Modeling the Efficiency of Public Service Delivery Using GDP Indicators

Macroeconomic indicators are quantitative metrics that provide critical insights into the overall state and dynamics of an economy at both national and regional levels. These indicators are indispensable tools for economists, policymakers, business leaders, and investors, aiding in the comprehensive analysis of the current economic environment and supporting informed decision-making processes. For example, Gross Domestic Product (GDP), a key macroeconomic indicator, measures the total market value of all goods and services produced within a country’s borders over a specific period, usually quarterly or annually. GDP serves as a comprehensive gauge of economic activity and growth trajectories. The scale of the population, labor force, and available land are critical indicators reflecting labor market conditions and economic resources. Government expenditures, primarily directed towards public services, constitute a significant portion of the state budget and often correlate with public sector employment levels. These indicators collectively provide a multidimensional view of economic performance, encompassing production, employment, trade, and public finances. However, the improvement of any single economic indicator does not fully capture the evaluation of a citizen’s quality of life. Instead, quality of life depends on the effective management of the state budget, equitable resource distribution, and achieving income growth satisfaction. Each household can attain satisfactory living standards by aligning its expenditures with its income. Underlying this philosophy is the belief that every nation has the potential to enhance its economic prosperity and happiness index through prudent fiscal planning aligned with its wealth generation capacity. Guided by this principle, countries are assessed based on the size of their Gross Domestic Product (GDP), in accordance with the United Nations Sustainable Development Policy framework. Our focus is on evaluating the provision of public services, using key indicators to measure progress in this domain.

• Labor Force
• Public Servants
• Cluster Sampling
• Sustainable Development

1. Introduction

The quantity of public sector employment (PSE) significantly influences the state budget, yet it also underpins the effective provision of essential public services, encompassing health care, education, infrastructure, and social welfare. The extent of public sector employment directly impacts the implementation of public policies, enforcement of regulations, and provision of public goods. Moreover, an expansion in public sector employment plays a pivotal role in fostering social cohesion and community development by generating employment opportunities, alleviating unemployment, and instilling a sense of security among citizens. Public sector jobs often offer stable wages and benefits, thereby contributing to income equality and poverty alleviation. Furthermore, the number of public sector employment shapes citizens’ trust in governmental institutions. During crises such as natural disasters or pandemics, the presence of government personnel becomes indispensable for facilitating prompt and effective response and recovery efforts. While quantifying the precise impact of PSE numbers on budget expenditures proves challenging, the efficacy of public institutions and governance significantly influences the promotion of social well-being and happiness. There are numerous researchers, policymakers, and experts who might discuss or study this topic, including academics specializing in public administration, government officials involved in public service management, and consultants in the field of organizational efficiency. Christopher Hood, a renowned political scientist, who specializes in public administration, governance, and public sector reform, delves into the efficient and effective delivery of public services ( Hood, 2000 ). Similarly, scholars such as Kahn (1983) , Moore (1995) , Ostrom (2015) , and Donahue & Zeckhauser (2011) have produced significant works in this field. Through their research, publications, and policy recommendations, these experts have substantially contributed to understanding and enhancing the efficiency of public services. Anjula Gurtoo and Colin C. Williams examined the status of public service in developing countries, in the sectors of health, infrastructure, labor and marginalized populations, rural economy and public administration ( Gurtoo & Williams, 2015 ).

The study encompassed 108 countries with comprehensive data sourced from official releases by the International Labor Organization and other online resources in 2022 (see Table A1 in Appendix). The data to be used in the research was not complete for some countries and it was inconsistent with some sources. Therefore, the sample was created from those countries for which quantitative data were complete. These countries were categorized based on their GDP rankings: 24 nations with GDPs up to 30,000 million USD were classified as low income; 33 countries with GDPs ranging from 30,000 million USD to 200,000 million USD were deemed below average; 25 nations with GDPs between 200,000 million USD and 500,000 million USD were categorized as average income; 10 countries with GDPs exceeding 1,000,000 million USD were classified as above average; 14 nations with GDPs between 1,000,000 million USD and 5,000,000 million USD were designated as high income; and 2 countries with GDPs surpassing 5000 billion USD were labeled as extremely high income. The average GDP among these 108 countries amounted to 480,000 million USD. The world’s 108 countries have been categorized into six clusters based on their GDP levels: low, below average, average, above average, high, and extremely high.

Table 1 illustrates that 56% of the countries analyzed exhibit low or below-average GDP levels, with the United States and China, positioned in the very high GDP cluster, contributing a mere 1%.

Table 1

Table 1. Clusters on GDP for considering 108 countries.

