Modeling the interrelation between formation factors of labor demand and its supply

There is a persisting problem of an imbalance of the demand for labor and its supply in the Russian economy: it is manifested in quantitative and qualitative imbalances on the labor market [1; 2]. On the one hand, there are unclaimed workers with certain qualifications and knowledge on the labor market; on the other hand, there is a shortage of workers in specific professions and specialties. It limits the growth of labor productivity and, ultimately, hinders economic development [3]. Since 2007, the share of the working-age population has been declining annually, and it had fallen from 63.0% to 55.9% by 2019. Even considering increased retirement age, according to the Rosstat forecast1, it will not exceed the level of 2007 (60.1– 62.5%, depending on the forecast version) by 2035. Population’s ageing in the future will exacerbate the unbalance problem on the Russian labor market [4; 5]. According to A.G. Korovkin [2], there might be a shortage of labor even at low rates of economic growth, when the aggregate demand for labor stagnates.

The lack of balance between the demand for labor and its supply leads to big economic losses, so it is important to look for new and improve existing tools to realize the potential of using the main

1 Estimated Population of the Russian Federation until 2035: Stat. Bull. Moscow, Rosstat, 2020. Available at: (accessed: December production factor – labor. It is believed that implementation of active longevity strategy is an efficient tool for solving current and future problems associated with population’s aging [6; 7]. According to studies [8], a certain share of older age cohorts retains their resource potential in Russia – health, a high level of education, and significant intelligence. Moreover, the labor activity of pensioners is not a new phenomenon for Russia. However, many experts are concerned that older workers may face problems when looking for a new job and maintaining their current workplace [9]. The analysis of age discrimination [10] showed that the chances of employment for a person at the age of 29 are 1.8–2.5 times higher than at the age of 48. Accordingly, the change of working capacity limits in Russia poses new challenges for the labor market, related to this labor force and its need on the labor market [11]. The study of the interaction of factors of the demand formation for labor and its supply will allow us to assess possible further trends on the labor market, which is especially important when the ageing of population becomes a significant constraint in the formation of employment.

Approach

Due to a weak, for objective reasons, statistical security of the studied issue at the macroeconomic level [12], researchers face the problem of assessing and formalizing the concepts of labor demand and supply. As a rule, a number of employees and vacancies are used for the analysis of labor demand, and size of the labor force and a number of unemployed – for the supply of labor. Discrepancy between labor demand and labor supply is estimated by comparing the values of these indicators [13; 14; 15]. This approach is included in A. G. Korovkin’s model of coordinating labor demand and its supply [16]. This model describes the interaction between a number of potential employees (difference between working-age population and those employed in the economy) and vacant jobs. It takes into account demographic processes, factor of movement of employees and jobs. Such approaches are widely used in assessing the balance of labor supply and demand, but they have a disadvantage associated with the statistical accounting methodology. Thus, shortcomings of the use of capital and labor, inefficiency of the labor market functioning lead to a deviation of the real employment indicator from the demand for labor2. In addition, depending on the data source, there may be quite serious discrepancies in the estimate of a number of employees [15]. The declared need for employees in the form of vacancies, as V. E. Gimpelson notes [17], is far from being identical with the efficient demand for labor and the creation of jobs. Considering the aforementioned, we propose an original solution to the formalization of the concepts of labor demand and supply. The demand for labor and its supply are described using two sets (vectors) of indicators – factors of demand and supply formation on the labor market.

