Factors Impacting Technical Efficiency in Mexican WUOs: A DEA with a Spatial Component

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Evaluating the efficiency of water utility organizations and identifying factors that cause inefficiency is essential. Expanding the target of this analysis to developing countries is also necessary.

My concern is the lack of explanations regarding the method and results of the Tobit analysis. The authors need to supply further details.

-         The dependent variable of the regression, yi* (line 295, page 7), needs a clear definition. Although the text reads this as “the efficiency scores of the WUOs,” no definition is provided. This definition is vital to understand why yi* is left censored at 0.

-         The independent variable of “microregions1” needs a definition, too. I referred to reference [70] but could not find the definition of “microregions1.” A table of the independent variables, which were categorized as “microregions1,” and their representative values should be included in this paper.

-         “(Intercept):1” and “(Intercept):2” that appear on page 10 should be defined within the Tobit regression equations on page 7.

-         The Tobit analysis results on page 10 should provide a table of model estimates to show the independent variables' statistical significance levels and how they were tested (Wald tests?).

Abbreviations should be spelled out when they first appear. The abbreviations CRS and VRS appear at the beginning of the paper and are spelled out later on page 6.

Author Response

To the esteemed Editor and Reviewers,

We sincerely thank you for your precious feedback on our manuscript (ID: sustainability-3459066). Substantial revisions have been made in order to address all the concerns raised, laying special emphasis on improvements that may significantly affect the explanation and presentation of Tobit analysis.

The Tobit methodology has been clarified in the revised version. It has now been made quite clear that the dependent variable modeled is the technical inefficiency (one less the DEA efficiency), explaining that it is a function of an underlying latent inefficiency and justifying the treatment of the lower threshold as zero. The geographic unit "microregions" is clearly defined by a new table detailing the composition of the regions used. Further, the meaning of the two major parameters related to the intercept (base level and the deviation of error) is now also explained within the methodological description with reference to average case outputs possible from the software. Importantly, we have supplanted the narrative account of Tobit findings by a formal table in the Results section that shows model estimates, indicators of statistical significance, and goodness-of-fit measures. Also, we made sure that all the definitions of key abbreviations (the ones concerning returns to scale) appear in their first use.

Aside from these specific changes, the manuscript has been further revised to improve scientific writing, clarity, and argument strength, with references to relevant and recent literature. We hope that these changes address your concerns satisfactorily and strengthen our manuscript.

Reviewer 2 Report

Comments and Suggestions for Authors

The paper covers an important topic and the achievements can be very useful for other case studies. The authors investigated the technical efficiency of 49 Water Utility Organizations (WUOs) through a combined Data Envelopment Analysis (DEA) and Tobit Model approach. The paper has potential, but some aspects must be taken into account before publication:

• The abstract could be improved, for example including the location of the study and more achievements;
• In the keywords, the word “Mexico” could be included (replacing the “determinant”);
• The introduction can be improved. The authors must highlight the novelty and contributions to the literature;
• Literature review can also be improved (for example supporting the importance of operational environment on efficiency analysis);
• The methodology can be better justified, including also major limitations (for example, the presence of outliers);
• More information can be provided about the case study (population, population density, GDP per capita, …);
• All sources of information must be included in the text;
• Units must be included in table 2. Include the currency;
• Regarding the efficiency analysis, I would expect some analysis per region;
• Explain also the main reasons for inefficiency among the utilities;
• The limitations of the study and future research can be highlighted in the conclusions;
• More recommendations for decision makers were expected in the conclusions.

Author Response

Dear Editor and Reviewers,

We thank you for your detailed review and encouraging comments on the relevance of our study on efficiency in Mexican water utilities. All the main points raised were diligently addressed to enrich the manuscript.

The abstract was edited to include the location (i.e., Mexico) and better summarize the findings. In addition, "Mexico" was added to the keyword list. The introduction and literature review were improved to emphasize the novelty of the study and reinforce the importance of the operating environment and governance, respectively. The rationale for the choice of methods was considerably strengthened, and limitations (including variable selection, geographic data granularity, and cross-sectional nature) were explicitly addressed in the Conclusions, as suggested.

We acknowledge the limited information in the case study, although we explain the limitations of the available data (PIGOO); this vague contextual presentation is largely interpreted as a limitation. We also confirm that all sources are cited and that units (including the MXN) have been added to the descriptive tables. While we do not include an analysis of average regional efficiency, we clarify that the Tobit analysis statistically assessed these regional differences without significant effects. A new section has been added to the Discussion to explore the causes of inefficiency (managerial factors, institutional factors, infrastructure). Finally, the Conclusions are enriched with more specific recommendations for decision-makers and more clearly outline future research.

We trust that this draft has comprehensively addressed all your suggestions.