GDP/US billion $/	0 - 30	30 - 200	200 - 500	500 - 1000	1000 - 5000	5000-up
GDP clusters	I Low	II Below average	III Average	IV Above average	V High	VI Veryhigh
Number of countries	24	33	25	10	14	2
Probability	0.23	0.33	0.22	0.09	0.12	0.01

2. A Research Methodology

The sample research method, a cornerstone of research methodology, entails selecting a subset (sample) from a larger population to study and generalize findings about the entire population. Given the impracticality of studying the entire population, sampling enables researchers to draw valid inferences from a representative and manageable group. In the study, we used a cluster sampling method and employed a first-order linear regression model with four factors. Thus,

$\hat{Y}=c_0+c_1\cdot x_1+c_2\cdot x_2+c_3\cdot x_3+c_4\cdot x_4$.(1)

Here $x_1,x_2,x_3$ and $x_4$—sample values or factors, $c_0,c_1,c_2,c_3$ and $c_5$—parameters of the model, $\hat{Y}$—estimated values of the sample regression. The joint effects of the factors were not considered in the sample regression model, as the impact of these factors on the number of public sector employees was examined separately. The parameters were estimated using the method of least squares during the construction of a multivariate regression model. Subsequently, we applied the following criteria as filters.

Criterion. A value meets the criteria if the absolute difference between its actual value () and its estimated value ( $\hat{Y}$) is less than σ.

$\left|Y-\hat{Y}\right|<\sigma$.(2)

Here, $Y-\hat{Y}$ were the residuals, and σ were the standard deviation for each level.

We began by clustering the sample values and subsequently developed a regression model for each cluster. After filtering the model’s outcomes based on criterion (2), our objective was to refine the most suitable cluster model. This approach to cluster regression effectively illustrates the trend of the factor in a straightforward manner.

3. The Estimation of Public Sector Employment Numbers

PSE plays a pivotal role in providing essential services to the populace. Within each cluster, we analyze the correlation between the number of public sector employees in a country and factors such as population size, area size, labor force, and GDP. We utilized MS Excel and EViews to perform the calculations.

3.1. Calculations for Cluster I

In this cluster, the analysis focuses on modeling the number of PSE in the 24 countries with low GDP, considering population, area size, labor force, and GDP. Among these variables, there is a weakly positive correlation of 32.9% between the number of public sector employees and the labor force, a very weakly positive correlation of 21% with population size, a very weakly negative correlation of 8% with area size, and a strong negative correlation of 52.1% with GDP size, indicating an overall negative relationship on average. For the models, x₁—GDP (million USD), x₂—number of labor force, x₃—population, x₄—area size (square kilometre) and Y—number of PSE are noted. A regression model was constructed using Equation (1) with sample values corresponding to cluster I. Thus,

$\begin{array}{c}\hat{Y}=1096622.984-49.56463\cdot x_1+0.128730\cdot x_2\\ -0.003542\cdot x_3-0.392865\cdot x_4\end{array}$.(3)

According to the statistical parameters of Equation (3) for Cluster I, the coefficient of determination (R² = 0.417109) indicates that the four selected factors explain approximately 42% of the variance in public sector employment. The Durbin-Watson statistic (DW = 1.469647) suggests an autocorrelation of residuals. According to the analysis, all the coefficients except for the coefficient of x₁ are weakly significant, and also according to F-statistic, the model (3) does not obey the normal distribution law (see Table 2 ).

Table 2

Table 2. Statistical outputs of model (3) in Cluster I.

Variable	Coefficient	Std. Error	t-statistic	Probability
GDP	−49.56463	17.56019	−2.822557	0.0109
Labor force	0.128730	0.107074	1.202252	0.2440
Population	−0.003542	0.028518	−0.124196	0.9025
Area size	−0.392865	0.498023	−0.788849	0.4399
C	1096622.984	378004.1	2.901087	0.0092
R-squared	0.417109	Mean dependent variable		534073.2
Standard error of regression	569581.0	Std. Deviation dependent var		678070.0
Sum squared residual	6.16E+12	F-statistic		3.399030
Durbin-Watson statistic	1.469647	Probability of F-statistics		0.029430

The model indicates that a one billion US dollar increase in GDP results in a decrease of 49 public sector employees. Conversely, an increase of 1000 in the labor force corresponds to an increase of 128 public sector employees, while a population increase of 10,000 leads to a decrease of 35 public sector employees. In this cluster, the average number of PSE is 534,073 with a standard deviation of 678,070. According to the single sigma rule, the acceptable range for the number of PSE is between 0 and 1,212,143. If the condition $Y-\hat{Y}\ge \sigma$ is fulfilled, the number of PSE in the country is considered too large, and if the condition $Y-\hat{Y}\le -\sigma$ is fulfilled, the number is considered too small. Based on criterion (2), Cuba has an excessively high number of PSE, whereas Madagascar and Rwanda have too small (see Figure 1 ). This range is designated as Level A for Cluster I.

Figure 1

Figure 1. Comparison of actual and estimated values for cluster I.

