The Role of Statistical Methods in the Estimation of Management Efficiency

Journal of Environmental Treatment Techniques

2019, Special Issue on Environment, Management and Economy, Pages: 1089-1092

J. Environ. Treat. Tech.

ISSN: 2309-1185

Journal web link: http://www.jett.dormaj.com

The Role of Statistical Methods in the Estimation

of Management Efficiency

Ekaterina A. Grigoreva , Elvira A. Polovkina, Tatiana N. Gubaidullina

Institute of Management, Economics and Finance, Kazan Federal University, Kazan, Russia

Received: 13/09/2019

Accepted: 22/11/2019

Published: 20/12/2019

Abstract

One of the tasks set for economic science is the study of the theoretical foundations for further improving production efficiency,

which serves as the fundamental basis for modern economic development. A lot of work has been devoted to questions of the

methodology for statistical studies on production efficiency and labour productivity. Nevertheless, some problems remain

insufficiently studied, in particular, questions on a generalizing indicator of economic efficiency, and analysis of management

efficiency growth factors. The authors of the paper consider the possibility of using statistical methods to identify the influence of

organizational factors on improving production efficiency, and propose methods for calculating the impact of management on

production efficiency. The paper discusses the methodology of statistical study of management effectiveness. Much attention is paid

to the correlation and regression analysis. A model is proposed, making it possible to adequately use systematic approaches to the

problem of the statistical study of the production and management.

Keywords: efficiency, factor analysis, production function, fixed assets, correlation and regression analysis, regression,

management.

materialized labour in the field of management and on the

Introduction

results achieved in the same field. Management effectiveness

in the broad sense involves the study of the contribution of

management itself to the final results of the production and

economic activities of the respective units. The study of

management effectiveness in the narrow sense is of

independent interest.

Management is part of the entire production process. It is

called upon to ensure the fullest use and development of the

productive forces potential in order to satisfy the whole

complex of social needs and achieve social goals with the

least expenditure of total labour. From these positions, the

category of management efficiency should reflect the

contribution of management to the overall results of

production and economic activity.

2 Methods

At the same time, management is a relatively independent

sphere of productive labour application, which is

characterized by the size of management resources and the

value of total labour costs. In this regard, the results of

managerial activity can be considered in two aspects: from

the standpoint of the governing system itself as a subject of

management and from the standpoint of the entire

management system as an organic unity of the subject and the

object of management (1). Accordingly, one can distinguish

two approaches to assessing management effectiveness:

assessing management effectiveness in the narrow and broad

sense of the interpretation of this term.

To improve management, an assessment and analysis of

its effectiveness is required. Of particular relevance are the

issues of evaluating management effectiveness in the context

of the work progress to strengthen an integrated approach to

planning in economic sectors and solving major economic

and social problems. It is important here already at the

project stage to evaluate the effectiveness of the planned set

of measures to improve management (2).

In recent years, many methods have been created in the

field of evaluating management effectiveness. They

highlighted a number of factors of management effectiveness,

examined the issues of grouping these factors, and proposed

indicators. This, for example, is an indicator being the ratio

of the management expenditures growth volume to the

production growth volume obtained by increasing labour

productivity, or an indicator being the ratio of the sum of

management expenditures to the net product output, etc. (3).

Along with certain advantages, each technique contains

controversial provisions. Analysis of existing methods for

Management efficiency in the narrow sense characterizes

management as an independent sphere of labour application

and is focused on studying the costs of living and

Corresponding author: Ekaterina A. Grigoreva, Kazan

Federal University. Email: ekaterina_kazan@mail.ru.

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Journal of Environmental Treatment Techniques

2019, Special Issue on Environment, Management and Economy, Pages: 1089-1092

assessing management effectiveness leads to the conclusion

that their main drawback is the lack of a systematic approach

to the construction of indicators.

average annual value of production assets, minus the value of

fixed assets of the management apparatus. A function of the

form (2) allows us to evaluate the contribution of

management to the overall results of production activities. It

is a particular type of production and management function.

