The Quest for an ESG Country Rank: A Performance Contribution Analysis/MCDM Approach

Abstract

Utilizing Multi-Criteria Decision Analysis (MCDA) methods based on environmental, social, and governance (ESG) factors to rank countries according to these criteria aims to evaluate and prioritize countries based on their performance in environmental, social, and governance aspects. The contemporary world is influenced by a multitude of factors, which consequently impact our lives. Various models are devised to assess company performance, with the intention of enhancing quality of life. An exemplary case is the ESG framework, encompassing environmental, social, and governmental dimensions. Implementing this framework is intricate, and many nations are keen on understanding their global ranking and avenues for enhancement. Different statistical and mathematical methods have been employed to represent these rankings. This research endeavors to examine both types of methods to ascertain the one yielding the optimal outcome. The ESG model comprises eleven factors, each contributing to its efficacy. We employ the Performance Contribution Analysis (PCA), Clifford algebra method, and entropy weight technique to rank these factors, aiming to identify the most influential factor in countries’ ESG-based rankings. Based on prioritization results, political stability (PSAV) and the voice of accountability (VA) emerge as pivotal elements. In light of the ESG model and MCDA methods, the following countries exhibit significant societal impact: Sweden, Finland, New Zealand, Luxembourg, Switzerland, Denmark, India, Norway, Canada, Germany, Austria, and Australia. This research contributes in two distinct dimensions, considering the global context and MCDA methods employed. Undoubtedly, a research gap is identified, necessitating the development of a novel model for the comparative evaluation of countries in relation to prior studies.

1. Introduction

ESG stands for Environmental, Social, and Governance, signifying a set of criteria employed to evaluate the performance of companies or organizations in terms of non-financial metrics. Environmental criteria encompass aspects such as a company’s ecological impact, including its carbon footprint and water consumption [1]. Social criteria relate to the influence of the company on society, involving its interactions with employees, customers, and the local communities it operates within [2]. Governance criteria direct attention to the internal management and oversight of a company, addressing factors such as board composition and executive remuneration [3]. The concept of ESG holds profound implications for socio-economic development, as it compels companies and organizations to contemplate their broader influence beyond mere financial performance [4]. By integrating environmental, social, and governance aspects, companies can foster more sustainable and conscientious business practices, benefiting not only shareholders, but also employees, customers, and the larger community [5]. Furthermore, a growing number of investors and consumers display heightened interest in supporting companies that prioritize ESG considerations [6]. Consequently, companies that prioritize ESG stand to gain a competitive edge in attracting investments and customers, as well as in recruiting and retaining top talent.

At the national level, numerous endeavors are made to assess ESG. Among the most recognized and widely utilized metrics is the ESG Country Rating by MSCI, a global provider of investment research and analysis [7]. The MSCI ESG Country Rating assesses countries based on their performance concerning environmental, social, and governance factors [8]. It takes into account diverse indicators, encompassing carbon emissions, utilization of renewable energy, labor rights, political stability, and corruption [9]. Other entities, such as the World Bank and the United Nations, also generate indices reflecting sustainability and social responsibility on a country-wide scale [10]. For instance, the World Bank’s Country Policy and Institutional Assessment (CPIA) evaluates a country’s policies and institutions across various sectors, including social inclusion, public sector management, and environmental sustainability [11]. While ESG indicators at the country level can provide valuable insights into a country’s sustainability and social responsibility, there are several methodological drawbacks that need to be considered. One of the main challenges is the lack of standardization and consistency across different measures. Organizations may use different indicators and methodologies, making it difficult to compare results across countries or over time. This can also lead to issues of subjectivity and bias, as different organizations may prioritize different factors or weight them differently [12]. Another challenge is the availability and reliability of data. ESG indicators often rely on self-reported data from companies and government agencies, which can be incomplete or unreliable. This can lead to inaccuracies or biases in the ratings. Moreover, the indicators may need to capture the complex and interconnected nature of sustainability and social responsibility. For example, a country may perform well on environmental indicators, but poorly on social or governance indicators, or vice versa. The indicators may also need to capture the nuanced and context-specific factors that can influence a country’s ESG performance [13]. This research aims at shedding some light into these issues by proposing a novel MCDM model based on information entropy for criteria weighting and on Clifford algebra for linearly decomposing overall scores for each country into its partial criteria contributions.

• Within this novel model, namely Performance Contribution Analysis (PCA), the use of information entropy for criteria weighting could help address subjectivity and bias in current ESG indicators. Information entropy provides a measure of the uncertainty or variability in the data, which can be used to objectively weigh the importance of different criteria when composing or computing final scores [14]
• On the other hand, using Clifford algebra to decompose overall scores into partial criteria contributions can help address the issue of transparency and consistency in current ESG indicators [15].
• By decomposing the overall score into partial contributions from each criterion, the model can provide a more detailed and nuanced understanding of how a country’s performance is numerically built upon different ESG factors. This can help identify areas of strength and weakness, as well as potential trade-offs and synergies between different criteria [16].
• This score composition (using information entropy weights) with further decomposition (using Clifford algebra) could help in generating a PCA 2 × 2 matrix for decision-makers in prioritizing ESG policies at the country level. Criteria with high information entropy and high contribution to the overall country’s score would be considered key criteria for policy formulation, as they are both important and uncertain [17].
• On the other hand, criteria with low information entropy and low contribution to the overall score would receive lower priorities in policy formulation, as they are less important and more predictable. This paper also contributes to considering many countries across multiple continents worldwide. Previously, studies have been limited to specific regions or countries, but in this paper, we attempt to cover the majority of the countries globally in comparison to previous studies [18].

The remainder of this paper is divided into five Sections, which will be discussed in more detail below. After the Introduction Section, there will be a brief overview of the Literature Review, where you will find a summary of the study, its contributions, the gaps in the literature and methods, and a review of the study’s purpose. The purpose of this Section is to evaluate previous studies to identify the research gaps that need addressing in this study. This Section also provides an overview of the literature related to mathematical methods, including PCA, Clifford, and information entropy weights, along with a description of the research methodology involved in their development. It is important to note that Section Four of this chapter is dedicated to discussing how the data has been analyzed according to the methods and equations presented in Section Three of this paper. The final part of this Section includes a conclusion, limitations, a discussion of future research, and a summary of the research questions.

2. Literature Review

Due to growing concerns regarding sustainability operation and development, companies have been focusing on various aspects of their performance, including economic, social, and governance (ESG) performance. The so-called ESG performance has also attracted significant attention from academic scholars over the recent decade, as reflected by a growing number of research articles investigating this issue from different perspectives. From empirical perspectives, research has investigated the relationship between corporate culture and ESG performance [12] the impact of climate change on ESG performance [19], board gender diversity and ESG performance [20], and the impact of environmental uncertainty on ESG performance [21] among others.

