Modeling labor markets. Mathematical modeling and forecasting of the organized labor market of the region Relevance of the research topic

25.11.2023

As a manuscript

GOLYATIN ANDREY OLEGOVICH

MATHEMATICAL MODELING AND FORECASTING OF THE ORGANIZED LABOR MARKET OF THE REGION

Speciality

08.00.13 – Mathematical and instrumental methods of economics

dissertation for the degree of candidate of economic sciences

Ivanovo 2007

The work was carried out at the State Educational Institution of Higher Professional Education "Ivanovo State Chemical-Technological University"

Scientific adviser: Doctor of Economic Sciences

Ermolaev Mikhail Borisovich

Official opponents: Doctor of Economic Sciences, Professor

Karyakin Alexander Mikhailovich

Candidate of Economic Sciences, Associate Professor

Kanakina Galina Vitalievna

Lead organization: State Educational Institution of Higher Professional Education "Perm"

State University"

The defense will take place on February 9, 2008 at 11.00 at a meeting of the dissertation council D 212.063.04 at the State Educational Institution of Higher Professional Education “Ivanovo State Chemical-Technological University” at the address: 153000 Ivanovo, F. Engels Ave., 7, main building , audience G 101.

The dissertation can be found in the library of the State Educational Institution of Higher Professional Education "Ivanovo State University of Chemical Technology"

Scientific Secretary

dissertation council S.E. Dubova

GENERAL DESCRIPTION OF WORK

RELEVANCE OF THE RESEARCH TOPIC

The problems of the functioning of the labor market have received considerable attention, both in world and domestic economic science. This is due to the special significance of the processes occurring in this market for the effective functioning of the economy as a whole, as well as the presence of a large number of specific features that are unique to the labor market and thereby distinguish it from other markets.

The labor market occupies a central place in a market economy, since labor is a decisive factor of production, in its own way a non-alternative resource. Labor relations are basic, fundamental in the system of economic relations of society.

The Russian labor market has experienced numerous shocks that accompanied the process of systemic transformation of the country's economy. At the moment, it is represented by a set of fairly isolated regional markets, which explains the growing interest in studying the latter.

The basic concepts when describing the functioning mechanism of any market are supply and demand. In the labor market, which is a very specific market, supply is formed by workers (sellers), and employers (buyers) act as demand providers. Consideration of the joint dynamics of labor demand and supply is undoubtedly relevant both theoretically and practically.

The most important task of economic science is the analysis and forecasting of socio-economic processes for targeted influence on them. Modern science has a wide arsenal of relevant tools, among which a special place is occupied by economic and mathematical modeling, which is relatively free from subjective ideas and biases. It is economic and mathematical methods and models that are designed to help understand the current situation in the labor market and select adequate tools for its regulation.

An analysis of the scientific literature shows that most labor market research is qualitative in nature, and the use of quantitative methods is aimed at solving individual particular problems. In this case, it seems necessary to use the principle of consistency when developing economic and mathematical models of the labor market.

In this regard, the construction of a complex of economic and mathematical models for analyzing and forecasting the demand and supply of labor for the purpose of managing the process of socio-economic development of the region is undoubtedly an urgent task.

DEGREE OF DEVELOPMENT OF THE PROBLEM

Mathematical modeling of the labor market as a socio-economic system naturally relies on a fairly extensive and deeply developed apparatus of economic and mathematical methods and models. Of particular importance for the purposes of this study are works on statistical modeling and forecasting of economic processes - the works of S.A. Ayvazyan, T. Anderson, J. Box, G. Jenkins, M. Kendal, Y.R. Magnus, V.S. Mkhitaryan, G. Teyla and others.

An analysis of works devoted to the actual problems of the labor market in general and its modeling in particular allows us to identify two major areas of research.

The first direction includes research developing the general provisions of the economic theory of labor, namely the organization, functioning and results of the relevant markets. Along with the fundamental works of recognized authorities of economic science - A. Smith, K. Marx, A. Marshall, J. M. Keynes, etc., whose merits extend far beyond the boundaries of labor theory, this area includes the works of labor relations theorists themselves - G Becker, R. Ehrenberg, R. Smith, R.K. Filera, D.S. Khameriesha, A.E. Rees, L. Robbins, R. Gronau, etc. Among the Russian authors who deeply develop the theoretical aspects of the functioning of the labor market, we can highlight V.S. Bulanova, N.A. Volgin, I. Zaslavsky, A. Kotlyar, R.I. Kapelyushnikova, K.G. Kyazimov, A. Nikiforov, Y. Odegov, V.A. Pavlenkova, G.E. Slesinger and others. The concepts of the functioning of the labor market of the authors listed above, in fact, represent the most general models that reflect the main approaches to the study of labor processes.

The second direction is empirical research and the actual economic and mathematical modeling of labor markets. Here we should highlight the works of S. Commander, R. Layard, C. Olivetti, B. Petrongolou, A. Richter, V.E. Gimpelson, R.B. Freeman, M.E. Shafer, J. Earl, etc.

Research by A.V. is also devoted to modeling processes occurring in the labor market. Andryunina, V. Bragina, A.G. Korovkina, T.D. Lapina, L. Nivorozhkina, V. Osakovsky K.V. Parbuzina A.V. Polezhaeva, K.N. Sabiryanova, L.S. Chizhova and others.

For the most part, this is statistical modeling and forecasting based on classical correlation-regression or cluster analysis.

The studies of these scientists developed a wide range of theoretical and practical aspects of modeling labor market processes. However, regional features in relation to modeling the organized labor market have not yet been sufficiently studied.

THE PURPOSE AND OBJECTIVES OF DISSERTATION RESEARCH

The purpose of the dissertation research is the development of a complex of economic and mathematical models for analyzing and forecasting the demand and supply of labor in the organized regional labor market.

In accordance with the purpose of the dissertation, the following are set and resolved: tasks:

research into the theoretical foundations of the functioning of the labor market, as well as the specific features of the formation and development of the Russian labor market, in particular at the regional level;
analysis and generalization of existing methods of economic and mathematical modeling of the labor market, including indicators of labor demand and supply;
development of a set of models for analyzing and forecasting demand and supply of labor in the organized regional labor market;
econometric analysis of the dynamics of regional registered unemployment and the number of vacant jobs reported to the employment service;
building a model for the functioning of the employment service as a queuing system.

THEORETICAL AND METHODOLOGICAL BASIS The research included the works of foreign and domestic economists and mathematicians on modeling and forecasting socio-economic systems using correlation and regression analysis, time series analysis, the theory of random processes and elements of mathematical statistics; works on the problems of the labor market and modeling of its individual components; legislative and regulatory acts on the regulation of employment in the Russian Federation, documents of the International Labor Organization (ILO).

INFORMATION BASE The research was based on statistical data from the Federal Employment Service, Rosstat of the Russian Federation for the Ivanovo Region, Rodnikovsky District Employment Center, periodical press materials and data from socio-economic studies of the labor market from the regional Employment Center.

SUBJECT OF THE STUDY is an economic and mathematical modeling of labor supply and demand in the organized labor market at the regional level.

OBJECT OF STUDY represented by the regional labor market (using the example of the Ivanovo region).

The dissertation work was completed in accordance with clause 1.9. – “Development and development of mathematical methods and models for analysis and forecasting of socio-economic processes of public life: demographic processes, labor market and employment, quality of life of the population, etc.” Specialty certificates 08.00.13 – mathematical and instrumental methods of economics.

SCIENTIFIC NOVELTY OF THE DISSERTATION RESEARCH, revealing the achievement of the goal, is as follows:

a system of economic and mathematical models for analyzing and forecasting demand and supply of labor in the organized regional labor market has been proposed;
a theoretical model of the dynamics of labor demand and supply was developed based on a system of nonlinear differential equations;
for the stages of development of the organized regional labor market identified by the author, econometric models of time series of registered unemployed people and vacant jobs reported to the employment service were constructed, taking into account both the trend-seasonal nature of the dynamics and the presence of autocorrelation in random residuals;
Based on the theory of queuing systems, an approach to modeling the functioning of the employment service, which is the main intermediary institution of the organized labor market, was developed and tested on the basis of empirical data.

THEORETICAL AND PRACTICAL SIGNIFICANCE

The complex of economic and mathematical models proposed in the work can be used by regional employment services, as well as government bodies at various levels to assess current and future changes in the demand and supply of labor in the regional labor market, as well as in areas related to it in order to develop a strategy for social - economic development of the region for the future.

Some research results can be used in the development of educational and methodological literature in the disciplines “Methods and models in economics”, “Statistical methods of forecasting”, “Econometrics”.

APPROBATION OF RESEARCH RESULTS

The results of individual stages of the dissertation research are reflected in publications in various scientific collections and journals, and were presented at the VII All-Russian Symposium on Applied and Industrial Mathematics, as well as regional scientific and practical conferences.

PUBLICATIONS

The main results of the dissertation research were reflected in 7 publications with a total volume of 3.65 conventional units. oven sheet, including the contribution of the applicant - 3.40 conventional units. oven leaf.

STRUCTURE OF THE DISSERTATION

The dissertation consists of an introduction, four chapters, a conclusion, a bibliographic list of references from 182 sources, and appendices. The main content of the scientific research is presented on 138 pages of typewritten text. The work is illustrated with 38 drawings, contains 2 tables, 44 formulas.

MAIN CONTENT OF THE WORK

In the introduction the relevance of the chosen topic of the dissertation research, the degree of scientific development of the problem are substantiated, the purpose and objectives of the work are determined, the subject and object of the research are revealed, the scientific novelty is noted, as well as the theoretical significance and testing of the results.

In the first chapter“THEORETICAL FOUNDATIONS OF ORGANIZATION AND FUNCTIONING OF THE LABOR MARKET” an analysis of the main approaches to defining the concept of “labor market” was carried out; the basic concepts of the functioning of this market are considered; the existing methods for determining the number of unemployed and vacant jobs as the main indicators of supply and demand in the current labor market are analyzed, and an assessment is given of the state and development of the labor market in the Ivanovo region for the period 1992-2006.

To date, there has not been a single definition of the concept of “labor market” in Russian economic science. A number of works have formed a view of the labor market as a system of socio-economic relations between subjects of the labor market regarding the entire complex of labor relations. At the same time, a number of authors focus their attention on certain aspects of the functioning of the social and labor sphere, which makes a certain contribution to clarifying the essence of the labor market.

Other definitions are also common. Some of them are based on an analysis of the components that make up the labor market, and define it as the total demand and supply of labor; in a number of works, the labor market is defined as a mechanism of interaction between labor market subjects operating within a certain economic space.

As a result of comparing the views and positions existing in the economic literature regarding the essence of the labor market, the following definition can be given: the labor market is a system of relations and a socio-economic mechanism for interaction between employers, employees and social partners regarding the formation, distribution and use of labor in conditions of its marketability.

The organized labor market in the scientific literature is understood as a labor market characterized by structuring and institutionalization. The concept revealed in this way can be designated as an organized labor market in a broad sense.

From the point of view of the process of interaction between the demand and supply of labor, the organized labor market can be defined more narrowly. The organization of the market, and more specifically the process of meeting sellers and buyers of any product, is given by the presence of certain institutions that mediate the conclusion of a transaction. Those. A necessary sign of organization is the presence of a specialized intermediary institution. For the labor market, such intermediaries in the meeting between supply and demand are the state employment service and non-state employment services (recruitment agencies).

Rice. 1. Intermediary institutions of the organized labor market.

Thus, the organized labor market in the narrow sense is a system of socio-economic relations between the providers of demand and supply of labor, the mechanism of interaction of which is mediated by specialized institutions.

The most important indicators of the labor market, like any other market, are the quantities of supply and demand, and the study of their interaction is the most interesting and relevant both theoretical and practical task. The main quantitative indicators of supply and demand in the current labor market are the number of unemployed and vacant jobs in the economic system under consideration.

In Russian statistics, as well as throughout the world, two methods of measuring unemployment are used. The first is based on registrations of the unemployed in the State Employment Service (SES), the second is based on the results of regular labor force surveys, in which the status of the unemployed is determined based on ILO criteria. Information about available jobs also comes primarily from two sources. The first is the statistical reporting of large and medium-sized enterprises and organizations, accumulated in Rosstat of the Russian Federation, the second is the accounting data of the State Service of the Russian Federation.

The dissertation research explores the advantages and disadvantages of each method, and also highlights the specifics of the SPSS data and justifies their use to study the coordination of labor supply and demand in the organized regional labor market.

In the second chapter“ECONOMIC-MATHEMATICAL MODELING AS A TOOL FOR STUDYING LABOR MARKET PROCESSES” the basic concepts of economic and mathematical modeling as the main method of studying complex systems are considered; an overview of the application of economic and mathematical modeling methods to the study of labor market processes is given; an approach to modeling the interaction of demand and supply of labor in an organized regional labor market based on a set of models was formulated, a model of the dynamics of demand and supply of labor was developed based on a system of nonlinear differential equations.

The labor market belongs to the class of complex probabilistic dynamic systems. The main method for studying such systems is the modeling method, i.e. a method of theoretical and practical action aimed at developing and using models.

The labor market as an object of economic and mathematical modeling is quite complex and diverse. The range of specific problems in the field of labor market research is very wide. Accordingly, the formulation of tasks and the specification of labor market processes that are objects of modeling determine the specifics of the methods used in the study.

In the case of studying patterns and relationships based on statistical data related to labor market processes and allowing to describe phenomena in this area from a quantitative side, econometric methods are used, primarily models and methods of regression analysis and time series analysis.

When setting optimization problems, when it is necessary to select the optimal one from the possible solution options in terms of the selected optimality criteria, various mathematical programming methods are used: linear, nonlinear, dynamic, stochastic, integer, etc.

A special place in the study of the labor market is occupied by balance models, both static and dynamic. They are used to model the inter-industry balance of labor costs, when studying the movement of population and labor resources, etc.

When solving a number of problems within the framework of the labor market, methods and models of queuing theory and game theory are used. The modeling of intersectoral and interregional labor migration is based on stochastic models based on Markov processes.

The direct object of the study is the interaction of labor supply and demand in the organized regional labor market.

For the purpose of analyzing and forecasting the dynamics of labor supply and demand, the work proposes a set of models presented in Fig. 2.

Rice. 2. Complex of analysis and forecasting models

labor supply and demand

The structure of the proposed complex is based on the following considerations:

1) A theoretical model based on a system of nonlinear differential equations (DE) in its most general form reflects the essence of the process of interaction between supply and demand at various stages of development of the regional labor market.

2) A set of time series models of the main indicators of demand and supply of labor in the organized labor market represents the primary level of processing and analysis of empirical data, without affecting the actual functioning mechanism of the relevant institutions.

3) Finally, the generalized model of the employment service (SE) as a queuing system (QS) and its simulation explores the internal side of the interaction between the providers of labor demand and supply and quite adequately reflects this process.

Testing of models within the framework of the formulated complex was carried out using data from the State Social Security Service as the main intermediary institution in the labor market. At the same time, the proposed set of models has signs of universality, i.e. the developed models can also be used to model processes occurring in the non-state segment of the organized labor market (in the work of recruitment agencies).

The last paragraph of the chapter is devoted to the development of a deterministic model of the dynamics of labor demand and supply in the form of a system of nonlinear control systems:

(1)

where is the number of potential workers (unemployed in accordance with the ILO methodology), is the number of vacant jobs (unfilled vacancies), is the number of economically active population.

An approach to modeling the coordination of labor supply and demand using the apparatus of differential equations was developed in the works of A.G. Korovkin. and his students and tested on empirical data from the labor markets of Russia and Moscow.

It seems that the model developed in the study based on the system of equations (1) is devoid of the identified shortcomings and more adequately describes the dynamics of demand and supply of labor in the labor market.

The main factors influencing changes in labor demand and supply are the following: demographic, investment and interaction factors. In the system of equations (1), the influence of these factors is described by the following components:

1) Demographic component of the increase in potential employees.

2) Investment components: – increase in the number of potential employees due to a reduction in existing vacancies, – change in the number of vacancies in the economic system, determined by the dynamics of capital (closing existing and creating new jobs).

3) Components of interaction: – occupation of existing vacant jobs by potential employees, – dismissal of an employee (his transfer to the category of potential with the simultaneous release of a vacancy).

The work formulates the conditions for the existence of stationary states of system (1).

Accordingly, the relationship between the signs and values of the model parameters will determine the current state of the labor market conditions and make it possible to predict the development of the market in question for the future.

The proposed model based on a system of nonlinear control systems is applicable both for the general labor market and for the organized market. In the latter case, the model can be modified by introducing into it an additional coefficient for the parameter, characterizing the ratio of registered and total unemployment in the labor market conditions of a particular region.

