Review Reports

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The study analyzes the relationship between economic performance and multidimensional well-being in 19 Italian regions between 2012 and 2023, using the ISTAT BES (Benessere, Equo and Sostenibile) framework and machine learning and clustering techniques. I find the topic of the paper very interesting and relevant. Below I provide several comments.

1. In the introduction, I miss a more general framing of the paper, with a deeper discussion of the well‑known problems associated with using GDP as an indicator of economic and social progress, as well as its limitations.
2. I do not consider Table 1 necessary, since the text already provides an exhaustive explanation of the literature and its connection to the BES framework.
3. It is not entirely clear how many Italian regions have been analyzed in the paper.
4. A stronger justification of the variables used throughout Section 5 is needed.
5. The paper is excessively long and becomes difficult to read; I believe the authors should make an effort to shorten it without losing clarity.
6. The authors use too many techniques (panel models, KNN, Boosting, hierarchical clustering, among others). It would be useful to better justify why each technique is appropriate and how they fit together within a coherent methodological framework.
7. In some cases, the result tables are excessively detailed. The authors should try to simplify them, keeping only the most significant results.
8. The paper would benefit from including some economic policy implications derived from the empirical findings.

Author Response

Point to Point Answers to Reviewer 1

Q1. The study analyzes the relationship between economic performance and multidimensional well-being in 19 Italian regions between 2012 and 2023, using the ISTAT BES (Benessere, Equo and Sostenibile) framework and machine learning and clustering techniques. I find the topic of the paper very interesting and relevant. Below I provide several comments.

A1. Thanks dear reviewer.

Q2. In the introduction, I miss a more general framing of the paper, with a deeper discussion of the well‑known problems associated with using GDP as an indicator of economic and social progress, as well as its limitations.

 

A2. We appreciate the reviewer’s insightful and constructive remark. There is wide consensus that the Introduction needed to be improved by introducing a broader perspective on the conceptual and empirical issues associated with the use of GDP as a measure of economic development and well-being. To that end, we have substantially rewritten the introduction. Specifically, we have included more information about the conceptual and empirical problems with the use of GDP in capturing income inequality, sustainability, institutions, and overall well-being. We also explain in detail how growth in GDP may not necessarily correspond to improvement in people’s quality of life in developed and diverse regions. Additionally, we make a clear link between those problems and why there is a need for a multidimensional approach. The BES approach is introduced to explain why it makes sense to adopt a multidimensional approach and discuss its logic and assumptions. Overall, the revised introduction makes the theoretical background of the paper clearer and better justified.

 

Q3. I do not consider Table 1 necessary, since the text already provides an exhaustive explanation of the literature and its connection to the BES framework.

 

A3. Table 1 has been remade as follows:

Macro-theme	Core idea	Key contributions from the literature	Link with BES framework
Environment & sustainability	Natural resources, energy systems and climate risks shape long-term growth	Ahammed et al.; Berberoglu et al.; Chengliang et al.; Du et al.; Insaidoo et al.; Wu et al.	Environment and sustainability as structural drivers of GDP
Social well-being & human capital	Health, well-being, education and demographic factors influence productivity and growth	Anauati et al.; Barbier & Mensah; Hussien et al.; Mohamed et al.; Zhou et al.	Well-being and human capital as inputs in GDP generation
Institutions & equity	Governance, inequality, poverty and inclusion shape development paths	Akinlo & Okunlola; Kunawotor et al.; Natanael; Okogun & Hiwatari	Institutional quality and equity explain regional divergence
Social & territorial dynamics	Social capital, participation, geography and infrastructure affect economic outcomes	Mažeikaitė; Crozet et al.; Mikheeva; Tan et al.	Social cohesion and territorial factors explain GDP heterogeneity
Innovation & development models	Innovation, finance and post-growth approaches redefine economic development	Lobonț et al.; Tiwari et al.; Buscemi; Chakori et al.	BES as a multidimensional alternative to GDP

 

 

Q4. It is not entirely clear how many Italian regions have been analyzed in the paper.

