Volume 20
Issue 4
Economics
JOURNAL OF
POLISH
AGRICULTURAL
UNIVERSITIES
Available Online: http://www.ejpau.media.pl/volume20/issue4/art03.html
TWOFACTORIAL FUNCTIONAL ANALYSIS OF ECONOMIC DEVELOPMENT IN THE REGIONS OF AZERBAIJAN
Sugra İ. Humbatova^{1}, Natig GO. Hajiyev^{2}
^{1} Price and Apprecation Department, Azerbaijan State University of Economics (UNEC), Baku, Azerbaijan
^{2} Regulation of Economy Department, Azerbaijan State University of Economics (UNEC), Baku, Azerbaijan
This article is about analysis of the dependence of industrial and agricultural production in the regions of Azerbaijan on two main factors: capital funds and workforce. It was mainly used the CobbDouglas production function and linear function in this analysis. The CobbDouglas production and linear functions that have economical and statistical meaning are used during analysis. In the analysis, it is decided not to take account of the main funds that indirectly used in the production and to improve the statistical database because the main funds that indirectly used in the production and the lack of statistical database create some hardships for making exact decisions and calculation.
Key words: regional development, agricultural production, industrial production, capital funds and workforce, CobbDouglas production function.
INTRODUCTION
The agricultural branch, in our opinion, is one of the basic branches of a developed state. Under the conditions of scientific and technical progress the role of agriculture increases in connection with the development of technologies of cultivation, with development and perfection of agricultural machinery and population growth, all of it causing intensive manufacture and consequently increased consumption of agricultural produce.
For this reason, we have decided to develop a model of production function for the agricultural branch.
The production function takes an important place in the economic theory as a model that directly concerns not the process of exchange, but the process of manufacture connected with consumption of various resources (raw materials, energy, work, the equipment etc.).
The construction of production function, that reveals the actual technological interrelations in manufacture, is one of the major economic problems. The economic analysis of manufacture investigates the relation between expenses and output. This relation also defines the maximum volume of output at certain combinations of factors of manufacture.
Production function research is applied in various fields of knowledge and to a wide type of the data. Functions can concern technological processes in the industry or agriculture. At work with production function there are various problems: a choice of appropriate explaining variables, preparation of the corresponding data, a choice of mathematical function, a statistical estimation, and interpretation of results. Consideration of two factors of manufacture is proved at the industrial production analysis, as the enterprises, branches, and national, world economy. Agriculture represents a particular interest for research.
For the research, the data on the total cost of production in the agriculture of the Azerbaijan economic region for 11 years (2005–2015), comprising labor (L) and capital (K), has been used.
LITERATURE REVIEW
The development of rural areas covers the prosperity of rural industry, land use, professional staff in agriculture and income growth per capita.
Most of the time, a number of researchers specialized in doing research at the international and national level have identified three main factors affected on economic development:
 Natural resources (water, land quality, ecology),
 Accumulation of human and physical capital (education of workforce, infrastructure),
 Economic geography (proximity to and distance from the market entry and exit).
Giannias and Liargovas have developed a model for the location decisions of firms and applied to study spatial variations of economic development in 17 Arab countries [9].
Redding and Venables have studied a mutual connection between salary and income per person [11], Gallup and Jeffrey have explored the regression between national income per capita and other variables including transport costs and distance from the center [8].
While different firms make a decision about location, they are obliged to consider not only human capital but also the existing level of the infrastructure. If they are exogenous variables, then, they are important for research of the human and physical capital that will enable us to study how human and physical capital and enhancement of the infrastructure have an influence on economic development [21].
Ruttan, during his research, has identified that, the growth of average income of the farmer families and total farmer income are not related to upgrowth of labor productivity, but connected with the level of development of the industry in the regions as well as access to nonagricultural activities of the farmer families [12]. At the same time, it was identified in other researches devoted to study the farmer’s income in the regions that it is expedient to direct the policy of rural development towards the profits of agricultural activities and the prices of production as well as for the development of nonrural economy [10].We can come to a conclusion from abovementioned statements that village development does not correspond to the agricultural growth and as a result, commercial agricultural activity develops and the villagers move to the cities [7]. Many economists in agrarian and regional spheres confirmed the diversity of the rural areas but they didn’t identify the longterm development of these places with static concept of the prosperity of the sector [3].
Besides, in the result of other researches the concept of "distribution" of effects has been included. It transforms economic growth in the regions into the new centers of independent economic development through the requirements of the agricultural products and the raw materials [15]. On the other hand the appeal of convenience and potential advantage has been mentioned based on empiric researches and supposed that ecological policy and preservation of natural territories are of great importance for the development of rural areas [6].
I would like to focus on the Poland scientists in this area. Mieczysław Adamowicz [1] has studied the basic theoretical aspects of the adaptation of household into the transformed economic system in rural areas at the regional level especially where the former collective farms are still exist, and explained the basic aspects of the manpower and the capital in order to get reasonable income. Subsequently, the analysis of empiric researches to identify competitiveness for organizational groups of agricultural producers in the market around 5 areas (Lubelskie, Świętokrzyskie, Mazowieckie, KujawskoPomorskie and Podlaskie) [16]. The standard of the household living has been analyzed within the period of economic recovery in Mazowieckie and 4 sub regions of Poland as well as 3 countries: Poland, Slovakia and Hungary [22]. Furthermore, the implementation of regional development strategy in transition period based on the operative programs (support for entrepreneurship and innovation) in West Pomeranian of Poland has been illustrated. In this article subjects, technical and social infrastructures as well as institutional associations have been mentioned as the main creators of the special systems for economic relations at the national and regional level.
Furthermore, it was noted that the government used general tools in order to realize mentioned policy on economic system. Beside these tools, the government diversified economic policy tools on national economic sector and developed regions with different socialeconomic characters.