From a methodological perspective, in order to develop the ESG framework, Zopounidis et al. [22] employed Multi-Criteria Decision Analysis (MCDA), utilizing a combination of qualitative and quantitative criteria in the evaluation process, along with the Preference Ranking Organization Method for Enrichment of Evaluations (PROMETHEE) II to enhance the evaluation process. Su and Sun [23] developed an improved Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method for applying ESG to mining enterprises, demonstrating its application to a mining enterprise in China for investment decisions.

Meng and Shaikh [24] employed the Fuzzy Analytic Hierarchy Process (AHP) and Weighted Aggregated Sum Product Assessment (WASPAS) methodology to assess investment risk in green finance. Quayson et al. [25] utilized the Ordinal Priority Approach (OPA) and Multi-Criteria Decision Making (MCDM) to analyze the impact of ESG on natural resources as part of their application of ESG for sustainable development. Escrig-Olmedo et al. [26] showcased the integration of ESG investors and sustainable investment through the use of fuzzy MCDM methods, highlighting its advantages and application in prioritizing ESG management factors based on country-specific variables.

Park and Jang [27] employed the AHP method to determine investment decisions based on country-specific ESG management factors, aiming to show the best results for institutional investors. Additionally, an analysis by Plastun et al. [28] demonstrated a correlation between ESG disclosure regulations and the competitiveness of countries, utilizing various statistical methods such as Student’s T-test, ANOVA analysis, Mann–Whitney analysis, simple average analysis, and regression analysis.

Costantiello and Leogrande [29] conducted research to determine the impact of R&D expenditures on the global economy’s ESG model, utilizing various economics techniques such as Pooled Ordinary Least Squares (OLS), Panel Data with random effects and fixed effects, and Weighted Least Squares (WLS). Based on the results, it was evident that R&D had the greatest positive impact, while the health index had the greatest negative impact. The impact of accountability and voice in ESG from a global perspective was displayed by Costantiello and Leogrande [30].

Reig-Mullor et al. [31] used the neutrosophic AHP in conjunction with the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) for the evaluation of ESG corporates, implementing their model in the oil and gas industry as well. Using fuzzy MCDM, Escrig-Olmedo et al. [26] evaluated sustainable ESG investors to find the best among them. Xidonas and Essner [32] demonstrated how a multi-objective optimization approach can be used to select ESG portfolios based on diverse criteria.

Camargo et al. [33] are credited with improving the financial condition of healthcare through the implementation of Robust Compromise (RoCo), which can be used to improve the financial situation of healthcare. By utilizing the RoCo method, they prioritized financial health according to capital adequacy, asset quality, management, earnings, liquidity, and sensitivity (CAMELS), along with environmental, social, and governance factors.

3. Methodology

Considering the potential complexity of using information entropy and Clifford algebra, we provide more detailed information on the steps we take for the proposed methodology used in the current paper, represented by the following Figure 1.

3.1. Background

The proposed approach, Performance Contribution Analysis, involves implementing a Multi-Criteria Decision Analysis (MCDA) technique based on Clifford algebra [34]. Clifford algebra extends the concept of a vector to include not only its magnitude and direction, but also its orientation, or “handedness.” This is achieved by introducing a set of “basis elements” representing the different possible orientations of a vector in a given space. The approach aims to score the performance of a set of alternatives based on a set of criteria while allowing for the linear decomposition of the scores of each alternative in terms of each criterion [35]. Clifford algebra proves useful in linear decomposition, especially in multilinear algebra, where it simplifies complex geometrical operations.

For instance, in three-dimensional space, a vector can be represented as a sum of scalar and bivector elements, where the bivector represents the plane in which the vector lies [36]. Similarly, a plane in three-dimensional space can be represented as a sum of scalar, vector, and bivector elements. This representation enables linear decomposition using geometric product and dot product operations, facilitating the separation of multivector components into simpler geometric elements. A key distinction between Performance Contribution Analysis (PCA) and other MCDM methods is that PCA can also serve as a post hoc analysis technique, whereas most other MCDM methods are used for decision-making a priori. PCA’s linear decomposition of performance scores allows for monitoring the improvement paths of decisions or solutions after implementation by focusing on each criterion’s contributions to overall performance. In contrast, other MCDM methods like Analytic Hierarchy Process (AHP) or Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) are exclusively used to evaluate and compare alternatives before decision-making. Furthermore, PCA enables an in-depth analysis of each criterion’s contribution to overall performance, whereas other MCDM methods aim directly to identify the best alternative or a ranking of alternatives based on criteria. Nonetheless, PCA can complement other MCDM methods to provide a comprehensive understanding of the selected alternative’s performance both before and after decision-making.

3.2. Clifford Algebra Applied to MCDM

Suppose a nxm MCDM matrix, consisting of n alternatives and m criteria [37]. Let us formalize the following derivations using elements of Clifford algebra, which is the most suitable framework for representing and manipulating geometric objects and their required transformations in a unified manner, within the context of the novel proposed approach [38].

Let us start by representing each alternative in the MCDM matrix as a vector in a Euclidean space of dimension m (i.e., the number of criteria). We can express each alternative vector as:

$${\mathrm{a}}_{\mathrm{i}}={\mathrm{a}}_{\mathrm{i}1}{\mathrm{e}}_1+{\mathrm{a}}_{\mathrm{i}2}{\mathrm{e}}_2+\dots +{\mathrm{a}}_{\mathrm{i}\mathrm{m}}{\mathrm{e}}_{\mathrm{m}}$$

(1)

where ${\mathrm{e}}_1$, ${\mathrm{e}}_2$, …,${\mathrm{e}}_{\mathrm{m}}$ are the basis vectors of the Euclidean space and ${\mathrm{a}}_{\mathrm{i}\mathrm{j}}$ is the j-th criterion value of the i-th alternative. We can stack all the alternative vectors into a matrix A:

$$\mathbf{A}=\left[{\mathbf{a}}_1{\mathbf{a}}_2\dots .{\mathbf{a}}_{\mathbf{n}}\right]$$

(2)

Similarly, we can represent each criterion as a vector in a Euclidean space of dimension n (i.e., the number of alternatives). We can write each criterion vector as:

$${\mathbf{c}}_{\mathbf{j}}={\mathbf{c}}_{1\mathbf{j}}{\mathbf{e}}_1+{\mathbf{c}}_{2\mathbf{j}}{\mathbf{e}}_2+\dots +{\mathbf{c}}_{\mathbf{n}\mathbf{j}}{\mathbf{e}}_{\mathbf{n}}$$