 

A4. The authors would like to express gratitude to the reviewer for the helpful comment. Indeed, the initial version of the paper failed to clearly state the number of Italian regions taken into consideration. Therefore, the manuscript was modified, and it was made more explicit about the territorial boundaries of the dataset. The new definition of the analysis states that it involves 21 territorial entities, which include 19 Italian regions and two autonomous provinces of Trento and Bolzano from 2012 till 2023. Furthermore, a special subsection named “Data Description and Regional Scope” was included to better explain the matter and give it some context. A new figure was created (Figure 1) in order to represent the geographical diversity of GDP in Italy.

 

Q5. A stronger justification of the variables used throughout Section 5 is needed.

 

A5. Thank you very much for the reviewer’s crucial comment. Indeed, the variables used in Section 5 need further justification. To address this issue, we have expanded our presentation to cover the reasons for selecting the variables for each component of Section 5 (panel econometric analysis, machine learning, and clustering analysis). Specifically, the econometric equation relies only on a few key E-Equo variables – youth exclusion, disposable income, and difficulties accessing services – to keep the model parsimonious and to estimate it stably. Meanwhile, the machine-learning and clustering parts employ a wide range of BES equity-related variables. At the same time, we have discussed the importance of using the variables in question from the theoretical perspective of the BES framework, which focuses on social inclusion, material well-being, poverty risks, labor-market participation, and access to opportunities.

 

Q6. The paper is excessively long and becomes difficult to read; I believe the authors should make an effort to shorten it without losing clarity.

 

A6. We thank the Reviewer for the insightful comment on the issue of length and clarity of the paper. To address this point, we have made major changes to the manuscript, resulting in a more concise presentation of its material. We have reduced the total number of pages from about 50 to 39. This has been achieved through eliminating redundant parts and consolidating the relevant results. We believe that our modifications will make the paper more accessible without diminishing its scientific value. Thank you once again for your suggestion.

 

Q7. The authors use too many techniques (panel models, KNN, Boosting, hierarchical clustering, among others). It would be useful to better justify why each technique is appropriate and how they fit together within a coherent methodological framework.

 

A7. We appreciate the valuable comments made by the Reviewer. As a result, a section titled “Methodological Framework and Motivation” has been incorporated into our study to substantiate the need for using various approaches and clarify their respective functions. In particular, panel modeling is used to find cause-and-effect relations, machine learning is applied to find nonlinearities, and clustering identifies differences across territories.

 

Q8. In some cases, the result tables are excessively detailed. The authors should try to simplify them, keeping only the most significant results.

 

A8. We are grateful to the reviewer for the useful comment made. Following that, we decided to significantly reorganize the presentation of empirical findings. Namely, the tables in the text were stripped down and contain only the most essential coefficients, variables, and measures of performance. Less essential statistics, diagnostics, and model outputs were moved into Appendices from the text. In particular, tables on econometric models now contain only the estimates of the coefficients and their significance, whereas tables on machine learning models present only the most important performance measures and variables. Decomposition tables are also simplified through presenting only the most important determinants of GDP. All the time, while presenting the more concise and readable findings, we provide all details and results in Appendixes A, B, and C. Thus, we can significantly improve readability without compromising accuracy or robustness.

 

 

Q9. The paper would benefit from including some economic policy implications derived from the empirical findings.

 

A9. Thank you for your important feedback. We have added a new section to the revised version, which is called “Policy Implications for Integrated and Inclusive Regional Development.” We formulated a set of policy implications that were deduced based on our empirical results and which explain the way in which well-being, equity, and sustainability operate as structural factors underlying regional development. The newly added discussion describes the importance of such aspects of growth as public safety, health care, transportation network, income distribution, and environmental policies as the elements of a growth strategy.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

An interesting article on a very important and ever-relevant issue concerning various aspects of economic growth – its determinants and the interrelationships between the level of development and the factors that determine it.
The text is logically structured, utilizes a wide range of diverse and innovative quantitative methods, and also has significant theoretical and application value with a degree of universality. The authors also place great emphasis on the consistency of the presented research results with their conclusions.
The article's main drawback is its length. Nearly 50 pages of text make it difficult to read, especially since the authors employ (as mentioned earlier) a wide range of research methods. As a result, the reader may be overwhelmed by the excess data and information, which require considerable concentration and verification. It seems that, without significantly detracting from the value of the text itself, the authors could have omitted descriptions of the tests of the fit of the various models tested to reality. Similarly, the description of some research results could have been more concise.
At the same time, despite the length of the article, some topics seem too briefly discussed, including the research concept itself. The research text indicates that the basis for the analyses is the ISAT BES model, which, as one might guess from the text, is a multi-indicator model describing various aspects of the level of economic development in Italy. However, the model itself is discussed very briefly; at one point, one might get the impression that it includes only three diagnostic variables (p. 8), while on the following pages it turns out there are many more. Therefore, a more comprehensive discussion seems advisable.

