An Evaluation of the Efficiency of Tertiary Education in the Explanation of the Performance of GDP per Capita Applying Data Envelopment Analysis (DEA)

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1.       Abstract - MAJOR

R.1.Maj.1.1

Line 24. "The DEA..." to line 27 "GDP per capita." This sentence about the fitness of this study can be explained in the methods part but it maybe too much to explain in the abstract. 

The sentence was shortened, more adequate to the abstract section.

R.1.Maj.1.2

What does it mean by "NUTS 2"? No description even in the introduction. 

It was introduced a brief explanation about EU NUTS 2 in abstract section.

R.1.Maj.1.3

Try to make it more precise. 

It was made more precise and shortened.

2.     Introduction - MAJOR

R.1.Maj.2.1

A short introductory description of NUTS 2 regions is missing.

In the abstract section (R.1.Maj.1.2) it was introduced a brief explanation about EU NUTS 2.

R.1.Maj.2.2

Line 73 to 87, a description of similar studies is provided. Is it possible to add to it what these studies missed? A research gap that is the base of your study? 

It was written a sentence about the novelty (research gap) of our study, considering the previous studies.

R.1.Maj.2.3

Line 88 starts explaining the methods adopted for this study until line 114. Should it be part of methods and materials? 

This part was moved to materials and methods section, it fills better in the starting of that section.

R.1.Maj.2.4

The purpose of this study is mentioned in 115 with some research questions and analysis. Should it also be part of methods and materials? 

In our opinion the research questions should be in the introduction section to justify the novelty and the gaps that the paper wants to respond.

R.1.Maj.2.5

surprisingly, from line 136, it starts again writing about the literature review. I think authors may choose to organize it in a much better way by combining disjunct parts of literature in one place.

The two parts of literature review in the introduction section were better organized to improve the sequence of the introduction.

R.1.Maj.2.6

Line 103-104. " The case study of Portuguese regions deserves a more detailed observation, analysis, and validation." why? Should the authors provide a reason for it that why the Portuguese region deserves more attention?. Otherwise, it shows biased writing/viewpoint of authors. 

We believe that the sentence is odd and exaggerated. We meant that we use the Portuguese regions to exemplify and understand the different types of efficiencies among regions and the regional asymmetries in EU NUTS 2. The sentence was removed.

3.     Materials and methods - MAJOR

R.1.Maj.3.1

Line 181, "GDP per capita is our main variable of interest". not tertiary education? From line 181 to 199, it all talks about GDP.  It provides a different outlook after reading the introduction where education was the main focus. 

The sentence was without meaning in the context of this manuscript. It was changed. In those parts of the text, we described the variables meaning and the GDP per capita as it is economically important and our explained variable, deserved a more detailed description than the percentage of tertiary education (which is easily calculated and understandable).

R.1.Maj.3.2

the methods part is not clear about how tertiary education is explaining the performance of GDP. 

Currently, with the changes made in R.1.Maj.2.3, in the material and methods section they are described. The econometric models explain how the percentage of tertiary education is used to explain the GDP per capita. Further, the models are detailed in “Spatial Regression Modeling” subsection.

4.     Results - MAJOR

R.1.Maj.4.1

similar to the methods part, results provide more information about the spatio-economic factors and less about education which does not justify with the paper title. 

The question is that the GDP per capita is the dependent variable we want to explain with the tertiary education and spatial lags of GDP per capita and at the same time is the output variable in the DEA optimization. Therefore, it is sometimes more analyzed in the results section than Tertiary Education and we can consider the hypothesis of changing the paper title.

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MAJOR

R.2.Maj.1

To use DEA models, the return to scale of the regions set should be determined first, and then the corresponding model should be selected and the efficiency calculated. But this is not done in this article.

We agree. It was introduced a scatter plot and a sentence about the linear or increasing relationship between the input and the output. The relationship is not clearly linear, so we decided to analyze the results of both models (CRS and VRS).

R.2.Maj.2

In this paper, there are 238 regions under evaluation with only one input and one output. The authors could have included more inputs and outputs. It is a simple form of Data set. Data envelopment analysis features are not used.

In this paper we are more concerned about the efficiency of Tertiary education for the levels of GDP per capita (only these two variables) and compare the results with the spatial econometric models which use the same variables.

R.2.Maj.3

Why are the simplest DEA models used? Why are models under increasing or decreasing returns to scale not used? Why are slack base models not used?

We used the VRS (variable returns to scale and CRS as well implemented in Python) model that can be suitable for increasing or decreasing returns to scale (but there are also the IRS and the DRS models) in the relationship among input and output and it does not seem to clearly reflect a proportional relationship. Slack base models could be used in this case and the paper be more focused only in DEA optimization methods, but we decided to compare the results of CRS and VRS models with the spatial econometric models.

R.2.Maj.4

After calculating the efficiency of different areas, they are categorized. On what basis are the categories selected? What are the characteristics of each category?

Considering the Moran’s spatial autocorrelation and Local scatter plot which plots the GDP per capita value of each region in the x-axis against the spatial lag of the GDP per capita value of each region in y-axis determined by their neighbors’ values of GDP per capita with a W (spatial weights) matrix, we classified the 4 quadrants showed in Figure 14 (previously 13), whose meanings are now better described in the text.

R.2.Maj.5

Have the outlier data been removed from the PPS? They can be very effective in the results. Please explain it in detail.

The outliers were not removed because we are studying 238 regions and we want to understand the spatial relationships between them, even when there are regions which have neighbors with substantially higher or lower performances for the socio-economic variables. We want to explain and understand the spatial patterns among all regions and the regions with significantly better and significantly worse performances.

R.2.Maj.6

Please use new references.

New references were added to the paper.

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MINOR

R.1.Min.1.1

The article requires improvement in writing impressions. In the introductory section, "the present article will be focused on SDG 4" -- it sounds like a research proposal. The article impressions sound better in the present form.   

The article was improved in writing impressions.

R.1.Min.1.2

The format of the article is not according to the given instructions to the authors on the journal website. 

The article was formatted according to the journal format.

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MAJOR

R.2.Min.1

the paper has potential to publish right now

Thank you so much.