(3)

where ${\mathbf{c}}_{\mathbf{i}\mathbf{j}}$ is the value of the j-th criterion for the i-th alternative. We can stack all the criterion vectors into a matrix C:

$$\mathbf{C}=\left[{\mathbf{c}}_1{\mathbf{c}}_2\dots .{\mathbf{c}}_{\mathbf{m}}\right]$$

(4)

To compute the dot product between a pair of alternative vectors ai and aj, we can use the geometric product of their corresponding multivectors A_i and A_j, defined as:

$${\mathbf{A}}_{\mathbf{i}}{\mathbf{A}}_{\mathbf{i}}=\frac{1}{2}\left({\mathbf{A}}_{\mathbf{i}}{\mathbf{A}}_{\mathbf{j}}+{\mathbf{A}}_{\mathbf{j}}{\mathbf{A}}_{\mathbf{i}}\right)$$

(5)

where A_i = ${\mathrm{a}}_{\mathrm{i}}+{\mathrm{e}}_{\mathrm{m}+1}$ and A_j = ${\mathrm{a}}_{\mathrm{j}}+{\mathrm{e}}_{\mathrm{m}+1}$ are multivectors in a Euclidean space of dimension m + 1, with an additional unit pseudoscalar ${\mathrm{e}}_{\mathrm{m}+1}$ that represents the orientation of the space.

The geometric product can be expanded using the distributive property and the following relations between the basis vectors:

$${\mathbf{e}}_{\mathbf{i}}{\mathbf{e}}_{\mathbf{j}}=-{\mathbf{e}}_{\mathbf{j}}{\mathbf{e}}_{\mathbf{i}},{\mathbf{e}}_{\mathbf{i}}{\mathbf{e}}_{\mathbf{j}}=1$$

(6)

We can show that the dot product of ${\mathrm{a}}_{\mathrm{i}}$ and ${\mathrm{a}}_{\mathrm{j}}$ is given by:

$${\mathbf{a}}_{\mathbf{i}}{\mathbf{a}}_{\mathbf{j}}=\frac{1}{2}\left({\mathbf{a}}_{\mathbf{i}}{\mathbf{a}}_{\mathbf{j}}+{\mathbf{a}}_{\mathbf{j}}{\mathbf{a}}_{\mathbf{i}}\right)$$

(7)

Using the outer product of the vectors representing the criteria, we obtain the grade-2 multivector:

$$\mathbf{A}={\sum }_{\mathbf{i},\mathbf{j}=1}^{\mathbf{m}}{\mathbf{a}}_{\mathbf{i}\mathbf{j}}{\mathbf{a}}_{\mathbf{i}}{^\mathbf{a}}_{\mathbf{j}}$$

(8)

which can be expanded as:

$$\mathbf{A}={\sum }_{\mathbf{i}=1}^{\mathbf{m}}{\mathbf{a}}_{\mathbf{i}\mathbf{i}}\left({\mathbf{a}}_{\mathbf{i}}^{\mathbf{a}}_{\mathbf{i}}\right)+{\sum }_{\mathbf{i}<\mathbf{j}}^{\mathbf{m}}{\mathbf{a}}_{\mathbf{i}\mathbf{j}}\left({\mathbf{a}}_{\mathbf{i}}^{\mathbf{a}}_{\mathbf{j}}+{\mathbf{a}}_{\mathbf{j}}^{\mathbf{a}}_{\mathbf{i}}\right)$$

(9)

where ∧ denotes the exterior product. The first term represents the diagonal elements of the matrix, while the second term represents the off-diagonal elements.

The norm of A is given by:

$$||\mathrm{A}||={\sum }_{\mathbf{i},\mathbf{j}=1}^{\mathbf{m}}{\mathbf{a}}_{\mathbf{i}\mathbf{j}}^2$$

(10)

3.3. Outer Product

Using the outer product of the vectors c representing the criteria, we obtain the grade-2 multivector:

$$\mathsf{\Gamma }={\wedge }_{\mathbf{j}=1}^{\mathbf{m}}{\mathbf{c}}_{\mathbf{j}}$$

(11)

where ⋀ denotes the outer product. This multivector represents the subspaces defined by the criteria vectors. In a similar way, we can use the outer product of the vectors a representing the alternatives to obtain the grade-2 multivector:

$$\mathsf{A}={\wedge }_{\mathbf{i}=1}^{\mathbf{n}}{\mathbf{a}}_{\mathbf{i}}$$

(12)

which represents the subspaces defined by the alternative vectors.

3.4. Performance Contribution Analysis

We can then define the Performance Contribution Analysis matrix as the contraction of these two multivectors:

$$∆=\mathsf{\Gamma }\cdot \mathsf{A}$$

(13)

where ⋅ denotes the geometric product or contraction. The elements of this matrix represent the dot products between the alternative vectors and the criterion vectors. We can also represent the alternative vectors, criterion vectors, and MCDM matrix as multivectors in the grade-1 and grade-2 subspaces of the Clifford algebra. The grade-1 subspaces represent the vectors, and the grade-2 subspaces represent the outer products of vectors.

To compute the partial performance measures for each alternative in terms of each criterion, we can use the projection of the alternative multivector onto each criterion subspace. The projection of the alternative multivector onto the subspace defined by the j-th criterion is given by:

$${\mathbf{p}}_{\mathbf{i}\mathbf{j}}\left({\mathbf{a}}_{\mathbf{i}}\right)=\frac{{\mathbf{a}}_{\mathbf{i}}\cdot {\mathbf{c}}_{\mathbf{j}}}{{\left|{\mathbf{c}}_{\mathbf{j}}\right|}^2}{\mathbf{c}}_{\mathbf{j}}$$

(14)

where ${\mathrm{a}}_{\mathrm{i}}$ is the multivector representing the i-th alternative, c_j is the multivector representing the j-th criterion, ⋅ denotes the geometric product or contraction, and ${\left|{\mathrm{c}}_{\mathrm{j}}\right|}^2$ is the squared magnitude of ${\mathrm{c}}_{\mathrm{j}}$. The numerator represents the dot product between the alternative vector and the criterion vector, and the denominator normalizes the projection vector to have unit magnitude. We can then compute the contribution of each alternative to each criterion by taking the magnitude of the projection vector:

$${\mathsf{\delta }}_{\mathbf{i}\mathbf{j}}=\left|{\mathbf{p}}_{\mathbf{i}\mathbf{j}}\left({\mathbf{a}}_{\mathbf{i}}\right)\right|$$

(15)

This represents the partial performance measure of the i-th alternative with respect to the j-th criterion.