Similarly, the greatest advantage of this article, namely the use of machine learning to select models describing the studied problem, is described too briefly. Given the potential inherent in this research approach, a more detailed description of the algorithms and linguistic tools used would be worthwhile, perhaps even in the form of a separate academic text.

In summary, this is an interesting and valuable text, primarily from a methodological perspective, but it requires a different focus on the topics discussed.

The text also requires minor linguistic corrections - there are spelling errors and unfinished or out-of-context sentences (e.g. page 7, line 18 from the bottom).

Comments on the Quality of English Language

Small corrections needed

Author Response

Point to Point Answers to Reviewer 2

Q1. An interesting article on a very important and ever-relevant issue concerning various aspects of economic growth – its determinants and the interrelationships between the level of development and the factors that determine it.

A1. Thanks dear reviewer.

Q2. The text is logically structured, utilizes a wide range of diverse and innovative quantitative methods, and also has significant theoretical and application value with a degree of universality. The authors also place great emphasis on the consistency of the presented research results with their conclusions.

A2. Thanks dear reviewer.

Q3. The article's main drawback is its length. Nearly 50 pages of text make it difficult to read, especially since the authors employ (as mentioned earlier) a wide range of research methods. As a result, the reader may be overwhelmed by the excess data and information, which require considerable concentration and verification.

A3. The authors appreciate the reviewer’s important observation regarding the length and clarity of the manuscript. We address this issue and revise the manuscript to make it clearer and shorter. Indeed, we shortened the manuscript from around 50 pages down to 40 pages. To make it easier for the reader to understand, the number of tables used in the text was reduced, with only relevant data kept in the table. All other complicated data and analyses were moved to new appendices. This helps reduce the cognitive load of the reader and presents the key findings in an understandable way.

Q4. It seems that, without significantly detracting from the value of the text itself, the authors could have omitted descriptions of the tests of the fit of the various models tested to reality.

A4. We thank the reviewer for his/her valuable comments. In reply to that, the way that we present model diagnostics and goodness-of-fit tests has been significantly streamlined across the paper. In particular, the discussion of the testing process itself as well as the reporting of numerical results from those tests has been omitted from the body of the paper in order to increase clarity and prevent the reader from being overwhelmed with too much technical information. In the new version, we have retained only brief descriptions of the robustness and validity of the models estimated, with the emphasis on the practical significance of the results. The results of all tests, together with any necessary diagnostic statistics and further assessment criteria, have been placed in the Appendices.

Q5. Similarly, the description of some research results could have been more concise.

A5. We sincerely thank the reviewer for his/her valuable comments regarding the need for improved clarity and conciseness. To this end, the manuscript has undergone revision in order to achieve these goals, especially pertaining to presentation of the empirical results. Various parts have become more concise through deletion of unnecessary repetitions and excessive information, especially pertaining to the machine learning and clustering techniques. The manuscript has focused on presenting key results and the economic relevance of such results. Moreover, various tables have been made more succinct through removal of irrelevant variables and inclusion of more detailed results in the Appendices. We believe that such changes greatly improve the clarity of the manuscript.

Q6. At the same time, despite the length of the article, some topics seem too briefly discussed, including the research concept itself.

A6. We appreciate this important suggestion from the reviewer. The presentation of the research idea and the theoretical foundations of our research have therefore been further improved across the manuscript. Firstly, the Introduction has been revised to clearly present the theoretical framework under which the study was conducted. It has been specified that rather than seeing the concepts of well-being, equity, and sustainability as the end results of economic development, they should be viewed as factors determining the economic performance of regions in the context of the Belt and Road Economic System (BES). Secondly, the Methodology has been revised to incorporate the link between the three methods used, namely, panel econometrics, machine learning, and clustering, and the theoretical framework presented above. Thus, the roles of these methods in investigating different aspects of the well-being–GDP nexus have been clarified, with each of the three methods examining linear dynamics, nonlinear relations, and territorial heterogeneity, respectively. These changes have helped to improve the presentation of our research idea and its theoretical significance.