Thus, the developed model of the dynamics of labor supply and demand based on a system of nonlinear differential equations can serve as an adequate tool for a qualitative general theoretical understanding of the labor market processes occurring in the economic system under consideration.

In the third chapter“ECONOMETRIC STUDY OF THE DYNAMICS OF LABOR SUPPLY AND DEMAND IN THE LABOR MARKET OF THE IVANOV REGION” examines the basic concepts of econometric modeling of time series with a description of the general scheme for constructing a time series model; Based on empirical data, adequate models of time series of the number of unemployed and vacancies declared in the labor market for the labor market of the Ivanovo region were found for the time interval 1992-2006.

An analysis of the dynamics of the number of registered unemployed and vacancies announced in the labor market made it possible to identify three qualitatively different stages in the formation and development of the labor market in the Ivanovo region. The joint dynamics of the numbers of unemployed and vacancies is presented in Fig. 3.

Stage 1(January 1992 – April 1996 – for the dynamics of the unemployed, January 1992 – December 1996 – for the dynamics of vacancies). "Spontaneous labor market." The regional labor market responded to the beginning of economic transformations and the introduction of market economic methods with a sharp increase in registered unemployment.

The increase in the number of unemployed was accompanied by a significant reduction in the number of vacant jobs reported in the SZ. Tension in the registered regional labor market has reached critical proportions. Thus, in April 1996, 190 unemployed people applied for one vacancy.

Rice. 3. Dynamics of the number of registered unemployed and vacancies declared in the labor protection sector in the Ivanovo region for the period 1992-2006.

The dynamics of the number of registered unemployed at this stage is described by a statistically significant linear trend with the coefficient of determination R2=0.993.

For the number of registered unemployed at this stage, the additive nature of the seasonal component was revealed. The behavior of the seasonal wave is such that it increases until April, and then gradually decreases with a slight increase towards December (Fig. 4).

Rice. 4. Seasonal wave in the number of registered unemployed

To model a number of residuals, 1st and 2nd order autoregressive models (AR(1) and AR(2)) were applied. The choice was made in favor of a 2nd order autoregressive model based on the criterion of minimum average approximation error.

The dynamics of vacancies at this stage is described by a downward exponential trend with the coefficient of determination R2=0.578. The seasonal component for a number of vacancies is multiplicative in nature. The seasonal wave for the number of declared vacancies at the first stage is presented in Fig. 5. The peak supply of vacant jobs occurs in the summer-autumn period, which is caused by both the increased demand for labor in the warm season and the reaction to the pendulum migration of labor resources.

Rice. 5. Seasonal wave in the number of vacancies announced in the health center

For a number of vacancies, autocorrelation in the residuals was also discovered; the AR(1) model was used to simulate the stationary series.

Stage 2(May 1996 – December 2000 – for the dynamics of the unemployed, January 1997 – December 2001 – for the dynamics of vacancies). "Self-regulating labor market." For the number of unemployed people, since mid-1996 there has been a change in the main trend - a sharp decrease in registered unemployment.

The trend for the number of unemployed at this stage is best described by a second-degree polynomial with R2=0.973. The identified seasonal component in terms of the nature of intra-annual fluctuations was similar to that described above and differed only in greater intensity. Autoregressive models of the 1st and 2nd orders were used to model a number of residuals. The choice was made in favor of AR(2): .

The time series of the number of vacancies at this stage is characterized by an exponential trend with R2=0.827. The seasonal component has similar intensity and character to the previous stage. For this series, autocorrelation in the residuals was also discovered; the AR(1) model was used to model the stationary series.

Stage 3(for the dynamics of the unemployed - from January 2001, for the dynamics of vacancies from January 2002 to the present). "Stable labor market." This stage can be characterized as the functioning of a kind of “civilized” labor market. The processes taking place there at the moment can be described as being determined to a greater extent by market factors.

Tension in the regional labor market is characterized by a “reasonable” (ranging from 1 to 3) number of unemployed people applying for one vacant job, i.e. Unlike previous stages, the numbers of unemployed and vacancies become comparable.

During 2001-2005. the number of registered unemployed tended to increase. The regular component is described by a linear trend with R2=0.735. Positive autocorrelation was found in the residuals obtained as a result of the trend-seasonal decomposition of the time series. To eliminate it, the AR(1) model was applied.

Since 2006, the dynamics of the registered unemployed has been described by a downward linear trend with R2=0.478. Due to the lack of qualitative prerequisites for changing the nature of seasonality, we used the seasonality indices of the previous stage for calculation. Both a priori and a posteriori (forecast for the 4th quarter of 2006) quality of the trend-seasonal model can be considered very good (average error of approximation less than 5%).

Dynamics of vacancies in 2002-2004 is described by a weak linear downward trend with pronounced seasonal fluctuations. Since 2005, the number of vacancies announced in SZ begins to increase. The time series at this stage is successfully described (with an average approximation error of less than 10%) by a trend-seasonal autoregressive model.

At the moment, the processes taking place in the labor market are, to a greater extent, than during the 1990s, subject to economic laws. The organized regional market responded with a certain lag, but predictably, to the increase in the number of vacancies since 2005 with a decrease in the number of registered unemployed.

The constructed econometric models of time series of the main indicators of the organized regional labor market adequately describe the dynamics of the processes occurring on it and can serve as an effective tool for short-term forecasting.

In the fourth chapter“MODELING OF EMPLOYMENT SERVICES BASED ON THE THEORY OF QUEUE SYSTEMS” the tasks and specifics of the functioning of the state employment service are considered; features that characterize the operation of the SZ as a queuing system have been identified; the basic concepts of queuing theory and QS simulation modeling are considered; The results of testing the approach to modeling the SZ as a non-classical QS are presented.

The employment service is the main institution that mediates the meeting of sellers and buyers of labor in the organized regional labor market. The main purpose of its functioning is to assist citizens in finding suitable work, and employers in selecting the necessary workers, i.e. SZ is a system that implements repeated execution of similar tasks. Some citizens who apply to SZ find employment for a certain period of time. It is quite obvious that, for a number of reasons, SZ cannot employ all the citizens who apply to it. Accordingly, some people leave SZ unemployed.

Thus, the activities of the employment service can be represented as a model of a queuing system. All the necessary attributes of a QS are available here:

incoming flow of demands (citizens contacting the employment service regarding employment issues);
a specific service structure that provides a variety of assistance in employment;
two outgoing streams of serviced claims (employed citizens and citizens who left the system unemployed).

The requirement flows of the above system can be represented as the following diagram.

Rice. 6. Flows of requirements passing through the SZ.

The same system attributes are present in the work of any recruitment agency. Therefore, despite some differences in the goals and strategies of public and private intermediary institutions, it seems possible to build a general descriptive model of the activities of an organization that provides services for coordinating the interests of those who are looking for work and those who are looking for workers.

The choice of the form of the QS model, reflecting the features of the functioning of the SZ, is based on the following considerations. Firstly, this is a health service with unlimited capacity, covering the totality of citizens who apply to the health service and wait for suitable vacancies for a certain time. Secondly, when selecting a model, one should take into account the very significant proportion of citizens who applied to the health protection system, but then left it unemployed. Thirdly, the specificity of the activities of the SZ is such that any citizen registered in it immediately begins to be served by this system. It is in principle impossible for a request to remain passively in the queue and wait for it to free up some channel.

Infinite-channel QS with an overflowing incoming flow and QS with a limitation on the time spent in the system have the necessary properties.

Analytical methods can be used to study a relatively narrow range of queuing problems. The system under consideration cannot be satisfactorily described by one of the elementary QS. The flow of citizens applying to the health center in order to find work is not the simplest (Poisson).

The use of mathematical tools to obtain analytical solutions in this case becomes dramatically more complicated. Only in relatively rare cases, rather as an exception, is it possible to obtain an analytical solution in a simple closed form.

The way out of this situation seems to be the use of simulation modeling, in which implementations of the QS operation process are simulated on a computer using a series of random variables.

To test the model, statistical data from one of the regional Employment Centers (ECCs) were used:

1. Weekly data for 2004-2006. on the number of registered citizens.

2. Weekly data for 2004-2006. about the number of citizens deregistered, including for reasons: they found a job (profitable occupation); registered for early retirement; aimed at vocational training; for other reasons.

As studies have shown, the flow of incoming requirements is best described (with the lowest level of significance of Pearson's criterion 2) by a gamma distribution with parameters =6.69, =9.30.

Fig.7. Distribution of the number of citizens registered with the CZN.

For probabilistic descriptions of the outgoing flow of employed citizens and the outgoing flow of those who left the system unemployed, gamma distributions with parameters =5.86, =8.90 and =1.69, =5.85, respectively, were found as the best (according to the Pearson agreement criterion).

A simulation model of the functioning of the employment service as a self-service organization was implemented in MS Excel. Using a random number generator and probability distributions obtained on the basis of empirical data for flows in the system, the weekly numbers of registered, employed and deregistered citizens for other reasons were modeled.

The resulting simulation model allows us to outline a probabilistic picture of the dynamics of the number of unemployed citizens in the system under consideration, and thereby assess the financial (budgetary) load of the employment service in question both at the current time and in the future.

MAIN PUBLICATIONS ON THE TOPIC OF THE DISSERTATION:

Publications in journals listed by the Higher Attestation Commission

1. Golyatin, A.O. Econometric study of the dynamics of the registered labor market in the Ivanovo region / A.O. Golyatin // Regional economics: theory and practice. – 2007. –№9. – P. 168–172, 0.70 pp.

2. Golyatin, A.O. Modeling of employment service based on the theory of queuing systems / A.O. Golyatin // Review of Applied and Industrial Mathematics. – 2006. – Volume 13. – Issue 5. – P. 846, 0.10 pp.

Other publications

3. Golyatin, A.O. Modeling the functioning of the employment service as a queuing system / A.O. Golyatin // Problems of economics, finance and production management: collection of articles. scientific works of Russian universities. Vol. 22. – Ivanovo: ISUTU. – 2007. – P. 272–276, 0.50 pp.

4. Golyatin, A.O. Labor market: some approaches to modeling the coordination of labor supply and demand / A.O. Golyatin // Social and humanitarian sciences in the XXI century: Materials of the international scientific conference in 3 T. T.I. Economic organizations: functioning and management / Ed. Doctor of Economics sciences, prof. G.V. Ulyanov. – Kovrov: KSTA. – 2006. – P. 247–254, 0.65 pp.

5. Golyatin, A.O. Mathematical analysis of a model for matching labor supply and demand based on a system of nonlinear differential equations of the Volterra-Lotka type / A.O. Golyatin // Problems of economics, finance and production management: collection of articles. scientific works of Russian universities. Vol. 19. – Ivanovo: ISUTU. – 2005. – P. 303–307, 0.55 pp.

6. Golyatin A.O. Statistical study of the dynamics of registered unemployment in the labor market of the Ivanovo region / A.O. Golyatin // Problems of economics, finance and production management: collection of articles. scientific works of Russian universities. Vol. 18. – Ivanovo: ISU. – 2005. – P. 304–309, 0.65 pp.

7. Golyatin, A.O. Modeling macroeconomic dynamics using cycle theory / A.O. Golyatin, S.M. Komolov // Problems of economics, finance and production management: collection of articles. scientific works of Russian universities. Vol. 10. – Ivanovo: ISU. – 2002. – P. 234–238, 0.50 pp. (auth. 0.25 p.l.).

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Golyatin Andrey Olegovich. Mathematical modeling and forecasting of the organized labor market of the region: dissertation... Candidate of Economic Sciences: 08.00.13 / Golyatin Andrey Olegovich; [Place of protection: Ivan. state chemical technology University]. - Ivanovo, 2007. - 154 p. : ill. RSL OD, 61:07-8/5918

Introduction

Chapter 1. Theoretical foundations of the organization and functioning of the labor market 11

1.1. Labor market: essence and basic concepts 11

1.2. The mechanism of functioning of the labor market 23

1.3. The number of unemployed and vacant jobs as the main indicators of the organized labor market 33

1.4. Labor market of the Ivanovo region in 1992-2006. 42

Chapter 2. Mathematical modeling as a tool for studying labor market processes 52

2.1. Basic concepts of mathematical modeling 52

2.2. Economic and mathematical modeling of labor market processes 60

2.3. Model of the dynamics of labor supply and demand based on a system of nonlinear differential equations 67

Chapter 3. Econometric study of the dynamics of labor supply and demand in the labor market of the Ivanovo region 78

3.1. Basic concepts of econometric time series modeling 78

3.2. Models for analysis and forecasting of unemployment in the region 93

3.3. Vacancies and tension in the regional labor market: analysis and forecasting 102

Chapter 4. Modeling the functioning of Employment Service 109 based on the theory of queuing systems

4.1. State employment service: tasks and specifics of functioning 109

4.2. Basic concepts of the theory of queuing systems 117

4.3. Simulation modeling SMO 124

4.4. Functioning of the Employment Service as a queuing system: construction and testing of a model 129

Conclusion 136

List of used literature

Introduction to the work

Relevance of the research topic

The Russian labor market has experienced numerous shocks that accompanied the process of systemic transformation of the country's economy. Historically, it is not yet possible to talk about a single all-Russian labor market; it is rather represented by a set of fairly isolated regional markets, which explains the growing interest in studying the latter.

The basic concepts when describing the functioning mechanism of any market are supply and demand. In the labor market, which is a very specific market, supply is formed by workers (sellers), and employers (buyers) act as demand providers. Consideration of the joint dynamics of labor demand and supply at the regional level is undoubtedly relevant both theoretically and practically.

The most important task of economic science is the analysis and forecasting of socio-economic processes for targeted influence on them. Modern science has a wide arsenal of relevant

5 tools, among which a special place is occupied by economic and mathematical modeling, relatively free from subjective ideas and biases. It is economic and mathematical methods and models that are designed to help understand the current situation in the labor market and select adequate tools for its regulation.

An analysis of the scientific literature shows that most labor market research is qualitative in nature, and the use of quantitative methods is aimed at solving individual problems. In this case, it seems necessary to use the principle of consistency when developing economic and mathematical models of the labor market.

In this regard, the construction of a set of economic and mathematical models for analyzing and forecasting the demand and supply of labor to substantiate regional plans for socio-economic development is undoubtedly an urgent task.

The degree of scientific development of the problem.

Mathematical modeling of the labor market as a socio-economic system is naturally based on a fairly extensive and deeply developed apparatus of economic and mathematical methods and models. Of particular importance for the purposes of our research are works on statistical modeling and forecasting of economic processes - the works of S.A. Ayvazyan, T. Anderson, D. Brillinger, J. Box, G. Jenkins, J. Johnston, K. Dougherty, M. Kendal, G. Kramer, Y.R. Magnus, E. Malenvo, B.C. Mkhitaryan, R. Otnes, G. Theil, D. Enokson and others.

General approaches to mathematical modeling of socio-economic systems, their stability and management were developed in the works of R. Allen, A. Bergstrom, V.-B. Zanga, M. Intriligator, L.V. Kantorovich, V.I. Kitaygorodsky, N.B. Kobeleva, N.E. Kobrinsky, V.A. Kolemaeva, V.V. Leontief, J. von Neumann, B.C. Nemchinova, Yu.M. Plotinsky, I. Ekland and others.

An analysis of works devoted to the actual problems of the labor market in general and its modeling in particular allows us to identify two major areas of research.

First direction includes studies that develop the general principles of the economic theory of labor, namely the organization, functioning and results of the relevant markets. First of all, this includes the fundamental works of recognized authorities of economic science - A. Smith, K. Marx, A. Pigou, A. Marshall, J.M. Keynes, P. Samuelson, K.R. McConnell and others, whose merits extend far beyond the boundaries of labor theory, as well as the work of labor relations theorists themselves - G. Becker, R. Ehrenberg, R. Smith, R.K. Filera, D.S. Khameriesha, A.E. Rees, L. Robbins, R. Gronau and others. Among Russian authors who deeply develop the theoretical aspects of the functioning of the labor market, we can highlight B.C. Bulanova, N.A. Volgin, I. Zaslavsky, A. Kotlyar, R.I. Kapelyushnikova, K.G. Kyazimov, A. Nikiforov, IO. Odegova, V.A. Pavlenkova, T.O. Razumov, S.Yu. Roshchina, G.E. Slesinger, T. Chetvernin, Shlender P.E. etc. The concepts of the functioning of the labor market of the authors listed above, in fact, represent the most general models that reflect the main approaches to the study of labor processes.