The Polish scientist includes some measures such as the development of various regions, the improvement of quality and standard of living, the satisfaction of local consumption, the formation of suitable condition to increase competitiveness of the local associations, the compensation of diversity in the development of various regions of the state, the decrease of lagging of less developed regions with more adverse conditions etc. The scientist comes to a conclusion that, the amalgamation of associations that are responsible for regional development as well as the formation of regional economic policy is very important. The central bodies of the state together with selfgoverned institutions possess the chance to realize strategic and operative purposes at the expense of using local resources, and through the promotion of social cooperation. The development of regions will be defined by the growth of entrepreneurship relations. For this reason, it is necessary to support the measures serving to the development of these relations, especially paves the way to create institutional bases of entrepreneurship [17].
Market economy causes the necessity to find effective decisions as a result of expansion of the competition. First of all, it is concerned to agriculture and agroindustry complex, especially farmers. That’s why, Wasilewski, scientist in economics, has touched this problem and identified interdependence between agricultural incomes of farmers, endproduct, agricultural and nonagricultural products in Wielkopolskie and KujawskoPomorskie Voivodships regions [19].
The researcher has estimated the availability of conditions for economic activities in nonagricultural sphere in rural areas (Podkarpacki region). Later he has decided that in dense populated regions it is desirable for inhabitants to develop nonagricultural economic activities. He also mentioned that there is no any considerable difference in the estimation of the factors influenced on nonagricultural economic activities and entrepreneurship in other sectors of agriculture [14].
Furthermore the role of cooperative banks in household economy and their economic activities has been analyzed in rural areas (Lublin region). He realized that in spite of the globalization, the local enterprises and institutions always keep their places. He has pointed out in his researches that the high rate of unemployment as well as the absence of the effective state policy and different business activities are the main causes of negative factors for the development of the banks in these regions [2].
It has been analyzed the relations between agricultural lands, efficiency of farms and financial situations in the centralwestern macroregion – Wielkopolskie and KujawskoPomorskie Voivodships. During the analysis, economic efficiency and profitability of labor and capital were closely examined [20]. One of the primary goals of current economic policy is related to agriculture. We are witnesses of land use and other natural resources as commercial purposes in the abovementioned sector. But the primary goal of the agrarian sector is: production of enough food [18].
BłażejczykMajka, Kala and Maciejewski, Polish scientists, studied interconnection between the fixed capital and the labor in agriculture in 9 countries of the European Union. Substitution elasticity for these production factors under the condition of the neutrality of technical progress has been estimated by means of CES – production function and influence of price changes on capital and labor in agriculture has been analyzed. The evaluation of parameters of CES dynamic function on the basis of years meets the typical difficulties related to its nonlinear function [4]. The abovementioned scientists have also carried out the analysis of regional labor productivity. Agriculture exposes natural and social factors apart from economic laws due to its specific characters [5].
The cluster analysis have been done in Mądry, Gozdowski, RoszkowskaMądra, Dąbrowski and Lupa Klukowo and Kulesze Koœcielne located in a western part of Podlasie province in Poland [13].
METHODS
The formation of the theory about production functions is referred to 1927 when American economist P. Douglas and mathematician D. Cobb wrote an article about "Theory of production". They determined the influence of capital and labor on production volume in the USA manufacturers. The formula has been defined as the following:
Philip Wicksteed put forward this module before them but Cobb and Douglas analyzed it by empiric method. That’s why it is of great economic importance. The greater K and L the less economic importance is noted.
The kinetic function y = AK^{α}L^{β}e^{γ}(where γ is the rate of technical progress per time unit) is the answer to the abovementioned function (norm of technological progress) that makes the CobbDouglas function important.
Elasticity on capital and labor is the following:(2) 
Analogically, it can be explained like (day/DL)/(y/L) equals β.
In macroeconomic level, expenditures and production are usually measured by special values. In other words, this is the sum of the volume of the resources and production price.
linear model (mutual substitution function)
(3) 
(4) 
The production function of the CobbDouglas model provided α + β = 1
(5) 
(6) 
The production function of the CobbDouglas model provided α + β ≠ 1
(7) 
(8) 
The production function of the CobbDouglas model provided
α + β = 1
by taking R&D into account
(9) 
(10) 
The production function of the CobbDouglas model provided α + β ≠ 1
by
taking R&D into account
(11) 
(12) 
ANALYSIS
The calculations have been done by the support of the Gretl software and all information was taken from the data of the State Statistical Committee of the Republic of Azerbaijan. We analyze the data taken from equation of linear regression by means of the methods of least square. Regression is used for analysis of influence on 1 dependent and 1 or several independent variables. As a result, we get the following indicators:
The production function of the CobbDouglas model provided α + β = 1, the production function of the CobbDouglas model provided α + β ≠ 1 and the linear model (mutual substitution function) from the production function of the CobbDouglas model provided α + β = 1 and the production function of the CobbDouglas model provided α + β ≠ 1, the production function of the CobbDouglas model provided α + β = 1 by taking R&D into account, the production function of the CobbDouglas model provided α + β ≠ 1 by taking R&D into account are of great economic importance that reflect the dependence of production on capital and labor for the industry sector in Absheron region.
So, we choose α + β = 1 CobbDouglas production function between them that possesses both economical and statistical meaning.
The main preference was given to those that have greater R^{2} while selecting functions. Then we choose a function that is of great importance both economical and statistical side. So, K (capital) and L (labor) are considered unimportant because of their negative () elasticity. For this reason, CobbDouglas production function where the elasticity is negative () was deleted, abbreviated. The rest of the functions were sorted out for the greatest correlation factor (R^{2} – max) as noted above. So, the tstatistic test, in other words statistic importance of St. Error (min), tstatistics (max), pvalue (p < 0.001, p < 0.01, p < 0.05 (1%, 5%, 10%)) was taken into account. The DW indicators have been in the field of uncertainty in some functions.
Among these formulas, we choose the production function of the CobbDouglas model provided α + β = 1 because it is of great importance both economical and statistical aspects.
Dependent variables: Ln (Y/L) 
const 
0.0147

