A Copula-Based Meta-Stochastic Frontier Analysis for Comparing Traditional and HDPE Geomembranes Technology in Sea Salt Farming among Farmers in Phetchaburi, Thailand

Round 1

Reviewer 1 Report

1)    How the applied method differs from some other techniques that have already been applied to the analyzed problem?
2)    What is the novelty and “value added” of this research?
3)    Eq. in L. 567 must be corrected.
4)    Tab. 3 caption should contain the name of the statistical test.
5)    Assumed significance level for testing should be provided in the text.
6)    Transformations/creations of variables in Tab. 4 must be explained. For instance, multiplication by 1, etc.
7)    Source “Calculation” should be replace by “Own calculations” or similar.
8)    L. 738 should be made into a full sentence without “:”.

Author Response

Dear Reviewer 1,

I am submitting a revised version of our manuscript titled “A Copula-Based Meta-stochastic Frontier Analysis of Sea Salt Production”, which addresses the comments and suggestions provided by the reviewers. I appreciate the valuable feedback and have made significant revisions to improve the manuscript's quality.

Point 1: How the applied method differs from some other techniques that have already been applied to the analyzed problem?

Response 1: We have added a detailed explanation in the sub-section of the Meta-frontier Efficiency Model to describe how the applied method differs from some other techniques that have already been applied to the analyzed problem in lines 380 – 385 [“Although copula-based stochastic frontier models are useful in assessing technical efficiency, they cannot be used to compare technical efficiency between different groups or samples with varying levels of technology. Therefore, to address this limitation, the copula-based meta-frontier approach is preferred over the copula-based stochastic frontier models. Consequently, we propose utilizing the meta-frontier approach to compare the technical efficiency of different technologies.” [Line 382 - 387].

Point 2: What is the novelty and “value added” of this research?

Response 2: I have included the novelty and contribution in the introduction that highlights the novelty and contribution of my research [“This article's novelty is in its use of a copula-based meta-stochastic frontier analysis to compare the technical efficiency of traditional and HDPE GMB technology of sea salt farmers in Phetchaburi, Thailand. This method provides a more accurate assessment of technical efficiency by considering the interdependence between error components and technology differences. Furthermore, this study contributes to the literature on sea salt farming by identifying the factors affecting technical efficiency and opportunities for improvement. Decision makers can use these findings to enhance efficiency, competitiveness, and profitability in agricultural development, which will ultimately improve the sustainable agricultural system and the livelihood of Thailand’s sea salt farmers.”] in Line 162 – 171].

Point 3: Eq. in L. 567 must be corrected.

Response 3: I have corrected the equation in L. 567.

Point 4: Tab. 3 caption should contain the name of the statistical test.

Response 4: I have updated the name for Table 3 to include the name of the LR-test used.

Point 5: Assumed significance level for testing should be provided in the text.

Response 5: I have provided the symbols ***, **, and * represents significance at 1%, 5%, and 10% levels in Table 3, 5, and 7. Additionally, I have added a note under each of these tables that states “Note: ***, **, and * represent significance at 1%, 5%, and 10% levels, respectively.”. I believe that this change will make it easier for readers to understand the statistical significance of the results presented in these tables.).

Point 6: Transformations/creations of variables in Tab. 4 must be explained. For instance, multiplication by 1, etc.

Response 6: The purpose of Tab. 4 is to display the AIC and BIC values for each copula family model that we tested. We have already provided an explanation of this under the table and in Figure 5.

 The best copula-based meta-frontier production model is Gaussian Copula.  Therefore, we explained the meaning of the parameters of the inputs under Table 5 to further clarify the analysis and discussion in the manuscript [Line 636 – 680].

Point 7: Source “Calculation” should be replaced by “Own calculations” or similar.

Response 7: I have updated the source to "Own calculations" in the appropriate tables of the manuscript.

Point 8: L. 738 should be made into a full sentence without “:”.

Response 8: I have rephrased L. 738 to make it into a full sentence without “:”.