In order to improve the model, countries that do not meet the criteria for the Level A model will be excluded. A new linear regression model will then be built for the remaining countries, designated as Level B. This process will continue, creating Level C and so on, until a model with a high coefficient of determination and satisfactory Durbin-Watson (DW) analysis is achieved. Initially, 21 countries were modeled, excluding Cuba (too large at Level A) and Madagascar and Rwanda (too low). At Level B, Yemen and Botswana were also excluded due to severity, leaving 19 countries for Level C. At this level, Tajikistan, Georgia, and Zambia were above the criterion, while Moldova, Nicaragua, and Albania were below it, resulting in 13 countries for Level D after excluding these six. Finally, Laos and Zimbabwe did not meet the criteria at Level D, leading to a Level E model with the remaining 11 countries. Consequently, Liberia and Senegal were excluded from the E-level countries, while nine countries—Kyrgyzstan, Niger, Afghanistan, Mali, Armenia, Haiti, Guinea, Bosnia and Herzegovina, and Trinidad and Tobago—qualified. Since all these countries met the criteria, the calculations were concluded. A regression model was then constructed for each of the five levels, and these equations were subsequently combined. Thus,

${\hat{Y}}_1=\left(\begin{array}{c}{\hat{Y}}_{1A}\\ {\hat{Y}}_{1B}\\ {\hat{Y}}_{1C}\\ {\hat{Y}}_{1D}\\ {\hat{Y}}_{1E}\end{array}\right)=\left(\begin{array}{cccc}-49.564& 0.128& -0.003& -0.392\\ -10.177& -0.013& 0.034& -0.64\\ -10.255& -0.01& 0.031& -0.642\\ -15.237& -0.037& 0.036& -0.756\\ -14.695& -0.045& 0.038& -0.773\end{array}\right)\left(\begin{array}{c}{x}_1\\ x_2\\ x_3\\ x_4\end{array}\right)+\left(\begin{array}{c}1096622.984\\ 430301.568\\ 425659.469\\ 563251.076\\ 546207.072\end{array}\right)$(4)

In system (4), the first equation corresponds to level A, and so on, with the fifth and last equation corresponding to level E. The determination coefficients (R²) of the regression models for Cluster I were 0.417, 0.748, 0.773, 0.978, and 0.995 for levels A, B, C, D, and E, respectively. Additionally, the Durbin-Watson (DW) indices were 1.469, 1.995, 1.815, 2.017, and 1.885 for these levels. Notably, at level E, the DW index was very close to 2, indicating that the regression model for the last level is highly reliable. The coefficients of determination improved progressively from level A to level E, reaching 0.995, which signifies that the four selected factors account for 99.5% of the variation in the numbers of PSE. In the final model based on Equation (4), all the coefficients are highly significant (see Table 2 ). In Cluster I, countries at level E met the criterion (2). Among the countries in Cluster I, Armenia leads in this indicator (see Table 3 ).

Table 3

Table 3. The model (4) results.

Cluster I		The number of public sector employments		24countries
		Too large	Too little
Levels	А	Cuba	Madagascar, Rwanda	3
	В	Yemen, Botswana	-	2
	С	Tajikistan,Zambia, Georgia	Moldova,Nicaragua, Albania	6
	D	Laos, Zimbabwe	-	2
	E	Liberia	Senegal	2
Eligible countries		Kyrgyzstan, Niger, Afghanistan, Mali, Armenia, Haiti, Guinea, Bosnia and Herzegovina, Trinidad and Tobago		9

At each level of Cluster I, the model was refined by excluding countries that did not meet the quantitative criteria for public sector employment. Among countries with low GDP, those remaining at the E level demonstrate the best and most appropriate development trends for GDP, population, labor force, and area size. In this cluster, Armenia best met the criteria. For countries with low GDP, the size of the land showed a very weak correlation with the number of public sector employments. This near-irrelevance suggests that government activities are not effectively reaching the population or are creating an excessive burden. The same methodology was applied to further model the other clusters.

3.2. Calculations for Cluster II

Cluster II comprises 33 countries with below-average GDP income. Within this cluster, Cameroon, Jordan, Belarus, Venezuela, and Ukraine exceed the criteria, while Ethiopia and Kuwait fall below. At level B, out of 26 countries, Uzbekistan, Guatemala, Oman, and Morocco surpass the criteria, whereas Tanzania, Luxembourg, and Ecuador fall short. Moving to level C, among the remaining 19 countries, Serbia and Azerbaijan stand as outliers, while Costa Rica and Uruguay underperform. Of the 15 countries progressing to level D, Latvia and Croatia exceed expectations, whereas Bahrain and Slovenia lag behind. If these four countries were excluded and evaluated at level E, Bulgaria would not meet the criteria. Among the model-tested characteristics of the remaining 10 countries at the subsequent F level, Paraguay overachieves, while Lithuania underachieves. Lastly, all of the remaining eight countries meet the criteria for modeling at level G. The models for each of these levels were integrated to create the following system of equations.

