https://doi.org/10.53656/str2024-3s-8-dyn

Резюме. This article presents a dynamic determined factor analysis of labour productivity in the Bulgarian energy subsector for the period 2013 – 2022. The purpose of this article is to reveal the quantitative influences of the factors operating revenues and number of employed persons on the development of the indicator labour productivity in the Bulgarian energy subsector through the averaged chain substitution method. The quantitative influences of operating revenues and number of employed persons on the deviation of the labour productivity indicator in the energy subsector are outlined. The results of the deterministic factor analysis make it possible to draw reasonable conclusions and to reveal the trends in the development of the factors operating revenues and number of employed persons, as well as the indicator of labour productivity in the Bulgarian energy subsector.

Ключови думи: energy subsector; labour productivity; dynamic determined factor analysis; averaged chain substitution method

Introduction

The energy subsector is one of the main subsectors of the national economy in the Statistical Classification of Economic Activities for the European Community. According to the Classification of Economic Activities 2008, it includes the following subsectors:

– Production, transmission, and distribution of electrical energy.

– Production and distribution of gaseous fuels along gas distribution networks.

– Heat energy production and distribution.

According to (Sterev & Biolcheva 2022) “The energy sector is subject to increased strategic geo-political and economic interests, both within the country and abroad”.

In recent years, the Bulgarian energy subsector has achieved one of the highest labour productivity in the Industry sector, as well as in our national economy. The lack of specialized developments related to the analysis of labour productivity in the Bulgarian energy industry make it difficult to practically solve the specific and complex problems related to the effective management of human resources, staff motivation and factors affecting labour productivity in enterprises from the energy subsector. It is necessary to clearly outline the trends in the development of the labour productivity indicator in the Bulgarian energy subsector.

Now, we have sufficient statistical information of a macro- and microeconomic nature about the processes and phenomena that occurred in the past, on the basis of which we can build trends and forecasts for the future development of the labour productivity indicator in the Bulgarian energy subsector.

The purpose of this article is to present the results and to reveal the quantitative influences of the factors operating revenues and number of employed persons of the enterprises from the Bulgarian energy subsector on the result indicator of labour productivity through the averaged method of chain substitutions for the period 2013 – 2022.

1. Main economic indicators of the Bulgarian energy subsector for the period 2013 – 2022

According to the information officially published by the National Statistical Institute (NSI), and according to data by the INFOSTAT information system of the NSI (INFOSTAT 2024), given in Table 1, most of Bulgarian energy companies currently achieve good production and economic results.

According to the data in Table 1, 4368 companies and organisations in the field of energy subsector and related activities and services were active in the energy industry in 2022. 32668 people were directly employed in the energy industry. The value of non-current assets exceeded BGN 15.6 billion.

Within the analysed period, the implemented financial result of the activity of the energy enterprises in 2022 has been the highest, namely 4.4 billion BGN, formed by 76.8 billion BGN in operating revenues and 72.4 billion BGN in operating expenses.

It is worth noting that the number of enterprises in the energy subsector in 2022 is growing steadily throughout the analysed period.

The other key indicators realised by the energy subsector for the entire analysed period in 2022 reached their highest value. The most significant growth in 2022 is achieved by operating revenues, operating expenses, and operating profit.

2. Research methods and methodology

According to (Bartholomew 1984): “Deterministic modelling of factor systems is an easy and effective means of formalizing the relationship of economic indicators, which will serve as a basis for quantifying the quantitative influence of individual factors in the change of the performance indicator”. If we can add according to: (Joreskog & Sorbom 1979) and (Angelova 2018): “Because deterministic factor analysis is aimed at identifying the influence of the change in the factors involved on the change in the value of the outcome measure of interest, excluding errors, and is most suitable for practical application in market conditions”.

According to still other authors (Bobinaite et al, 2022) and (Angelova & Kuzmov 2018), “Labour productivity is an economic indicator reflecting the performance of an economic system in terms of the quantity of goods and services produced over a given period of time with the use of given resources, per worker or per hour worked”.

The labour productivity indicator of the Bulgarian energy industry is characterized by the two-factor multiple (relative) model, which has the following form:

The labour productivity indicator of the Bulgarian energy industry is characterized by the two-factor multiple (relative) model, which has the following form:

(1) \(L P=\cfrac{R}{N}\)

were:

\(R\) is the operating revenues of the energy subsector, in BGN thousands;

\(N_{-}\)is the number of persons employed in the energy subsector.

For the purposes of dynamic deterministic factor analysis, the analysed period is divided into sub-periods.