**


Ln(K/L) 
0.0471

**


Rsquare 
0.452641  Corr. Rsquare 
0.374447  
Parameter rho 
0.097682  Stat. DurbinWatson 
1.727505 
We get d_{l} = 0.927 and d_{u} = 1.324 on DurbinWatson significance table. Then 4 – 1.324 = 2.676. So, it satisfies with d_{u} < DW < 4 – d_{u} (1.324 < 1.727 < 2.676). It means hypothesis about the absence of autocorrelation of the rest in 0.05 significance level is refused. It shows the high quality of this model.
It was determined that industrial production has increased 2.229 times, basic production assets 2.219 times, and the number of employees 1.130 times based on the analysis of industrial production in Absheron region during 2005–2015. The dependence of industrial production on fixed assets and labor for Absheron region is expressed by the following multiplicative production function:
(13) 
Let’s appraise the influence of efficiency and size of production on industrial manufacturing:
Relative elasticity of fixed assets 0.606832 and relative elasticity of labor 0.393168.
Individual efficiency of fixed assets E_{K} = 1.005 and individual efficiency of labor E_{L} = 1.005.
Now let’s define the total efficiency index of production (This formula is calculated as the geometric mean of the individual efficiency indices on fixed assets and labor):
(14) 
Now let’s focus on the size of production (This formula is calculated as the geometric mean of the growth rate on fixed assets and labor):
(15) 
Thus, the growth in Absheron region by 2.229 times between 2005–2015 was the reason of the increase of the industrial efficiency by 1.301 times and its volume by 1.702 times.
Fig. 1. Industrial production of Absheron
region.
Source: author’s
own compilation, calculations 
As for the agricultural sector, the linear model is opted for estimation.
Dependent variable: Y 
const 
0.3425


L 
0.4087


K 
0.0228

**


R square  0.625154  Corr. R square  0.500205  
Parameter rho  0.388063  Stat. DurbinWatson  2.769855 
(16) 
We get d_{l} = 0.927 and d_{u} = 1.324 on DurbinWatson significance table. Then 4 – 1.324 = 2.676. So, it doesn’t satisfy with d_{u} < DW < 4 – d_{u} (1.324 < 2.769 > 2.676) and it belongs to the uncertainity field. It means hypothesis about the absence of autocorrelation of residuals in 0.05 significance level isn’t refused. It doesn’t confirm the high quality of this model.
Fig. 2. Agricultural production of Absheron region. Source: author’s own compilation, calculations 
The same formulas are made for other economic regions by the same way.
For GanjaGazakh region, the production function of the CobbDouglas model provided α + β = 1 has been chosen among the abovementioned models in order to reflect the dependence of industrial production on fixed assets and labor.
Dependent variable: Ln(Y/L) 
Pvalue