${\hat{Y}}_2=\left(\begin{array}{ccc}5.973& 0.388& -\begin{array}{cc}0.135& 0.347\end{array}\\ 7.641& 0.369& \begin{array}{cc}-0.119& 0.106\end{array}\\ \begin{array}{c}6.692\\ 6.996\\ \begin{array}{c}7.002\\ 7.056\\ 7.159\end{array}\end{array}& \begin{array}{c}0.307\\ 0.122\\ \begin{array}{c}0.063\\ 0.041\\ 0.008\end{array}\end{array}& \begin{array}{cc}\begin{array}{c}-0.096\\ -0.032\\ \begin{array}{c}-0.112\\ -0.004\\ 0.007\end{array}\end{array}& \begin{array}{c}0.097\\ 0.093\\ \begin{array}{c}0.074\\ 0.065\\ 0.053\end{array}\end{array}\end{array}\end{array}\right)\left(\begin{array}{c}{x}_1\\ x_2\\ x_3\\ x_4\end{array}\right)+\left(\begin{array}{c}70019.526\\ -291073.501\\ \begin{array}{c}-219093.611\\ -174200.064\\ \begin{array}{c}-137932.054\\ -121807.281\\ -108277.298\end{array}\end{array}\end{array}\right)$(5)

In Cluster II, the determination coefficients (R²) of regression models were 0.669, 0.862, 0.838, 0.958, 0.993, 0.995, and 0.998 for levels A, B, C, D, E, F, and G, respectively. The coefficient notably increased to 0.999 at the final level, indicating a substantial enhancement in the model’s explanatory power. Correspondingly, the Durbin-Watson (DW) indices were 1.981, 2.483, 2.437, 1.552, 2.361, 2.785, and 2.306 for these seven levels, respectively, with the index nearing 2 at the G level, affirming the robustness of the last-level regression model. Countries at level G within Cluster II—El Salvador, Estonia, Bolivia, Uganda, Mongolia, Ghana, Slovakia, and Hungary—all adhere to the criteria for public sector employments (see Table 4 ). Mongolia leads among these countries in terms of this indicator within the cluster.

Table 4

Table 4. Some results of the model (5) on Cluster II.

Cluster II		The number of public sector employments		33countries
		Too large	Too little
Levels	А	Cameroon, Jordan, Belarus, Venezuela and Ukraine	Ethiopia, Kuwait	7
	В	Uzbekistan, Guatemala,Oman, and Morocco	Tanzania, Luxembourg,and Ecuador	7
	С	Serbia, Azerbaijan	Costa Rica, Uruguay	4
	D	Latvia, Croatia	Bahrain, Slovenia	4
	E	-	Bulgaria	1
	F	Paraguay	Lithuania	2
	G	El Salvador, Estonia, Bolivia, Uganda, Mongolia, Ghana,Slovakia and Hungary (Eligible countries)		8

3.3. Calculations for Cluster III

This cluster comprises 25 countries with an average GDP. Like the preceding cluster, as the levels progress from A onward, all seven remaining countries at level F successfully met the criteria for modeling. These models for each level were then integrated to create the following system of equations. Thus,

${\hat{Y}}_3=\left(\begin{array}{ccc}1.93& 0.009& \begin{array}{cc}0.015& 0.739\end{array}\\ 1.354& 0.001& \begin{array}{cc}0.033& 0.386\end{array}\\ \begin{array}{c}0.385\\ 0.439\\ \begin{array}{c}-0.208\\ -1.306\end{array}\end{array}& \begin{array}{c}-0.013\\ -0.006\\ \begin{array}{c}-0.015\\ -0.016\end{array}\end{array}& \begin{array}{c}\begin{array}{cc}0.047& 0.272\end{array}\\ \begin{array}{cc}0.043& 0.412\end{array}\\ \begin{array}{c}\begin{array}{cc}0.047& 0.377\end{array}\\ \begin{array}{cc}0.048& 0.321\end{array}\end{array}\end{array}\end{array}\right)\left(\begin{array}{c}{x}_1\\ x_2\\ x_3\\ x_4\end{array}\right)+\left(\begin{array}{c}-16010.815\\ -139000.26\\ \begin{array}{c}139251.202\\ 94583.336\\ \begin{array}{c}339480.901\\ 725254.859\end{array}\end{array}\end{array}\right)$(6)

In Cluster III, the determination coefficients (R²) of regression models were 0.626, 0.874, 0.946, 0.981, 0.993, and 0.999 for levels A, B, C, D, E, and F, respectively. Notably, the coefficient reached 0.999 at the final level, signifying a significant enhancement in the model’s explanatory power. Additionally, the Durbin-Watson (DW) indices were 2.706, 2.594, 1.69, 1.715, 2.227, and 2.117 for these levels, respectively, with the index nearing 2 at the C level, indicating the high quality of the last-level regression model. Within Cluster III, the countries at level F—Kazakhstan, Portugal, Finland, Czech Republic, Iran, Vietnam, and Singapore—all meet the criteria (see Table 5 ). Additionally, Kazakhstan leads among the countries in this cluster regarding this indicator.

