Social Housing and Affordable Rent: The Effectiveness of Legal Thresholds of Rents in Two Italian Metropolitan Cities

Round 1

Reviewer 1 Report

Dear author, thank you for an engaging article. You provide an in-depth analysis of HS in Italy. The data section of this piece contains  valuable results and conclusions. Nevertheless, your target audience is unclear to me: are you trying to explain what an SH is to someone who has very little knowledge about it? If I understand correctly, this is not the goal of your article. 

In the introduction, you attempt to offer an extensive overview of SH situation across Europe and ‚developing countries‘. Yet, again, I do not understand why is there a need for that in your article focused on thresholds of rents in two Italian metropolitan cities.

You provide rigorous analysis, yet sometimes you tend to essentialize concepts (terms) like ‚foreigner‘, ‚Western world‘. At time, your phrasing needs work. What do you mean by 'treated mainly by the Western world'. What do you mean by the Western world? 

Author Response

We would like to thank the Reviewers and Editor for their detailed comments and suggestions for the manuscript.

We believe that the comments have identified important areas which required improvement.

After completion of the suggested edits, the revised manuscript has benefitted from an improvement in the overall presentation and clarity.

Below, you will find a point by point description of how each comment was addressed in the manuscript; original reviewer comments in black color and responses in red color.

Point 1

Reviewer

Dear author, thank you for an engaging article. You provide an in-depth analysis of HS in Italy. The data section of this piece contains valuable results and conclusions.

Authors

Thank you for your positive comments.

Point 2

Reviewer

Nevertheless, your target audience is unclear to me: are you trying to explain what an SH is to someone who has very little knowledge about it? If I understand correctly, this is not the goal of your article. 

Authors

Thank you for your comment. Our study focused on the internal and external fairness of thresholds of Social Housing rents. This is a very specific topic but is also strictly related to housing policy and Social Housing, so we decided to provide an overview of SH in Italy and Europe to present it in a broader context.

Point 3

Reviewer

In the introduction, you attempt to offer an extensive overview of SH situation across Europe and‚ developing countries’. Yet, again, I do not understand why is there a need for that in your article focused on thresholds of rents in two Italian metropolitan cities.

Authors

The Introduction section was actually too long. We moved a part of it to a new section, called Social Housing in The European Union and United Kingdom, according to another reviewer’s suggestion. However, as we mentioned above, we still want to provide an overview of SH in Europe to present the topic of our research in a broader context.

Point 5

Reviewer

You provide rigorous analysis, yet sometimes you tend to essentialize concepts (terms) like ‚foreigner‘, ‚Western world‘. At time, your phrasing needs work. What do you mean by 'treated mainly by the Western world'. What do you mean by the Western world? 

Authors

Thank you for reporting it. We rephrase this part of the section.

Thank you very much for your attention

Sincerely yours,

Authors

Reviewer 2 Report

Dear Authors,

Your complex paper "Social Housing and affordable rent. The effectiveness of legal thresholds of rents in two Italian metropolitan cities" is supported by a coherent and reliable argumentation and it is based on extensive literature review. The weak point is the methodology. Even if it is clearly explained and extensively exemplified by the case studies, important parts are copy-pasted from theory which is a major weakness, leading to suspicion of plagiarism. The disparate sections of the methodology should form a unitary whole. Below are detailed recommendations referring to various aspects which should be taken into account:

- Introduction should be shorter, the first section can be split into two parts, the second one with the title "Social Housing in the EU and United Kingdom" for instance;

- It is necessary to eliminate minor grammar errors, e.g.:

 "it worth mentioning" -> "it is worth mentioning", title of Chart 1, "social housin" -> "social housing", "In the literature, there are many studies dealings" -> "... dealing", "Zona3-Peripheral" -> Zone 3, "however there are numerous areas or municipalities where they are strong or very strong dissimilarity" -> "... where there are strong or very strong dissimilarities".

etc.

- "In fact, in 2019, around three tenths (30.2%) of the EU-27 population lived in rented dwellings, although this share ranged from 4.2% in Romania up to 58.4% in Switzerland". Some comments are needed here, for instance not all rentals are transposed into legal leases, especially in countries where tax evasion is high.

It should also be mentioned that there is no direct correlation between the percentage of social housing in the stock of residential properties and the percentage of the population at risk of poverty in the total population.

- Source of Table 1 is missing.