const 
0.0439

**


Ln(K/L) 
0.0101

**


Rsquare  Corr. Rsquare


Parameter rho  Stat. DurbinWatson

We get d_{l} = 0.927 and d_{u} = 1.324 on DurbinWatson significance table. Then 4 – 1.324 = 2.676. So, it doesn’t satisfy with d_{u} < DW < 4 – d_{u} (1.324 < 2.908 > 2.676) and it belongs to the uncertainity field. It means hypothesis about the absence of autocorrelation of residuals in 0.05 significance level isn’t refused. It doesn’t confirm the high quality of this model.
It was determined that industrial production has increased 1.798 times, basic production assets 1.893 times, and the number of employees 0.961 times based on the analysis of industrial production in GanjaKazakh region during 2005–2015. The dependence of industrial production on fixed assets and labor for GanjaKazakh region is expressed by the following multiplicative production function:
(17) 
Let’s appraise the influence of efficiency and size of production on industrial manufacturing:
Relative elasticity of fixed assets 0.78516 and relative elasticity of labor 0.21484.
Individual efficiency of fixed assets E_{K} = 0.949 and individual efficiency of labor E_{L} = 1.870.
Now let’s define the total efficiency index of production (This formula is calculated as the geometric mean of the individual efficiency indices on fixed assets and labor):
(18) 
Now let’s focus on the size of production (This formula is calculated as the geometric mean of the growth rate on fixed assets and labor):
(19) 
Thus, the growth in GanjaKazakh region by 1.798 times between 2005–2015 was the reason of the increase of the industrial efficiency by times and its volume by times.
Fig. 3. Industrial production of GanjaKazakh region. Source: author’s own compilation, calculations 
We choose the linear model for agriculture.
Dependent variable: Y 
const 

L 

K 

Rsquare  0.213427  Corr. Rsquare  0.048764  
Parameter rho  0.056829  Stat. DurbinWatson  1.303332 
(20) 
We get d_{l} = 0.927 and d_{u} = 1.324 on DurbinWatson significance table. Then Then 4 – 1.324 = 2.676. So, it doesn’t satisfy with d_{u} < DW < 4 – d_{u} (1.324 < 1.303 > 2.676) and it belongs to the uncertainity field. It means hypothesis about the absence of autocorrelation of residuals in 0.05 significance level isn’t refused. It doesn’t confirm the high quality of this model.
Fig. 4. Agricultural production of GanjaKazakh region. Source: author’s own compilation, calculations 
For ShekiZagatala region, the production function of the CobbDouglas model provided α + β = 1 has been chosen in order to reflect the dependence of industrial production on fixed assets and labor.
Dependent variable: Ln(Y/L) 
Pvalue  
const 
0.3984 

Ln(K/L) 
0.0006 
***  
Rsquare  0.835662  Corr. Rsquare  0.812185  
Parameter rho  0.108588  Stat. DurbinWatson  2.209766 
Fig. 5. Industrial production of ShekiZakatala region. Source: author’s own compilation, calculations 
We get d_{l} = 0.927 and d_{u} = 1.324 on DurbinWatson significance table. Then 4 – 1.324 = 2.676. So, it satisfies with d_{u} < DW < 4 – d_{u} (1.324 < 2.210 < 2.676). It means hypothesis about the absence of autocorrelation of the rest in 0.05 significance level is refused. It shows the high quality of this model.
It was determined that industrial production has increased 14.792 times, basic production assets – 1.198 times, and the number of employees – 3.562 times based on the analysis of industrial production in ShekiZakatala region during 2005–2015. The dependence of industrial production on fixed assets and labor for ShekiZakatala region is expressed by the following multiplicative production function:
(21) 
Let’s appraise the influence of efficiency and size of production on industrial manufacturing:
Relative elasticity of fixed assets 0.748536 and relative elasticity of labor 0.251464.
Individual efficiency of fixed assets E_{K} = 12.347 and individual efficiency of labor E_{L} = 4.152.
Now let’s define the total efficiency index of production (This formula is calculated as the geometric mean of the individual efficiency indices on fixed assets and labor):
(22) 
Now let’s focus on the size of production (This formula is calculated as the geometric mean of the growth rate on fixed assets and labor):
(23) 
Thus, the growth in ShekiZakatala region by 14.792 times between 2005–2015 was the reason of the increase of the industrial efficiency by 9.383 times and its volume by 1.574 times.
We choose the linear model for agriculture.
Dependent variable: Y 
const

0.0021

***


L

0.0080

***


K

0.0172

**


Rsquare

Corr. Rsquare


Parameter rho

Stat. DurbinWatson

(24) 
We get d_{l} = 0.927 and d_{u} = 1.324 on DurbinWatson significance table. Then 4 – 1.324 = 2.676. So, it satisfies with d_{u} < DW < 4 – d_{u} (1.324 < 1.792 < 2.676). It means hypothesis about the absence of autocorrelation of the rest in 0.05 significance level is refused. It shows the high quality of this model.
Fig. 6. Agricultural production of ShekiZakatala region. Source: author’s own compilation, calculations 
For GubaKhachmaz region, the production function of the CobbDouglas model provided α + β = 1 has been chosen in order to reflect the dependence of industrial production on fixed assets and labor.
Dependent variable: Ln(Y/L) 
const

<0.0001 
***


Ln(K/L)