The changes of the resultative indicator ( \(\triangle L P\) ) and of the participating factor variables operating revenues (\(\Delta R\) ) and number of employed persons (\(\Delta N\) ) during the analysed sub-periods can be represented by the following expressions:

(2) \(\Delta L P_t=L P_{t}-L P_{t-1} \)

(3) \(\Delta R_{t}=R_{t}-R_{t-1} \)

(4) \( \Delta N_{t}=N_{t}-N_{t-1} \)

where:

\(t\) is the index of the \(t^{\text {th }}\) value of the performance indicator and of the participating factor variables over time, \(t=0,1,2, \ldots, T\);

\(t_{0}\) and \(t_{T}\) are the beginning and the end of the whole analysed period respectively;

\(t_{t-1}\) and \(t_{t}\) are the beginning and the end of the \(t^{\text {th }}\) sub-period respectively.

The index of the \(t^{\text {th }}\) sub-period takes values between \(0 \div 1\) and \(t-1 \div T\) \((t-1 \div t=0 \div 1,1 \div 2,2 \div 3, \ldots)\).

From here, it is easy to perform a dynamic DFA of the performance indicator for the whole period and for individual sub-periods.

The averaged chain substitution method is a new method for deterministic factor analysis (DFA), which is characterized by absolute accuracy and unequivocalness of the obtained results and has universal applicability, regarding all types of factor models.

For multiple factor models, such as the mathematical model of labour productivity, it is characteristic that the averaged chain substitution method is the only accurate method of all remaining DFA methods. It was developed and published by the author in the period \(2020 \div 2023\). The individual quantitative influences of the change of the factor variables on the change of the resultative indicator, according to: (Mitev 2020, 2021, 2022, 2023), are determined by the following expressions:

(4) \(\begin{aligned} & \Delta L P_{(R)}=\cfrac{\Delta R}{2}\left(\cfrac{1}{N_{0}}+\cfrac{1}{N_{1}}\right) \\ \end{aligned}\) ;

(5) \(\begin{aligned} & \Delta L P_{(N)}=\cfrac{R_{1}+R_{0}}{2}\left(\cfrac{1}{N_{1}}-\cfrac{1}{N_{0}}\right) \end{aligned}\) .

The methods applied in the development of this study were: the methods of analysis and synthesis, a systematic approach, the method of comparison, and the averaged chain substitution method.

3. Dynamic deterministic factor analysis of the operating revenues of one employed person in the Bulgarian energy subsector for the period \(2013 \boldsymbol{\div} \mathbf{2 0 2 2}\)

3.1. Input Data and empirical findings

The necessary data for performing the dynamic deterministic factor analysis of labour productivity in the Bulgarian energy subsector for the period \(2013 \div\) 2022 were taken from the INFOSTAT system of the National Statistical Institute of Bulgaria.

The determination of the absolute changes in labour productivity as a result of the absolute changes in the factor variable operating revenues and the number of persons employed used the averaged chain substitution method. The quantitative impact of the change in operating revenues on the absolute change in labour productivity is determined by formula 4. Accordingly, the quantitative impact of the change in the number of persons employed on the absolute change in labour productivity is determined by formula 5.

The input data and the results obtained from the dynamic deterministic factor analysis using the averaged chain substitution method of the indicator operating revenues of one employed person in the Bulgarian energy subsector by years and for the entire period \(2013 \div 2022\) are presented in table 2.

Figure 1 presents the quantitative factor influences of the factors operating revenues and number of employed persons on the quantitative change of labour productivity in the energy subsector.

3.2.. Discussion of Results

For the entire analysed period 2013 – 2022, the operating revenues of one employed person in the Bulgarian energy subsector increased by BGN 1834.311 thousand or by \(354.04 \%\). The increase in operating revenues by BGN \(59,930,811\) thou- sand or by \(354.19 \%\) improves labour productivity by BGN 1,834,795 thousand/ employed or by \(354.13 \%\). The increase in the number of employed persons by 11 employed persons or by \(0.03 \%\) slightly impairs labour productivity by BGN 0.483 thousand/employed person or by \(0.09 \%\).

A check that the absolute change in the performance indicator is equal to the sum of the two-factor influences shows some minor errors far behind the decimal point. This confirms the high accuracy of the averaged chain substitution method.

Conclusions and summary

As can be seen from Table 2 and Figure 1, the main factor for increasing labour productivity in the energy subsector for the entire analysed period is the significant increase in operating revenues. The weak increase in the number of persons employed during the period 2013 – 2022 insignificantly worsens labour productivity.

Hence, the increase in the operating revenues during the analysed period in the Bulgarian energy subsector plays a key role in increasing labour productivity. The increase in the number of employed persons by 11 during the analysed period, it had a negligible negative impact on the increase in labour productivity.

The results of the dynamic deterministic factor analysis show that the Bulgarian energy subsector managed to significantly increase the level of labour productivity during the analysed period. The high growth of operating revenues is the main factor for the improvement of labour productivity in the Bulgarian energy industry.

REFERENCES

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