To propose an improvement path for each alternative, we can use the contribution values to identify the criteria with the highest and lowest values for each alternative. The alternative should focus on improving its performance on the criteria with the lowest contribution values to move towards the performance of the highest-ranked alternative.

We can also represent the improvement path as a multivector in the grade-2 subspace, using the outer product of the vectors representing the criteria with the lowest and highest contribution values. This represents the subspace defined by the criteria that the alternative should focus on improving to move towards the performance of the highest-ranked alternative.

The partial contributions of each criterion to each alternative are then divided by the sum of the contributions of all criteria for that alternative to obtain the normalized contributions, which are denoted by $\dot{{\delta }_{ij}}$. Thus, we have:

$$\dot{{\mathit{\delta }}_{\mathit{i}\mathit{j}}}=\frac{{\mathit{\delta }}_{\mathit{i}\mathit{j}}}{\sum _{\mathit{k}=1}^{\mathit{m}}{\mathit{\delta }}_{\mathit{i}\mathit{k}}}$$

(16)

where n is the number of alternatives, m is the number of criteria, and ${\delta }_{ij}$ is the partial contribution of criterion j to alternative i.

3.5. Information Entropy Weights for Each Criterion

The information entropy of a column vector u can be computed based on the entropy of its individual entries. If the coordinates of a column-vector are more dispersed or varied, this will generally result in a higher entropy value [38]. This is because a higher degree of variability or randomness in the entries implies a higher level of uncertainty or unpredictability. Hence, the entropy weight $w_j$ of criterion j is calculated as follows:

$${\mathit{H}}_{\mathit{j}}=-{\sum }_{\mathit{i}=1}^{\mathit{n}}{\mathit{x}}_{\mathit{i}\mathit{j}}\mathbf{l}\mathbf{o}\mathbf{g}\left({\mathit{x}}_{\mathit{i}\mathit{j}}\right),\mathrm{j}=1..\mathrm{m}$$

(17)

$${\mathit{w}}_{\mathit{j}}=\frac{{\mathit{H}}_{\mathit{j}}}{{\sum }_{\mathit{k}=1}^{\mathit{m}}{\mathit{H}}_{\mathit{k}}}$$

(18)

where $H_j$ is the entropy of criterion j, and $w_j$ is the weight of criterion j.

3.6. Overall Performance Score per Alternative and Linear Decomposition

Finally, the overall performance score Si of alternative i is computed as the weighted sum of its normalized criteria values, i.e.,

$${\mathit{S}}_{\mathit{i}}={\sum }_{\mathit{j}=1}^{\mathit{m}}{\mathit{w}}_{\mathit{j}}{\mathit{x}}_{\mathit{i}\mathit{j}},\mathrm{i}=1..\mathrm{n}$$

(19)

where $x_{ij}$ is the normalized value of alternative i on criterion j—entries of the MCDM matrix—and $w_j$ is the weight of criterion j. The linear decomposition of the overall performance score $S_i$ per each criterion is obtained via the outer product of S and $∆$, S∧$∆=\mathrm{S}$⊗$∆$ − $∆$⊗S. The R code for implementing these computations is available to readers upon request.

3.7. Limitations of Methods and Assumptions

3.7.1. Limitations

The interpretation of entropy measures can be subjective, particularly in decision-making scenarios where the selection of the entropy formulation or calculation method can impact the outcome of decisions. The presence of subjectivity can result in conflicts between decision-makers and stakeholders. Entropy-based models frequently depend on assumptions and simplifications regarding the underlying system, including variable independence and the validity of probabilistic distributions. Departures from these assumptions can impact the precision and dependability of analyses based on entropy [39].

Entropy measures offer insights into the present state of a system but may offer limited predictive capabilities for future states or outcomes, particularly in dynamic or evolving systems influenced by external factors or feedback mechanisms. The understanding of entropy measures is contingent upon the context and the selection of the reference frame or probability distribution. Diverse formulations of entropy can yield varying conclusions regarding the behavior of the system, thus posing a challenge when comparing results across studies or applications. Accurate estimation of probability distributions in entropy-based analyses often necessitates a substantial amount of data, especially in high-dimensional or intricate systems. In certain real-world scenarios, acquiring enough data for entropy calculations may prove to be impractical or expensive [40].

3.7.2. Assumptions

The assumptions underlying Clifford algebra are as follows:

In the context of Clifford algebra, it is commonly assumed that the underlying space possesses the Euclidean properties of distance, angles, and orthogonality. Although it is possible to extend it to non-Euclidean spaces, many applications primarily utilize Euclidean geometry for the sake of simplicity. Nevertheless, it is important to note that this assumption may not be applicable in all situations, and the incorporation of non-orthogonal bases can introduce further intricacies. Although the definition of Clifford algebra extends to infinite-dimensional spaces, practical applications mostly focus on finite-dimensional vector spaces due to computational restrictions and modeling limitations. Certain applications of Clifford algebra center around homogeneous geometries, such as projective geometry or conformal geometry. These geometries possess distinct properties that facilitate specific computations and allow for geometric interpretations. The utilization of Clifford algebra techniques assumes the smoothness and continuity of geometric objects and transformations, thereby enabling the implementation of differential geometric methods. Departures from these assumptions may necessitate the use of alternative modeling methodologies.

The underlying assumptions of entropy are as follows:

In entropy calculations, it is commonly assumed that the random variables being analyzed are independent and identically distributed. This process streamlines the analysis of probability distributions and computations. Any deviations from this assumption may necessitate adjustments to entropy formulations. The presence of non-stationarity can add complexity to entropy estimates and necessitate the use of adaptive methods. Although the concept of entropy can be applied to continuous random variables, its practical computations often focus on discrete or discretized state spaces. This assumption serves to streamline probability distributions and enhance computational calculations. In the calculation of entropy, it is customary to have prior knowledge about the probability distribution that governs the system being analyzed. The process of estimating probability distributions from data entails the introduction of uncertainties and often necessitates assumptions about data generating processes. In the case of entropy measures like Shannon entropy, it is assumed that memoryless processes exist, wherein the independence of future states from past states is guaranteed given the current state. When dealing with systems that possess memory effects or dependencies, it may be necessary to consider alternative formulations of entropy. The employment of the Clifford algebra and entropy methods is contingent upon mathematical formulations and definitions which may not always accurately depict real-world phenomena. The usage of these formulations implies implicit assumptions about their applicability and validity. The Clifford algebra and entropy methods are employed in specific domains and contexts where their assumptions are deemed reasonable. The extension of these methods to new domains necessitates meticulous evaluation of underlying assumptions and their repercussions. The practical implications of both Clifford algebra and entropy methods are contingent upon the data’s quality and the validity of the underlying models. The correct interpretation of results relies heavily on assumptions regarding data accuracy, completeness, and model validity.