Q7. The research text indicates that the basis for the analyses is the ISAT BES model, which, as one might guess from the text, is a multi-indicator model describing various aspects of the level of economic development in Italy. However, the model itself is discussed very briefly; at one point, one might get the impression that it includes only three diagnostic variables (p. 8), while on the following pages it turns out there are many more. Therefore, a more comprehensive discussion seems advisable.

A7. We would like to thank the reviewer for making such an important point. As a result of the reviewer's feedback, we have made several adjustments to the manuscript and provided a more complete explanation of the BES framework. First, we have further developed the description of the BES framework in the Introduction section. It is now clearly stated that the BES framework represents a multidimensional system of many indicators associated with different aspects of well-being, which include health, education, security, income, social relationships, institutions, and environmental sustainability. We have also noted that, for the purpose of analysis, these indicators are grouped into three major dimensions: Benessere (B), Equità (E), and Sostenibilità (S). Furthermore, we have emphasized that the regression analysis utilizes subsets of indicators, rather than a limited number of variables, chosen from the general BES framework. We have done so by specifying it in the variables section and including a note explaining this issue in the footnotes of the main tables. Such changes help to ensure greater clarity in the paper.

Q8. Similarly, the greatest advantage of this article, namely the use of machine learning to select models describing the studied problem, is described too briefly. Given the potential inherent in this research approach, a more detailed description of the algorithms and linguistic tools used would be worthwhile, perhaps even in the form of a separate academic text.

A8. Thank you very much for this helpful comment. We have significantly extended the methodological part of the manuscript to clarify the machine learning procedure used in our study. First, we specify the list of regression algorithms we use, which includes Boosting, Decision Tree, K-Nearest Neighbors (KNN), Linear Regression, Random Forest, Regularized Linear Models, and Support Vector Machine (SVM). Clustering methods comprise Density-Based clustering, Fuzzy C-Means, Hierarchical clustering, Model-Based clustering, k-Means, and Random Forest-based clustering techniques. Furthermore, the procedure used for selecting models has been specified, which includes comparing different algorithms with each other based on multiple statistical performance criteria (RMSE, MAE, MAPE, R², and so forth), whereupon a final selection of an algorithm is made on the basis of weighted performance indicators. This process allows identifying the optimal model for each specific dimension of the BES framework. It should be noted that these amendments were designed to improve the clarity regarding the potential and methodological novelty of the ML approach applied in the current study.

Q9. In summary, this is an interesting and valuable text, primarily from a methodological perspective, but it requires a different focus on the topics discussed.

 

A9. We appreciate the reviewer's useful remarks regarding the method-substance balance in the article. Accordingly, the manuscript has been adjusted to ensure a more balanced consideration of methodological and substantive aspects in the analysis presented. While maintaining the integrated machine-learning approach, further emphasis has been placed on the economic interpretation of the findings reported in Sections 4 and 5, as well as on discussing their significance in terms of regional development, territorial heterogeneity, and the importance of well-being, equity, and sustainability as structural features defining economic success. Moreover, an effort has been made to clarify the contribution of the study not only from the methodological but also the substantive point of view in the Introduction and Conclusion sections. The main objective was to highlight the economic relevance of our findings and their policy implications, especially concerning place-based approaches to development and the alleviation of regional disparities in Italy.

 

Q10. The text also requires minor linguistic corrections - there are spelling errors and unfinished or out-of-context sentences (e.g. page 7, line 18 from the bottom).

A10. Thank you for your valuable suggestion. The manuscript has been revised to rectify any typing mistakes, grammatical inconsistencies, and to improve readability. In detail, the whole paper has been checked for grammatically inconsistent statements. The problem pointed out by the reviewer (page 7, line 18 from the bottom) has been fixed. The objective of the above corrections is to increase the readability of the paper.

 

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

Review Report: From Security to Sustainability: The BES Determinants of Italian Regional GDP.