Second direction represents empirical research and actual economic and mathematical modeling of labor markets. Here we should highlight the works of S. Commander, R. Layard, C. Olivetti, B. Petrongolou, A. Richter, V.E. Gimpelson, R.B. Freeman, M.E. Shafer, J. Earl, etc. .

For the most part, this is statistical modeling and forecasting based on classical correlation-regression or cluster analysis. Of particular interest are the works of A.G. Korovkin and his students on modeling the coordination of the dynamics of demand and supply of labor based on a system of differential equations of the Volterra-Lotka type.

The purpose of the dissertation research is the development of a complex of economic and mathematical models for analyzing and forecasting the demand and supply of labor in the organized regional labor market.

In accordance with the purpose of the dissertation, the following are set and resolved: tasks:

research of the theoretical foundations of the functioning of the labor market, as well as the specific features of the formation and development of the Russian labor market, V particularly at the regional level;

analysis and generalization of existing methods of economic and mathematical modeling of the labor market, including indicators of labor demand and supply;

development of a set of models for analyzing and forecasting demand and supply of labor in the organized regional labor market;

econometric analysis of the dynamics of regional registered unemployment and the number of vacant jobs reported to the employment service;

building a model for the functioning of the employment service as a queuing system.

Subject of research is an economic and mathematical modeling of labor supply and demand in the organized labor market at the regional level.

Object of study represented by the regional labor market (using the example of the Ivanovo region).

Information base The research was based on statistical data from the Federal Employment Service, Rosstat of the Russian Federation for the Ivanovo Region, Rodnikovsky District Employment Center, periodical press materials and data from socio-economic studies of the labor market from the regional Employment Center.

Theoretical and methodological basis The research included the works of foreign and domestic economists and mathematicians on modeling and forecasting socio-economic systems using correlation and regression analysis, time series analysis, the theory of random processes and elements of mathematical statistics; works on the problems of the labor market and modeling of its individual components; legislative and regulatory acts on the regulation of employment in the Russian Federation, documents of the International Labor Organization (ILO).

The dissertation work was completed in accordance with clause 1.9. - “Development and development of mathematical methods and models for analysis and forecasting of socio-economic processes of public life: demographic processes, labor market and employment, quality of life of the population, etc.” Passports of specialty 08.00.13 - mathematical and instrumental methods of economics.

Scientific novelty dissertation research, revealing the achievement of the goal, is as follows:

A system of economic and mathematical models for analyzing and forecasting demand and supply of labor in the organized regional labor market is proposed;

a theoretical model of the dynamics of labor demand and supply was developed based on a system of nonlinear differential equations;

for the stages of development of the organized regional labor market identified by the author, econometric models of time series of registered unemployed people and vacant jobs reported to the employment service were constructed, taking into account both the trend-seasonal nature of the dynamics and the presence of autocorrelation in random residuals;

Based on the theory of queuing systems, an approach to modeling the functioning of the employment service, which is the main intermediary institution of the organized labor market, was developed and tested on the basis of empirical data.

Practical significance and testing of the research results.

The complex of economic and mathematical models proposed in the work can be used by regional employment services, as well as government bodies at various levels, “to assess current and future changes in the demand and supply of labor in the regional labor market, as well as in areas interconnected with it in order to develop strategies for the socio-economic development of the region for the future.

Some research results can be used in the development of educational and methodological literature in the disciplines “Methods and models of economics” and “Statistical methods of forecasting”.

Work structure. The dissertation consists of four chapters.

IN first chapter an analysis of literary sources in the field of labor market research was carried out, the main approaches to determining

10 the labor market as an economic category, the basic concepts of the functioning of this market were studied, the existing methods for determining the number of unemployed and vacant jobs as the main indicators of supply and demand in the current labor market were analyzed, the state and development of the labor market in the Ivanovo region for the period 1992-2006 was assessed.

In second chapter the basic concepts of economic and mathematical modeling as the main method of studying complex systems are considered; an overview of the application of economic and mathematical modeling methods to the study of labor market processes is given; a set of models for analyzing and forecasting the demand and supply of labor in the organized regional labor market has been proposed; a model of the dynamics of demand and supply of labor has been developed based on a system of nonlinear differential equations.

IN third chapter the basic concepts of econometric modeling of time series are considered, based on empirical data, an econometric analysis of indicators of labor supply and demand in the organized labor market of the Ivanovo region is carried out in the time interval 1992-2006.

IN fourth chapter the tasks and specifics of the functioning of the State Employment Service were analyzed, an approach to modeling the functioning of the Employment Service was proposed based on the theory of queuing, and a simulation model of the regional Employment Center was built on the basis of empirical data.

The mechanism of functioning of the labor market

World economic thought contains many attempts to provide an adequate theoretical description of the functioning mechanism of both the entire labor market and its individual components. With all the variety of such descriptions, the most significant and widespread are two: classical and Keynesian. Let us briefly describe each of them.

Classic concept. By classical theory in non-Marxist economic literature we mean primarily the theory of English and American economists, based on the teachings going from A. Smith and D. Ricardo to A. Marshall, A. Pig and other scientists who devoted themselves to developing the theory of general economic equilibrium. Classical employment theory involves constructing functions of aggregate demand for labor and aggregate supply of labor applicable to conditions of perfect competition. These complex functions are obtained by aggregating the demand functions of individual entrepreneurs and the supply functions of individual workers. The subjects in the labor market will be business and the state, and the subjects of supply will be households.

According to the classical concept, the labor market is a self-regulating system. The main factor in market balance is the price of labor. The orthodox classical model assumes that the labor chain is absolutely flexible and freely responds to any changes in supply and demand, maintaining a state of equilibrium.

This model can be presented in the form of a graph (Fig. 2), where the LS curve of labor supply, which increases with increasing wages, intersects with the descending LD curve of labor demand at equilibrium point E.

At point E, the demand for labor is equal to the supply of labor, that is, the labor market is in equilibrium. This means that all entrepreneurs who agree to pay wages W/PxE find the required amount of labor on the market, their demand for labor is fully satisfied. In a market equilibrium position, all workers are fully employed and are ready to offer their services at W/PxE wages. Therefore, point E determines the position of full employment.

Under any other wage conditions other than W/PxE, the equilibrium in the labor market is disturbed. Wages are the equilibrium price in the labor market.

Of course, the possibility of emergency circumstances (wars, political upheavals, drought, etc.) that take the economy away from the path of full employment is recognized. At the same time, it is argued that the inherent weakness of the market system for automatic self-regulation soon automatically restores production and employment levels in the economy. State intervention in the functioning of the labor market and the entire economy as a whole is considered unnecessary, and, moreover, harmful. The cause of unemployment is a wage level that is too high, exceeding the equilibrium value, at which there is an excess supply of labor (unemployment). Meanwhile, the reduction of wages is hampered by the demands of the workers themselves, who do not want to work for a wage equal to the marginal product of labor or when the “burden of labor,” in their assessment, is higher than the offered wage. Thus, essentially, unemployment cannot be involuntary.

Thus, from the point of view of the economic role of the state, the classical model is based on the assumption that the market system is capable of automatic self-regulation. The best economic policy in this case is a policy of non-intervention by the state.

A natural and, in a sense, complete development of the stated point of view is the neoclassical concept, formally described by the theory of general equilibrium of L. Walras. In it, the economy is represented by two sectors: production and consumption. The manufacturing sector is assumed to produce a finite range of products using a finite set of factors. The rationality of the behavior of economic entities is postulated. Consumers, within the framework of budget constraints, in accordance with their utility function, strive to obtain maximum satisfaction from the chosen range of products, and producers strive to maximize profits from the release of goods. The economy is considered perfectly competitive, i.e. Each economic entity passively accepts the existing price system without trying to influence it. The central question of the Walras model is the existence of equilibrium prices for goods and primary factors (including labor), in which producers and consumers, acting in the best way for themselves and in accordance with budget constraints, ensure a state of affairs where demand for each product and the factor does not exceed his proposal. A rigorous mathematical proof of the existence of equilibrium prices in the general equilibrium model was obtained only in the middle of the 20th century. subject to some additional natural restrictions.

Among the proven modifications of the Walras model, the Arrow-Debreu model has the greatest generality and chronological priority.

Another important issue of neoclassical models is the problem of the attainability of equilibrium - a necessary condition for stability and normal functioning of the economy. Walras himself believed that in a market economy, the market (“auctioneer”) acts as a regulator, coordinating the actions of all participants and establishing equilibrium prices. As a result of the “groping” process, a gradual step-by-step approach initially occurs. selected prices to equilibrium ones, the so-called cobweb model.

Economic and mathematical modeling of labor market processes

Moving on to consider the problems of the labor market as an object of mathematical modeling and forecasting, it should be noted that this market fully possesses all the basic properties of the socio-economic systems discussed above.

It should be noted that the labor market as an object of economic and mathematical modeling is quite complex and diverse. The range of specific tasks in the field of studying labor market processes is very wide, and even an overview description of them can be the topic of a separate study. Nevertheless, we will try to briefly characterize the range of the main, in our opinion, tasks, in solving which the tools of economic and mathematical modeling could be used.

The main objectives of research in the field of the labor market are the following: ? analysis of the composition and indicators of the number of labor resources, including analysis of employment and unemployment; ? analysis of working time indicators, including issues of scientific organization of labor and analysis of labor costs; ? calculation of actual and planned labor productivity, analysis of factors influencing labor productivity; ? analysis of forms and systems of remuneration, distribution of workers by salary level; ? analysis of the dynamics of labor remuneration and productivity while studying the influence of their ratio on the cost and competitiveness of products; ? building a system of labor balances, including the balance of labor resources, the balance of the use of working time, the balance of the movement of the number of employees, the intersectoral balance of labor costs; ? study of the main indicators of the standard of living of the population, including analysis of patterns and connections between income and consumption; ? modeling of industry dynamics of labor resources; ? analysis of labor migration, etc.

In other words, having chosen the labor market as an object of study, it is necessary to decide on the specific task of studying individual processes and phenomena occurring on it.

The listed main tasks in the field of the labor market determine the methodological basis for studying this market. These fundamentals include general scientific methods (system analysis, integrated approach, program-target planning), analytical and prognostic methods (mathematical programming, probability theory and mathematical statistics, queuing theory, expert assessment methods, etc.), as well as methods borrowed from other fields of knowledge, such as sociology, psychology, ecology, etc. The specified methodological foundations for labor market research determine the features of the use of economic and mathematical modeling and forecasting to solve the above problems.

First of all, it should be noted that statistical data related to labor market processes (cross-sectional data, time series) serve as the basis for studying phenomena in this area from a quantitative perspective, and, therefore, the establishment of patterns should occur on the basis of econometrics, which uses the methods of theory probability and mathematical statistics. Therefore, when modeling labor market problems, one cannot do without the basic concepts and methods of these sciences: random variable, mathematical expectation, dispersion, general and sample populations, statistical criteria of agreement, laws and distribution curves, etc.

It should be noted here that econometric methods are perhaps the most common in studying the labor market.

Thus, the method of correlation-regression analysis (CRA) is widely used in the works of A.G. Korovkin, A.V. Polezhaev. Andryunina A.V. Lapina T.D., Podorvanova Yu.A. Parbuzina K.V., Zaitseva N.M. for assessing the dependence of sectoral employment on macroeconomic factors - the volume of gross domestic product and fixed assets, for assessing the functions of demand and supply of labor, the relationship between wages and unemployment, tax burden and employment efficiency, empirical assessment of production functions. In addition to classical multiple regression analysis, more advanced econometric methods are also used in these works: the use of dummy variables and autoregressive transformation in regression analysis.

Bragin V. and Osakovsky V. to estimate the natural level of unemployment in Russia used the apparatus of discrete dependent variables, i.e. logit and probit models.

An extensive study of the dependence of employment on the most important macroeconomic indicators, as well as analysis and forecasting of regional employment dynamics using econometric methods are presented in the work

It should be noted that the use of econometric methods in the works of foreign authors is a priori a guarantee of high quality and scientific significance of research work (research paper, discussion paper).

Models for analysis and forecasting of unemployment in the region

A visual analysis of the dynamics of the number of registered unemployed made it possible to identify three qualitatively different stages in the formation and development of the labor market in the Ivanovo region, covered by the periods: January 1992 - April 1996, May 1996 - December 2000, from January 2001 to the present.

Stage 1 (January 1992 - April 1996). "Spontaneous labor market." Which is quite natural, the regional labor market responded to the beginning of economic transformations and the introduction of market economic methods with a sharp increase in registered unemployment. This process was also significantly influenced by the almost single-industry specialization of the region's economy, which was a legacy of the planned economy. During this period, the number of unemployed people registered in the SZ increased from 3,297 people. in January 1992 to 91,190 people. in April 1996

Both visual analysis and statistical verification of the presence of a trend in the time series of registered unemployed using the criterion of ascending and descending series at this interval showed a clear presence of an upward trend.

The dynamics of the number of registered unemployed at this stage is described by a statistically significant linear trend: y = -10066.58+1687.44? (statistic value -1.73 and 83.34). Determination coefficient L2 = 0.993 (the overall quality of the regression equation was assessed using the F-significance indicator = 2.54E-55).

For the number of registered unemployed at this stage, the additive nature of the seasonal component was revealed. The behavior of the seasonal wave of registered unemployed is such that it increases until April, and then gradually decreases with a slight increase by December. JIII Feb March Apr May June July Aug

The calculated Durbin-Watson (DW) statistic was found to be 0.24, indicating the presence of positive autocorrelation. Consequently, the error time series contains statistical dependencies that can be modeled.

To model a number of residuals, 1st and 2nd order autoregressive models (AR(1) and AR(2)) were applied. As can be seen from Fig. 16, the values of the coefficients of the autocorrelation function (ACF) of a number of residuals decay monotonically, and the partial autocorrelation function (PACF) has outliers (peaks) in the first two lags (Fig. 17).

Such a decrease in the number of registered unemployed can be explained by a number of reasons. Firstly, these are institutional reasons associated with significant changes in the functioning of employment services during this period. Thus, the reduction in registered unemployment was significantly influenced by the growth of the employment fund deficit and, for this reason, the reduction in the ability of the employment service to provide assistance to the unemployed. Meager benefits, strict conditions for receiving them and constant delays in payments have led to a significant outflow of those wishing to register as unemployed. Very indicative in this case is the Resolution of the Head of the Regional Administration. dated December 16, 1996 No. 708 “On limiting the amount of payment of unemployment benefits, scholarships during the period of professional training, advanced training, retraining in the direction of the employment service authorities”, defining the limitation of the monthly amount of payment of unemployment benefits, as well as maintaining the replacement procedure (with the consent of unemployed) unemployment benefits in food, industrial goods and services. We cannot ignore the processes of partial stabilization of the country's economy, accompanied by an increase in demand for labor. The outflow of part of the working-age population to economically more favorable neighboring regions also had an impact. In other words, the processes of self-regulation at this stage of development of the labor market in the Ivanovo region played a dominant role, labor resources gradually adapted, assimilating new “rules of the economic game.”

The trend for the dynamics of the number of unemployed at this stage is best described by a polynomial of the second degree. actually). Coefficient of determination R =0.973 (F-significance = 3.4E-42).

The seasonal wave for this period has the most pronounced pattern of fluctuations in the number of registered unemployed during the year (Fig. 19). This situation is explained by the seasonal nature of a number of jobs (construction workers, road workers, etc.); in the summer season, the pendulum migration of labor resources makes itself felt significantly, when workers rush to work in neighboring regions. With the end of the season, “returnees” again join the ranks of the unemployed.

Basic concepts of the theory of queuing systems

In many areas of economics, finance, production and everyday life, systems of a special type that implement repeated execution of similar tasks play an important role. Such systems are called queuing systems (QS). Let's consider the basic concepts of the theory of queuing systems.

Mathematical schemes of queuing theory are characterized by the fact that at certain moments of time (random or deterministic) requests for service arise and there are special devices (devices, instruments, channels) for servicing these requests, operating according to a certain law.

In the classical queuing theory, the mathematical functioning of the QS is described using the apparatus of finite systems of differential equations, as a result of which it is possible to express in explicit form the main characteristics of the efficiency of the QS through its parameters and the parameters of the flow of requests. Any QS includes the following elements: ? source of requirements; ? incoming flow of requirements; ? service system (service channels); ? outgoing flow of requirements.

In many cases, a possible queue of requests awaiting service within the QS is added to this list.

Depending on the location of the sources of requirements, QS systems are divided into open ones, for which the sources of requirements are located outside the system, and closed ones, in which the sources of requirements are located inside the system. Depending on the number of service channels, single-channel and multi-channel QS systems are distinguished (sometimes specifying the number of available channels). Finally, depending on whether queue formation is possible in the QS or not, systems are divided into:

1) QS with failures (zero wait or obvious losses), in which an application received at the entrance to the QS at the moment when all channels are busy receives a “refusal” and leaves the QS (“disappears”).