Table 5

Table 5. Some results of the model (6) on Cluster III.

Cluster III		The number of public sector employments		25 countries
		Too large	Too little
Levels	А	Iraq, Pakistan, Egypt	Bangladesh, Nigeria	5
	В	South Africa	Colombia, Philippines	3
	С	Greece, Romania	Peru, Chile	4
	D	Denmark, Thailand	New Zealand, Austria	4
	E	Malaysia	Qatar	2
	F	Kazakhstan, Portugal, Finland, Czech Republic,Iran, Vietnam and Singapore		7

3.4. Calculations for Cluster IV

This cluster comprises 10 countries with above-average GDP. As with the previous cluster, all seven remaining countries at level C met the criteria for modeling, following a sequential improvement from level A. The models for each of these levels were then integrated to create the following system of equations. Thus,

${\hat{Y}}_4=\left(\begin{array}{ccc}-0.711& 0.402& \begin{array}{cc}-0.086& -0.033\end{array}\\ 0.606& 0.1& \begin{array}{cc}0.008& 0.175\end{array}\\ 0.786& 0.074& \begin{array}{cc}0.016& 0.199\end{array}\end{array}\right)\left(\begin{array}{c}{x}_1\\ x_2\\ x_3\\ x_4\end{array}\right)+\left(\begin{array}{c}437048.504\\ 115551.183\\ 47407.401\end{array}\right)$(7)

The determination coefficients for regression models within Cluster IV were 0.928, 0.992, and 0.999 for levels A, B, and C, respectively. Notably, the coefficient reached its highest value of 0.999 at level C, signifying a substantial improvement in the model’s explanatory power. Additionally, the Durbin-Watson (DW) indicators exhibited values of 2.245, 2.496, and 1.864 for levels A, B, and C, correspondingly. Remarkably, the indicator approached the desired threshold of 2 in the final C level, indicating enhanced model performance.

The countries classified as C level within Cluster IV—Belgium, Norway, Sweden, Argentina, Türkiye, and the Netherlands—each meet the criteria for PSE numbers, as outlined in Table 6 . Notably, the Netherlands has emerged as the frontrunner in this cluster, surpassing its counterparts in this particular indicator.

Table 6

Table 6. Some results of the model (7) on Cluster IV.

ClusterIV		The number of public sector employments		10 countries
		Too large	Too little
Levels	A	Poland	United Arab Emirates	2
	B	Israel	Ireland	2
	C	Belgium, Norway, Sweden, Argentina, Türkiye, and Netherlands		6

3.5. Calculations for Cluster V

This cluster includes 14 high-income countries. It is improved successively from A level to D level. Calculation results:

${\hat{Y}}_5=\left(\begin{array}{ccc}0.819& 0.161& \begin{array}{cc}-0.043& 1.031\end{array}\\ 0.136& 0.11& \begin{array}{cc}-0.027& 0.545\end{array}\\ \begin{array}{c}0.467\\ 0.198\end{array}& \begin{array}{c}0.128\\ 0.129\end{array}& \begin{array}{cc}\begin{array}{c}-0.033\\ -0.033\end{array}& \begin{array}{c}0.516\\ 0.489\end{array}\end{array}\end{array}\right)\left(\begin{array}{c}{x}_1\\ x_2\\ x_3\\ x_4\end{array}\right)+\left(\begin{array}{c}-1338139.007\\ 2381032.023\\ \begin{array}{c}1335355.596\\ 1835313.419\end{array}\end{array}\right)$.(8)

The determination coefficients for regression models within Cluster V were 0.769, 0.929, 0.981, and 0.995 for levels A, B, C, and D, respectively. Notably, the coefficient reached its peak at 0.995 in the final level, indicating a significant enhancement in the model’s explanatory capability. Additionally, the Durbin-Watson (DW) indices were recorded at 2.256, 1.409, 2.148, and 2.679 for levels A, B, C, and D, respectively. However, it’s worth noting that in the last C level, the index showed less stability, suggesting potential areas for further investigation.

In Table 7 , Indonesia, Spain, Mexico, Brazil, Italy, India, and Germany—comprising the final D level of this cluster—all meet the specified criteria. Particularly noteworthy is India, which exhibits the most favorable indicators for PSE numbers. Moreover, we opted not to develop a dedicated model for the USA and China, as they are very high-GDP countries included in Cluster VI.

Table 7

Table 7. Some results of the model (8) on Cluster V.

Cluster V		The number of public sector employments		14 countries
		Too large	Too little
Levels	A	Russia	Austral, Canada	3
	B	United Kingdom	Japan	2
	C	France	South Korea	2
	D	Indonesia, Spain, Mexico, Brazil, Italy, India, and Germany		7

4. Analysis of Cluster Model Findings

Figure 2

Figure 2. Correlation between number of PSE and other factors/Cluster I/.