3.8. Selecting Factor

Take into account stakeholders’ needs and expectations. Identify key ESG factors for stakeholders and prioritize variable selection accordingly. Consult GRI, SASB, SDGs, or PRI for ESG best practices. These resources offer ESG factor and metric guidance. Identify significant ESG issues through a materiality assessment for your organization or portfolio. Materiality assessments evaluate how ESG factors affect financial performance, reputation, and stakeholder relationships. ESG factors differ by industry and sector. Material factors vary between industries. Evaluate data availability and quality for potential ESG variables in each industry. Factors to consider include data coverage, accuracy, timeliness, and consistency. Focus on variables with reliable data access. Evaluate the financial importance of ESG factors by analyzing their impact on company performance, valuation, and risk. Give priority to factors with a proven impact on financial outcomes in ESG modeling. Ensure inclusive decision-making through collaboration with experts and stakeholders. ESG model variable selection is iterative. Regularly update variable selection based on trends, feedback, regulations, and priorities [41].

3.9. Type of Data

Entropy can be applied to continuous data, such as environmental indicators (e.g., carbon emissions, air quality index, biodiversity metrics), social metrics (e.g., income inequality, poverty rates, education levels), and governance indicators (e.g., corruption index, political stability index). It can also be extended to discrete data, such as categorical variables representing various dimensions of ESG performance (e.g., the existence of human rights safeguards, compliance with environmental regulations, governance frameworks). Clifford algebra is often used in geometric algebra, allowing for the representation of diverse geometric entities like points, lines, planes, and volumes. Techniques in Clifford algebra facilitate the analysis of geometric data, including spatial coordinates, vectors, and shapes. One approach is to represent ESG data as a multidimensional matrix, where each dimension corresponds to a specific factor or criterion [42].

4. Analysis and Discussion of Results

4.1. Data and Variable Classification

The dataset utilized in this research was collected from various sources and covers the years 2009 to 2020, spanning multiple countries globally. Initially, this compilation resulted in an aggregate dataset consisting of 550 observations, encompassing seven positive criteria and four negative criteria. After removing missing values, the resulting aggregate dataset forms an imbalanced panel, comprising 546 observations and a total of 11 criteria. Supplementary contextual variables, including those related to time, GDP per capita, population, and foreign trade as a percentage of GDP, complement the dataset. These variables are detailed in

Table 1. Descriptive stats for the positive and negative criteria.

Criteria	Direction	Acronym	Mean	SD	CV	Max	Min	Skewness	Kurtosis	Entropy
Control of Corruption	positive	CC	0.94	0.72	0.77	2.40	-	0.59	(1.07)	7.36
Government Effectiveness	positive	GE	0.89	0.65	0.74	2.24	-	0.32	(1.19)	7.30
Voice and Accountability	positive	VA	0.92	0.53	0.58	2.12	-	(0.11)	(1.25)	7.17
Political Stability and Absence of Violence	positive	PSAV	0.70	0.42	0.60	2.01	0.01	0.20	(0.88)	7.04
Patent	positive	PAT	18,556.36	128,190.17	6.91	1,393,815	2.00	8.57	75.90	8.74
Gross Enrollment Ratio—Primary School	positive	GERPS	102.61	6.00	0.06	128.64	84.47	0.64	2.40	9.09
Bottom 50% share—pre-tax national income	positive	BOT50	0.17	0.05	0.30	0.26	0.05	(0.46)	(0.55)	8.59
CO2 emissions (kg per USD of GDP [43])	negative	CO2	0.43	0.33	0.76	2.07	0.05	1.48	2.27	9.09
Top 10% share—pre-tax national income	negative	TOP10	0.42	0.10	0.24	0.68	0.27	0.92	(0.09)	8.66
Top 1% share—pre-tax national income	negative	TOP10	0.15	0.05	0.33	0.31	0.07	1.20	1.20	8.55
Population ages 65 and above	negative	POP > 65	0.13	0.06	0.42	0.22	0.03	(0.26)	(1.33)	9.09

,

Table 2. Descriptive stats for the continuous contextual variables.

	Mean	SD	CV	Max	Min	Skewness	Kurtosis	Entropy
GDP per capita	31,137.60	21,400.91	0.69	116,283.70	1047.59	1.40	2.89	9.09
Population	75,847,211.84	250,939,932.49	3.31	1,407,745,000.00	318,041.00	4.76	21.20	9.09
Foreign trade/GDP	101.02	66.39	0.66	379.10	22.49	2.19	5.34	9.09

and

Table 3. Frequency counts for the categorical contextual variables.

Country Count
Armenia	10	Finland	10	Mozambique	10
Australia	10	France	10	NewZealand	10
Austria	10	Georgia	10	Norway	10
Azerbaijan	10	Germany	10	Peru	10
Belarus	10	Greece	10	Portugal	10
Belgium	10	Guatemala	10	Romania	10
Bulgaria	10	Hungary	10	Serbia	10
Canada	10	India	10	Singapore	10
Chile	10	Indonesia	9	Slovakia	10
China	10	Ireland	10	SouthAfrica	10
Colombia	10	Israel	10	Spain	10
CostaRica	10	Latvia	10	Sweden	10
Croatia	9	Lithuania	10	Switzerland	10
Cyprus	10	Luxembourg	10	Thailand	10
CzechRepublic	10	Malaysia	10	Turkey	10
Denmark	8	Malta	10	UnitedKingdom	10
Ecuador	10	Mexico	10	Uzbekistan	10
Estonia	10	Morocco	10	Vietnam	10
Year Count
2010	55	2014	55	2018	55
2011	53	2015	55	2019	55
2012	53	2016	55
2013	55	2017	55

. Table 1 presents positive and negative criteria from various sources. Continuous contextual variables are listed in Table 2. Table 3 displays frequency counts of categorical contextual variables.

Regarding the positive and negative criteria outlined in Table 1, the analysis utilizes variables sourced from three distinct databases. Data on control of corruption, government effectiveness, voice and accountability, and political stability and absence of violence are extracted from the Worldwide Governance Indicators database. Information on patents, CO₂ emissions, gross enrollment ratio, and total population aged 65 and above are sourced from the World Bank’s open data repository. Additionally, data on the Top 1%, Top 10%, and bottom 50% shares of pre-tax national income are obtained from the World Inequality Indicators database.