2) QS with waiting (unlimited waiting or queue). In such systems, a request that arrives when all channels are busy is placed in a queue and waits for the channel to become available and accept it for service. Each application received at the entrance will eventually be serviced.

3) SMO of mixed type (with limited OE/sitting). These are systems in which some restrictions are imposed on the application’s stay in the queue. These restrictions may be imposed on the length of the queue, the time spent in the queue or in the QS, etc.

In QS with waiting and in QS of mixed type, different schemes for servicing requests from the queue are used, i.e. Such QSs have a certain queue discipline. Service can be ordered, when applications from the queue are serviced in the order they arrive in the system, and unordered, when applications from the queue are serviced in random order. Sometimes priority service is used, when some requests from the queue are considered priority and therefore are serviced first.

The universal classification of queuing systems is based on a listing of the key characteristics of their elements. As a rule, the following expression is accepted for designating a QS: A/B/n/m/l, where A is a symbolic image of the probabilistic distribution of time intervals between adjacent requirements, B is a designation of the probabilistic distribution of time for servicing one request by one channel, n is the number of serving channels in the QS, m is the restriction on the length of the queue (either in the form of the maximum possible number of requirements in the queue, or in the form of the maximum possible time the requirement remains in the queue), / is the number of sources of requirements.

The main indicators of the effectiveness of the QS include: probability of Rotk failure, i.e. the probability that the current request will leave the system unserved; ? relative capacity Q, i.e. the average share of requirements served by the system out of the total number; ? absolute capacity A, i.e. the average number of requests served by the system per unit of time; ? average number of occupied channels km (for multi-channel QS); ? average queue length L04, (average number of requests in the queue); ? average number of requirements in the system, Lcucm.\ ? average time a request stays in the Goch queue; ? average time a request stays in the Tsist system (for service or in queue), etc.

The input flow of applications (requirements for service) is characterized by a certain organization and a number of parameters: the intensity of receipt of applications, i.e. the number of applications received on average per unit of time, and the law of probability distribution of the moments of arrival of applications into the system.

The servicing system represents a set of devices (channels, devices) that provide service to an application that has entered the system. The serving system is characterized by throughput (service speed), i.e. the number of applications served per unit of time, and the law of distribution of time for servicing applications.

The output flow of requests is the flow of serviced requests leaving the serving system. The output flow parameter is intensity.

Let us dwell in more detail on the characteristics of the input stream of applications. A flow of homogeneous events is the time sequence of appearance of requests for service, provided that all requests are equal. There are also flows of heterogeneous events when one or another application has some kind of priority.

If the flow is homogeneous, then each event is characterized only by the moment of its occurrence t). There are two ways to define homogeneous events. The first way is to list all known moments tj. The second method is to indicate a dependency that allows you to calculate t) from previous values.

FEDERAL AGENCY FOR EDUCATION OF THE RF

STATE EDUCATIONAL INSTITUTION OF HIGHER

PROFESSIONAL EDUCATION

KAZAN STATE TECHNOLOGICAL UNIVERSITY

FACULTY OF ECONOMICS, MANAGEMENT AND LAW

COURSE WORK

in the discipline: “Economic and mathematical modeling”

on the topic: “Economic and mathematical modeling of the processes of labor migration and unemployment”

Completed: Lobanova E.V.

Work protected "__" _____ 2011

Supervisor _________________

KAZAN 2011

Introduction

1. Theoretical foundations of the organization and functioning of the labor market

2. Economic and mathematical modeling as a tool for studying labor market processes

3. Unemployment

3.1. Concept and consequences of unemployment

3.2. Registration of the unemployed

3.3. Types of unemployment

3.4. Costs of unemployment

3.5. Classical and Keynesian models of unemployment. State measures to regulate unemployment

4. Migration4.1. Migration theory4.2. Integration theory4.3. Conclusions from practice4.4. Simple migration models4.4.1. Harris-Todaro model4.4.2. “Advantage vector” model4.4.3. Model of human capital theory4.4.4. Conclusion from the model4.5. Impact of labor movement on comparative advantage and welfare4.5.1. Benefits of the “receiving” country from immigration4.5.2. Negative manifestations of immigration for the “receiving” country4.5.3. Benefits from the movement of labor for the country of emigration4.5.4. Negative consequences for the country of emigrationConclusionReferences

Introduction

My course work concerns such problems as labor migration and unemployment, or rather, economic and mathematical modeling of these processes. Migration as a phenomenon was known back in the 10th century. Throughout time, it has undergone changes due to the fact that the social system has changed, and, consequently, the worldview of people. States were already making attempts to manage, systematize and record migration processes. And only nowadays these attempts lead to positive results. In my opinion, the problem of migration is very relevant now, because many have the opportunity to freely enter the territory of foreign countries. For the most part, people travel to the territory of another country (or their own city) in an attempt to find at least temporary or better-paid work. The process of internationalization of production, which is actively occurring throughout the world, is accompanied by the internationalization of the workforce. Labor migration has become part of international economic relations. Migration flows rush from one region and country to another. Giving rise to certain problems, labor migration provides undoubted advantages to countries receiving labor and supplying it. One of the manifestations of internationalization and democratization of the economic and socio-cultural life of mankind, as well as the consequences of acute ethnic contradictions, direct clashes between countries and peoples, emergency situations and natural disasters disasters are large-scale intra- and inter-country movements of population and labor resources in various forms. These are voluntary migrants who take advantage of the rights and opportunities provided to them by world civilization and international labor markets to choose a place of residence and work. These are refugees and forced migrants who leave their home not of their own free will, but under the pressure of “circumstances.” The world community, which until recently did not directly feel the size, characteristics and consequences of migration processes at the international level, was faced with the need to coordinate the efforts of many countries to resolve acute situations and collective regulation of migration flows.

The transition to market relations currently taking place in Russia is associated with great difficulties and the emergence of many socio-economic problems. One of them is the problem of employment, which is inextricably linked with people and their production activities.

The market presents and demands a completely different level of labor relations at each enterprise. However, effective mechanisms for the use of labor resources have not yet been created, new employment problems are arising and old ones are worsening, and unemployment is growing.

Mass poverty and social vulnerability of large sections of the population are our reality.

The transition to a market economy inevitably led to great changes in the use of labor resources. With the restructuring of the country's economic life, many factors have emerged that influence the qualitative characteristics of the labor market. Emigration of the population to non-CIS countries mainly involves highly qualified personnel, specialists who are able to withstand competition in the global labor market. For Russia, it will have a twofold consequence - on the one hand, the supply of labor will decrease, on the other, its quality will deteriorate.

The regulatory role of the state should be to constantly maintain a balance between economic and employment priorities in economic transformation programs.

Mathematical modeling of the labor market as a socio-economic system naturally relies on a fairly extensive and deeply developed apparatus of economic and mathematical methods and models.

The goal that I set in my course work is to consider economic and mathematical models of the processes of labor migration and unemployment. In this regard, my tasks included consideration of such points as: the theoretical foundations of the organization and functioning of the labor market, economic and mathematical modeling as a tool for studying labor market processes, unemployment (the concept and consequences of unemployment, accounting for the unemployed, types of unemployment, costs of unemployment, classical and Keynesian models of unemployment, government measures to regulate unemployment), migration (migration theory, integration theory, conclusions from practice, simple migration models (Harris-Todaro Model, “Advantage Vector” Model, Human Capital Theory Model)), the impact of worker movement forces on comparative advantage and welfare (benefits of the “host” country from immigration, negative consequences of immigration for the “host” country, benefits from the movement of labor for the country of emigration, negative consequences for the country of emigration).

1. Theoretical foundations of the organization and functioning of the labor market

Rice. 1. Intermediary institutions of the organized labor market.

2. Economic and mathematical modeling as a tool for studying labor market processes

The labor market belongs to the class of complex probabilistic dynamic systems. The main method for studying such systems is the modeling method , those. a method of theoretical and practical action aimed at developing and using models.

The direct object of the study is the interaction of labor supply and demand in the organized regional labor market.

There is a set of models for analyzing and forecasting labor supply and demand (Fig. 2.

Rice. 2. A set of models for analyzing and forecasting labor demand and supply

A deterministic model of the dynamics of labor demand and supply was also developed in the form of a system of nonlinear control systems:

(1)

where is the number of potential workers (unemployed in accordance with the ILO methodology), is the number of vacant jobs (unfilled vacancies), is the number of economically active population.

3. Unemployment

3.1. Concept and consequences of unemployment

Unemployment- a social phenomenon that involves the lack of work among people who make up the economically active population.

According to the definition of the International Labor Organization, a person aged 10-72 years (in Russia 15-72 years old) is considered unemployed if, during the critical week of the population survey on employment problems, he simultaneously:

Didn't have a job

Looking for a job

Was ready to start work

Consequences of unemployment

Decrease in income

Mental health problems

Loss of qualifications

Economic consequences (loss of GDP)

Worsening crime situation

3.2. Registration of the unemployed

In modern Russia, accounting of the employed population is carried out using two methods:

According to the Ministry of Health and Social Development of the Russian Federation, based on applications from the unemployed to the employment service. Since a large part of the population has no incentive to register their status as unemployed, the aggregate data is incorrect. Such summary data are published in statistical collections for reference.

According to a population survey on employment problems. Previously, such a survey was carried out once a quarter, but starting from September 2009, it was transferred to a monthly basis. The sample size for surveys is determined at 0.06% of the population aged 15-72 years per quarter and 0.24% per year. Population census materials are used as the sampling frame. The annual sample size for Russia as a whole is about 260 thousand people aged 15-72 years (approximately 120 thousand households), which corresponds to 0.24% of the population of this age. Every quarter in Russia as a whole, about 65 thousand people aged 15-72 years (about 30 thousand households), or 0.06% of the population of this age, are examined. The data obtained as a result of such a survey is published by Rosstat.

3.3. Types of unemployment

The following types of unemployment are distinguished:

- Voluntary- is associated with people’s reluctance to work, for example, in conditions of lower wages. Voluntary unemployment increases during an economic boom and decreases during a recession; its scale and duration vary among people of different professions, skill levels, as well as among different socio-demographic groups of the population.

- Forced (unemployment waiting) - occurs when an employee is able and willing to work at a given wage level, but cannot find a job. The reason is an imbalance in the labor market due to the inflexibility of wages (due to minimum wage laws, the work of trade unions, raising wages to improve the quality of labor, etc.). When real wages are above the level corresponding to the equilibrium of supply and demand, supply in the labor market exceeds demand for it. The number of applicants for a limited number of jobs increases, and the likelihood of actual employment decreases, which increases the unemployment rate. Types of involuntary unemployment:

- cyclical- caused by repeated declines in production in a country or region. It represents the difference between the unemployment rate at the current moment of the economic cycle and the natural unemployment rate. It is natural for different countries to have different levels of unemployment.

- seasonal- depends on fluctuations in the level of economic activity during the year, characteristic of certain sectors of the economy.

- technological- unemployment associated with mechanization and automation of production, as a result of which part of the workforce becomes redundant or requires a higher level of qualifications.

Unemployment registered- unemployed population searching for work and officially registered.

Unemployment marginal- unemployment of weakly protected segments of the population (youth, women, disabled people) and the lower social classes.

Unemployment unstable- caused by temporary reasons (for example, when employees voluntarily change jobs or quit in seasonal industries).

Unemployment structural- is caused by changes in the structure of demand for labor, when a structural mismatch is formed between the qualifications of the unemployed and the demand for available jobs. Structural unemployment is caused by large-scale restructuring of the economy, changes in the structure of demand for consumer goods and production technology, the elimination of obsolete industries and professions, and there are 2 types of structural unemployment: stimulating and destructive.

Unemployment institutional- unemployment that occurs when the state or trade unions intervene in establishing wage rates different from those that could be formed in a natural market economy.

Unemployment frictional- the time of voluntary search by an employee for a new job that suits him to a greater extent than his previous workplace.

3.4 Costs of unemployment

Lost output is the deviation of actual GDP from potential as a result of underutilization of the total labor force (the higher the unemployment rate, the greater the gap in GDP);

Reduction in federal budget revenues as a result of decreased tax revenues and decreased revenue from the sale of goods;

Direct losses in personal disposable income and a decrease in the standard of living of persons who become unemployed and members of their families;

Increased costs for society to protect workers from losses caused by unemployment: payment of benefits, implementation of programs to stimulate employment growth, professional retraining and employment of the unemployed, etc.

3.5. Keynesian and classical models of unemployment. State measures to regulate unemployment.

Macroeconomics is a branch of economic science that studies the behavior of the economy as a whole from the point of view of ensuring conditions for sustainable economic growth, full employment of resources, minimizing inflation and balance of payments. Macroeconomic policy instruments are fiscal (fiscal) policy and monetary (monetary) policy.

Macroeconomic models are formalized (logical, graphical and algebraic) descriptions of various economic phenomena and processes in order to identify functional relationships between them. Any model is a simplified, abstract reflection of reality, because all the variety of specific details cannot be simultaneously taken into account when conducting research. Therefore, no macroeconomic model is absolute; it does not give the only correct answers. However, with the help of such generalized models, a set of alternative ways to control the dynamics of employment levels, inflation and other economic variables is determined.

The term “classical economists” was introduced into scientific circulation by K. Marx, referring mainly to the English economists A. Smith and D. Ricardo. However, later Western scientists began to interpret this term much more broadly. J. Keynes, in particular, included the followers of D. Ricardo in the classical school, i.e. those who adopted and further developed the Ricardian economic teaching, including J. Mill, A. Marshall and A. Pigou. A number of other authors include K. Marx himself among the classics.

Currently, in Western economic literature, the classical school includes the followers of A. Smith and D. Ricardo, primarily J. Say, T. Malthus, J. Mill, K. Marx, right up to the economists of the late 19th century.

There are no economic and mathematical models in the works of the classics. Their verbal characteristics of a market economy were translated into the language of mathematical models later, after the appearance of the theory of John Keynes, to compare the views of the classics and Keynesians. Moreover, at present it would be wrong to regard classical theory only as an important stage in the history of economic thought. Many provisions of the classics have acquired particular relevance today.

The main macroeconomic indicators are the volume of national production, the inflation rate and the unemployment rate.

Unemployment is an integral property of a market economic system. The number of unemployed increases significantly during periods of crisis and decreases during periods of recovery.

The number of unemployed is an important indicator, but it exists in isolation from the number of economically active population. Therefore, the main indicator of the use of labor resources is the unemployment rate in the country. The unemployment rate is the ratio of the number of unemployed people to the economically active population, expressed as a percentage.

In the USSR, for about six decades (early 30s - late 80s), the existence of unemployment in the country was not officially noted, and sufficiently complete statistical records of the processes occurring in the field of employment were not kept. And only in the late 80s - early 90s, attention to this problem both from the state and from economic science increased significantly. At the same time, using only the number of officially received unemployed status does not provide a sufficiently accurate picture of the situation on the labor market.

Firstly, much depends on the methodology for determining the unemployed. If, to calculate the unemployment rate, only the number of officially registered unemployed is taken, then the unemployment rate is underestimated compared to the actual one - not everyone who is unemployed and who is looking for it turns to the appropriate services; and the procedure for obtaining unemployed status itself does not seem quite simple, and therefore not even all of those who apply to the employment services manage to complete it.

Secondly, the problem is accounting for partial unemployment or underemployment. On the one hand, enterprise managers hoped for favorable changes in the situation in the future and tried to retain qualified personnel. On the other hand, people in similar situations simply did not have a better choice in many cases.

Determining the number of unemployed and the unemployment rate is an important task, since we are talking about one of the most important macroeconomic indicators, but the methodology, the technique of calculation itself is not sufficiently perfect.

Full employment is the absence of cyclical unemployment.

The most widespread in Western economic science are the neoclassical and Keynesian theories of unemployment.

Classical employment theory , (D. Ricardo, J. Mill, A. Marshall and other economists of the 19th century), is based on the belief that the market has sufficient capabilities to effectively coordinate all processes occurring in the field of employment, ensuring full use of the labor resources that are available in society. According to the classics, the reason for unemployment is too high wages, which creates an excess supply of labor. This is the result of certain requirements of the employees themselves. The free play of market forces - demand, supply, wages - will ensure the necessary coordination in the field of employment. Classical economists argued that wage rates should and would fall. A general decrease in demand for products will be reflected in a decrease in demand for labor and other resources. If wage rates are maintained, this will immediately lead to the emergence of surplus labor, i.e. will cause unemployment. However, not wanting to hire all workers at the original wage rates, producers find it profitable to hire these workers at lower wage rates. The demand for labor falls, and workers who cannot be hired at the old, higher rates will have to agree to work at the new, lower rates. If there is an excess supply of labor, then a decrease in wages should reduce it, but, at the same time, increase the demand for labor. If wages in this situation do not decrease, this is prevented by the workers themselves and their trade unions, then they “voluntarily” agree to the existence of a certain number of unemployed.