In the scientific literature, the question of a set of factors that form the demand for labor and its supply is not debatable. The textbooks3 highlight such macroeconomic factors of labor demand as the level of economic development, investment activity, state of production factors, and the unemployment level. The supply, according to the theory of labor economics, reflects the willingness of workers to sell their labor for a certain reward, so it depends on the availability of labor and the level of its education and qualifications4 [18]. In various scientific studies, this list of supply and demand factors is similar, but, depending on the scientific goals, it is supplemented considering the specifics or features of the labor market segment. Thus, for a complete and adequate assessment of the employment dynamics and the labor market, presented by scientists from the Institute of Economic Forecasting of RAS and the Moscow School of Economics at the Lomonosov Moscow State University5, a total demand of the economy for labor is determined by the volume of production and investment, and a total supply – by demographic trends and the labor potential quality. In the analysis of the relationship between supply and demand on the labor market considering the gender structure of the labor force, I. B. Korolev [19] additionally identified such factors as the size of the public sector and the service sector. In studying the process of coordinating supply and demand taking into account educational features of the labor force [20], a set of factors that affect demand was significantly expanded (the level of technologies used, parameters of state policy in the field of education, availability of education, etc.; Fig. 1).

During a decline in working-age population, the problem of determining alternative sources of labor resources, as well as opportunities to make up for numerical labor losses, is important [21]. Therefore, for the purpose of our study, labor migration, informal employment, and labor activity of elderly population are also considered labor supply factors. These factors characterize a satisfied need (demand) for labor; each of these employment types

• Figure 1.    Factors of the formation of demand for labor and its supply

  
  
  

Source: own compilation.

occupies a specific segment, a “niche” on the labor market [22–26]. At the same time, they ensure replenishment of the deficit and the balance on the labor market, which characterizes the potential supply of labor. The inclusion of these factors in the model will allow assessing their impact on the balance between labor demand and its supply.

Research data

The statistical basis of the study is Rosstat data for 2006–2018 for the regions of Russia, including the results of sample surveys of the labor force. The corresponding indicators are selected for the chosen factors of the formation of labor demand and its supply (Tab. 1) .

Table 1. Indicators of supply and demand factors on the labor market

Indicator designation	Indicator, measurement unit
Indicators of demand factors
X 1	Degree of depreciation of fixed assets for the full range of organizations, %
X 2	Indices of the physical volume of investments in fixed capital, in comparable prices, as a percentage of the previous year
X 3	Unemployment rate of population aged 15–72 years, %
X 4	Labor productivity index, as a percentage of the previous year
X 5	Index of the physical volume of the gross regional product, in constant prices, as a percentage of the previous year
X 6	Labor market tension coefficient, units
Indicators of supply factors
Y 1	Employed in the informal sector, as a percentage of a total employed population*
Y 2	Labor force participation rate of population aged 15–72, %**
Y 3	Population with higher and secondary vocational education, as a percentage of the workforce**
Y 4	Number of employed people entering work, as a percentage of a number of employed people in a corresponding region
Y 5	Employment of population aged 60–72 years, %
* The indicator partially describes informal employment. ** Considering changes in the terminology of statistical accounting of Rosstat. Source: own compilation.

The model does not include regions that do not have statistical data on the selected indicators, as well as regions with indicator values that deviate more than twice from the average value for a year. As a result, a sample of 68 entities of the Russian Federation was obtained.

Model

The employment level of population aged 60– 72 years is one of the indicators of supply factors on the labor market. However, the labor market is a relationship between two sets (vectors) of indicators – supply and demand. There is no output variable here, so it is difficult to use regression analysis. In this case, one of the tools can be the coefficient of closeness of interdependence between random vectors, earlier introduced in the study [27]. For a particular case, when vectors X = ( X ₁,..., X m ) and Y = (Y 1 , ..., Y l) have joint normal distributions, the coefficient of closeness of the interdependence between random vectors X and Y is determined by the formula:

D e ( X , Y ) = 1 -

R X ∪ Y

R X ⋅ R Y

where: |R X| , |R Y| , |R_{X uY}| are determinants of correlation matrices of random vectors X, Y, Z = X и Y = ( X ! ,..., X m , Y 1 ,..., Y l ) , 0 <  D e ( X , Y ) <  1 .

The higher the coefficient value D_e(X, Y) , tighter the relationship between the random vectors X and Y is. Value D_e(X, Y) = 1 indicates the presence of a linear functional relationship between, at least, two components of the vectors X and Y. If D_e (X, У) = 0 , then random vectors X and Y are linearly independent.