In addition to the revisions made to our manuscript in response to the reviewer's comments, I would like to inform you that I have also utilized the English editing services listed at https://www.mdpi.com/authors/english to improve the language quality of my manuscript. I have attached the English Editing Certificate to this email as proof of our use of these editing services.

I believe that these revisions have significantly improved the quality and impact of our manuscript and we hope that you will find the revised version suitable for publication in “Agriculture”. I appreciate your time and consideration and look forward to hearing from you soon.

Best regards,

Roengchai

Author Response File: Author Response.docx

Reviewer 2 Report

The paper sheds light on Sea Salt Production in Phetchaburi province (Thailand). To this end, a Copula-Based Meta-stochastic Frontier Analysis was utilized to assess technical efficiency and the technology gap between traditional technology and High-Density Polyethylene Geomembranes (HDPE GMBs) technology.

The proposed paper is well written with good use of the English language. The paper begins with an informative and well-structured abstract. 

The Introduction follows helping the reader to get into the subject immediately. In the Introduction and in the second section, in my opinion, the literature that was used is appropriate for the subject of the paper being conducted on academic articles.

The data collection and analysis methods used in the research are almost clearly explained; indeed, more information on the variables used in the model is needed so that other researchers could repeat the analysis.

The results are presented in a comprehensive way, but there is a lack of use of scientific literature in their discussion. All data presented in tables and figures are easily understandable.

The paper does not present limitations of the research, theoretical and practical implications, or future research which would provide immediate takeaways for academics and producers.

There is a need for some minor corrections in order to improve the quality of the paper:

-row 489: please, correct 2222 in 2022

-rows: 490-495: what about section D of the questionnaire?

-What are the hypotheses tested? they are not clearly stated in the text

-I recommend shortening the "conclusions" section: there is no need to summarise the whole paper (as done in lines 721-735). It is important to identify the implications of the results achieved. Theoretical implications relating to the model used and practical implications relating to the production technologies tested. In addition, the limitations of the study and future research directions should be indicated

Author Response

Dear Reviewer 2,

I am submitting a revised version of our manuscript titled “A Copula-Based Meta-stochastic Frontier Analysis of Sea Salt Production”, which addresses the comments and suggestions provided by the reviewers. I appreciate the valuable feedback and have made significant revisions to improve the manuscript's quality.

Point 1: The data collection and analysis methods used in the research are almost clearly explained; indeed, more information on the variables used in the model is needed so that other researchers could repeat the analysis.

Response 1: I have revised the methods section to provide more information on the variables used in the model. Specifically, we have included a detailed explanation of the variables included in the model and have provided additional information on their measurement [Line 440 – 477].

Point 2: The results are presented in a comprehensive way, but there is a lack of use of scientific literature in their discussion. All data presented in tables and figures are easily understandable.

Response 2: In able 5 and 7, I have revised the discussion section to include more references to relevant literature. Specifically, we have included more detailed explanations of how our results align or differ from previous research. [Table 5: Line 628 – 680] [Table 7: Line 716 – 776]

Point 3: The paper does not present limitations of the research, theoretical and practical implications, or future research which would provide immediate takeaways for academics and producers.

Response 3: -     I have included the implications, “To increase HDPE GMB technology adoption in salt farming, relevant public and private sector agencies should promote greater access to this technology through government subsidies with low-interest conversion. Additionally, educating and demonstrating salt farming techniques with HDPE technology can help increase farmers' acceptance of this technology, leading to improved salt quality, yields, and prices and greater production efficiency through reduced labor and fuel usage. Although HDPE GMB technology has been successful in improving sea salt production, traditional salt farming practices continue to be prevalent in many areas. To overcome weather related yield failures, farmers should receive training to become more resilient and adaptable to changing conditions. In addition, promoting traditional salt farming practices for inclusion in the Globally Important Agricultural Heritage Systems (GIAHS) can help increase their value and recognition, highlighting the importance of local expertise and potentially attracting more consumer interest and demand.” [Line 792 – 804].