Will workers be willing to work at reduced rates? According to classical economists, competition from the unemployed forces them to do this. By competing for available jobs, the unemployed will help lower wage rates until these rates are so low that it becomes profitable for employers to hire all available workers. Therefore, classical economists came to the conclusion that involuntary unemployment is impossible. Anyone willing to work at a market-determined wage rate can easily find a job.

Neoclassical concept unemployment in its most consistent form was presented by the famous English economist A. Pigou in his book “The Theory of Unemployment,” published in 1933.

The main provisions of A. Pigou boil down to the following:

a) the number of workers employed in production is inversely related to the level of wages, i.e., the higher the wages, the lower the employment;

b) existed before the First World War of 1914-1918. the balance between the level of wages and the level of employment is explained by the fact that wages were set as a result of free competition between workers at a level that ensured almost full employment;

c) the strengthening of the role of trade unions after the First World War and the introduction of a state unemployment insurance system made wages inflexible and kept at too high a level, which was the cause of mass unemployment;

D) to achieve full employment, wages must be reduced.

Equilibrium in the labor market in the neoclassical model is determined through the function of demand for labor and the function of its supply, where real wages act as the price of labor P.L.. Labor demand curve D.L. is decreasing in nature, since firms that demand this factor of production will be able to hire more workers at lower wages. If the level of wages increases, the number of attracted labor will decrease. DL = f(PL).

Labor supply in the labor market SL also depends on real wages: the higher PL, the more workers will offer their labor on the market, and, conversely, the lower the wage, the fewer of them will be willing to get a job. Therefore, labor supply is viewed as an increasing function of real wages and the labor supply curve has a positive slope:

SL=f(PL).

By combining the demand and supply graphs, we obtain a neoclassical labor market model, showing that everyone who wants to work can find a job at the current equilibrium wage rate PLE. If labor supply increases (curve shift SL to position S'L), then this leads to a reduction in wages to PLF and equilibrium in the labor market is established at the point F.

Thus, in the neoclassical model, a market economy is able to use all labor resources, but only if wages are flexible.

Full employment in this case means that everyone who wants to sell a certain amount of labor at the prevailing wage rate at the moment can fulfill his desire. If the salary PLK is established above the market equilibrium level (at the request of trade unions or with government intervention), this will lead to the fact that the demand for labor will be significantly less than the supply of labor and a certain part of workers will find themselves unemployed. The number of unemployed is shown in the bar KM. Consequently, in the neoclassical model, unemployment is real, but it does not follow from the laws of the market, but arises as a result of their violation, intervention in the competitive mechanism of either the state or trade unions, i.e. non-market forces. These forces do not allow wages to fall to the equilibrium level, due to which entrepreneurs will not be able to offer work to everyone at the required wage rate.

Therefore, according to neoclassics, in a market economy there can only be voluntary unemployment, that is, that which is caused by the demands of high wages. Workers themselves choose unemployment for the sake of higher earnings. If the state regulates wages, it violates the competitive market mechanism. Hence the demands of economists in this direction - to eliminate unemployment, it is necessary to achieve competition in the labor market and wage flexibility.

The neoclassical concept of voluntary unemployment, set out in the book of A. Pigou, became the subject of serious criticism by J. Keynes in his fundamental work “The General Theory of Employment, Interest and Money”.

Keynesian employment theory formed mainly in the 30s of the XX century. She is associated with the name of the English economist J.M. Keynes, the most prominent researcher in the field of macroeconomics. Keynes is the founder of modern employment theory. In 1936, in his work “The General Theory of Employment, Interest and Money,” he proposed a fundamentally new explanation of unemployment. Keynesian employment theory differs sharply from the classical approach. The hard conclusion of this theory is that under capitalism there is no mechanism to guarantee full employment. Full employment is more random than regular.

The classics did not see unemployment as any serious problem. However, the events that actually took place corresponded less and less to the classical postulates. A massive explosion of unemployment occurred in the early 1930s during the Great Depression.

The Keynesian concept of employment consistently and thoroughly proves that in a market economy, unemployment is not voluntary (in the neoclassical sense), but forced. According to Keynes, neoclassical theory is valid only within the sectoral, microeconomic level, and therefore it is not able to answer the question of what determines the actual level of employment in the economy as a whole . Keynes showed that the volume of employment is in a certain way related to the volume of effective demand, and the presence of underemployment, i.e., unemployment, is due to limited demand for goods.

Expressing his views, J. Keynes refutes the theory of A. Pigou and shows that unemployment is inherent in a market economy and follows from its very laws. In the Keynesian concept, the labor market can be in a state of equilibrium not only with full employment, but also with unemployment. This is because the labor supply , according to Keynes, depends on the value of nominal wages, and not on its real level, as the neoclassics believed. Consequently, if prices rise and real wages fall, workers do not refuse to work. The demand for labor presented on the market by entrepreneurs is a function of real wages, which changes with changes in the price level: when prices rise, workers will be able to buy fewer goods and services and vice versa. As a result, Keynes comes to the conclusion that the volume of employment depends to a greater extent not on workers, but on entrepreneurs, since the demand for labor is determined not by the price of labor, but by the amount of effective demand for goods and services. If effective demand in a society is insufficient because it is determined primarily by the marginal propensity to consume, which falls as income rises, then employment reaches an equilibrium level at a point below full employment.

In addition, the employment of a significant part of the labor force is determined by such a component of total expenditure as investment. The relationship between increased employment and increased investment is characterized by an employment multiplier equal to the demand multiplier. An increase in investment leads to an increase in primary employment in industries directly related to investment, which, in turn, has an impact on industries producing consumer goods, and as a result, all this leads to an increase in demand, and therefore in total employment, the increase in which exceeds increase in primary employment directly related to additional investments.

Employment according to Keynes is a function of the volume of national production (income), the share of consumption and savings in income. Therefore, to ensure full employment, it is necessary to maintain a certain proportionality between the costs of creating GNP and its volume and savings and investments.

If the cost of producing GNP is insufficient to ensure full employment, unemployment occurs in the society. If they exceed the required size, inflation occurs.

In relation to "savings - investment", if S > I, then the flow of capital investment, growth in production and supply, on the one hand, and low current demand (due to large savings) on the other, will lead to a crisis of overproduction, a fall in demand for labor and unemployment. Excess of investments over savings I > S leads to the fact that productive demand is not satisfied due to a lack of savings. The downside of low savings is a high propensity to consume, which ultimately leads to an increase in the price level, i.e. inflation.

The Keynesian concept makes two important conclusions:

a) flexibility of prices in the commodity and money markets, as well as wages in the labor market, is not a condition for full employment. Even if they were decreasing, this would not lead to a reduction in unemployment, as the neoclassics believed, since when prices fall, the expectations of capital owners regarding future profits fall;

b) to increase the level of employment in society, active government intervention is necessary, since market prices are not able to maintain equilibrium at full employment. By changing taxes and budget expenditures, the government can influence aggregate demand and the unemployment rate.

The labor market is a specific sector of the economy. It differs from all other markets in that it is not goods that move on it, but living people. Therefore, its regulation has enormous socio-economic and political significance and is a special concern of the state. However, the task of the state is not to provide everyone with a job, as this increases inflation, but to keep unemployment at a natural level, which means achieving full employment.

The consequences of unemployment falling below the natural rate can be seen on the Phillips curve. A. Phillips established an inverse relationship between unemployment U and inflation P. On the graph, this dependence takes the form of a curve.

The Phillips curve shows that as demand for labor increases and unemployment decreases, the price level in the economy rises. Unemployment limits the possibilities for wage growth, and therefore costs, which affect the price level.

The Phillips curve describes the relationship between inflation and unemployment only in the short term, where a reduction in unemployment is impossible without an increase in inflation. Over the long term, the Phillips curve transforms into a stagflation curve, which shows a simultaneous increase in inflation and unemployment.

If the natural rate of unemployment in an economy is represented by a line U*U*, then on the Phillips curve this level corresponds to the point A, and inflation - P*. If actual unemployment in the economy is higher than the natural norm and amounts to U1, then inflation will drop to the level n1 .

If the state, in order to reduce losses in the economy, first reduces unemployment to U*, and then to U2(by increasing the money supply, expanding investment, etc.), the price level will rise to n2. The current situation will be reflected on the Phillips curve by point C.

After some time, trade unions will demand indexation of wages, in response to which entrepreneurs will lay off some workers (in order to prevent rising costs). Unemployment will return to its natural level and the Phillips curve will shift to the right, passing through the point A".

If the government takes new steps to reduce unemployment to the level U3, then the inflation rate will already be n3. On the Phillips curve combinations U3-p3 will correspond to the point D. After wage indexation and employment reduction to U* The Phillips curve will shift to the right again and pass through the point A". Further similar government actions will have similar consequences: every attempt to reduce unemployment will be followed by a rise in prices and a return of unemployment to the natural norm.

By its actions, the state provokes not only a rise in prices, but also an increase in unemployment. The curve passing through points C is D is the stagflation curve.

State employment policy should be based primarily on determining the type of unemployment. The state should not fight against any unemployment, but only against cyclical unemployment. To reduce unemployment and increase employment, the state uses the following methods:

a) improving the information system on available jobs;

b) creation and improvement of the activities of labor exchanges;

c) development of a personnel retraining system;

d) creating conditions for the development of small and medium-sized businesses;

e) development of special targeted employment programs for youth, women and workers in restructuring industries.

Unemployment sometimes causes labor migration, so in the next chapter of this work we will look at population migration, migration patterns, benefits and costs of labor movement.
4. Migration

Population migration(lat. migration- relocation) - the movement of people from one region (country, world) to another, in some cases in large groups and over long distances. People who migrate are called migrants, or, depending on the nature of the migration, emigrants, immigrants or settlers. Migration within a country is called internal, and between countries - external.

According to a report by the International Organization for Migration, the number of international migrants in 2010 was 214 million, or 3.1% of the world's population. If the growth of this indicator continues at the same rate, then by 2050 it will reach 405 million. Migration is partly due to such reasons as wars (emigration from Iraq and Bosnia to the USA and Great Britain), political conflicts (emigration from Zimbabwe to the USA) and natural disasters (migration from Montserrat to UK due to volcanic eruption). However, the main reasons for migration remain economic, namely the difference in profits that can be received for the same work in different countries of the world. In addition, a factor causing migration may be a shortage of specialists in a particular profession in a certain region. For example, economically motivated migration is observed within the European Union, where barriers to movement between countries have been practically eliminated. Here, high-income countries - France, Germany, Italy, Great Britain - serve as host countries for migrants from Greece, Hungary, Lithuania, Poland and Romania.

Forced migration can serve as a means of social control for authoritarian regimes, while voluntary migration is a means of social adaptation and a cause of urban population growth.

4.1. Migration theory

Research at the microeconomic level identify factors that predetermine individual decisions on migration (probabilistic, behavioral models have been developed) or encourage employers to hire foreign labor. Significant incentives for emigration include the difference between income available and expected in the country of immigration, the opportunity to find a reliable job, and subsequently obtain a residence permit, and the duration of residence depends on the degree to which expectations are realized.

Employers are interested in using migrant labor not only in connection with the expansion of production capabilities. Foreign labor, by increasing the supply in the labor market in a certain skill segment of the country, facilitates the survival of enterprises that are under competitive pressure but have limited capital to invest in rationalization.

It is possible to focus on the multinational nature of production or increase the capital intensity of an enterprise in order to increase labor productivity (which is reflected in the qualification structure of demand for labor within the country).

Research shows that migration is based on differences in the social and tax systems of the country of origin and the country of immigration, and the structure of immigration is determined by the qualifications and origin of the labor force.

According to territorial-structural According to models, the scale of intercountry migration flows is determined by a combination of factors in the emigration region, such as unemployment, population growth, poverty, economic stagnation, and in the immigration region, labor shortages, rapid economic growth and employment growth. There are also factors of a significant gap in wages between the region of emigration and immigration, as well as geographical remoteness, linguistic and cultural distances.

The arguments supporting these models fit well with the neoclassical theory that migration can level out regional wage differences. Although analysis of data, primarily for the UK, shows that migration does not play a big role in reducing regional differences in wages and unemployment. Labor markets are segmented and regulated, so migration can only act as one factor in equalizing wages and unemployment. However, within the United States, internal migration is credited with an important function of leveling regional imbalances. Within the EU there are different models, which in some regions are similar to the US, and in others similar to the British model.

Analysis of time series shows what exactly determines the employment of foreign labor. Differences in sectoral development of production, the ratio between capital and labor, and the level of protectionism are identified as influencing factors, as well as institutional mechanisms for recruiting labor.

Research into the welfare effects of migration in countries of emigration and immigration deserves attention. We are talking about the impact of labor migration on wages and income distribution in the country of immigration. In empirical studies, the effect of some reduction in wage levels for support workers and apprentices is largely attributed to labor migration. This effect is pronounced in countries that use foreign labor.

When assessing the impact of labor migration on wages and overall economic productivity, a key question is whether migrant workers replace or complement a given country's workforce, and if so, to what extent. In Austria, for example, the risk of a decline in wages is low, and unemployment is rising due to expanding foreign employment, especially in seasonal work and foreigners living here for a long time.

Countries of emigration appear to benefit less than expected from the outflow of their labor force (reduced unemployment, inflow of remittances, higher skill levels of workers upon return, etc.).

4.2. Integration theory

Theoretically, labor migration occurs until the marginal productivity of labor and, thus, wages are equalized in the integration space. The prerequisite for this is the absence of barriers to migration, mutual recognition of skill levels and the condition that cultural and linguistic differences are not decisive.

The importance of socio-cultural affiliation in the decision to migrate is poorly taken into account in this theory, although, as evidenced by the various migration models applied to EU citizens, traditional relationships (the historical dimension) are very important in determining the size and direction of migration flows.

Contrary to the provisions of integration theory, the movement of capital and goods has become a more important tool for smoothing out differences in wages and productivity than labor migration.

Before the creation of the Common Market, 44% of the foreign labor force came from the region that later formed the “six” of the EEC. In the “nine” of the EEC in 1980, about 47% of the total foreign labor force came from the EEC. This share decreased in the late 80s and early 90s. In 1995, only 42% of the approximately 6.5 million foreign workers employed in the 15 EU countries came from EU regions.

The degree of overlap between labor markets in the EU (the share of citizens of EU member countries in the total number of employed) is very low and currently amounts to about 2% (in Germany - 1.8%, France - 2.4, Great Britain - 1.6, Austria – 0.9%). The share of all foreign labor in total employment in the EU in 1996 was 5%. This dynamic is consistent with the EU's intentions: the creation of the EU internal market should not be linked to a sharp increase in labor migration. Equalizing interregional differences in income and wages should first of all be carried out through flows of capital and goods and only then through labor migration.

4.3. Conclusions from practice

In the 60s and early 70s, the use of foreign labor was an important component of economic development. During this period, the number of foreigners working in the “six” of the EEC increased from approximately 1.8 million to almost 4.4 million people.

Much of the immigration was the result of targeted labor recruitment carried out in countries of immigration. Recruitment (as a stimulus for immigration) is important if there are no traditional migration relations between the country of emigration and the country of immigration.

The increasing globalization of production in the 70s and 80s, as well as the growth of the tertiary sector, affected the influx of labor. From 1975 to 1995 the number of labor migrants in the founding countries of the EEC increased by approximately 400 thousand people. The share of hired workers from the “six” countries in the total number of all foreign workers decreased from 48 to 42%.

Currently, about 6.5 million foreigners are employed in 15 EU member countries.

In the 80s, a new core was formed that formed the economic basis of employment - high-tech industries, such as the sphere of highly specialized services (central branches of concerns with departments for planning, organizing and controlling a geographically differentiated decentralized production system, financial consultants, technical consultants, etc.) . In addition to the growing demand for labor in the areas of high technology and production-oriented services, types of low-paid labor have emerged (care services, courier services, gardeners, dry cleaners, security services, etc.), for which demand from the labor force is increasing. high level of income. In the process of eliminating the economic backwardness of countries, the supply of cheap and mobile labor has decreased. In this sense, the CEE countries have gained importance, as have the newly industrialized countries of Asia.