Moreover, these factors exhibit a limited influence on the number of government employees, while the size of the GDP appears to correlate with a decrease in the provision of government services. Notably, within Cluster I, the correlation coefficient between PSE and the labor force demonstrates a progressive increase with each level shift (see Figure 2 ). In this cluster of countries, the public service aims to bolster the workforce, aligning with an economic policy rooted in agriculture and traditional production.

Table 8

Table 8. Correlation between the number of PSE and other factors for Cluster II.

Factors	Levels in Cluster II							Average
	A	B	C	D	E	F	G
GDP	0.416	0.353	0.764	0.85	0.88	0.889	0.887	0.720
Labor force	0.629	0.634	0.453	0.472	0.388	0.391	0.347	0.473
Population	0.543	0.553	0.425	0.455	0.373	0.376	0.326	0.436
Area size	0.374	0.163	−0.201	−0.045	−0.218	−0.222	−0.273	−0.060

In Cluster II, the majority of countries are in the developing phase, with economies predominantly reliant on resource extraction and low-tech manufacturing. Consequently, the influence of capital flight on GDP and foreign trade balance is anticipated to be significant. Mongolia, the primary representative of this cluster, relies heavily on the mining sector, which accounts for over 80% of its GDP, posing challenges to long-term sustainable development policies.

Conversely, other factors exhibit correlations below the average. Notably, as the level shifts within this cluster, the correlation of GDP with these factors diminishes, while the correlation with other variables increases. In these countries, all factors exhibited a positive and beneficial impact on PSE numbers. Nevertheless, with each level change, the correlation between PSE number and GDP size decreased, while the influence of other factors steadily ascended. Notably, a robust correlation was observed between PSE and population size.

Despite the fluctuating effect of GDP size on public sector employment, the impact of other factors consistently grows with increasing levels. The 10 countries within this cluster are indisputably highly developed nations, characterized by policies tailored to their populations and workforces, ensuring access to public services commensurate with their geographical areas and settlements.

Their mean values were 0.169, 0.764, 0.697 and 0.638 respectively. Notably, the average correlation coefficients in the table reveal a very weak influence of GDP size on public sector employment, a trend linked to the developed nature of these countries and their high economic potential. Here, it is evident that sustainable services are prioritized, with a focus on both the workforce and the population.

5. Conclusion

A methodology for improving the model was adopted by passing criteria from one level to another within the cluster. As a result, we were able to construct the best-fitting model for each cluster. It also identifies the countries that best fit the cluster. However, this study does not aim to rank countries in any way.

In Cluster I, there is a noted deficiency in public service accessibility, overshadowed by potent political, economic, and geopolitical influences. Armenia, serving as the primary representative, leans towards implementing public services rooted in local customs and traditional lifestyles. Cluster II countries prioritize leveraging GDP growth to allocate state budget resources towards future capital formation, judicious use of land and underground resources, and directing public services towards enhancing education and workforce capabilities, alongside implementing long-term sustainable development policies. Mongolia, the cluster’s key representative, grapples with these challenges presently. Conversely, in Cluster III nations, the emphasis on public service implementation tailored to their populations and labor forces yields positive outcomes for sustainable development in these developing countries. Kazakhstan, the cluster’s main representative, experiences rapid development fueled by its land resources and geopolitical advantages. Cluster IV countries exemplify a superior model of public services, serving as a benchmark for others, with direct implications on the happiness index of nations. The Netherlands, the primary representative of this cluster, stands as a global leader in banking, financial services, and the implementation of optimal policies for sustainable development. Cluster V countries serve as exemplary models in delivering public services to remote areas compared to counterparts in other clusters. Notably, India, the cluster’s main representative, holds the title of the world’s most populous country and has emerged as a significant player in IT industry workforce training. It can be inferred that this conducive public service environment enables these countries to embrace modern technologies and sustain robust economic development over the long term by fostering workforce skills.

This study utilized data from 108 countries. With our developed methodology, it becomes feasible to estimate the number of public sector employments in other nations. For instance, as of 2022, Switzerland’s workforce stands at 4,968,223, with approximately 723.1 thousand in public sector employment (according to the Labor Force Survey in ILOSTAT Explorer). The country’s population is 8779 thousand, with a gross domestic product of $818.4 billion and an area spanning 41,285 square kilometers. Based on our classification, Switzerland falls into cluster IV. According to the latest model of this cluster, the projected number of public sector employments in the country is 1,218,125.

Appendix

Table 9

Table A1. The data sourced by international organizations in 2022.