                              -              I have included a new section 6 on the limitations of the study and future research directions

               “6. Limitations and Future Recommendations

This study has some limitations to consider. Firstly, the empirical model used in this study could be biased due to the possibility of an omitted variables problem. Secondly, the limited sample size could affect the model estimation’s accuracy. Thirdly, the data collection period coincided with the COVID-19 pandemic and the harvest season in 2022, which could have increased the difficulty of collecting data through questionnaires. Lastly, corresponding with respondents in the targeted areas may have been challenging due to the use of local languages. Future studies should also consider the cost of HDPE GMB and apply cost-oriented and profit-oriented approaches to pro-vide a more comprehensive analysis of the sea salt production process. To conduct a comprehensive sustainability study in sea salt production, future studies should collect panel data to analyze the changes in production efficiency and sustainability over time and identify trends and patterns. Modeling panel data can also identify factors that contribute to sustainability and efficiency, informing targeted interventions and policy changes to promote sustainable practices.” [Line 805 – 819].

Point 4: There is a need for some minor corrections in order to improve the quality of the paper:

       -   row 489: please, correct 2222 in 2022

       -   rows: 490-495: what about section D of the questionnaire?

               -              What are the hypotheses tested? they are not clearly stated in the text.

Response 4: -     I have corrected the typo and changed "2222" to "2022".

                                 -          Regarding the comment on rows 490-495, I found the typo and change from 4 parts to three parts at line 499, so I did not have section D.

                                -            I have revised the text to state the hypotheses tested explicitly and have provided more detailed explanations of their formulation at [Line 565-579]. “To assess the specified meta-frontier model’s suitability, the hypotheses are investigated. These hypotheses aim to evaluate the model’s adequacy and determine whether it can effectively explain the variations in technical efficiency between different groups. The relevance of exogenous variables to explain inefficiency was also assessed using this testing process. The first test  involves examining whether the coefficients of the second-order variable in the translog model, (β_ij) are equal to zero. If the result indicates that the coefficients are zero, then the Cobb‒Douglas function can be considered a statistically valid representation of the data. The second test, , involves testing whether inefficiency effects are present in the models at any level. If the result shows that inefficiency effects are absent from the models at all levels, then the model can be considered accurate in capturing the variations in technical efficiency between different groups. The third test, , involves assessing whether there is a significant difference between the traditional and HDPE GMB technology. A non-significant result would suggest that there is no need for specifying the meta-frontier production model.”

Point 5: I recommend shortening the "conclusions" section: there is no need to summarise the whole paper (as done in lines 721-735).

Response 5: I have revised the conclusions section to focus on the key findings of the study and their significance. We have eliminated the summary of the entire paper. “This study analyzed and compared traditional and HDPE GMB technology in sea salt production in the Phetchaburi province using a copula-based meta-stochastic frontier technique with a sample size of 250 farmers. Various copula families were employed to analyze the dependence structure of the two error components. The Gaussian copula-based meta-frontier model with a translog production function was the best fit, suggesting that the assumption of independence between the two error components in the stochastic frontier model can be relaxed. Land, labor, and fuel energy were the most significant input variables. The study found that producers operating under the HDPE GMB technology system are more technically efficient than those operating under traditional technology. The study identified the driver factors of technical inefficiency, which included land, market, sex, and experience for traditional technology production and land, sex, and experience for HDPE GMB production technology. The factors affecting technical inefficiency for traditional technology production were land, market, sex, and experience, while, for HDPE GMB production technology, the factors were land, sex, and experience.” [Line 777 – 791].