The professional and qualification structure of labor migration of a certain country gives an idea of its position in the international division of labor. Recruitment strategies on a European scale are increasingly being used, especially in management, finance and insurance, as well as in technical professions (engineering).

4.4. Simple Migration Models 4.4.1. Harris-Todaro model

The number of migrants during a fixed period t is defined as a function: , Where

Number of migrants from country A to country B,
- salary in country A,
- expected salary in country B,
- reaction function.

In this case, the expected salary in a new place depends on the probability of employment p: ( - salary in country B), that is, on the situation on the labor market. If the unemployment rate in the host country increases, then expected incomes will naturally decrease and the number of migrants will also decrease.

4.4.2. “Advantage vector” model

Another migration model involves taking into account a number of expected benefits (in the form of a “vector of benefits”): , Where

M t - number of migrants,
D - distance between countries,
X = (X 1, ..., X n) - all factors inducing migration,
a, b - model parameters.

In this model, as can be seen, in addition to benefits, costs are also taken into account - the distance factor certainly has a negative impact on the number of migrants.

4.4.3. Human Capital Theory Model

Migration is an investment; certain costs in the short term must be compensated by an increase in income in the long term, otherwise such a decision is economically meaningless. When deciding to move, a person compares the given expected income and expenses for emigration:

, Where

C - direct costs (costs of moving, purchasing new housing, transporting property, etc.),
Y i B , Y i A - income in year i in countries B and A, respectively,
M - moment of moving,
R - year of termination of labor activity,
r is the individual discount rate.

In the above inequality, implicit costs are the alternative income that the worker could have received without leaving his homeland (Y A). Individual characteristics of the employee - discount rate ρ.

Conclusion from the model:

· Migrants are relatively young people. Investments are always more profitable the longer they receive returns (the larger the value (R - M) in the model).

· Migration is more profitable, the greater the expected difference in income (Y B - Y A).

· The decision to migrate depends on the direct costs of moving.

There are quite a large number of models of population and labor movement, based on a variety of assumptions about the nature of intergroup flows and designed to obtain a wide range of conclusions about population mobility.

4.5. The Impact of Labor Movements on Comparative Advantage and Welfare 4.5.1. Benefits of the “receiving” country from immigration

· Growth of labor resources, GDP volume, total income of workers and aggregate demand in the economy, tax revenues to the state budget. Elimination of structural imbalances in the labor market.

· The ability to hide (or maintain at the same level) unemployment.

· For receiving states, especially the “aging” countries of Northern and Central Europe, another aspect is important: migrants (partially or fully) compensate for natural population decline, they themselves, on average, are usually younger than residents of the receiving country, and the birth rate in their families are higher. This means an increase in the country’s labor resources not only in the short term, but also in the long term, and therefore potential output also increases.

4. 5 . 2 . Negative manifestations of immigration for the “receiving” country

· Sociocultural factors. Temporary nature of migration, lack of assimilation with the indigenous population.

· There is a widespread misconception in society, which economists are fighting in vain: it is generally accepted that the number of jobs in the economy is limited, which means that newcomers are taking away jobs from local residents.

· Mass migration creates additional strain on the budget of the host country.

4. 5 . 3 . Benefits of labor movement for the country of emigration

· The loss of part of the labor force can have a positive effect in conditions of mass unemployment. Tension in the local labor market is decreasing and unemployment is falling.

· Emigrants not only improve their own and their family’s living conditions, but also ease the burden on the budget. The state now does not need to spend money on their treatment, education of children, etc.

· Those working and living abroad regularly send money home to their family and friends. As a result, there is a constant influx of funds from migrant workers into the donor country. Migrant remittances play a very important role, becoming a significant addition to national income.

4. 5 . 4 . Negative consequences for the country of emigration

This is a "brain-drain" problem. Some of the emigrants are the most educated and gifted professionals. For developing economies, educated specialists are the most limited productive resource, and therefore their value is very high.

However, this process is not irreversible. History has already shown that specialists who have worked in Europe and America, received additional education and work skills, and are familiar with the latest technologies return to countries where significant economic growth begins. Here at home, they can now apply for better jobs. Therefore, for poor countries with abundant labor resources, labor migration is more a positive than a negative phenomenon.

Conclusion

So, based on the work I have done, some conclusions can be drawn, namely:

The problem of unemployment is one of the fundamental ones in the development and functioning of human society. Unemployment is a phenomenon characteristic of the stage of commodity production.

Unemployment is predetermined by various factors: scientific and technological progress causes a reduction, first of all, of manual workers; structural changes in the economy cause a decrease in the number of employees in certain sectors of production; an increase in labor productivity also leads to a decrease in the number of people employed; The reduction of living labor is facilitated by the law of saving time. In the context of worsening economic problems, some production facilities that pollute the environment are also being closed. All these are objective factors that occur in all countries, regardless of their economic system. Unemployment often causes migration.

Migration has a significant impact on the socio-economic and demographic development of almost all regions of Russia and foreign countries. This is one of the most complex demographic processes, since the migration behavior of the population is influenced by a complex of interethnic, political, economic and social factors. Labor migration is the relocation of the working population from one state to another for a period of more than a year, caused by economic and other reasons. Developed countries are the main destination for immigration, while developing countries are the main destination for emigration. State regulation of the international labor market is carried out on the basis of the national legislation of the host countries exporting labor, on the basis of agreements between them, as well as on the basis of ILO conventions and recommendations.

Also, in my course work, I tried to solve all the problems posed in the introduction, that is, they considered: the theoretical foundations of the organization and functioning of the labor market, economic and mathematical modeling as a tool for studying labor market processes, unemployment (the concept and consequences of unemployment, accounting for the unemployed, types of unemployment , costs of unemployment, classical and Keynesian models of unemployment, government measures to resolve unemployment), migration (migration theory, integration theory, conclusions from practice, simple migration models (Harris-Todaro Model, “Advantage Vector” Model, Human Capital Theory Model)) , the impact of labor movement on comparative advantage and welfare (benefits and costs of labor movement: a simple graphical model for two economies, the benefits of immigration for the “receiving” country, the negative effects of immigration for the “host” country, the benefits of labor movement for the emigrating country , negative consequences for the country of emigration).

I believe that the tasks I set in the introduction are fully disclosed in the work; the goal of the work has been achieved. Bibliography 1. Alexey Kireev. International Economics. Part 1. – M.: “International Relations”, 1999. - 416 p.

2. A. Ananyev “New processes in employment in the transition to a market economy”, “Economic Issues”, No. 5 - 1995

3. D.J. Bartholomew. Stochastic models of social processes. - M.: Finance and Statistics, 1985.

4. I. Zaslavsky “On the benefits of the labor market”, “Questions of Economics” No. 9 - 1991

5. G. Mankiw “Macroeconomics” M.: MSU, 1994

6. A. G. Korovkin “Dynamics of employment and labor market: issues of macroeconomic analysis and forecasting” - M: MAKSPress, 2001

7. S. Kotlyar “Methodology for assessing unemployment”, “Man and Labor”, No. 8 - 1993

8. Wikipedia.org

9. Keynes J.M. General theory of employment, interest and money. M.: Progress, 1978

10. Agapova T.A., Seregina S.F. “Macroeconomics” Moscow 1999.

11. S. N. Ivashkovsky “Economics: macro- and microanalysis” Moscow 1999.

12.”Course of Economic Theory”, ed. Chepurina, Kiseleva Kirov 1994.

13. Campbell R. McConnell, Stanley L. Brew “Economics” Moscow 1992

14. Labor Economics: (social and labor relations) / Ed. N.A. Volgina, Yu.G. Odegova. – M.: “Exam”, 2002. – 736 p.15. E.F. Avdokushin. International economic relations. – M.: “Yurist”, 1999. – 366 p.16. L. Kostin, Doctor of Economics, prof. Migration and migrants. // Man and labor. -№8 2001. – p. 61-64

17. P. Heine “Economic way of thinking” M.: News, 1991

Modeling is one of the main methods used in scientific and applied research. Modeling is the process of constructing, studying and applying models.

Economic modeling is the construction and study of economic objects, processes and phenomena in artificially created conditions (natural modeling), or using mathematical tools (mathematical modeling).

A mathematical model of an object is its representation in the form of a set of equations, inequalities, graphs, etc., a certain image of an object created to simplify its study, obtain new knowledge about it, analyze and evaluate decisions made in various situations.

Among the objects of modeling, models characterizing the labor market are widely represented. The labor market is one of the main components of a market economy, which can be illustrated using the model of V. Leontiev. This model is represented by four sectors of economic activity - households, manufacturing, the government sector, other countries - and the functional relationships between the volume of output, labor costs, capital and total economic efficiency, which are formalized in a system of equations and identities that describe the production function. At the same time, the labor market acts as a subsystem that has a direct impact on the dynamics of economic growth, macroeconomic proportions and macroeconomic equilibrium, and at the same time is, directly or indirectly, under the influence of all macroeconomic components and the dynamics of economic growth as a whole. From V. Leontiev’s model it is clear that the labor market can be isolated from the macroeconomic system and presented as an independent economic system of a lower order, formally described in V. Leontiev’s model by a system of equations

1. Balance sheet identity of the cost of labor costs

(1 – TL)–(PLD LD + PLGE – LGE + PLGG LOG + PLR LR) = PL – R. (5.1)

2. Balance equation of labor

L = LD + LGE + LGG + LR + LU. (5.2)

3. Balance equation of time

LH = L + LI, (5.3)

where L – labor costs; PL – deflator of monetary expression of labor costs; PLD – monetary deflator of labor costs in the private sector; PLGE – deflator of the monetary expression of labor costs in state-owned enterprises; PPLGG – deflator of monetary expression of labor costs in government institutions; PLR – deflator of the monetary expression of labor costs in the production of export goods; LD – labor costs in the private sector; LGE – labor costs at state enterprises; LGG – labor costs in government institutions; LR – net export of labor inputs; LU – unemployment; LH – total fund of working and non-working time; LI – free time; TL is the current payroll tax rate.

Now let's look at an example of modeling unemployment and introduce some notation. Let L be the economically active population, E be the employed, U be the unemployed, then

L=E+U . (5.4)

Let's assume that L=const, then s is an indicator of the level of dismissal of workers, i.e., this is the proportion of employed people who lose their jobs every month.

Let j be an indicator of the level of employment, i.e. the proportion of unemployed people who find work every month, then during this month the number of people hired is jU, and sE is the number of people who have lost their jobs.

The unemployment rate is the ratio of the number of unemployed to the economically active population: U/L.

If the unemployment rate is constant and equal to the value – U/L, then the number of people hired should coincide with the number of people fired, i.e. The following equality must be satisfied:

jU = sE; jU = (L – U). (5.5)

This means: J (U/ L) = s(1 – U/ L), => U/ L = s/(s + j) unemployment rate (in percent).

The unemployment rate is one of the key macroeconomic indicators, and its correct determination is necessary for understanding and predicting the results of socio-economic policies. At the same time, the modern labor market is characterized by constant dynamic changes, the flow of labor from one state of employment to another.

Assessing dynamic flows in the labor market allows us to identify the factors that most determine changes in the structure of unemployment. Thus, its high level in any socio-economic group of the population may be associated not only with a high probability of job loss, but also with frequent changes of place of work, low socio-economic mobility and insufficient activity in searching for work, a long period of unemployment, low the likelihood of maintaining the received job, etc. For the purposes of macroeconomic policy, it is important not only to correctly assess the level of unemployment in a particular population group, but also to establish which of the labor flows in the labor market lead to such a level of unemployment.

The main population movements between the states of employment (E), unemployment (U) and economic inactivity (N) can be represented in the form of the following diagram (see Fig. 5.1)1

Pen

Peu

Pue

Pun

U Economically

Unemployed inactive

Pnu

population

Rice. 5.1. Main flows in the labor market

Рij shows the transition probability, i.e. the probability with which representatives of a certain population group will move from the i-th state to the j-th over a certain period of time. The transition probability is defined as the proportion of individuals who moved from the i-th state to the j-th over a period of time (t, t + 1) in the total population that was in the initial state i at time t. For example, P and e reflects the share of unemployed people who got a job over a certain period of time.

In conditions of equilibrium in the labor market, when the number of persons who left the category of unemployed is equal to the number of persons who became unemployed, the unemployment rate (UR) can be directly expressed in terms of transition probabilities:

(5.6)

UR=

(Pne+Pnu)Pue + PnePun (Pne+Pnu)Peu + PnuPen



This equation is derived from the following two conditions: PenE = PneN (the number of the employed population that has become part of the economically inactive population is equal to the number of economically inactive population that has moved into the category of the employed population) and (Pun+Pue)U = PueE+PnuN. Hence (Pun + Pue)URT = (Pue + Pnu)(1 – UR)T, where T is the number of economically active population (T = E + U), UR is the unemployment rate (UR = U/T = 1 – E/ T).

In other words, the unemployment rate is a certain function of the probabilities of the population transition from one alternative state to another (employment, unemployment and economic inactivity):

(5.7)

UR =

+ - - + + -

f(Pen, Pne, Pun, Pnu, Peu, Pue).

A plus sign above a variable means that its growth causes an increase in the unemployment rate, a minus sign means that an increase in this variable contributes to a decrease in the unemployment rate. Thus, the unemployment rate will be higher the lower the probability of outflow from the category of unemployed (Pue and Pun) and the entry into work of persons who were not previously part of the labor force (Pne), as well as the higher the probability of voluntary or involuntary departure from work (Pen and Peu). From equations (5.6) and (5.7) it follows that when assessing the impact of government regulation measures on the unemployment rate, it is necessary to take into account changes in all six transition probabilities due to their close relationship.

It should be noted that the issues of modeling labor indicators (including employment, unemployment, etc.) are studied in detail within the framework of a separate discipline “Analysis and modeling of labor indicators”1. From the point of view of a more in-depth study of the issues under consideration and the current state of the Russian economy (a certain growth of the domestic economy), modeling the processes of economic growth is of interest. Let's consider the most famous models.

Keynesian models of economic growth. Until the end of the 1930s. Western macroeconomic theory practically did not study the mechanism of economic growth. Only in 1939 was the work of the English economist R. Harrod published, and a few years later - by the American economist E. Domar. Both authors were supporters of the Keynesian model. Although Harrod's work has been published previously, it is useful to consider Domar's simpler model first.

Domar model. Domar, as a representative of American Keynesianism, was interested in the dynamic aspects of this theory, i.e. he was interested in the problem of ensuring full employment not for a short period of time (like Keynes), but for a long period. Thus, Domar believed that achieving full employment is not a static problem, but a dynamic one. The fact is that the level of aggregate demand that ensures full employment in a given period of time may be insufficient to achieve full employment in a subsequent period. Consequently, in a developing economic system, aggregate demand should increase in proportion to its production capabilities. This condition is written as follows:

P − P = Y − Y (5.8)

where P and P are production possibilities, respectively, in period and ; Y and Y are the total income during these periods.

Domar expresses the left side of this equation as

P − P = I A, (5.9)

where I is the volume of net investment in period t; A is the increase in production capabilities per unit of investment (assumed to be a constant value in the model).

In reality, however, the increase will be less than I A, since the creation of new production capabilities presupposes the disposal of old ones; therefore, the real increase will be

P − P = I V, (5.10)

where in – potential average social productivity of investment (also assumed to be constant).

Analyzing the right side of equation (5.8), Domar considers the increase in total income through the investment multiplier effect. At the same time, the marginal propensity to save is also assumed to be constant. In this case, the level of income is a value proportional to the level of investment. From this, Domar concludes that full employment in the economy will be stably maintained over the long term if investment and total income grow at the same rate, equal to the product of the marginal propensity to save and the average social productivity of investment.

Y = I = sB.(5.11)

Harrord's model. Domar's model could not fully reveal the mechanism of economic growth, since it lacks a detailed theory of investment. The Harrod model does not have this drawback. It includes the endogenous theory of investment. It is characterized by two features. The first is taking into account the expectations of entrepreneurs. It is assumed that in any period of time they plan the supply of goods based on the degree to which their forecasts correspond to the actual level of demand in the previous period. If their forecasts turned out to be correct, and aggregate demand coincided with aggregate supply, then supply growth rates will be planned equal to those previously achieved. If the planned supply turns out to be higher than demand, then the rate of supply growth will be reduced. If, on the contrary, the planned supply turned out to be insufficient in relation to demand, then the rate of supply growth will be increased.

The second feature of Harrod’s investment theory is the introduction of the marginal “capital/product” ratio into the model: this is the increase in capital that is necessary for the value of the product to increase by one.