	Countries	Population	Areasize	Lavor force	Numberof PSE	GDP
	Cluster I. Low GDP
1	Cuba	11,194,449	106,440	5,233,000	3,401,450	2020
2	Liberia	5,418,377	96,320	1,372,000	552,916	4001
3	Tajikistan	10,143,543	139,960	2,209,000	728,970	10,492
4	Kyrgyzstan	6,735,347	191,800	2,344,000	398,480	10,931
5	Rwanda	14,094,683	24,670	4,446,000	248,976	13,313
6	Niger	27,202,843	1,266,700	4,688,000	168,768	13,970
7	Moldova	3,435,931	32,850	1,327,000	214,974	14,421
8	Afghanistan	42,239,854	652,860	7,512,000	1,096,752	14,939
9	Madagascar	30,325,732	581,795	9,504,000	380,160	14,955
10	Nicaragua	7,046,310	120,340	3,039,000	246,159	15,672
11	Laos	7,633,779	230,800	3,337,000	380,418	15,724
12	Yemen	34,449,825	527,970	7,100,000	1,370,300	16,940
13	Mali	23,293,698	1,220,190	3,241,000	77,784	18,827
14	Albania	2,832,439	27,400	1,090,000	156,960	18,882
15	Armenia	2,777,970	28,470	1,394,000	270,436	19,503
16	Haiti	11,724,763	27,560	4,810,000	432,900	20,254
17	Botswana	2,675,352	566,730	1,308,000	235,440	20,352
18	Zimbabwe	16,665,409	386,850	3,939,000	476,619	20,678
19	Guinea	14,190,612	245,720	5,409,000	367,812	21,228
20	Bosnia andHerzegovina	3,210,847	51,000	1,026,337	251,453	24,528
21	Georgia	3,728,282	69,490	1,959,000	413,349	24,605
22	Senegal	17,763,163	192,530	6,096,000	384,048	27,684
23	Trinidad and Tobago	1,534,937	5130	621,000	142,209	27,899
24	Zambia	20,569,737	743,390	6,275,000	420,425	29,784
	Cluster II. Below average GDP
1	El Salvador	6,364,943	20,720	2,738,000	221,778	32,489
2	Estonia	1,322,765	42,390	692,900	164,910	38,101
3	Latvia	1,830,211	62,200	1,022,000	296,380	41,154
4	Paraguay	6,861,524	397,300	3,190,000	334,950	41,722
5	Bolivia	12,388,571	1,083,300	4,992,000	384,384	43,069
6	Cameroon	28,647,293	472,710	8,426,000	825,748	44,342
7	Bahrain	1,485,509	760	716,500	68,784	44,391
8	Uganda	48,582,334	199,810	17,400,000	713,400	45,559
9	Jordan	11,337,052	88,780	1,898,000	461,214	47,452
10	Mongolia	3,447,157	1,553,560	1,068,000	390,888	52,989
11	Slovenia	2,119,675	20,140	913,400	190,901	62,118
12	Serbia	7,149,077	87,460	2,920,000	680,360	63,502
13	Costa Rica	5,212,173	51,060	2,222,000	275,528	68,381
14	Lithuania	2,718,352	62,674	1,452,000	390,588	70,334
15	Croatia	4,008,617	55,960	1,715,000	511,070	70,965
16	Uruguay	3,423,108	175,020	1,700,000	266,900	71,177
17	Belarus	9,498,238	202,910	5,000,000	3,600,000	72,793
18	Ghana	34,121,985	227,540	12,070,000	772,480	72,839
19	Tanzania	67,438,106	885,800	24,890,000	1,144,940	75,709
20	Azerbaijan	10,412,651	82,658	4,680,000	1,024,920	78,721
21	Uzbekistan	35,163,944	425,400	18,120,000	3,297,840	80,392
22	Luxembourg	654,768	2590	208,800	24,430	82,275
23	Bulgaria	6,687,717	108,560	2,551,000	538,261	89,040
24	Guatemala	18,092,026	107,160	4,465,000	272,365	95,003
25	Venezuela	28,838,499	882,050	14,010,000	3,404,430	102,328
26	Oman	4,644,384	309,500	968,800	762,446	114,667
27	Ecuador	18,190,484	248,360	6,953,000	486,710	115,049
28	Slovakia	5,795,199	48,088	2,727,000	763,560	115,469
29	Ethiopia	126,527,060	1,000,000	52,820,000	3,486,120	126,783
30	Morocco	37,840,044	446,300	11,730,000	985,320	134,182
31	Ukraine	36,744,634	579,320	17,990,000	4,803,330	160,503
32	Hungary	10,156,239	90,530	4,263,000	1,295,952	178,789
33	Kuwait	4,310,108	17,820	2,380,000	442,680	184,558
	Cluster III. Average GDP
1	Greece	10,341,277	128,900	4,918,000	1,047,534	219,066
2	Kazakhstan	19,606,633	2,699,700	9,022,000	2,102,126	220,623
3	Qatar	2,716,391	11,610	1,424,000	160,912	237,296
4	Peru	34,352,719	1,280,000	16,160,000	1,325,120	242,632
5	New Zealand	5,228,100	263,310	2,413,000	277,495	247,234
6	Portugal	10,247,605	91,590	5,395,000	793,065	251,945