It is advisable to especially highlight in the composition

of fixed assets the computer equipment and study their

influence on the achieved production results. A sufficiently

large number of factors can be included into production

functions, that is, they are quite suitable for describing

multifactorial economic processes. In the general case, the

production and management function have the form:

With a systematic approach, management at any level is

considered, on the one hand, as a system that includes a

number of subsystems of a lower level, and on the other

hand, as a subsystem included in a more complex formation,

namely production. This determines the need, firstly, for a

systematic comprehensive assessment of management

efficiency, which would allow taking into account all the

essential aspects of management as a system, and the

influence of individual factors on the overall level of

efficiency. Such an assessment should include the use of a

hierarchical system of indicators and a study of the

effectiveness factors themselves. Secondly, it is necessary to

take into account the specifics of management as a subsystem

of social production. This means that the constructed system

of indicators should take into account the dual nature of

managerial activity in the system of social production, that is,

it should be presented as indicators characterizing the

influence of management on production results, and

indicators of the control system effectiveness itself. Thirdly,

the methodological linking of management performance

indicators with social production efficiency indicators is

mandatory. In particular, the subsystem of management

performance indicators should be an organic part of the

system of social production effectiveness indicators; a

generalized management efficiency indicator should be

calculated in such a way that it is simultaneously a parameter

of a generalized production efficiency indicator (4, 11).

To implement this approach, statistical methods and

modern technologies can be used. In particular, it seems

promising to use production functions in combination with

correlation and regression analysis to evaluate the

management effectiveness of the apparatus of production

functions.

(3)

where

are expended production factors;

expended management factors. For

function of the form (3) that is non-negative, continuous, and

differentiable with respect to all arguments, a number of

characteristics of control efficiency can be calculated:

The marginal rate of effectiveness for each factor

(4)

Which will show the change in the result of the

production activity of a object when the production or

managerial factor changes by one and at the fixed values of

the remaining factors;

Change in the result of the production activity of

the system due to the cumulative change in production

factors:

(

Results and Discussion

The production function is a model of the production

Change in the result of production and economic

activity due to the cumulative change in management factors

results dependence on expended production factors. In the

study of economic development using production functions,

two main factors are usually distinguished: expended living

labour estimated by the number of industrial production

(6)

personnel , and the average annual value of fixed assets

Marginal rate of substitution for factor

with factor

(1)

(7)

If we take into account that the result of the production

and economic activity of a object is determined not only by

the costs of production resources, but also depends on the so-

called managerial factors, then the allocation of these

components or the use of production and management

functions of the form seems reasonable:

Management efficiency indicator in the form of the ratio

of the production growth volume resulting from the

strengthening of intensive growth factors to the managerial

resource expenditures growth volume

(2)

(8)

where Y is the result of the production activities of the object;

is the number of workers; L is the number of

administrative personnel; C is the average annual value of

fixed assets of the management apparatus; and C is the

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Journal of Environmental Treatment Techniques

2019, Special Issue on Environment, Management and Economy, Pages: 1089-1092

where I is a set of indices of all intensive production volume

factors. In this case, it is often necessary to identify factors

assigning them to one or another group. As a rule, a scheme

for classifying factors has already been set. However, it is

often more useful in the construction of classification to go

based on the object’s properties in their diversity and not

based on a predetermined scheme to the natural types, which

often leads to a result having a great heuristic value. In this

case, the apparatus of cluster analysis can be successfully

used (7). It is not necessary to express factors in

quantitatively similar assessments; moreover, the use of

appropriate similarity factors opens up the possibility of the

simultaneous use of quantitative and qualitative

characteristics. The type of grouping obtained depends on a

given criterion for the optimality of the grouping or objective

function. Thus, depending on the objective function, various

partitions of the initial set of factors and objects can be

obtained (8, 13).