Point 6: It is important to identify the implications of the results achieved. Theoretical implications relating to the model used and practical implications relating to the production technologies tested. In addition, the limitations of the study and future research directions should be indicated

Response 6: -     I have included the implications, “To increase HDPE GMB technology adoption in salt farming, relevant public and private sector agencies should promote greater access to this technology through government subsidies with low-interest conversion. Additionally, educating and demonstrating salt farming techniques with HDPE technology can help increase farmers' acceptance of this technology, leading to improved salt quality, yields, and prices and greater production efficiency through reduced labor and fuel usage. Although HDPE GMB technology has been successful in improving sea salt production, traditional salt farming practices continue to be prevalent in many areas. To overcome weather related yield failures, farmers should receive training to become more resilient and adaptable to changing conditions. In addition, promoting traditional salt farming practices for inclusion in the Globally Important Agricultural Heritage Systems (GIAHS) can help increase their value and recognition, highlighting the importance of local expertise and potentially attracting more consumer interest and demand.” [Line 792 – 804].

-              I have included a new section 6 on the limitations of the study and future research directions

“6. Limitations and Future Recommendations

This study has some limitations to consider. Firstly, the empirical model used in this study could be biased due to the possibility of an omitted variables problem. Secondly, the limited sample size could affect the model estimation’s accuracy. Thirdly, the data collection period coincided with the COVID-19 pandemic and the harvest season in 2022, which could have increased the difficulty of collecting data through questionnaires. Lastly, corresponding with respondents in the targeted areas may have been challenging due to the use of local languages. Future studies should also consider the cost of HDPE GMB and apply cost-oriented and profit-oriented approaches to provide a more comprehensive analysis of the sea salt production process. To conduct a comprehensive sustainability study in sea salt production, future studies should collect panel data to analyze the changes in production efficiency and sustainability over time and identify trends and patterns. Modeling panel data can also identify factors that contribute to sustainability and efficiency, informing targeted interventions and policy changes to promote sustainable practices.” [Line 805 – 819].

In addition to the revisions made to our manuscript in response to the reviewer's comments, I would like to inform you that I have also utilized the English editing services listed at https://www.mdpi.com/authors/english to improve the language quality of my manuscript. I have attached the English Editing Certificate to this email as proof of our use of these editing services.

I believe that these revisions have significantly improved the quality and impact of our manuscript and we hope that you will find the revised version suitable for publication in “Agriculture”. I appreciate your time and consideration and look forward to hearing from you soon.

Best regards,

Roengchai

Author Response File: Author Response.docx

Reviewer 3 Report

This is an interesting paper focusing on the production of sea salt and it's production efficiency in Thailand provinces. I have few suggestions/comments for the sole aim of improving the final version of this study. 

From the title, there is a need for the author to modify it. Kindly include the provinces/country of study. Also, you need to add sea salt farmers as part of the title.

In the abstract, salient findings of this study are conspicuously missing. In line 25, use "performance instead of "success".

In the introduction, there is a need for author to present a more robust background information focusing on the keywords in the title. Is Thailand the only country producing salt? You need to make that assertion here and if not, you need to include global production statistics of salt/sea salt.

In line 84-86, support it with references. From the introduction to literature review, why it all about Thai sea salt production? You may need to lt your readers have understanding of sea salt production in other regions and countries. Studies from other countries should be included. 

In all figures and tables presented in this study, kindly add the source at the bottom of each of them. In line 483, instead of 174 was "chosen", kindly use 174 was "selected".

In Table 3 you're expected to firstly state the study hypotheses at the tail end of the introduction before presenting the results and discussion. This is conspicuously missing. In Table 5&7, include the p-values in the table headings. 

I discover that most of the findings of this study was not discussed using previous empirical studies either to support or refute the findings. Please, kindly do thorough discussion using empirical studies (relevant and recent references).

Before the conclusion section, kindly present a sub-section with the heading"limitations of the study and"areas for further studies".

After conclusion, present some recommendations enamating from this study. You may merge the two together.

Thank you.

Author Response

Dear Reviewer 3,

I am submitting a revised version of our manuscript titled “A Copula-Based Meta-stochastic Frontier Analysis of Sea Salt Production”, which addresses the comments and suggestions provided by the reviewers. I appreciate the valuable feedback and have made significant revisions to improve the manuscript's quality.