Corruption is a critical determinant of a country’s governance and economic health. By including this criterion, the MCDA aims to evaluate a country’s efforts to maintain transparency, accountability, and the rule of law in both public and private sectors. Low corruption levels are associated with stable institutions, favorable business environments, and sustainable development. Government effectiveness assesses the efficiency and capacity of a government in formulating and implementing policies that drive positive outcomes for citizens. Government effectiveness reflects the ability to deliver essential public services, promote social welfare, and maintain a stable economic environment. Voice and accountability reflect the significance of citizens’ participation and their ability to influence decision-making processes in their country. A strong voice and accountability score indicate open political systems, respect for human rights, and the protection of civil liberties. Political stability and absence of violence are crucial for sustainable development. This criterion assesses a country’s internal conflicts, political stability, and the absence of violent incidents. Political stability fosters investor confidence, economic growth, and social well-being. The patent criterion highlights a country’s innovation and intellectual property protection capabilities. Nations that encourage innovation through robust patent systems promote economic diversification, technological progress, and competitiveness on the global stage. Education is a fundamental driver of social development and human capital formation. The gross enrollment ratio in primary school provides insights into a country’s commitment to quality education and equal access to learning opportunities for its citizens. The bottom 50% share of pre-tax national income addresses income inequality and inclusivity. Evaluating the income share of the bottom 50% of the population helps gauge a country’s efforts to ensure that economic growth translates into tangible benefits for all segments of society.

Incorporating CO₂ emissions as a negative criterion reflects the pressing need to combat climate change and reduce environmental harm [43]. High levels of carbon dioxide emissions are associated with increased greenhouse gas concentrations and contribute to global warming and environmental degradation. By including CO₂ emissions as a negative criterion, the MCDA underscores the importance of transitioning to cleaner energy sources, adopting sustainable practices, and minimizing carbon footprints [44]. The top 10% share of pre-tax national income aims to address income inequality and wealth concentration. A disproportionately high share of national income held by the top 10% of the population can lead to social disparities, reduced social cohesion, and unequal access to opportunities. Evaluating this negative criterion signals the importance of fostering equitable economic growth and ensuring that prosperity is shared more broadly among citizens. Similar to the top 10% share, the top 1% share of pre-tax national income highlights extreme wealth concentration and potential social inequality. An excessively high income share among the top 1% may exacerbate income disparities and limit economic mobility for the rest of the population. This criterion underscores the need for progressive taxation, inclusive economic policies, and measures to promote social equity. The total population aged 65 and above acknowledges the challenges associated with aging populations and the need for adequate social support systems. A high percentage of the population aged 65 and above can strain healthcare systems, pension schemes, and social services. Assessing this criterion emphasizes the importance of long-term planning for aging demographics, ensuring healthcare access, and promoting intergenerational equity.

Regarding the contextual variables detailed in Table 2, their inherent roles as endogenous drivers for achieving higher or lower country-level ESG scores are discussed below. Contextual variables such as GDP per capita, population, and foreign trade as a percentage of GDP can potentially influence ESG scores diversely, with no predetermined conclusion. GDP per capita serves as a gauge of a nation’s economic advancement, and a higher GDP per capita can potentially correlate with elevated ESG scores. This is due to wealthier nations having greater resources to invest in sustainable technologies and practices, as well as stronger institutions and regulations promoting environmental and social responsibility. However, higher GDP per capita might also correspond with augmented consumption and production levels, contributing to negative environmental and social repercussions. Thus, the impact of GDP per capita on ESG scores hinges on wealth generation and utilization.

Population size also has implications for country-level ESG scores. Larger populations could lead to amplified resource consumption, environmental degradation, and social and economic inequality. Nonetheless, larger populations might generate economies of scale, enhancing the viability and cost-effectiveness of sustainable technologies and practices. Moreover, a sizable population could foster social and political mobilization around ESG concerns, driving transformative change. Foreign trade as a percentage of GDP can equally affect country-level ESG scores. Countries heavily reliant on foreign trade could face environmental and social risks linked to global supply chains, encompassing deforestation, labor exploitation, and human rights violations [45]. Conversely, foreign trade can facilitate knowledge and technology transfer, motivating companies to adopt more sustainable practices aligned with international standards and regulations.

4.2. Results of the PCA and the Comparison between PCA and Other Methods

Results from the PCA (Performance Contribution Analysis) method applied to the positive/negative criteria in Table 1 are depicted in Figure 1. An output-oriented approach with varying returns to scale was used for the DEA results in Figure 1. For SFA scores, a simple output average was adopted, and the TOPSIS model assumed equal weights. Notably, due to the criteria’s scale, many with mean values below one, SFA regression results did not detect inefficiency, explaining the higher-than-one efficiency scores [46]. Nonetheless, correlation outcomes shown in

Table 4. Correlation results between scores.

	PCA	DEA	SFA	TOPSIS	Average
PCA	1.0000	0.4678	0.7739	0.5290	0.6927
DEA	0.4678	1.0000	0.5202	0.5084	0.6241
SFA	0.7739	0.5202	1.0000	0.3543	0.6621
TOPSIS	0.5290	0.5084	0.3543	1.0000	0.5979

demonstrate that the proposed PCA model maintains isotonicity in scores compared to alternative approaches (all correlations are positive). For comparison purposes,

Table 5. Descriptive statistics for the scores.

	Mean	SD	CV	Max	Min	Skewness	Kurtosis	Entropy
DEA	0.835	0.153	0.183	1.000	0.392	(0.680)	(0.529)	7.666
PCA	0.360	0.084	0.233	0.587	0.186	0.387	(0.685)	9.093
SFA	1.060	0.020	0.018	1.164	1.029	0.955	1.594	9.093
TOPSIS	0.303	0.057	0.188	0.731	0.183	2.944	19.147	9.093

presents descriptive statistics for these scores, revealing that PCA scores exhibit the highest coefficient of variation and lowest skewness while yielding the second-lowest mean values [47].

Table 6. Ridge regression results for the impact of contextual variables on ESG scores.

	Coefficient	t-Value	p-Value
(Intercept)	0.3588050388 *	76.95958153	3.70 × 10−121
Trend	−0.0004424813	−0.02089351	9.83 × 105
Trend2	−0.0016312695	−0.07695365	9.39 × 105
GDP per capita	0.0638894040 *	10.54915716	4.98 × 10−14
Population	0.0044968509	0.92006019	3.59 × 105
Foreign trade	−0.0132574130 *	−2.21560559	2.81 × 104

(*) Asterisk denotes a significant relationship at the 0.05 level. Adj R-squared = 0.4216. Best lambda = 0.006049645. MSE = 0.0035664934.

presents the findings of Ridge regression for the PCA scores linked to the contextual variables outlined in Table 2. Before delving into the results, it is important to grasp the distinctions between Ridge and Lasso regressions, and the rationale for favoring the former over the latter. Both are regularization techniques aimed at preventing overfitting in linear regression models. Ridge regression applies an L2 penalty, adding a penalty term equal to the square of the coefficient magnitude, while Lasso regression employs an L1 penalty, adding a penalty term equal to the absolute value of the coefficients. Ridge regression shrinks all variable coefficients toward zero without excluding any from the model, whereas Lasso regression facilitates feature selection by often setting coefficients of less important variables to zero. Additionally, Ridge regression has a closed-form solution based on linear algebra, whereas Lasso regression necessitates an iterative optimization algorithm. Ridge regression generally yields lower variance and higher bias compared to Lasso regression, with the latter resulting in higher variance and lower bias. Notably, when variables outnumber the sample size, Ridge regression remains viable, while Lasso regression can falter due to the L1 penalty’s nature. In summary, Ridge regression suits scenarios with similarly important explanatory variables or few predictors, while Lasso regression suits scenarios with a subset of crucial variables and less significant ones (attributable to a multitude of predictors).