7	Iraq	45,504,560	434,320	8,900,000	3,328,600	264,182
8	Finland	5,545,475	303,890	2,685,000	700,785	280,826
9	Czech Republic	10,495,295	77,240	5,304,000	816,816	290,924
10	Chile	19,629,590	743,532	8,367,000	786,498	301,025
11	Romania	19,892,812	230,170	9,451,000	1,512,160	301,262
12	Colombia	52,085,168	1,109,500	25,760,000	1,081,920	343,939
13	Pakistan	240,485,658	770,880	108,800,000	7,942,400	376,533
14	Iran	89,172,767	1,628,550	30,500,000	4,544,500	388,544
15	Denmark	5,910,913	42,430	2,795,000	844,090	395,404
16	Philippines	117,337,368	298,170	42,780,000	3,892,980	404,284
17	South Africa	60,414,495	1,213,090	22,190,000	3,483,830	405,870
18	Malaysia	34,308,525	328,550	13,190,000	1,991,690	406,306
19	Vietnam	98,858,950	310,070	54,800,000	4,164,800	408,802
20	Bangladesh	172,954,319	130,170	65,000,000	2,015,000	460,201
21	Singapore	6,014,723	700	3,444,000	340,956	466,789
22	Austria	8,958,960	82,409	4,707,000	376,560	471,400
23	Egypt	112,716,598	995,450	29,950,000	6,349,400	476,748
24	Nigeria	223,804,632	910,770	83,200,000	2,995,200	477,386
25	Thailand	71,801,279	510,890	38,370,000	3,683,520	495,341
	Cluster IV. Above average GDP
1	UnitedArab Emirates	9,516,871	83,600	5,340,000	544,680	507,535
2	Israel	9,174,520	21,640	3,493,000	1,096,802	522,023
3	Ireland	5,056,935	68,890	2,161,000	473,259	529,245
4	Belgium	11,686,140	30,280	5,150,000	1,086,650	578,604
5	Norway	5,474,360	365,268	2,707,000	871,654	579,267
6	Sweden	10,549,347	450,295	5,600,661	1,200,000	591,189
7	Argentina	45,773,884	2,736,690	18,000,000	3,204,000	632,770
8	Poland	41,026,067	306,230	17,600,000	4,153,600	688,177
9	Türkiye	85,816,199	769,630	31,300,000	4,695,000	905,988
10	Netherlands	17,618,299	33,720	9,090,000	1,808,910	991,115
	Cluster V. High GDP
1	Indonesia	277,534,122	1,811,570	150,000,000	13,050,000	1,319,100
2	Spain	47,519,628	498,800	8,528,000	1,262,144	1,397,509
3	Mexico	128,455,567	1,943,950	54,510,000	6,432,180	1,414,187
4	South Korea	51,784,059	97,230	27,750,000	2,858,250	1,665,246
5	Australia	26,439,111	7,682,300	12,440,000	3,595,160	1,675,419
6	Brazil	216,422,446	8,358,140	110,000,000	13,310,000	1,920,096
7	Italy	58,870,762	294,140	25,940,000	4,150,400	2,010,432
8	Canada	38,781,291	9,093,510	19,520,000	4,138,240	2,139,840
9	Russia	144,444,359	16,376,870	78,000,000	31,668,000	2,240,422
10	France	64,756,584	547,557	30,680,000	6,136,000	2,782,905
11	United Kingdom	67,736,802	241,930	33,500,000	7,537,500	3,070,668
12	India	1,428,627,663	2,973,190	475,000,000	18,050,000	3,385,090
13	Germany	83,294,633	348,560	45,900,000	5,921,100	4,072,192
14	Japan	123,294,513	364,555	70,000,000	5,390,000	4,231,141
	Cluster VI. Very high GDP
1	China	1,425,671,352	9,388,211	878,000,000	69,274,200	17,963,171
2	United States	339,996,563	9,147,420	164,400,000	22,029,600	25,462,700

References

1. Donahue, J. D.,&Zeckhauser, R. J. (2011). Collaborative Governance: Private Roles for Public Goals in Turbulent Times. Princeton University Press. >https://doi.org/10.1515/9781400838103

2. Gurtoo, A.,&Williams, C. C. (2015). Developing Country Perspectives on Public Service Delivery. Springer (India) Pvt. Ltd. >https://doi.org/10.1007/978-81-322-2160-9

3. Hood, C. (2000). The Art of Statecraft: Culture, Oratory, and Public Administration. Clarendon Press. >https://doi.org/10.1093/0198297653.001.0001

4. Kahn, A. E. (1983). Political Economy of Deregulation: Interest Groups in the Regulatory Process. AEI Press.

5. Moore, M. H. (1995). Creating Public Value: Strategic Management in Government. Harvard University Press.

6. Ostrom, E. (2015). Governing the Common. Cambridge University Press. >https://doi.org/10.1017/CBO9781316423936