0.0125

**


Rsquare

Corr. Rsquare


Parameter rho

Stat. DurbinWatson

We get d_{l} = 0.927 and d_{u} = 1.324 on DurbinWatson significance table. Then 4 – 1.324 = 2.676. So, it satisfies with d_{u} < DW < 4 – d_{u} (1.324 < 1.874 < 2.676). It means hypothesis about the absence of autocorrelation of the rest in 0.05 significance level is refused. It shows the high quality of this model.
It was determined that industrial production has increased 2.167 times, basic production assets 1.139 times, and the number of employees 3.244 times based on the analysis of industrial production in CubaHachmaz region during 2005–2015. The dependence of industrial production on fixed assets and labor for CubaHachmaz region is expressed by the following multiplicative production function:
(25) 
Let’s appraise the influence of efficiency and size of production on industrial manufacturing:
Relative elasticity of fixed assets 0.59765 and relative elasticity of labor 0.40235.
Individual efficiency of fixed assets E_{K} = 1.902 and individual efficiency of labor E_{L} = 4.152.
Now let’s define the total efficiency index of production (This formula is calculated as the geometric mean of the individual efficiency indices on fixed assets and labor):
(26) 
Now let’s focus on the size of production (This formula is calculated as the geometric mean of the growth rate on fixed assets and labor):
(27) 
Thus, the growth in CubaHachmaz region by 2.167 times between 2005–2015 was the reason of the increase of the industrial efficiency by 1.247 times and its volume by 1.733 times.
Fig. 7. Industrial production of CubaHachmaz region. Source: author’s own compilation, calculations 
For agriculture, the production function of the CobbDouglas model provided α + β ≠ 1 has been chosen in order to reflect the dependence of agriculture production on fixed assets and labor.
Dependent variable: LnY 
const 
0.0787

*  
LnK 
0.0040

***  
LnL 
0.1574


Rsquare  0.939289  Corr. Rsquare  0.919051  
Parameter rho  0.053485  Stat. DurbinWatson  1.842938 
We get d_{l} = 0.927 and d_{u} = 1.324 on DurbinWatson significance table. Then 4 – 1.324 = 2.676. So, it satisfies with d_{u} < DW < 4 – d_{u} (1.324 < 1.843 < 2.676). It means hypothesis about the absence of autocorrelation of the rest in 0.05 significance level is refused. It shows the high quality of this model.
It was determined that industrial production has increased 3.144 times, basic production assets 2.306 times, and the number of employees 1.283 times based on the analysis of industrial production in CubaHachmaz region during 2005–2015. The dependence of industrial production on fixed assets and labor for CubaHachmaz region is expressed by the following multiplicative production function:
(28) 
Let’s appraise the influence of efficiency and size of production on industrial manufacturing:
Relative elasticity of fixed assets 0.4563791 and relative elasticity of labor 0.5436209.
Individual efficiency of fixed assets E_{K} = 1.363 and individual efficiency of labor E_{L} = 2.450.
Now let’s define the total efficiency index of production (This formula is calculated as the geometric mean of the individual efficiency indices on fixed assets and labor):
(29) 
Now let’s focus on the size of production (This formula is calculated as the geometric mean of the growth rate on fixed assets and labor):
(30) 
Thus, the growth in CubaHachmaz region by 3.144 times between 2005–2015 was the reason of the increase of the industrial efficiency by 1.872 times and its volume by 1.676 times.
Fig. 8. Agricultural production of CubaHachmaz region. Source: author’s own compilation, calculations 
For Aran region, the production function of the CobbDouglas model provided α + β = 1 has been chosen in order to reflect the dependence of industrial production on fixed assets and labor.
Dependent variable: Ln(Y/L) 
const

0.0009

***


Ln(K/L)

0.0047

***


Rsquare

Corr. Rsquare


Parameter rho

0.033201  Stat. DurbinWatson

We get d_{l} = 0.927 and d_{u} = 1.324 on DurbinWatson significance table. Then 4 – 1.324 = 2.676. So, it satisfies with d_{u} < DW < 4 – d_{u} (1.324 < 1.440 < 2.676). It means hypothesis about the absence of autocorrelation of the rest in 0.05 significance level is refused. It shows the high quality of this model.
It was determined that industrial production has increased 2.299 times, basic production assets 2.780 times, and the number of employees 1.050 times based on the analysis of industrial production in Aran region during 2005–2015. The dependence of industrial production on fixed assets and labor for Aran region is expressed by the following multiplicative production function:
(31) 
Let’s appraise the influence of efficiency and size of production on industrial manufacturing:
Relative elasticity of fixed assets 0.560246 and relative elasticity of labor 0.439754.
Individual efficiency of fixed assets E_{K} = 0.826 and individual efficiency of labor E_{L} = 2.450.
Now let’s define the total efficiency index of production (This formula is calculated as the geometric mean of the individual efficiency indices on fixed assets and labor):
(32) 
Now let’s focus on the size of production (This formula is calculated as the geometric mean of the growth rate on fixed assets and labor):
(33) 
Thus, the growth in Aran region by 2.299 times between 2005–2015 was the reason of the increase of the industrial efficiency by 1.449 times and its volume by 1.810 times.
Fig. 9. Industrial production of Aran region. Source: author’s own compilation, calculations 
For agriculture, the production function of the CobbDouglas model provided α + β = 1 has been chosen in order to reflect the dependence of agriculture production on fixed assets and labor.
Dependent variable: Ln(Y/L) 
const 
0.8509