Point 1: From the title, there is a need for the author to modify it. Kindly include the provinces/country of study. Also, you need to add sea salt farmers as part of the title

Response 1: I have revised the title of our manuscript to " A Copula-Based Meta-stochastic Frontier Analysis for Com-paring Traditional and HDPE Geomembranes Technology in Sea Salt Farming among Farmers in Phetchaburi, Thailand".

Point 2: In the abstract, salient findings of this study are conspicuously missing. In line 25, use "performance instead of "success".

Response 2: -     I have revised the abstract to include a summary of the salient findings of our study. Specifically, we have included a brief overview of the key results and their significance [Line 9 – 24].

   - I have changed the word "success" to "performance" in line 22.

Point 3: In the introduction, there is a need for author to present a more robust background information focusing on the keywords in the title. Is Thailand the only country producing salt? You need to make that assertion here and if not, you need to include global production statistics of salt/sea salt.

Response 3: I have added additional information on sea salt production and trade in other countries from the Salt industry worldwide - statistics & facts (2022), and the U.S. Geological Survey database (2022).

Point 4: In line 84-86, support it with references. From the introduction to literature review, why it all about Thai sea salt production?

        You may need to let your readers have understanding of sea salt production in other regions and countries.

        Studies from other countries should be included.

Response 4: -     I have added references to support the claims made in lines 84-86.

-    I have added additional information on sea salt production and trade in other countries from the Salt industry worldwide - statistics & facts (2022), and the U.S. Geological Survey database (2022).

-    I have included more studies about the technical efficiency of sea salt production in from Guinea and Ghana [Line 302-305]

Point 5: In all figures and tables presented in this study, kindly add the source at the bottom of each of them. In line 483, instead of 174 was "chosen", kindly use 174 was "selected".

Response 5: -     I have added the source at the bottom of each figure and table presented in the study.

-      I have changed the word "chosen" to "selected" in line 483.

Point 6: In Table 3 you're expected to firstly state the study hypotheses at the tail end of the introduction before presenting the results and discussion. This is conspicuously missing.

 In Table 5&7, include the p-values in the table headings. 

Response 6: -     I have revised the text to state the hypotheses tested explicitly and have provided more detailed explanations of their formulation at [Line 565-579]. “To assess the specified meta-frontier model’s suitability, the hypotheses are investigated. These hypotheses aim to evaluate the model’s adequacy and determine whether it can effectively explain the variations in technical efficiency between different groups. The relevance of exogenous variables to explain inefficiency was also assessed using this testing process. The first test  involves examining whether the coefficients of the second-order variable in the translog model, (β_ij) are equal to zero. If the result indicates that the coefficients are zero, then the Cobb‒Douglas function can be considered a statistically valid representation of the data. The second test, , involves testing whether inefficiency effects are present in the models at any level. If the result shows that inefficiency effects are absent from the models at all levels, then the model can be considered accurate in capturing the variations in technical efficiency between different groups. The third test, , involves assessing whether there is a significant difference between the traditional and HDPE GMB technology. A non-significant result would suggest that there is no need for specifying the meta-frontier production model.”

-              I have included the p-values in the table headings for Tables 5 and 7.

Point 7: I found that sections 2 & 3 should be re‐organized and be shortened. It may be easier for the readers if the authors define properly the mixture of regression model and the class‐ membership equation first before moving to the computation of the GINI and of the Polarization of subgroups. Sections 2.1 and 2.2 are too long and can be significantly reduced. In section 2.1 the authors assume the condition u_k > u_j, but this does not appear anywhere else in the calculation of the mixture of regression model. After equation (10) all the other equations are not numbered.