The manuscript shows potential, and the attempt to integrate multiple analytical approaches is commendable. However, in its current form, the study suffers from conceptual ambiguity, methodological inconsistency, and overinterpretation of results. The distinction between association, prediction, and causation is not sufficiently maintained, and several methodological steps lack clarity and rigor. Therefore, I recommend major revision.

• The manuscript uses strong causal language, but the methods are observational and predictive. How do the authors justify causal interpretations given potential reverse causality between GDP and BES indicators?
• What is the actual novelty of the study, new theory, new evidence, or a combination of existing methods?
• The roles of panel regression, machine learning, and clustering are unclear. Please explain, what is the specific purpose of each method, and how do they complement rather than duplicate each other?
• Econometric issues e.g., heteroskedasticity, autocorrelation, cross-sectional dependence, are reported but not properly handled. How do these violations affect the reliability of the estimated coefficients and inference?
• The machine learning results show near perfect performance which is unrealistic result, so please explain how were training and testing conducted, and how was overfitting or data leakage avoided?
• How do the authors ensure that predictive relationships are not being misinterpreted as structural mechanisms?
• Which formal tests were used, and are the underlying assumptions satisfied?
• How stable are the clusters across different specifications, and why should they be interpreted beyond exploratory grouping?
• How does this study clearly differ from existing BES or regional GDP studies, particularly in the Italian context?
• Can the authors revise the text to reduce repetition and improve clarity, especially in the methodology section?

Author Response

Point to Point Answers to Reviewer 3

Review Report: From Security to Sustainability: The BES Determinants of Italian Regional GDP.

Q1. The manuscript shows potential, and the attempt to integrate multiple analytical approaches is commendable.

A1. Thanks dear reviewer.

Q2. However, in its current form, the study suffers from conceptual ambiguity, methodological inconsistency, and overinterpretation of results. The distinction between association, prediction, and causation is not sufficiently maintained, and several methodological steps lack clarity and rigor. Therefore, I recommend major revision.

A2. The reviewer's valuable comments are appreciated. The manuscript has been significantly revised in order to clarify the concepts, improve methodological coherence, and refine the interpretation of the empirical findings. First, the definitions of association, prediction, and causation have been elaborated upon, and the use of panel econometric models has been clarified as a means of uncovering structural associations between variables over time. On the other hand, machine-learning methods have been explained as predictive and descriptive methods designed to detect nonlinear relations and interactions in the data. Clustering analysis has been identified as an exploratory technique that enables one to uncover territorial regimes. Moreover, it has been specified that the findings should be interpreted in terms of associations rather than causal effects. Second, the description of the empirical framework has been enhanced by providing more information about the algorithms, the model selection, and the evaluation criteria utilized in this study. Third, the manuscript has been revised in order to avoid overinterpretation of the results. Causal formulations in expressions that implied causality have been corrected and replaced with formulations that are more appropriate and precise. In conclusion, these revisions have helped to improve the conceptual quality of the paper, increase methodological coherence, and avoid inappropriate interpretation of the empirical findings.

Q3. The manuscript uses strong causal language, but the methods are observational and predictive. How do the authors justify causal interpretations given potential reverse causality between GDP and BES indicators?

A3. Thank you very much for pointing out this critical issue concerning the usage of causal language and the problem of reverse causality between GDP and BES indicators. To address this concern, we have extensively revised the manuscript to ensure no causal interpretations were made about the empirical findings. Specifically, it has been made clear throughout the revised manuscript that while panel econometrics models can identify structural associations through time series, machine learning techniques provide ways to describe and predict non-linear interactions within data. Moreover, clustering analysis was considered as an exploratory method in the revised manuscript. Additionally, we have clearly acknowledged the existence of a bidirectional link between GDP and various BES indicators as higher economic performance can lead to better institutional, social, and environmental performance which would create reverse causality. To address this concern, we have elaborated on our empirical strategy by explicitly stating that our methods do not support any causal interpretation of results but rather associations are what should be taken into account. As a result, we have revised the whole manuscript to ensure all causal language has been properly changed to fit the methods utilized in our research. These revisions help to further improve the methodological framework of the paper and guarantee consistency in the methods used and conclusions drawn from them.

Q4. What is the actual novelty of the study, new theory, new evidence, or a combination of existing methods?