According to Harrod's findings, entrepreneurs' expectations will be fully satisfied when the production of goods increases at a rate equal to

T rg =(5.12)

where s is the marginal propensity to save (considered a constant); Cr− marginal capital/product ratio.

Expression Harrord calls it a guaranteed growth rate. However, the actual growth rate may not coincide with the guaranteed one. If such a deviation occurs in any direction, a mechanism will begin to operate, which at each new stage will help move the economy away from the equilibrium state. For example, if actual growth turns out to be greater than guaranteed, then there will be an excess of demand over supply. Then next year entrepreneurs will plan an even higher rate of production growth. However, demand will increase even more, and producers will once again find themselves unsatisfied and will be forced to further increase the rate of production growth. The situation will develop similarly when actual growth turns out to be less than guaranteed. As a result, aggregate demand will be less than aggregate supply. Then entrepreneurs will begin to reduce the rate of production growth, but the growth rate of aggregate demand will fall even more. Entrepreneurs will once again be deceived in their expectations and will be forced to further reduce production growth rates.

Thus, Harrod believed that the balance between supply and demand in the process of economic growth is extremely unstable.

Along with the concepts of actual and guaranteed growth, Harrod introduces the concept of the natural growth rate. This is the rate that is the maximum possible, allowed by the growth of the economically active population and technical progress. Considering natural growth, Harrod introduces into the model the proposition that technical progress is neutral, i.e. assumes that the general relationship between the amount of capital and the amount of product remains unchanged as long as the rate of interest on loans remains unchanged. With this assumption, it turns out that the improvement of technical knowledge is manifested in a constant increase in the productivity of living labor. Then, if there is no increase in the volume of capital, a situation may arise in which the same quantity of product will be produced with an ever-decreasing number of employed people. This will lead to an increase in the unemployment rate. Consequently, in order to increase employment, a constant increase in the volume of capital is necessary, and this must proceed at the same pace as technological progress.

Harrod introduces the following formula for the natural growth rate:

A = d+t+dt, (5.13)

Where d– growth rate of economic population; t– rate of growth of labor productivity; dt– an indicator characterizing the joint influence of both factors, since newly recruited workers, as a rule, have higher labor productivity.

An important point in Harrod's model is the study of the relationships between the growth rates considered. It is obvious that the growth rate of production and income cannot exceed the growth rate for a long time. However, if the economic system was in a state of depression for a certain period, then the actual growth rate for some period may exceed the natural one. But this period will be short-lived, then the actual growth rate will begin to decline.

If the guaranteed growth rate is higher than the natural one, then the actual growth rate over a long period of time will be less than the guaranteed one; As a result, entrepreneurs, experiencing constant disappointment in expectations, will reduce production plans and investment volumes. As a result, the economic system will fall into a state of depression.

If the guaranteed tempo is less than the natural tempo, then there is no reason for the actual tempo to consistently exceed the guaranteed tempo. With this approach, the expectations of entrepreneurs will be justified, they will expand production, and the economy will move into a state of recovery.

If the actual growth rate over a long period of time is equal to the guaranteed one, then such development completely satisfies entrepreneurs, but this situation cannot be considered optimal for the economic system, since the guaranteed growth rate in this case will always be less than natural. This means underutilization of labor resources and rising unemployment.

For an economic system, equality of all three growth rates is always optimal: actual, guaranteed and natural. In this case, all the expectations of entrepreneurs are met, full employment and a high level of production efficiency are ensured.

Neoclassical models of economic growth. They developed in the process of criticizing Keynesian models. At the same time, some truly vulnerable features of Keynesian models stood out:

1) production growth in these models was considered exclusively as a function of new capital investments, while growth can also be achieved by attracting new workers to use existing but unused capacity;

2) the models assumed the constant capital intensity of production, which did not make it possible to choose between more or less intensive production methods;

3) Keynesian growth theories could not be recommended for the development of countries that lack capital and have large labor resources.

Neoclassical models of economic growth are based on the mathematical apparatus of the production function. Previously, the latter was considered at short time intervals. Now it is necessary to analyze the production function and its role in studying the problems of macroeconomic dynamics.

The production function has the form

, (5.14)

where Y is the final product; X1, X2, …, Xn – the most important factors of production; A is a parameter that plays a dual role: it characterizes the share of factors not taken into account in the model and ensures reduction of all factors to a single dimension; a1, a2, ...,ap – elasticity coefficients characterizing the degree of influence of factor characteristics on the resultant one.

The sum of the elasticity coefficients can be greater than, less than, or equal to 1. If the sum of the elasticity coefficients is equal to 1, there are neutral returns to scale, i.e. final output grows at the same rate as the output of factors of production. When the sum of the elasticity coefficients is less than 1, there are negative returns to scale, i.e. the final volume of production increases to a lesser extent than the total volume of factors of production. If the sum of the elasticity coefficients is greater than 1, then they speak of positive returns to scale, i.e. final output grows faster than the output of factors of production.

The first model of economic growth based on a production function was the Cobb–Douglas production function, which was constructed by studying US manufacturing statistics for 1899–1922. The model examined the dependence of production volume on two factors: the volume of labor resources and fixed capital. The Cobb–Douglas function has the form

where L is the volume of labor resources; – labor elasticity coefficient; K – volume of fixed capital; – capital elasticity coefficient. In this model + =1.

This production function had a serious drawback: it considered only the option of extensive growth, without taking into account the influence of scientific and technological progress. In 1942, J. Tinbergen (Netherlands) introduced the NTP factor into the Cobb–Douglas function

A = e, (5.16)

where e is the base of natural logarithms; n – coefficient of elasticity of the NTP factor; t – time period for which growth parameters are determined.

Thus, NTP is described by an exponential function of time.

Such an adjustment to the production function allowed Tinbergen to quantify the impact of scientific and technical progress (i.e., the share of intensive factors) in the process of economic growth

n = Y – L – K.(5.17)

This approach to assessing the influence of NTP means that this factor is external (exogenous) in relation to other parameters of the function, i.e. it acts autonomously, taking on independent meanings. At the same time, there is another approach to assessing the NTP factor, when it is considered as an internal (endogenous) parameter. With this approach, NTP does not receive an independent expression, different from other parameters of the production function, but manifests itself within them. In this case, the problem of determining the influence of scientific and technical progress also arises. Her solution was proposed by J.R. Hicks. It consists of taking into account the effects of scientific and technical progress based on the study of elasticity coefficients of substitution and individual factors of production. A graphical illustration of this approach is presented in Fig. 5.2.

E3 E1 E2

F2 F1 F3

Rice. 5.2

On the ordinate axis K is the volume of capital; on the abscissa axis L is the volume of labor resources. The curves shown on the graph are called isoquants. They show different combinations of factors of production (labor and capital) that produce the same amount of output. When the isoquant shifts to the right (from E1F1 to E2F2), the volume of output increases, and when it shifts to the left (from E1F1 to E3F3), it decreases.

The value of the elasticity of substitution coefficient shows by how many percent the consumption of one factor will change when the costs of another change by one percent.

E = dKL / dLK,(5.18)

where − dK/dL – the marginal rate of substitution of one factor for another.

Formula (5.18) contains natural volumes of factors, while technological methods of production differ in their ratios. These ratios are determined by the marginal rate of substitution, each value of which corresponds to certain technologies. If L/R = P, dK/dL = q, then it turns out

E=(dPdq / Pq).(5.19)

Magnitude E shows the elasticity of substitution not of the factors themselves, but of their ratios: when the marginal rate of substitution changes by 1%, the ratio of production factors will change by E%.

If, when technology changes, the coefficient of elasticity of substitution does not change, then NTP is considered neutral, since the ratio of production factors remains the same. If the elasticity coefficient has changed, this indicates the effect of the NTP factor. With an increase in the share of capital, a labor-saving type takes place, and with an increase in the share of labor, a capital-saving type of scientific and technical progress takes place.

The debate between supporters of exogenous and endogenous setting of the STP parameter in the production function continues. Proponents of the exogenous interpretation justify their position by the fact that scientific and technical progress develops according to its own laws. Adherents of the endogenous interpretation draw attention to the fact that scientific and technical progress is inseparable from other factors of production, materializing in an increase in their quality.

Several neoclassical models of economic growth have been developed based on the production function. Among them, the models of the American economist R. Solow and the English economist D. Mead are especially famous.

Solow model. This model was developed in 1956. R. Solow believed that if a production function of a neoclassical type is introduced into Harrod’s model, then the contradictions associated with the instability of economic development and the possibility of constant growth with forced unemployment will be eliminated.

The structure of the Solow model is determined by the following equations:

Y = F(K,L); (5.20)

I = dK/dt; (5.22)

I= S; (5.23)

L(t) = L e ; (5.24)

dY/dL = w/P. (5.25)

Equation (5.20) is an already known aggregate production function of the neoclassical type. Equation (5.21) expresses the saving function, with the propensity to save assumed to be constant, as in the Domar and Harrod models. Expression (5.22) is essentially an identity: net investment is the change in the value of capital over time. Equation (5.23) represents the traditional equilibrium condition in the goods market. Equation (5.24) shows that labor resources increase at a constant rate n, as it was in the Harrod model, and L expresses the size of the labor force at the initial moment. Since this model does not take into account scientific and technical progress, the growth rate of the labor force coincides with the natural growth rate of the system. Finally, equation (5.25) is the well-known equilibrium condition for the entrepreneur, i.e. equality of real wages to the marginal product of labor.

After appropriate transformations we obtain

DK/dt = sF(KL e). (5.26)

This differential equation determines the rate of capital accumulation required to maintain full employment.

The mechanism of action of the Solow model is quite simple. Let's take an economic system during a certain period of time. The volumes of capital and labor are given. Since the relative prices of factors of production, i.e. wages and profits fluctuate in such a way as to ensure full use of both capital and labor, the production function determines the level of production. Moreover, once the level of production is determined, the savings function gives the amount of savings; since they are equal to capital investment, and capital investment is something other than a change in the amount of capital, then the rate of accumulation is known. In the next period, the amount of capital equal to the sum of the initial stock and net investment is obtained. The amount of available labor is given by equation (5.24), and the action of the described mechanism will be repeated again.

In the Solow model, the problem of achieving full employment is considered through changes in the value of the capital-labor ratio. After a series of transformations, we obtain the equation

dk/dt = sF(k,1) – nk. (5.27)

This differential equation determines the change over time in the capital-labor ratio, which guarantees the maintenance of full employment.

Let us consider equation (5.27) in more detail. Expression sF(k,1) denotes the amount of product received on average per employee, and sF(k,1) is, respectively, the amount of savings and new capital per employee. Expression nk represents the amount of capital required to equip new labor resources, which depends on the number of workers already employed.

If the growth in the volume of new capital per employed person is equal to the volume of capital per employed worker required to equip the new labor force, i.e. if sF(k,1) = nk, then full employment is ensured without any changes in the combination of production factors: dk/dt= 0. If the increase in the volume of capital per worker exceeds the amount of capital per employee required to equip the new labor force (sF(k,1) > nk), then the absorption of the entire increase in capital entails a transition to a new production combination that uses more capital and less labor. Then the rate of interest falls relative to the wage rate and entrepreneurs choose a new production combination with a more intensive use of capital. Finally, if the increase in capital per worker is less than the amount of capital per worker required to equip the new labor force (sF(k,1)< nk), then to achieve full employment it is necessary to use a different production combination that uses less capital and more labor. This is achieved as follows: maintaining the same combination of factors leads to unemployment, then wages decrease relative to the rate of interest, and entrepreneurs choose a combination with less use of capital and more intensive use of labor.

As a result, economic growth continues while maintaining full employment. Ultimately, the Solow model guarantees not only the possibility of equilibrium economic growth, i.e. development with full employment and full use of capital, but also the sustainability of this growth in the sense that when the system deviates from the line of equilibrium development, internal mechanisms come into play that can ensure the return of the economy to a state of equilibrium.

This is the fundamental difference between the Solow model and the Keynesian models of Harrod and Domar.

Mead's model. This model develops the problem of the functioning of an economic system of perfect competition, developing as a result of population growth, capital accumulation and technical progress.

The production function of the model under consideration is expressed as follows:

Y = F(K, L, t), (5.28)

Where Y, K, And L have already known meanings, t denotes time and shows that the state of technical knowledge improves over time. From the above production function it is clear that the level of production can increase over time due to three reasons: capital growth, active population growth and technological progress.

The equation that determines the contribution of each of these three factors to economic growth is

Y = Uk + Qq + r,(5.29)

Where Y– average annual growth rate of national income; U – the share of national income received by capital; TO - average annual rate of capital accumulation; Q– the share of national income received by labor; q– average annual growth rate of labor resources; r – average annual growth rate of national income under the influence of technological progress.

Subtracting from both sides of this equation the parameter q, we get the equation

Y – q = Uk – (1 – Q)g = r. (5.30)

It shows the annual growth rate of income per unit of labor, as well as the annual growth rate of per capita income, subject to , that a constant proportion of the population is employed in production. From equation (5.30) it is clear that the higher the rate of accumulation and technical progress and the lower the rate of population growth, the higher the income per unit of labor.

Having considered the factors that determine economic growth, J. E. Mead poses the problem of changing growth rates.

Knowing that the rate of population growth can depend on the rate of growth of per capita income ( Y–q)and that the rate of technological progress is influenced by the rate of capital accumulation, Mead assumes that these quantities are determined by factors external to the economic system. Therefore, these parameters are assumed constant in the model.

The scientist comes to the following conclusions. The rate of growth of national income, as well as (at a constant rate of population growth) the rate of growth of the standard of living of a given society, can increase if:

1) technical progress develops so quickly that it causes an increase in the “product / capital” ratio;

2) the nature of technical progress and the possibility of interchangeability of capital and labor in production are such that they cause a constant redistribution of income in favor of persons with a higher propensity to save (i.e., an increase in the share of profit in national income);

3) capital and labor are interchangeable, and factors of production grow at different rates;

4) technical progress intensifies to a greater extent that factor of production that grows faster.

Thus, the growth rate of national income depends on a number of circumstances. Mead further examines the question of whether it is possible to maintain a constant rate of income growth over time. The model gives a positive answer to this, naming the following conditions for stable growth:

1) the elasticity of factor substitution is equal to one;

2) technical progress is neutral;

3) the propensity to save among recipients of profits and wages remains constant.

Fulfillment of these conditions presupposes the achievement of a constant rate of capital accumulation. In Mead's model, the rate of capital accumulation should be equal to

Tn = (Qq + r) / (1 – u).(5.31)

Then national income will grow at a constant rate, also equal to Tn = (Qq + r).

In the future, the study of economic growth in the production function model involves taking into account an increasing number of factors, i.e. Multifactor models of economic growth become dominant. In the famous work of the American economist E. Denison, “A Study of Differences in Economic Growth Rates,” written in the mid-1960s. Based on materials showing the growth of national income in ten developed countries of the world for 1950–1962, the author analyzed 23 factors of economic growth. These include factors associated with the costs of labor (employment, hours worked, gender and age structure of the employed, education) and capital (structures and equipment, inventories, land, housing stock); influencing the increase in output per unit of cost (progress in knowledge, changes in the timing of their application, reducing the age of capital, progress in the distribution of resources, etc.); providing savings by increasing the scale of economic activity (growth of national local markets, elasticity of demand based on income).

The classification of factors proposed in the Mead model is the most detailed, and the growth model itself is for the first time based on specific statistical measurements.

Neoclassical models of economic growth are criticized by representatives of a number of economic theories. In particular, serious criticism is contained in the works of representatives of Marxist theory. They boil down to the following. A significant drawback of neoclassical theories of economic growth is that they completely bypass the problem of selling products, focusing on production costs and on obtaining maximum profits with a minimum of costs. They do not take into account the fact that a reduction in wages for these purposes leads to a relative decrease in demand and a deterioration in sales conditions. Neoclassicists tried to develop a model of balanced production growth without taking into account the sale of products, and this is the most vulnerable link in their concept. This theory is far from reality in the sense that it is based on the concept of stable equilibrium, which excludes economic crises; its supporters proceed from the presence of free competition and abstract from the existence of unemployment and underutilization of production capacity.