The results in Table 6 indicate that GDP per capita exerts a positive and significant influence on country-level ESG scores, whereas the foreign trade-to-GDP ratio exerts a negative and significant impact on these scores. Notably, the impact of population is deemed statistically insignificant. One plausible interpretation of these findings is that elevated GDP per capita may reflect heightened economic and institutional development, fostering resources and incentives for sustainable practices and policies. Conversely, increased foreign trade levels might correlate with heightened environmental and social risks, including pollution, labor exploitation, and human rights violations, thereby potentially lowering ESG scores. However, it is essential to note that these interpretations stem from variable correlations and do not necessarily imply causation.

Furthermore, underlying phenomena could underpin these results. For instance, nations heavily reliant on foreign trade might encounter international or domestic pressures that prioritize economic growth over sustainability and social responsibility, whereas countries with higher GDP per capita may possess more resources to invest in sustainable technologies and practices. Additionally, diverse countries may exhibit distinct cultural, social, and political norms and values that shape their ESG priorities and actions. However, it is worth considering that foreign trade must be approached with decarbonization goals in mind, aligning with the commitments of the Paris Agreement for global CO₂ emission reduction. Cultural, social, and political facets are pivotal in evaluating ESG. These factors can foster transparency in financial matters, and investment-seeking nations may strive to bolster direct and indirect investment to augment their Gross National Product (GNP), potentially reinforcing environmental commitments.

PCA stands out from other ESG evaluation methods due to its ability to reduce dimensionality, identify crucial factors, conduct unbiased analysis, provide quantitative insights, improve interpretability, offer flexibility, and seamlessly integrate with decision-making processes. Through the utilization of these strengths, PCA has the ability to significantly improve the effectiveness and rigor of ESG analysis and decision-making processes.

4.3. Results of the OLS

Nonetheless,

Table 7. OLS regression results for ESG rank at the country level.

	Estimate	Std. Error	t-Value	Pr (>|t|)	Sig.
(Intercept)	0.250	0.011	21.808	0.000	*
Sweden	0.276	0.015	18.916	0.000	*
Finland	0.255	0.015	17.492	0.000	*
New Zealand	0.240	0.015	16.465	0.000	*
Luxembourg	0.235	0.015	16.084	0.000	*
Switzerland	0.232	0.015	15.900	0.000	*
Denmark	0.230	0.015	15.777	0.000	*
India	0.223	0.015	15.287	0.000	*
Norway	0.222	0.015	15.190	0.000	*
Canada	0.216	0.015	14.782	0.000	*
Germany	0.213	0.015	14.586	0.000	*
Austria	0.200	0.015	13.724	0.000	*
Australia	0.186	0.015	12.772	0.000	*
United Kingdom	0.175	0.015	11.993	0.000	*
Chile	0.158	0.015	10.858	0.000	*
Singapore	0.156	0.015	10.708	0.000	*
Estonia	0.153	0.015	10.472	0.000	*
Belgium	0.148	0.015	10.180	0.000	*
Portugal	0.148	0.015	10.163	0.000	*
France	0.146	0.015	10.040	0.000	*
Uzbekistan	0.142	0.015	9.705	0.000	*
China	0.133	0.015	9.150	0.000	*
Malta	0.133	0.015	9.125	0.000	*
Czech Republic	0.127	0.015	8.689	0.000	*
Israel	0.114	0.015	7.821	0.000	*
Lithuania	0.107	0.015	7.364	0.000	*
Spain	0.106	0.015	7.264	0.000	*
Belarus	0.099	0.015	6.766	0.000	*
Cyprus	0.094	0.015	6.304	0.000	*
Mozambique	0.084	0.015	5.790	0.000	*
Thailand	0.084	0.015	5.762	0.000	*
Azerbaijan	0.084	0.015	5.725	0.000	*
Georgia	0.081	0.015	5.545	0.000	*
Hungary	0.079	0.015	5.418	0.000	*
Costa Rica	0.073	0.015	5.033	0.000	*
Slovakia	0.070	0.015	4.780	0.000	*
Vietnam	0.067	0.015	4.594	0.000	*
Latvia	0.066	0.015	4.497	0.000	*
Mexico	0.057	0.015	3.932	0.000	*
Turkey	0.056	0.015	3.872	0.000	*
Bulgaria	0.052	0.015	3.561	0.000	*
Serbia	0.041	0.015	2.837	0.005	*
Peru	0.038	0.015	2.636	0.009	*
Indonesia	0.038	0.015	2.591	0.010	*
Croatia	0.032	0.015	2.224	0.027	*
Guatemala	0.031	0.015	2.105	0.036	*
Malaysia	0.030	0.015	2.047	0.041	*
Colombia	0.021	0.015	1.465	0.144
Morocco	0.020	0.015	1.354	0.176
South Africa	0.018	0.015	1.259	0.209
Greece	0.018	0.015	1.246	0.213
Armenia	0.012	0.015	0.824	0.410
Ireland	0.008	0.015	0.558	0.577
Romania	0.006	0.015	0.430	0.668
Trend	0.000	0.002	0.131	0.896
Trend2	(0.000)	0.000	(0.230)	0.818

(*) Asterisk denotes a significant relationship at the 0.05 level.

presents the findings of Ordinary Least Squares (OLS) regression, highlighting ESG scores at the country level across the sampled nations. Ecuador serves as the reference category. Notably, many countries exhibit significant coefficients, suggesting that local regulatory policies, along with cultural and societal elements, significantly influence ESG scores. In essence, this underscores the significance of local cultural, social, and political norms alongside economic norms.