A4. Thank you to the reviewer for making an important remark about the originality of the research. To answer to his point, we modified the manuscript by making explicit what would be considered to be the originality of the paper. It should be noted that the novelty in this research paper comes from the application of a novel empirical approach which does not require the creation of a new theoretical perspective. The combination of panel econometrics, machine learning and clustering analysis methods used together gives an opportunity to examine the nonlinear structure and territorial heterogeneities of the multidimensional connection between well-being and economic growth. Using such an approach, it is possible to capture the complex interactions and effects which cannot be fully understood through a single methodological framework. Moreover, the use of this approach in the case of ISTAT BES indicators helps to identify new empirical evidence on the multidimensional structure of economic growth in Italy. The contributions of the paper are specified both in the Introduction and in the Abstract parts.

Q5. The roles of panel regression, machine learning, and clustering are unclear. Please explain, what is the specific purpose of each method, and how do they complement rather than duplicate each other?

A5. The reviewer raises this crucial point on the role played by the different empirical approaches used in this work. To clarify this aspect, in the revision process, we made sure that the specific objective of each methodological approach is better specified. Thus, panel econometric models are now introduced precisely as techniques to investigate the structural associations, accounting for unobserved regional heterogeneity, and obtaining the average relationship within regions. On the contrary, machine learning approaches are presented precisely as predictive and descriptive models used mainly to analyze non-linear and interaction effects among variables as well as the relative impact of factors under consideration. Clustering techniques are now presented precisely as an explorative approach useful to identify homogenous territorial regimes. In addition, we have stressed that each approach does not replicate the others but acts on different levels. While panel models offer the global perspective of the relation, machine learning offers insights into the local and non-linear relationship. Finally, clustering offers an insight into the hidden spatial structures of the relationship under study. All these aspects have been taken care of in the methodological section of the revised paper.

Q6. Econometric issues e.g., heteroskedasticity, autocorrelation, cross-sectional dependence, are reported but not properly handled. How do these violations affect the reliability of the estimated coefficients and inference?

A6. Thank you for your valuable comment. In the revision of our paper, we have discussed the problems of heteroskedasticity, autocorrelation, and cross-sectional dependence, highlighting the presence and implications of these econometric issues. First, a full range of tests has been conducted in order to identify whether there is a violation of the econometric issues. As the results show, econometric problems exist; moreover, they are common for macro-regional panels. According to the findings, the existence of violations has an impact only on the efficiency of estimators and accuracy of standard errors, but does not affect the consistency of estimated coefficients. Second, in order to correct for econometric violations, we use robust standard errors when running all estimations using panel data. Robustness provides validity of inferential statistics, especially testing of hypotheses at significance level. Third, the revised version of the manuscript contains a discussion of econometric issues, and also includes a full description of test results, . Moreover, a concise summary table presenting all results for three models was provided. Thus, in the revised version, the nature of econometric issues as well as their impact on estimation were discussed.

Q7. The machine learning results show near perfect performance which is unrealistic result, so please explain how were training and testing conducted, and how was overfitting or data leakage avoided?

 

A7.  The reviewer's comment is indeed valid. We would like to emphasize that the training, validation, and testing process is clearly outlined in the updated manuscript. Performance metrics are also discussed, and how they are interpreted is explained. First, the data sample is split into two parts, with 80% of observations being assigned to the estimation sample and 20% to the test sample. In addition, there is another step in estimating model parameters – a validation step. It means that there is a sequence of operations: training, validating, and testing. Second, model complexity is controlled via algorithm-specific techniques. For example, boosting uses shallow trees and shrinkage, k-nearest neighbors optimize the number of neighbors, and linear algorithms use regularization. The presence of the validation subset helps avoid overfitting when selecting the optimal hyperparameters of a specific model. Third, data leakage is explicitly excluded since there is always a strict separation of the train, validation, and test datasets. Lastly, it should be noted that the reason why performance metrics are exceptionally high is that they are normalized. In other words, the indicators such as R², RMSE, and MAE are given relative to the best-performing model in the sample. Hence, the proximity to one does not mean perfect prediction but only reflects relative performance. Additional explanations are provided in the updated manuscript and in the appendices.