Serious criticism of neoclassical theories of growth is expressed by representatives of English post-Keynesianism. They question the existence of the production function itself. From their point of view, establishing an unambiguous connection between factors such as labor and capital is impossible. The fact is that if we express the volumes of these factors in value terms, it turns out that the same values of the cost of labor and capital can have completely different physical values. To avoid this contradiction, these factors should be presented in physical units, which is possible for the quantity of labor but not applicable for capital. With any option for measuring the volume of capital, its value depends on the interest rate, i.e. from income distribution. But if it is impossible to measure capital in physical units, i.e. Regardless of the distribution of income, the production function, understood as a one-to-one relationship between certain quantities of factors of production and a certain amount of product, does not exist. Then the entire theory of distribution of the social product, based on the concept of marginal productivity and claiming to explain the distribution of income, considering the available quantities of factors of production as data, also loses all meaning. In other words; the theory of marginal productivity faces the following contradiction: if the distribution of income has not yet occurred, then it is impossible to talk about the existence of a particular amount of capital, since it depends on the distribution of income; if the distribution of income has already occurred, then we can talk about the amount of capital, but the theory of marginal productivity cannot be used to explain the distribution of income, since this distribution is considered as given. Post-Keynesian leader D. Robinson, criticizing neoclassical models of economic growth based on the production function, called them “golden age models.” By this she emphasized the discrepancy between the conclusions of these models and reality.

Post-Keynesianism (Cambridge School) is a relatively new direction in macroeconomic theory. Its representatives are English economists D. Robinson, N. Kaldor, P. Sraffa, D. Mirlis. This direction is based on two theoretical sources: Ricardo's labor theory of value and Keynes's theory. Cambridge School scholars criticize orthodox Keynesianism (Hicks, Hansen) for seriously distorting Keynes's views. They believe that the central tenet of Keynes's theory is the idea that the market economy is unstable, while Hicks and his supporters presented Keynes's theory as a model of macroeconomic equilibrium. In addition, representatives of the Cambridge school criticize Keynes's followers for ignoring monetary factors, the problem of distribution, and for considering Keynes's theory as static, although, according to post-Keynesians, it is fundamentally a dynamic theory.

Economists of the Cambridge School proposed their theory of distribution, which was substantiated in most detail by N. Kaldor. It assumes the use of the multiplier principle to construct a theory of income distribution under conditions of full employment, as well as the following conditions: the economy is in a state of full employment, so income in real terms can no longer increase; income is divided into salary and profit; profit recipients have a higher propensity to save; trade union agreements with entrepreneurs are concluded on the basis of nominal wages.

If entrepreneurs invest in an amount exceeding savings, then as a result of the multiplier effect, total income in monetary terms increases. Consequently, the general price level begins to rise. Since collective agreements fix nominal wage rates, real wages fall. As a result, the share of wages in total income is reduced, and the share of profit increases. Since profit recipients have a high propensity to save, the volume of savings in society increases, which equals the volume of investment, and equilibrium is restored in the economy.

The opposite situation is observed in the economy when the level of investment is less than the volume of savings. A decrease in demand at full employment causes a decrease in the price level, hence an increase in real wages and a decrease in profits. As a result, the share of wages in national income increases, which leads to a reduction in savings, since workers have a lower propensity to save than entrepreneurs. The economy is again experiencing an equalization of investment and savings.

N. Kaldor makes the following conclusion: if the values of the propensity to save among hired workers and entrepreneurs are given, then the share of profit in national income is directly dependent on the share of investment in it.

The economy always has a mechanism for redistributing income that guarantees a level of savings that will be sufficient to balance any volume of investment. Therefore, the rate of accumulation depends only on the decisions of entrepreneurs. N. Kaldor believed that an increase in growth rates could be achieved only through the redistribution of national income in favor of profit.

At the same time, within the framework of post-Keynesian theory, another point of view is expressed. D. Robinson believes that the most important stimulus for economic growth is the redistribution of national income in favor of wages. This will eliminate difficulties in implementation and increase the volume of aggregate demand.

Kaldor–Mirlis model. This post-Keynesian model of economic growth is a full employment model that incorporates Calrod's theory of distribution. It views investment as an active and saving as a passive element in the growth process. The decisive participants in the growth process are entrepreneurs who invest in a certain amount. The income redistribution mechanism guarantees constant equalization of the amount of investment and savings.

The most important feature of the model is a fundamentally new approach to technical progress. In all previously considered models, it was treated as a factor external to the economic system in the sense that its rates were determined independently of other parameters of the system. In this model, technical progress is studied in close connection with capital accumulation. Consideration of technological progress is based on two main principles:

1) analysis of the existing machine park by generation, since each new generation of equipment has higher productivity;

2) learning through experience.

The second principle assumes that entrepreneurs do not immediately find the optimal line of their behavior, but gradually approach it, accumulating experience in implementing the achievements of scientific and technical progress. However, the learning function is characterized by diminishing efficiency. Therefore, it is necessary to constantly introduce new ideas into the economic system.

Since the authors of the model consider technical progress in close connection with capital, they consider it impossible to separate these two parameters. The concept of capital is absent in the model, and the function of technical progress is expressed through two indicators:

– growth rate of investment per worker ( I);

– growth rate of labor productivity of workers employed on the latest generation machines (P ).

The technical progress function has the form

П = f(I) ,(5.32)

As the rate of growth of investment per unit of labor accelerates, labor productivity increases, but at a decreasing rate, since the use of existing technical knowledge has its limits. Therefore, accelerating the rate of growth depends both on the influx of new ideas and on the extent to which they are diffused through experiential learning. Thus, the main driving force of economic growth is the ability of society to realize the achievements of scientific and technical progress.

1) the total amount of net profit that they expect to receive during the entire period of operation of the machine park must be at least equal to the amount that other entrepreneurs receive in the entire economy;

2) only those projects are invested that guarantee the return of all invested funds within a certain time frame.

From a mathematical point of view, the Kaldor–Mirlis model is a complex system of 11 equations with 11 unknowns. As a result of its solution, the main condition for stable equilibrium development was formulated - equality of growth rates: investment per unit of labor (I), labor productivity on new generation machines ( P ) and real wages (W/R) .

I = P = (W/P).(5.33)

One of the most important areas of analysis of socio-economic phenomena and processes is not only their study in dynamics, which involves assessing actual changes in levels, identifying trends and patterns of their development, but also building forecasts based on them. Labor market forecasting should be considered as a process of quantitative and qualitative labor market research aimed at identifying labor market development trends and optimal calculation of supply and demand. In general, forecasting in the labor market can consist of various directions:

− supply of the economically active population. This direction allows us to determine the number of people entering the labor market;

− demand for the economically active population. This forecast consists of the number of jobs expected to be introduced in the forecast period and available jobs, taking into account possible changes.

− relationship between demand and direction. Characterizes the degree of tension in the labor market;

− distribution of the economically active population.

In modern conditions, in almost all countries, forecasting the situation on the labor market is very important. In all countries, population growth leads to an increase in the working age population, which places demand for jobs. At the same time, the development of modern technologies causes not only a relative, but also an absolute reduction in the need for workers in many enterprises. Therefore, to develop measures to combat unemployment, forecasting the size of the working-age and economically active population, as well as the number of employed and unemployed, is of great importance. This forecasting is based, first of all, on forecasting the total population of the country and its structure, taking into account possible changes in the coefficients of economic activity and employment of the working population. In addition, forecasting the size of the economically active, employed and unemployed population is carried out on the basis of extrapolation methods. The essence of extrapolation forecasting methods is as follows: based on the analysis of actual, time series of the economically active population, employed and unemployed of a particular country, a formal function (depending on time) is determined, called a growth curve, which most accurately describes the real process of changes in the number of forecasted indicators. Most often in practice, such functions are:1:

1) equation of a line

S t = S 0 + ΔS t; (5.34)

2) second order parabola equation

S t = a 0 + a 1 t + a 2 t 2 ; (5.35)

3) various power functions, for example:

S t = S 0 (1+k) t ; (5.36)

S t = S 0 (1+k / (1-0.5k)) t, (5.37)

where S t , S 0 are, respectively, the predicted and base level of this indicator (number of economically active, employed or unemployed population); t – forecast period (in years); k is the overall growth rate of the predicted indicator (number of economically active, employed or unemployed population); a 0 , a 1 , a 2 – parameters of the equation determined as a result of solving a system of normal equations.

More complex in implementation, but giving more accurate results, are mathematical models that take into account age-specific rates of economic activity, employment and unemployment of the population. They make it possible to reflect not only the dynamics of absolute predicted indicators, but also possible changes in age-specific relative indicators. In this case, the economic-mathematical model for predicting the number of economically active, employed and unemployed population in general looks like this:

P (t) = H 1 R T , (5.38) where P (t) is the distribution matrix of the absolute number of the predicted indicator at the end of the t-year period; H 1 – matrix of distribution of the total population of the country at the beginning of the forecast period; R – matrix of age-specific coefficients of mechanical population growth; E is the identity matrix; N and M are matrices of age-specific fertility and mortality rates, respectively; T – matrices of age-specific coefficients of predicted indicators (economic activity, employment and unemployment).

The construction of such models is possible if appropriate information is available. The labor market forecast is the basis for determining financial resources, and also allows us to determine employment policy priorities for the forecast period and develop specific measures aimed at reducing the unemployed, increasing competitiveness in the labor market and ensuring social guarantees.

Collection output:

MODELING OF LABOR MARKET DEVELOPMENT USING INTELLIGENT INFORMATION TECHNOLOGIES

Zhuk Marina Alekseevna

Ph.D. econ. Sciences, Associate Professor OSU, Orenburg

Omelchenko Tatyana Valentinovna

OSU, Orenburg

Currently, the processes occurring in regional labor markets are a relevant subject for research due to their high social significance in the post-crisis economic space of Russia. An analysis of the definitions of the labor market showed that the labor market can be defined as an economic environment or space, as a mechanism or as a system. Having carried out a comparative analysis of various definitions, and having studied the essence and features of the labor market, the following definition was formed: “The labor market is a dynamic economic system in which competing employers and employees enter into social and labor relations on mutually beneficial terms, as a result of which a certain level of employment and wages.”

The above definition reflects the essence of the labor market, but does not take into account the fact that the labor market performs many functions, the most important of which are social and economic. The labor market should not be completely self-regulating only due to its own mechanisms, since vulnerable sections of the population will not be able to consistently take part in social and labor relations. For these and other less significant reasons, the labor market should be regulated by the state.

The main subjects of the labor market are employers and their representatives, as well as employees. The state is also a subject of the labor market, which assumes the functions of regulating social and labor relations between employers and employees. The state, as an active participant in the labor market in a market economy, has the opportunity to create new jobs, thereby contributing to the development of the labor market and the economy as a whole.

The current state of the labor market in Russia does not meet the requirements of a growing economy, since the presence of a mismatch between supply and demand in the labor market is not temporary, but long-lasting.

The imbalance of supply and demand is expressed in two forms. The first implies a quantitative discrepancy between the demand and supply of labor, which is expressed in the form of unemployment or a shortage of labor resources. The second form is a discrepancy between the qualification structure of supply and demand, which is expressed in the form of a shortage of workers with the required qualifications or their excess.

For the Orenburg region, the level of registered unemployment has fluctuated around 1% for the last five years, which suggests that there is no pronounced quantitative discrepancy between supply and demand in the labor market. But this indicator fluctuates around the lower limit of the natural rate of unemployment, which borders on a situation of shortage in the labor market, leading to a slowdown in economic growth.

In conditions of shortages in the labor market, government regulatory measures should be taken to ensure maximum compliance between the structures of demand and supply in the labor market. On the one hand, the low unemployment rate indicates that almost the entire economically active population of the region is involved in labor relations, and in this case we can talk about full employment. But on the other hand, if we analyze the standard of living of the region’s population, we can conclude that employment is full, but not effective.

To regulate the labor market at the city level in order to achieve effective employment, modern information technologies should be used, which will not only help automate the collection, storage, processing and transmission of information, but also speed up and simplify the development of measures to regulate it. Such technologies include intelligent information technologies designed to solve unstructured and semi-structured problems, taking into account poorly formalized factors.

To solve the problems of regulating the labor market, it is necessary to store information about the labor market and promptly obtain information about the dynamics of its indicators and structure. All this is required to develop a set of measures to regulate the labor market. To determine a development strategy, detailed and summary information for a certain past period of time and forecast information on a number of indicators are required.

Forecasting must be based on statistical information, the collection and processing of which requires material and time costs. In addition, forecasts are made using mathematical and statistical models, the construction of which also takes time, and changing the parameters of the models may require their adaptation to new conditions.

The disadvantage of this approach is that it is costly and does not allow quickly obtaining information in the required sections, and also that it makes it possible to only partially increase the validity of decision-making, and the final management decision can only be obtained by a person. Intelligent information systems make it possible to develop decisions like a person and accumulate not only information, but also knowledge, as well as management experience in the form of knowledge.

The basis of intelligent information systems is a knowledge base and a logical inference mechanism. The knowledge base is organized on the basis of the selected knowledge representation model. The choice of model depends on the subject area, the functional purpose of the intelligent system and the complexity of the objects.

As part of the conducted labor market research and analysis of existing knowledge representation models, a frame model for knowledge representation was selected and developed. This model consists of two hierarchical frame structures of supply and demand.

The developed model allows you to store knowledge about labor market objects, their relationships, interaction conditions, possible situations that can happen to these objects. The frame model also makes it possible to store not just knowledge, but “deep” knowledge, which can affect not only the processes of recognizing emerging situations, but also processes such as thinking and imagination. Therefore, using the developed knowledge representation model, it is possible to model not only the current state of the labor market, but also “play out” various imaginary situations. This happens due to the fact that each object of the frame model has its own set of actions and a set of conditions under which they will be activated.

An important advantage of the frame model is that it simultaneously stores declarative and procedural knowledge, which makes it possible to fill the knowledge base through attached procedures. The knowledge base, in turn, can be replenished with some situations that occur in the labor market and can be considered stereotypical. Such situations, when included in the database, can be activated and, after checking the conditions, become objects of the knowledge base.

Logical inference in frame models is not strictly specified, which avoids constant changes and modifications of systems developed on the basis of these models. Another advantage of the model is that it can be implemented using standard DBMS.

The initially developed frame model was implemented using Microsoft Visual FoxPro 9.0. The created intelligent information system was workable, but had disadvantages:

– the development of the most intelligent information system took a lot of time and required significant effort;

– each frame, taking into account the peculiarities of its structure, was represented in the database as a separate table with many fields, standard for a certain class of objects and level of the frame hierarchical structure, as well as an unlimited number of rows, which increased as you worked with the system and depended on the number of relationships with others objects;

– the development of internal attached procedures was carried out in several stages, and their debugging took a lot of time;

– the execution of external procedures for comparing the hierarchical structures of supply and demand took a long time with a large number of frames;

– the sets of slots for describing frames were fixed, and changing them required rebuilding the program with repeated debugging and changes to the attached procedures.

In connection with the listed shortcomings of the developed system, an attempt was made to implement it using the 1C: Enterprise system, as one of the frequently used in small and medium-sized enterprises and having a wide range of functionality that can be used to implement frames. The choice of this system made it possible to significantly speed up and simplify the process of implementing a frame model for knowledge representation, improve methods for describing procedural and declarative knowledge, provide their visual representation, expand the functionality of the developed model and optimize the logical inference procedure.

The developed intelligent system is designed to perform the following main functions:

– collection, processing, storage, use and transmission of information on the state of the labor market at the city level;

– accumulation of knowledge about the labor market, emerging problems, experience in solving them and the effectiveness of applied measures to regulate the labor market;

– providing information on the structure of supply and demand in the labor market, inconsistencies in these structures;

– developing measures to regulate the labor market, taking into account changes occurring in both the structure of demand and supply, as well as possible trends in the development of these structures;

The developed system should be used in the employment service, which has data on the state of the labor market, existing unemployed people, available vacancies, and can also supplement information by receiving it from enterprises on available vacancies and already occupied jobs and from educational institutions on expected graduations.

The proposed intelligent system can be used in developing a set of measures to regulate the labor market, in developing strategies for socio-economic development, in determining the structure of enrollment in educational institutions, as well as in developing training and retraining programs for unemployed citizens.

Bibliography:

1. Andreychikov, A.V. Intelligent information systems / A.V. Andreychikov, O.N. Andreichikova. – M.: Finance and Statistics, 2004. – 424 p. – ISBN 5-279-02568-2.

2. Gavrilova, T.A. Knowledge bases of intelligent systems/ T.A. Gavrilova, V.F. Khoroshevsky - St. Petersburg: Peter, 2001. - 384 p. – ISBN 5-272-00071-4.

3. Kapelyushnikov, R.I. Russian labor market: adaptation without restructuring / R. I. Kapelyushnikov. – M.: State University Higher School of Economics, 2001. – 309 p. – ISBN 5-7598-0086-8.

4. Romanov, V.P. Intelligent information systems in economics: textbook / ed. Doctor of Economics, Prof. N.P. Tikhomirov. – M.: Exam, 2007. – 496 p. – ISBN 5-377-00090-0.