Ln(K/L) 
0.0007

***


Rsquare  0.822406  Corr. Rsquare  0.797036  
Parameter rho  0.302472  Stat. DurbinWatson  1.038468 
We get d_{l} = 0.927 and d_{u} = 1.324 on DurbinWatson significance table. Then 4 – 1.324 = 2.676. So, it doesn’t satisfy with d_{u} < DW < 4 – d_{u} (1.324 > 1.038 < 2.676) and it belongs to the uncertainity field. It means hypothesis about the absence of autocorrelation of residuals in 0.05 significance level isn’t refused. It doesn’t confirm the high quality of this model.
It was determined that industrial production has increased 8.355 times, basic production assets 2.306 times, and the number of employees 0.851 times based on the analysis of industrial production in Aran region during 2005–2015. The dependence of industrial production on fixed assets and labor for Aran region is expressed by the following multiplicative production function:
(34) 
Let’s appraise the influence of efficiency and size of production on industrial manufacturing:
Relative elasticity of fixed assets 0.80122 and relative elasticity of labor 0.19878.
Individual efficiency of fixed assets E_{K} = 3.623 and individual efficiency of labor E_{L} = 9.81.
Now let’s define the total efficiency index of production (This formula is calculated as the geometric mean of the individual efficiency indices on fixed assets and labor):
(35) 
Now let’s focus on the size of production (This formula is calculated as the geometric mean of the growth rate on fixed assets and labor):
(36) 
Thus, the growth in Aran region by 8.355 times between 2005–2015 was the reason of the increase of the industrial efficiency by 4.415 times and its volume by 1.890 times.
Fig. 10. Agricultural production of Aran region. Source: author’s own compilation, calculations 
For Yuxari Karabakh (literally means Upper Karabakh), the production function of the CobbDouglas model provided α + β = 1 has been chosen in order to reflect the dependence of industrial production on fixed assets and labor.
Dependent variable: Ln(Y/L) 
const 
<0.0001 
***


Ln(K/L) 
0.0017

***


Rsquare 
0.774767  Corr. Rsquare 
0.742590  
Parameter rho 
0.335586  Stat. DurbinWatson 
2.641094 
We get d_{l} = 0.927 and d_{u} = 1.324 on DurbinWatson significance table. Then 4 – 1.324 = 2.676. So, it satisfies with d_{u} < DW < 4 – d_{u} (1.324 < 2.641 < 2.676). It means hypothesis about the absence of autocorrelation of the rest in 0.05 significance level is refused. It shows the high quality of this model.
It was determined that industrial production has increased 4.858 times, basic production assets 6.135 times, and the number of employees 1.352 times based on the analysis of industrial production in UpperKarabakh region during 2005–2015. The dependence of industrial production on fixed assets and labor for UpperKarabakh region is expressed by the following multiplicative production function:
(37) 
Let’s appraise the influence of efficiency and size of production on industrial manufacturing:
Relative elasticity of fixed assets 0.758339 and relative elasticity of labor 0.241661.
Individual efficiency of fixed assets E_{K} = 0.791 and individual efficiency of labor E_{L} = 3.593.
Now let’s define the total efficiency index of production (This formula is calculated as the geometric mean of the individual efficiency indices on fixed assets and labor):
(38) 
Now let’s focus on the size of production (This formula is calculated as the geometric mean of the growth rate on fixed assets and labor):
(39) 
Thus, the growth in UpperKarabakh region by 4.858 times between 2005–2015 was the reason of the increase of the industrial efficiency by 1.139 times and its volume by 4.253 times.
Fig. 11. Industrial production of UpperKarabakh region. Source: author’s own compilation, calculations 
We choose the linear model for agriculture.
Dependent variable: Y 
const 
0.0386

**


L 
0.1522


K 
0.2473


Rsquare  0.334189  Corr. Rsquare  0.112252  
Parameter rho  0.187023  Stat. DurbinWatson  1.595281 
(40) 
We get d_{l} = 0.927 and d_{u} = 1.324 on DurbinWatson significance table. Then 4 – 1.324 = 2.676. So, it satisfies with d_{u} < DW < 4 – d_{u} (1.324 < 1.595 < 2.676). It means hypothesis about the absence of autocorrelation of the rest in 0.05 significance level is refused. It shows the high quality of this model.
Fig. 12. Agricultural production of UpperKarabakh region. Source: author’s own compilation, calculations 
For Dagliq Shirvan (literally means Mountainous Shirvan), the linear function has been chosen in order to reflect the dependence of industrial production on fixed assets and labor.
Dependent variable: Y 
const 
0.4865


L 
0.0235

**


K 
0.1967


Rsquare  0.618605  Corr. Rsquare  0.491473  
Parameter rho  0.132056  Stat. DurbinWatson  1.612718 
(41) 
We get d_{l} = 0.927 and d_{u} = 1.324 on DurbinWatson significance table. Then 4 – 1.324 = 2.676. So, it satisfies with d_{u} < DW < 4 – d_{u} (1.324 < 1.613 < 2.676). It means hypothesis about the absence of autocorrelation of the rest in 0.05 significance level is refused. It shows the high quality of this model.
Fig. 13. Industrial production of Mountainous Shirvan region. Source: author’s own compilation, calculations 
For agriculture, the production function of the CobbDouglas model provided has been chosen in order to reflect the dependence of industrial production on fixed assets and labor.
Dependent variable: Ln(Y/L) 
const 
0.2750