Q8. How do the authors ensure that predictive relationships are not being misinterpreted as structural mechanisms?

A8. The reviewers' remark on this point is well taken, and we would like to thank them for this valuable suggestion. In the new version of the paper, we have further specified the concept of predictive relationships vs. the structural interpretation to avoid misinterpretation. Namely, we have explicitly noted that machine learning tools are applied strictly from the perspective of predicting non-linear patterns and the relative variable importance. They are not used to draw conclusions about the existence of structural mechanisms or causalities in general. The latter can be done only using panel econometric analysis, which enables controlling for unobserved regional heterogeneity and analyzing dynamic associations. Moreover, we have revised the text such that roles of different methodological approaches are better

Q9. Which formal tests were used, and are the underlying assumptions satisfied?

A9. We appreciate the reviewer for his valuable comments. In our revised version of this manuscript, we have explicitly specified the diagnostic tests applied to check these issues in the empirical framework. The diagnostic tests that we apply include the Breusch-Pagan and Wald tests for checking heteroskedasticity; Wooldridge test for checking panel data autocorrelation; Pesaran CD test for cross-sectional dependence; and finally Hausman test for choosing between fixed and random effects models. All our models show heteroskedasticity, autocorrelation, and cross-sectional dependence. These problems are common in any macroeconomic regional panel data. However, their violation does not affect the consistency of coefficient estimates. The problem of heteroskedasticity and autocorrelation is solved by applying robust standard errors in all our models.

Q10. How stable are the clusters across different specifications, and why should they be interpreted beyond exploratory grouping?

Thank you for pointing out this interesting comment. Regarding the stability of the clustering results and its interpretations, in our revised manuscript, we further explain the stability of the territorial clusters and how they should be interpreted. Firstly, the stability of clusters is evaluated via the comparison of clustering results based on various methods. Although the hierarchical method offers better partition performance, the same territorial groups are found even if other clustering techniques are applied. Therefore, the identified territorial clustering pattern is not influenced by any specific algorithm but is derived from the characteristics of the data. Moreover, the measures of clustering quality presented, which include separation and compactness of the clusters, verify the reliability of the clustering results. Secondly, it should be noted that our clusters are not considered only for exploratory purposes. Rather, they reflect structural features of the economy and society and can be considered economic territorial regimes. In particular, each cluster represents distinct regional profiles with different levels of GDP and BES indicators, such as mobility, security, and health status. Thirdly, it should be emphasized that the obtained clusters can be useful for policymakers when designing policies to stimulate economic growth in regions with diverse economic and social development regimes.

Q11. How does this study clearly differ from existing BES or regional GDP studies, particularly in the Italian context?

A11. The authors thank the reviewer for his valuable observation. The revised manuscript explicitly addresses the differences between the current research and the existing literature on BES and regional GDP, especially in the Italian case. First, it is stressed that while the BES framework has gained considerable popularity in literature and has mostly served to describe well-being at different levels of aggregation, this study offers an empirical analysis of the linkages between well-being and GDP. From this perspective, this paper goes beyond the mere descriptive aspect of reporting data on well-being and focuses on establishing systematic links between multidimensional well-being and GDP. Second, compared to the bulk of traditional studies on regional GDP, which tend to utilize only a few macroeconomic indicators, the analysis involves a larger number of social, institutional, and environmental indicators representing a multi-dimensional construct of regional economic performance.

Q12. Can the authors revise the text to reduce repetition and improve clarity, especially in the methodology section?

A12. We appreciate the suggestion of the reviewer regarding this matter. The methodology part of our paper has been rewritten, and redundancy in the description of the methodology has been minimized. We have also consolidated the discussion about the complementary nature of the methodological tools used in our study. This has led to a much-improved presentation of the methodology part of the paper. Specifically, redundant paragraphs and technical details of the algorithm have been eliminated from the discussion. The complementary nature of panel data econometrics, machine learning, and clustering techniques is now discussed in an integrated manner.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors have made the suggested changes, and I think the paper has improved substantially and can be published in its current form.

Author Response

Point to Point Answers to Reviewer 1

 

Q1. The authors have made the suggested changes, and I think the paper has improved substantially and can be published in its current form.

A1. Thanks dear reviewer.

Author Response File: Author Response.docx