Reviewer 3 Report

Comments and Suggestions for Authors

I appreciate being part of this article's evaluation. I have a few comments that I hope will allow the researchers to strengthen the text.

1) Literature review: I consider that the authors cover a wide range of topics associated with their theoretical aspects of interest and that there is a balanced citation of works, recognizing the methodological limitations of DEA and the need to combine DEA with statistical models such as Tobit. However, I would like to make a few points:

-> The authors could include a more rigorous structural discussion of existing approaches in the DEA-Tobit combination. For example, there is no clear distinction between truncated and censored regression, nor are any articles referring to the subject mentioned in the text, as there is no distinction between bootstrap DEA and a second econometric stage. The authors note that geography could influence efficiency, but the methodological literature on spatial analysis or spatial econometrics is not examined in depth. In that sense, they do not address using SAR, SEM, or spatial Tobit models as more appropriate alternatives.
-> The authors could improve or make more explicit the methodological choices from a rigorous theoretical framework and not limit themselves to functional expositions.
Therefore, I will basically recommend a) Including key references that address methodological robustness and b) Expanding the review to include DEA with explicit spatial components.

2) Methodology: The authors adequately specify the model. The input-oriented model is consistent with common practices in public service analysis, which try to minimize resources while maintaining service quality.
-> Regarding the methodology, I have a few suggestions: a) it is mentioned that CRS is used to compare without scale restrictions, and VRS with variable returns. However, the text does not adequately justify the choice of orientation (input-oriented) in terms of the Mexican context of water management. Why not output-oriented or SBM?
b) I found no robustness analysis: how sensitive are the results to variable changes? Additionally, the authors do not discuss whether the extreme values of the variables generate outlier or super-efficient DMUs.
c) Although the censored model is specified, it is unclear why and how the censoring threshold was defined.
d) I believe that the use of Tobit on DEA efficiency results may violate the assumption of normality of the error, which requires bootstrap DEA or truncated regression as a robust alternative
-> The authors could include bootstrap DEA to obtain bias-corrected estimates.
I would also like to comment on the results and the discussion. Perhaps the authors could:
Increase the critical rigor in the discussion, recognizing the insufficiency of the simple Tobit model to explain differences in efficiency.
• Offer concrete proposals: how the regional analysis should be reformulated, what variables should be integrated into future studies, and what policies can be inferred from the map of efficiencies.
• Link the results more explicitly to the water governance framework in Mexico.

Congratulations and success with your evaluation.

Comments on the Quality of English Language

Some minor tweaks can improve the clarity.

Author Response

We sincerely appreciate your valuable suggestions, which have strengthened this work. The authors have addressed your concerns in the following ways:

Regarding the literature review, there is now a much more rigorous discussion of existing approaches to combining DEA and Tobit, clarifying the methodological choices against a solid theoretical foundation. Key references on methodological robustness were included, and the review was expanded to consider analyses with explicit spatial components, although our subsequent Tobit analysis does not show a significant effect of defined geographic microregions.

Regarding the methodology, we fully justify the choice of the DEA model's input orientation and demonstrate its appropriateness to the Mexican water management context, where the goal is to minimize resources while maintaining service quality. The Tobit model specification for the analysis of efficiency determinants was clarified, including the treatment of the censored variable.

In the results and discussion section, we critically discuss the limitations of the Tobit model used and the need for a more comprehensive geography to account for differences in efficiency. We analyze the implications of the findings, linking them more explicitly to the context of water governance in Mexico. We also offer specific suggestions on variables to include in future studies and how to reformulate regional analysis, emphasizing the importance of local management, institutional, or operational factors over overall geography.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors have addressed most of my concerns. There are minor issues to be resolved.

In equation Eq 5, the transpose operator should be applied to xi (I assume xi and beta are vertical vectors).

Table 5 should include estimated coefficients and statistical significance of the dummy variables for four microregions (with "Center" as the baseline). These are the most important variables to be presented on this table.

Author Response

Following the reviewer's valuable comments, we made two important adjustments to the manuscript.
First, we changed the mathematical notation used in equation five, which refers to the Tobit model, to properly incorporate the transposition operator, providing greater precision and formal accuracy.
Second, and much more substantially, we modified Table 5. This table now explicitly disaggregates and presents the individual estimated coefficients and statistical significance for each of the four dummy variables representing the geographic microregions (compared to the reference core region). This allows for a direct and detailed assessment of the individual effect of each geographic area, thus fully addressing the reviewer's request to include these key results.

Reviewer 2 Report

Comments and Suggestions for Authors

The authors met my expectations with the paper revision. So I am able to recommend the publication

Reviewer 3 Report

Comments and Suggestions for Authors

Thank you for your sustained effort to address my comments. I have no further observations.

Round 3

Reviewer 1 Report

Comments and Suggestions for Authors

The authors appropriately addressed my concerns in the previous review round.