Ln(K/L) 
0.0109

**


Rsquare  0.627742  Corr. Rsquare  0.574562  
Parameter rho  0.013929  Stat. DurbinWatson  1.839518 
We get d_{l} = 0.927 and d_{u} = 1.324 on DurbinWatson significance table. Then 4 – 1.324 = 2.676. So, it satisfies with d_{u} < DW < 4 – d_{u} (1.324 < 1.840 < 2.676). It means hypothesis about the absence of autocorrelation of the rest in 0.05 significance level is refused. It shows the high quality of this model.
It was determined that industrial production has increased 2.216 times, basic production assets 1.112 times, and the number of employees 1.416 times based on the analysis of industrial production in Mountainous Shirvan region during 2005–2015. The dependence of industrial production on fixed assets and labor for Mountainous Shirvan region is expressed by the following multiplicative production function:
(42) 
Let’s appraise the influence of efficiency and size of production on industrial manufacturing:
Relative elasticity of fixed assets 0.645743 and relative elasticity of labor 0.354257.
Individual efficiency of fixed assets E_{K} = 1.992 and individual efficiency of labor E_{L} = 1.564.
Now let’s define the total efficiency index of production (This formula is calculated as the geometric mean of the individual efficiency indices on fixed assets and labor):
(43) 
Now let’s focus on the size of production (This formula is calculated as the geometric mean of the growth rate on fixed assets and labor):
(44) 
Thus, the growth in Mountainous Shirvan region by 2.216 times between 2005–2015 was the reason of the increase of the industrial efficiency by 1.827 times and its volume by 1.210 times.
Fig. 14. Agricultural production of Mountainous Shirvan region. Source: author’s own compilation, calculations 
For Nakhchivan region, the production function of the CobbDouglas model provided α + β ≠ 1 has been chosen in order to reflect the dependence of industrial production on fixed assets and labor.
Dependent variable: LnY 
const 
0.0068

***


LnK 
0.7600


LnL 
0.0112

**


Rsquare  0.963289  Corr. Rsquare  0.951051  
Parameter rho  0.291922  Stat. DurbinWatson  1.346499 
We get d_{l} = 0.927 and d_{u} = 1.324 on DurbinWatson significance table. Then 4 – 1.324 = 2.676. So, it satisfies with d_{u} < DW < 4 – d_{u} (1.324 < 1.347 < 2.676). It means hypothesis about the absence of autocorrelation of the rest in 0.05 significance level is refused. It shows the high quality of this model.
It was determined that industrial production has increased 20.944 times, basic production assets 7.056 times, and the number of employees 4.009 times based on the analysis of industrial production in Nakhichevan region during 2005–2015. The dependence of industrial production on fixed assets and labor for Nakhichevan region is expressed by the following multiplicative production function:
(45) 
Let’s appraise the influence of efficiency and size of production on industrial manufacturing:
Relative elasticity of fixed assets 0.052444 and relative elasticity of labor 0.947555.
Individual efficiency of fixed assets E_{K} = 2.968 and individual efficiency of labor E_{L} = 5.224.
Now let’s define the total efficiency index of production (This formula is calculated as the geometric mean of the individual efficiency indices on fixed assets and labor):
(46) 
Now let’s focus on the size of production (This formula is calculated as the geometric mean of the growth rate on fixed assets and labor):
(47) 
Thus, the growth in Nakhichevan region by 20.944 times between 2005–2015 was the reason of the increase of the industrial efficiency by 5.067 times and its volume by 4.125 times.
Fig. 15. Industrial production of Nakhichevan region. Source: author’s own compilation, calculations 
For agriculture, the production function of the CobbDouglas model provided α + β = 1 has been chosen in order to reflect the dependence of agriculture production on fixed assets and labor.
Dependent variable: Ln(Y/L) 
const 
0.0068 
*** 

LnK 
0.7600 

LnL 
0.0112 
** 

Rsquare  0.963289  Corr. Rsquare  0.951051  
Parameter rho  0.291922  Stat. DurbinWatson  1.346499 
We get d_{l} = 0.927 and d_{u} = 1.324 on DurbinWatson significance table. Then 4 – 1.324 = 2.676. So, it doesn’t satisfy with d_{u} < DW < 4 – d_{u} (1.324 > 0.921 < 2.676) and it belongs to the uncertainity field. It means hypothesis about the absence of autocorrelation of residuals in 0.05 significance level isn’t refused. It doesn’t confirm the high quality of this model.
It was determined that industrial production has increased 8.319 times, basic production assets 29.466 times, and the number of employees 3.846 times based on the analysis of industrial production in Nakhichevan region during 2005–2015. The dependence of industrial production on fixed assets and labor for Nakhichevan region is expressed by the following multiplicative production function:
(48) 
Let’s appraise the influence of efficiency and size of production on industrial manufacturing:
Relative elasticity of fixed assets 0.443089 and relative elasticity of labor 0.556911.
Individual efficiency of fixed assets E_{K} = 0.282 and individual efficiency of labor E_{L} = 2.163.
Now let’s define the total efficiency index of production (This formula is calculated as the geometric mean of the individual efficiency indices on fixed assets and labor):
(49) 
Now let’s focus on the size of production (This formula is calculated as the geometric mean of the growth rate on fixed assets and labor):
(50) 
Thus, the growth in Nakhichevan region by 8.319 times between 2005–2015 was the reason of the increase of the industrial efficiency by 0.875 times and its volume by 9.477 times.
Fig. 16. Agricultural production of Nakhichevan region. Source: author’s own compilation, calculations 
For Lenkeran region, the production function of the CobbDouglas model provided α + β ≠ 1 has been chosen in order to reflect the dependence of industrial production on fixed assets and labor.
Dependent variable: LnY 
const 
0.9913