X _j

growth factors;

is an increment of j-th factor compared

to the baseline period or plan. If some factor j used in

formula (8) is not given in the form of expenditures, then it

can be reduced to them using values

showing how many

factor i increment units is equivalent to one factor j increment

unit. For example, if the value of the factor i interchangeable

with factor j expressed in the form of expenditures is known,

then the notional expenditures for achieving the actual value

of j factor will be:

(

Then the formula (8) will take the form:

(

10)

Conclusions

In real conditions, most economic phenomena are

where I

presented in the form of expenditures; and I

indices j of management factors presented in a different form,

moreover I +I =I.

is the set of all indices j of management factors

interconnected by certain dependencies. In addition, specific

modelling conditions may require aggregation of the initial

information about the object in question with minimal losses.

In this case, the problem arises of reducing the description of

a system consisting of many variables, some of which are

connected by dependencies, to the description of a system

consisting of a smaller number of independent derivatives of

variables. In this case, a factor analysis apparatus can be used

to determine the model parameters. The main advantages of

factor analysis are the ability to use dependent factors and

taking into account the hidden components of factors. If, for

example, technical and economic factors include the scale of

production, then when constructing a factor analysis model,

the hidden components of this factor are also taken into

account - the size of fixed assets, the number of employees,

and gross output. To establish the type of function f, multiple

correlation and regression analysis can be used (9, 12). The

mathematical basis for identifying the type of connection by

is the set of all

Summary

The proposed approach to the construction of a system of

management performance indicators ensures the

interconnection of production and management performance

indicators. It also opens up the possibility of creating a

system of indicators which are logically interconnected and

united by a single target area.

The use of multifactor production functions for each

particular case encounters two main difficulties: firstly, the

need for an analytical expression of the function f; secondly,

the need to select factors for building the model. Both of

these problems can be quite effectively solved using

statistical methods.

Several statistical methods can be used to select and

group the most significant production and managerial factors:

expert assessment methods, correlation analysis, cluster

analysis, and various versions of factor analysis (5,15,16).

To select the most significant factors, as a rule, the

method of correlation analysis is used: the matrix of pair

correlation coefficients between the considered factors,

including the effective one, are analysed, and the most

significant of them are selected on this basis. Correlation

analysis as a formal mathematical apparatus is advisable to

combine with expert methods, which allow, firstly, to obtain

informal assessments of specialists and, secondly, to assess

the impact of quantitatively immeasurable factors (6, 17).

When assessing the degree of influence of each factor on

the final indicator, it is advisable to use analysis of variance.

This method allows not only to evaluate the contribution of

each factor to the final indicator, to find out how significant

the influence of factors not included in the model is, but also,

without starting modelling, to study the combined effect of a

number of factors on the modelled indicator.

this method is the possibility of

representation of the response function f by a Tailor

polynomial Y:

a fairly accurate

mn

Y  a  a X  a X X  a X ...



i1

i j

i1

With

decomposition

coefficients

a , a , a ,..., a ,..., a ,...

Modelling allows us to get sample regression coefficients

b , b , b ,..., b ,..., b ,...,

which are sufficiently close

in their values to the coefficients of the theoretical expansion.

Correlation analysis is based on a number of prerequisites

necessary for its implementation: the availability of

information for a certain period of time, the independence of

factors, the uniformity of sample estimates, and some others

(

10, 14, 15). All of these conditions may be observed when

Modern requirements for the analysis of economic

development require consideration of all its significant

solving the task under consideration. For example, the

fulfilment of the independence condition can be achieved by

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Journal of Environmental Treatment Techniques

2019, Special Issue on Environment, Management and Economy, Pages: 1089-1092

switching from a model of indicators to a model of growth,

and by elimination of two strongly correlated factors the one

which is less correlated with the final indicator. After the

elimination of each factor, as well as after the final creation

of the model, it should be checked for adequacy to the real

process (significance) by any criterion (for example, by the

Fisher criterion). If a polynomial of the chosen degree does

not provide a sufficiently good approximation, then the

exponent should be increased (18, 19, 20).

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Acknowledgements

The work is performed according to the Russian

Government Program of Competitive Growth of Kazan

Federal University.

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