Response 7: I have revised the text to state the hypotheses tested explicitly and have provided more detailed explanations of their formulation at [Line 565-579]. “To assess the specified meta-frontier model’s suitability, the hypotheses are investigated. These hypotheses aim to evaluate the model’s adequacy and determine whether it can effectively explain the variations in technical efficiency between different groups. The relevance of exogenous variables to explain inefficiency was also assessed using this testing process. The first test  involves examining whether the coefficients of the second-order variable in the translog model, (β_ij) are equal to zero. If the result indicates that the coefficients are zero, then the Cobb‒Douglas function can be considered a statistically valid representation of the data. The second test, , involves testing whether inefficiency effects are present in the models at any level. If the result shows that inefficiency effects are absent from the models at all levels, then the model can be considered accurate in capturing the variations in technical efficiency between different groups. The third test, , involves assessing whether there is a significant difference between the traditional and HDPE GMB technology. A non-significant result would suggest that there is no need for specifying the meta-frontier production model.”

-    I have included the p-values in the table headings for Tables 5 and 7.

Point 8: I discover that most of the findings of this study was not discussed using previous empirical studies either to support or refute the findings. Please, kindly do thorough discussion using empirical studies (relevant and recent references).

Response 8: In Tables 5 and 7, I have revised the discussion section to include more references to relevant literature. Specifically, we have included more detailed explanations of how our results align or differ from previous research. [Table 5: Line 628 – 680] [Table 7: Line 716 – 776]

Point 9: Before the conclusion section, kindly present a sub-section with the heading "limitations of the study and "areas for further studies".

Response 9: -     I have included a new section 6 on the limitations of the study and future research directions

“6. Limitations and Future Recommendations

This study has some limitations to consider. Firstly, the empirical model used in this study could be biased due to the possibility of an omitted variables problem. Secondly, the limited sample size could affect the model estimation’s accuracy. Thirdly, the data collection period coincided with the COVID-19 pandemic and the harvest season in 2022, which could have increased the difficulty of collecting data through questionnaires. Lastly, corresponding with respondents in the targeted areas may have been challenging due to the use of local languages. Future studies should also consider the cost of HDPE GMB and apply cost-oriented and profit-oriented approaches to provide a more comprehensive analysis of the sea salt production process. To conduct a comprehensive sustainability study in sea salt production, future studies should collect panel data to analyze the changes in production efficiency and sustainability over time and identify trends and patterns. Modeling panel data can also identify factors that contribute to sustainability and efficiency, informing targeted interventions and policy changes to promote sustainable practices.” [Line 805 – 819].

Point 10: After conclusion, present some recommendations emanating from this study. You may merge the two together.

Response 10: I have included the recommendation, “To increase HDPE GMB technology adoption in salt farming, relevant public and private sector agencies should promote greater access to this technology through government subsidies with low-interest conversion. Additionally, educating and demonstrating salt farming techniques with HDPE technology can help increase farmers' acceptance of this technology, leading to improved salt quality, yields, and prices and greater production efficiency through reduced labor and fuel usage. Although HDPE GMB technology has been successful in improving sea salt production, traditional salt farming practices continue to be prevalent in many areas. To overcome weather-related yield failures, farmers should receive training to become more resilient and adaptable to changing conditions. In addition, promoting traditional salt farming practices for inclusion in the Globally Important Agricultural Heritage Systems (GIAHS) can help increase their value and recognition, highlighting the importance of local expertise and potentially attracting more consumer interest and demand.” [Line 792 – 804].

In addition to the revisions made to our manuscript in response to the reviewer's comments, I would like to inform you that I have also utilized the English editing services listed at https://www.mdpi.com/authors/english to improve the language quality of my manuscript. I have attached the English Editing Certificate to this email as proof of our use of these editing services.

I believe that these revisions have significantly improved the quality and impact of our manuscript and we hope that you will find the revised version suitable for publication in “Agriculture”. I appreciate your time and consideration and look forward to hearing from you soon.

Best regards,

Roengchai

Author Response File: Author Response.docx

Round 2

Reviewer 3 Report

The revised version of this manuscript reflected the huge improvement on the previous original manuscript. I feel the editor can make final publication decision on this revised version. Thank you.