In this case, we have vectors of indicators of demand X = ( X 1 ,..., X ₆) and supply Y = ( Y 1 , ..., Y ₅) factors. The analysis showed that they can be described by multidimensional normal distribution laws.

Along with (1), we also introduce an estimate of the contribution to the joint relationship of individual components of X and Y vectors:

A D e ( X \ X, , Y ) = D e ( X , Y ) - D e ( X \ X„ Y ), i = 1,2,..., 6, A D e ( X , Y \ Y j ) = D e ( X , Y ) - D e ( X , Y \ Y ), j = 1,2,...,5.

Results and discussion

Figure 2 shows the dynamics of the interdependence closenesscoefficient between the indicators of supply and demand factors on the labor market for 2006–2018. Since the need for labor varies significantly over time [1; 28], it is expected that the values of the interdependence closenesscoefficient between the indicators of labor demand and supply factors changed significantly during the studied period with the financial and economic crisis, economic downturn, sanctions against Russia, and countersanctions.

Thus, closeness of the interconnection significantly decreased in 2010, when a negative balance of the movement of jobs was formed after the implementation of several anti-crisis measures – organization of public works and the creation of temporary jobs (in 2009–2010, the economy lost 2.4 million jobs). On the one hand, these crisis measures stabilized the situation on the labor market. On the other hand, in the post-crisis period, they did not contribute to improving the efficiency of employment and economic development.

Since 2014, there has been a trend of establishing a balance on the labor market. O. I. Izryadnova explains such a reaction in difficult macroeconomic condition by the policy of retaining qualified personnel in the conditions of a real reduction in the labor cost, expectations of increased economic activity, and a shortage of labor supply due to demographic factors and the outflow of migrants [29].

The key feature of the Russian labor market is this adaptation to fluctuations of the economic environment that occurs due to changes of the labor price, rather than the level of employment and unemployment [30]. The labor market adapts not by freeing up the labor force, but by expanding the practices of labor relations. In most cases,

• Figure 2.    Dynamics of the interdependence closeness coefficient between indicators of supply and demand factors on the labor market, 2006–2018

0.8 0.7 0.7 0.6 0.6 0.5 0.5 0.4

2006        2008        2010        2012        2014        2016        2018

Source: own compilation.

while choosing between laying off employees and instability, a number of part-time workers increases transferring them to part-time work, employers [31]. According to Rosstat, in 2012–2018, the share selected the latter, and it allowed them to keep of such employees increased from 5.2 to 11.0% unemployment at the same level. During economic (Tab. 2) , and it continues to grow. The highest

Table 2. Change in the number of employees of organizations engaged in parttime work, by type of economic activity, in % to a list number of employees

2012     2014      2016	2018
Total                                                                                          5.2        9.9        10.7	11.0
Agriculture, hunting, and forestry                                                             3.7a        7.3         8.1	9.8b
Mining operations                                                                        2.3        6.9        8.3	8.8
Manufacturing industries                                                                 8.9       21.3       22.0	21.2
Production and distribution of electricity, gas, and water                                      2.0        6.1         7.0	7.2c
Construction                                                                                  5.6        15.4        18.1	17.6
Wholesale and retail trade; repair of motor vehicles, motorcycles, household goods, and 2.8        7.2         8.5 personal items	9.9d
Hotels and restaurants                                                                   n/d       21.6        26	29.8e
Transport and communications                                                        3.2       11.3       12.6	10.1f
Financial activities                                                                                   1.9         6.1          7.1	8.8g
Real estate transactions, rent, and provision of services                                       n/d        10.8        11.8	9.8h
Education                                                                                n/d        6.7        6.8	7.6
Healthcare and social services work                                                       n/d        6.3        7.0	8.1
Provision of other public, social, and personal services                                        n/d        8.7         9.7	12.0i

End of Table 2