LnK 
0.4375


LnL 
0.0129

**


Rsquare  0.870943  Corr. Rsquare  0.827924  
Parameter rho  0.130766  Stat. DurbinWatson  2.171435 
We get d_{l} = 0.927 and d_{u} = 1.324 on DurbinWatson significance table. Then 4 – 1.324 = 2.676. So, it satisfies with d_{u} < DW < 4 – d_{u} (1.324 < 2.171 < 2.676). It means hypothesis about the absence of autocorrelation of the rest in 0.05 significance level is refused. It shows the high quality of this model.
It was determined that industrial production has increased 3.623 times, basic production assets 2.158 times, and the number of employees 1.421 times based on the analysis of industrial production in Lenkoran region during 2005–2015. The dependence of industrial production on fixed assets and labor for Lenkoran region is expressed by the following multiplicative production function:
(51) 
Let’s appraise the influence of efficiency and size of production on industrial manufacturing:
Relative elasticity of fixed assets – 0.229659 and relative elasticity of labor – 0.770340.
Individual efficiency of fixed assets E_{K} = 1.678 and individual efficiency of labor E_{L} = 2.549.
Now let’s define the total efficiency index of production (This formula is calculated as the geometric mean of the individual efficiency indices on fixed assets and labor):
(52) 
Now let’s focus on the size of production (This formula is calculated as the geometric mean of the growth rate on fixed assets and labor):
(53) 
Thus, the growth in Lenkoran region by 3.623 times between 2005–2015 was the reason of the increase of the industrial efficiency by 2.315 times and its volume by 1.562 times.
Fig. 17. Industrial production of Lenkoran region. Source: author’s own compilation, calculations 
We choose the linear model for agriculture.
Dependent variable: Y 
const 
0.0457

**


L 
0.0796

*


K 
0.7619


Rsquare  0.436535  Corr. Rsquare  0.248713  
Parameter rho  0.099098  Stat. DurbinWatson  1.242750 
(54) 
We get d_{l} = 0.927 and d_{u} = 1.324 on DurbinWatson significance table. Then 4 – 1.324 = 2.676. So, it doesn’t satisfy with d_{u} < DW < 4 – d_{u} (1.324 > 1.243 < 2.676) and it belongs to the uncertainity field. It means hypothesis about the absence of autocorrelation of residuals in 0.05 significance level isn’t refused. It doesn’t confirm the high quality of this model.
Fig. 18. Agricultural production of Lenkoran region. Source: author’s own compilation, calculations 
Notes:
 ***, **, * – level of significance, respectively, 1%, 5%, 10%;
 z statistics in brackets.
Source: own calculations using statistical program STATA
CONCLUSIONS
Although there are a number of researches and achievements for the development of economic and mathematic tools, this science encounters with some serious criticism that challenge its application. These cases were always denied and are still being denied. It brings discrepancy to compromise on adaptation of theory and practice. One of the problems is to choose mathematic model for the application of economic object. We have to understand that there is no any universal model and perhaps can’t be. Selecting this or other functional dependences are formed under the influence of the factors stipulated with the features and purposes of the concrete duty.
It is important to note that using optimization and immitation methods are possible in the further steps of the research. So, the practical results achieved during this period enable to develop comprehensive approach to the formation of the single development strategy by practising statistical modeling methods at the regional level. To our mind, the practice of some proposals in this article can serve as a practical base not only for the formation of rural development strategy, but also for the development of economic and mathematical models of rural areas and regions.
 Nondirect capital funds in production shouldn’t be registered in order to use capital funds more efficiently.
 It is necessary to improve the compliance of the employees involved in the production sphere to their occupations.
 It is necessary to approach the economic development of lowland and mountainous areas geographically.
 It is essential to improve statistical data.
 Expansion of the development policy for agriculture and rural areas (the development of strategy, programs and measures and control of them. Strategic Road Map in Azerbaijan)
 Acceleration of the institutional development;
 Application of the innovations for supporting of agricultural producers, researches and the development of respective systems for providing consultation services;
 The development and improvement of agriculture and other initiatives that might cause raising the standard of living and bring benefits to villagers in the rural regions.
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Accepted for print: 24.10.2017
Sugra İ. Humbatova
Price and Apprecation Department, Azerbaijan State University of Economics (UNEC), Baku, Azerbaijan
AZ1001
Baku
Azerbaijan
email: s.qunbatova2012@yandex.com
Natig GO. Hajiyev
Regulation of Economy Department, Azerbaijan State University of Economics (UNEC), Baku, Azerbaijan
AZ1001
Baku
Azerbaijan
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