2)

where \({y}_{1}\), \({y}_{2}\) - total output of agricultural products in each of the regions, billion rubles;

\({x}_{1}\), \({x}_{5}\) - total cost of all capital assets in the agricultural sector in each of the regions, billion rubles;

\({x}_{2}\), \({x}_{6}\) - total labor costs of agricultural workers in each of the regions, billion rubles;

\({x}_{3}\), \({x}_{7}\) - ratio volume of crop production to livestock production in each of the regions;

\({x}_{4}\), \({x}_{8}\) - arable land area in each of the regions, thousand hectares.

Table 2 shows the analysis of the model’s quality. It presents the calculated values of the correlation and determination coefficients, Fisher-Snedecor and Student’s tests (column 2), as well as the significance of the Fisher-Snedecor test and p-values for Student’s test (column 3).

Table 2. Values of calculated statistics.
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The correlation coefficients more 0.9 and close to 1 in both regression models. Regression models are known to be of high quality when determination indexes are more than 0.8. The difference between 1 and this coefficient demonstrates the effect of variables not included in the regressions under consideration is 8.3%. The calculated statistic values (166 and 165) are higher than the table value of the Fisher-Snedecor test, which is 3.98 at a significance level of 0.05. For both regression models, all calculated Student test values for the coefficient and the exponents are in the range from 2.67 to 6.75; in absolute value they exceed the table amount, which is 1.99 at a significance level of 0.05. Results presented in Table 2 allow us to conclude that there is a high quality correlation between the resulting values and the four factors of the regression models (1) and (2). All levels of significance given in column 3 of Table 2 have values less than 0.01. Therefore, the coefficients of the developed regression models and the degree values in these regression models are statistically significant with the precision of 99%.

The data obtained allow us to make a general conclusion that the developed regression models (1) and (2) fully meet the econometric requirements and, therefore, can be used to describe the dependencies of agricultural production volumes in the regions from discussing factors. Consequently, the first hypothesis was confirmed.

5 Discussion

The developed regression models (1)–(2) prove the influence of fixed assets, wages, the ratio of the volume of crop production to the production of livestock products, the area of arable land on the volume of production of enterprises and entrepreneurs belonging to the rural sector. The developed regression models show the presence of established stable dependencies of agricultural production volumes in the regions on the factors under consideration for the period from 2017 to 2018. Thus, the second hypothesis was confirmed.

The degree values for the four factors in the developed models are greater than zero. Consequently, an increase in the values of each of the four factors can be used to increase the total volume of agricultural production. In the entire range of changes in the values of factors, the resulting indicators do not reach the maximum values. This indicates the possibility of increasing agricultural production in each of the regions of Russia under consideration. In all regions there are significant reserves for the further development of enterprises in this sector of the economy, including on the basis of the following measures:

  • increasing the number of enterprises and the number of employees employed in them;

  • increasing the volume of fixed assets;

  • increasing the ratio between crop production and animal husbandry;

  • expansion of the area of arable land or yield.

Factors of the total value of fixed assets of agricultural enterprises, as well as the volume of arable land available to them in both regression models affect turnover to a greater extent compared to the other two factors. This follows from the comparison of the values of the degrees in the first and second regression models. Thus, the third hypothesis was confirmed. Comparison of total output of agricultural products according to data for 2017 and 2018 shows that the values of this resulting indicator (equal to the sum of the values of degrees in regression models) are almost the same and amount to 0.795 (regression model 1) and 0.790 (regression model 2). This suggests that with the simultaneous increase of four factors, the growth of agricultural production over the years under review was almost the same. The return on scale in agriculture over the years under review was less than 1. This situation is due to the fact that most farmers have a small number of workers. Therefore, the possibilities of specialization of employees are limited, and they are forced to perform a variety of functions. As shown in [9], this leads to a relatively low level of personnel training, a decrease in labor productivity and, as a consequence, low resource efficiency at such enterprises.

To increase agricultural production in the Russian regions, it is advisable to ensure the simultaneous growth of all four factors.

A comparative analysis of the actual values of production volumes and the data predicted on the basis of the regression model (1) showed a high level of resource efficiency in 2017 in the following regions: Krasnodar territory (10.3%), Samara region (12.2%), Orenburg region (12.6%), Rostov region (12.6%), republic of Tatarstan (13.6%), Altai republic (13.8%), Saratov region (13.9%), Volgograd region (14.1%), Trans - Baikal territory (17.5%), Kurgan region (22.0%), republic of Kalmykia (23.7%), republic of Tyva (28.5%). The deviations of the actual values from the predicted values are indicated in parentheses. The low level of use of the considered factors of production was in such regions as Khabarovsk territory (−19.3%), Vologda region (−16.6), Tver region (−12.3%), Kirov region (−12.3%), Primorsky territory (−11.9%), Kostroma region (−11.8%), Vladimir region (−11.5%), Kaluga region (−11.5%), Yaroslavl region (−11.1%).

A comparative analysis of the actual values of production volumes and the data predicted on the basis of the regression model (2) showed a high level of resource efficiency in 2018 in the following regions: Krasnodar territory (10.1%), Orenburg region (10.8%), Rostov region (10.9%), Saratov region (11.1%), Volgograd region (11.7%), republic of Tatarstan (11.8%), Samara region (12.3%), Altai republic (13.2%), republic of Sakha (14.2%), Kurgan region (19.9%), republic of Kalmykia (21.6%), republic of Tyva (32.2%). The low level of use of the considered factors of production was in such regions as Vologda region (−15.8%), Khabarovsk territory (−15.8%), Primorsky territory (−13.9%), Kostroma region (−12.4%), Kirov region (−12.4%), Kaluga region (−11.2%), Yaroslavl region (−10.9%), Vladimir region (−10.7%), Tver region (−10.5%), Smolensk region (−10.1%). The above lists showed that most of the regions in 2018 retained their characteristics shown in 2017.

6 Conclusion

The conducted research has a certain scientific and practical significance. The scientific significance of the study is as follows:

  • methodology for the development of regression models demonstrating the dependence of the total volume of agricultural production on four factors - the total cost of all fixed assets in the agricultural sector, the total labor costs of agricultural workers in each of the regions, the ratio of crop production to livestock production, the area of arable land in the agricultural sector. The methodology provided for the use of spatial data by region, characterizing the values of the four factors under consideration according to the results for one year. In our study, these were 2017 and 2018.

  • two four-factor regression models were developed during the study. These regression models describe the dependence of production volumes in the agricultural sectors of each region on the factors under consideration.

  • an increase in production in the agricultural sector improves the possibility of replacing each of the four factors with another.

  • in our study, a ranking was conducted and regions were identified that are characterized by maximum and minimum use of resources.

The proposed regression models allow us to estimate the use of labor costs of agricultural workers, the cost of all fixed assets, the ratio of crop production to livestock production, the area of arable land in the agricultural sector. Therefore, it is advisable to use them when justifying programs and plans for the strategic development of regions. That is, to assess how effectively resources are being used. In addition, regression models allow us to identify an imbalance in the values of factors for each of the regions. Regression models can be used to justify programs to increase each of the four indicators, to form plans and programs for further development of agriculture.

There were limitations in the research process, since 65 regions of Russia were considered in which agricultural production has received significant development. At the same time, data on 17 regions of Russia in which the agricultural sector has not received significant development were not taken into account when constructing production functions. Further research may be related to the development of similar functions in the years following the publication of the relevant official statistics.