Ranking these significant coefficients in descending order reveals the top ESG country rankings: Sweden, Finland, New Zealand, Luxembourg, Switzerland, Denmark, India, Norway, Canada, Germany, Austria, and Australia. These results signify that these nations have displayed robust performance concerning environmental, social, and governance factors, as indicated by the incorporated PCA score indicators (dependent variable). Generally, these top-ranked countries share a commitment to sustainability, social responsibility, and human rights. They have set ambitious goals for emissions reduction, renewable energy adoption, and have implemented policies promoting sustainable practices. Strong welfare states and dedication to social equality and non-discrimination are also apparent. Conversely, Morocco, South Africa, Greece, Armenia, Ireland, and Romania emerged as relatively less influential countries. For instance, Morocco has the world’s lowest human rights rating. South Africa leads in income inequality and poverty. Greece grapples with high unemployment rates in the European Union. Armenia’s struggles extend across several areas, often aggravated by conflicts with Azerbaijan. Ireland grapples with elevated CO₂ emissions. Romanians perceive increasing corruption trends.

4.4. PCA and Information Entropy

Figure 2 illuminates potential paths for other countries to ascend the ESG ranks. Information entropy weights (Figure 2, top; Equations (17) and (18)) reveal higher country heterogeneity concerning primary school enrollment, wealth concentration among the top 1% and 10%, political stability, absence of violence, and voice and accountability. Utilizing these weights to compute overall ESG scores and their components (Figure 2, middle; Equations (13)–(16) and (19)), insights emerge. Population above 65 years, bottom 50% wealth distribution, political stability, absence of violence, and government effectiveness constitute the most impactful criteria in ESG score composition. This analysis encompasses two dimensions: prioritizing criteria with higher inter-country heterogeneity for ESG rank improvement, and focusing on major influential criteria despite potentially lower heterogeneity. Therefore, Figure 3 illustrates a proposed matrix, positioning research criteria against these two dimensions of analysis. The top-right quadrant highlights priority criteria. Results emphasize that among these, political stability and absence of violence (PSAV) and voice and accountability (VA) hold the greatest significance. Consequently, ranking these countries based on these two factors strongly influences their rankings. Conversely, patents (PAT), CO₂ emissions (CO₂), and control of corruption (CC) exhibit lower importance among all criteria.

PCA outcomes have the potential to shed light on the fundamental data structure and assist in the identification of crucial variables. Subsequently, the 2 × 2 decision matrix (Figure 4) can be employed for the assessment of alternatives or decisions, considering the variables and their relative significance, potentially utilizing the insights derived from PCA and information entropy weights. We add a comparative analysis in the Appendix A that more explicitly demonstrates the advantages of PCA over other ESG evaluation methods. Also, in order to demonstrate the advantages of PCA over other ESG evaluation methods more explicitly, we add a case study in Appendix A.

5. Conclusions

It is increasingly crucial to address methodological limitations at the country level to enhance the comprehension of a country’s sustainability and social responsibility [48]. In the field of ESG, a significant challenge lies in the lack of standardization and consistency across diverse measures [49]. This study aims to prioritize countries using ESG models at the country level. Various attempts have been made to gauge ESG on a country level. Among these, MSCI’s ESG Country Ratings are widely used. These ratings evaluate countries based on their environmental, social, and governance performance. Criteria encompass carbon emissions, renewable energy utilization, labor rights, and political stability. Organizations such as the World Bank and the United Nations also produce national-level sustainability and social responsibility metrics. The Country Policy and Institutional Assessments (CPIA) evaluate country policies and institutions across sectors like social inclusion, public sector management, and environmental sustainability.

This research introduces a novel Multi-Criteria Decision Making (MCDM) model called Performance Contribution Analysis (PCA), which combines information entropy for criteria weighting and Clifford algebra for decomposing overall scores into partial criteria contributions. By utilizing information entropy, the model addresses subjectivity and bias in current Environmental, Social, and Governance (ESG) indicators, providing an objective method for weighting criteria importance. Additionally, employing Clifford algebra enables the decomposition of overall scores, offering transparency and consistency in ESG indicators. The PCA model offers a detailed understanding of country performance based on different ESG factors, identifying strengths, weaknesses, and potential trade-offs. Furthermore, by prioritizing criteria with high information entropy and contribution to overall scores, the model aids decision-makers in formulating ESG policies at the country level. Notably, this study contributes to the broader scope by considering numerous countries across continents, providing a comprehensive analysis unparalleled by previous regional or country-specific studies. The application of Multi-Criteria Decision Analysis (MCDA) methods that incorporate environmental, social, and governance (ESG) factors to rank countries holds substantial practical implications across diverse fields. Policymakers have the potential to improve the efficacy of interventions and resource allocation through the identification of areas exhibiting both strong and weak performance among different countries. Investors are increasingly prioritizing ESG factors when making investment decisions. The use of MCDA methods for rankings can aid investors in identifying nations with strong ESG performance, thereby highlighting potential pathways for sustainable investments. Conversely, countries that rank low may face challenges in attracting investments, which motivates them to improve their ESG performance to remain competitive. This data can be utilized for making informed decisions pertaining to market entry, risk management, and corporate social responsibility initiatives. Countries that obtain favorable ESG rankings may experience an enhanced global reputation, which can contribute to their diplomatic stature and soft power. These nations have the opportunity to assess their ESG performance in relation to other countries and adopt successful practices from diverse regions. The purpose of the comparative analysis is to identify areas that can be improved and foster knowledge sharing and collaboration among countries. The ESG rankings align with the Sustainable Development Goals (SDGs) established by the United Nations, providing a framework for evaluating progress towards global sustainability targets. By prioritizing ESG factors, nations can effectively track their progress in attaining the SDGs and identify specific areas requiring further attention. This information provides stakeholders with the means to champion positive transformations and ensure governmental accountability.

Research outcomes indicate that Sweden, Finland, and New Zealand, among others, excel in country-level ESG implementation, incorporating both MCDA and other methods. The potential for benchmarking lower-ranking countries against higher-performing ones is evident. Countries can focus on crucial factors, such as GDP per capita, population, and foreign trade percentage of GDP, to uplift their ESG performance. Although the study contributes to the literature in measuring ESG performance at the country level, it suffers from a number of limitations: (1) The data period is not updated. The current paper uses a dataset covering a number of countries between 2009 and 2020. Considering that we have already passed the first quarter of 2024, the data is a bit outdated. (2) In terms of the second-stage analysis to investigate the impact of contextual variables on ESG performance, ridge regression was used. This second-stage analysis lacks a robustness check. Based on these limitations, future research can focus on: (1) expanding the data period to the most recent year to further see the robustness and difference of the results compared to the ones of the current study; and (2) using alternative methods to check the robustness of the results in the second-stage analysis. A couple of recommendations regarding the alternative methods include the Multi-Layer Perception/Hidden Markov model [49] and the robust endogenous neural network analysis [50].