- "In each zone, rents have been divided into 3 levels, i.e. sub 1, sub 2 and sub 3, concerning the characteristics of the dwelling, for an overall total of 314 agreed rents" - my question is: have you divided rents into three categories or is it an official classification?

- "By cluster analysis we mean a multivariate statistical technique, through which it is possible to obtain a groups structure from a certain population of data, that is, by grouping several similar units together in a certain number of groups". Please reformulate: cluster analysis is a multivariate statistical technique. Instead of "population of data", population data.

- "Homogeneity (heterogeneity) and heterogeneity (diversity)" -> Homogeneity (uniformity), not Homogeneity (heterogeneity).

- You should pay attention to sources, a whole part of the methodology is copy-pasted from the following links

http://www.math.le.ac.uk/people/ag153/homepage/KmeansKmedoids/Kmeans_Kmedoids.html

Please find a way to to avoid suspicions of plagiarism.

"k-medoids is also a partitioning technique of clustering that clusters the data set of objects into k clusters with k known a priori. A useful tool for determining k is the silhouette.

It could be more robust to noise and outliers as compared to k-means because it minimizes a sum of general pairwise dissimilarities instead of a sum of squared Euclidean distances. The possible choice of the dissimilarity function is very rich, the most used is the Euclidean distance.

A medoid of a finite dataset is a data point from this set, whose average dissimilarity to all the data points is minimal i.e. it is the most centrally located point in the set.

The most common realisation of k-medoid clustering is the Partitioning Around Medoids (PAM) algorithm and is as follows:

1. Initialize: randomly select k of the n data points as the medoid.
2. Assignment step: Associate each data point to the closest medoid.
3. Update step: For each medoid m and each data point o associated to m swap m and o and compute the total cost of the configuration (that is, the average dissimilarity of o to all the data points associated to m). Select the medoid o with the lowest cost of the configuration".

https://www.ncss.com/software/ncss/clustering-in-ncss/

"In the second phase, possible alternatives to the k objects selected in phase one are considered in an iterative manner. At each step, the algorithm searches the unselected objects for the one that if exchanged with one of the k selected objects will lower the objective function the most. The exchange is made, and the step is repeated. These iterations continue until no exchanges can be found that will lower the objective function.

Note that all potential swaps are considered, and that the algorithm does not depend on the order of the objects on the database".

Repeat alternating steps 2 and 3 until there is no change in the assignments".

You can synthesize the methodology as it is supposed to be well known by scholars and formulate it synthetically in your own words.

- The SC has to be defined the first time it is mentioned, at page 15, it is not enough the description "The maximum average silhouette across all values of k are denoted by SC".

- PAM (Partition Around Medoids) acronym is detailed four times.

- In Tables 4 and 5, you have to explain how you selected the 13/269 elements for Milan and 12/45 elements for Bari and as Table notes, the .... meaning that the rest of data are not included due to lack of space or other reasons.

- For the following

Figure 19b shows the distance of the agreed rent considered with the centroid or reference agreed rent for cluster 2, i.e. with Bitonto and sub-zone 2.

Figure 19c shows the distance of the agreed rent considered with the centroid or reference agreed rent for cluster 2, i.e. with Bitonto and sub-zone 3.

Figure 19d shows the distance of the agreed rent considered with the centroid or reference agreed rent for cluster 2, i.e. with Bitonto and sub-zone 4.

Figure 19e shows the distance of the agreed rent considered with the centroid or reference agreed rent for cluster 2, i.e. with Bitonto and sub-zone 5.

Figure 19f shows the distance of the agreed rent considered with the centroid or reference agreed rent for cluster 2, i.e. with Bitonto and sub-zones 6-7-8-9 that characterize only in the municipality of Bari.

are needed some explanations, even if concise and brief.

- In the section of Conclusions

"Public administrations must set a rule to limit SH rents that is easy to apply but also flexible and updatable. In the case of Italian law, these limits are based on local territorial agreements between landlord and tenant associations. These agreed rents have the advantage of being renewed every year and of being diversified by city and area, although they are not mandatory and do not exist for all Italian municipalities".

Which kind of limitation? As value? Please reformulate.

This section has to be more detailed.

- Which are the limitations of your research?

- You mention in text Appendix 1, 2 and 3, but you present only Appendix A.

I recommend the publication of the paper after revisions. It is necessary to make significant changes in order to avoid any suspicion of plagiarism and also carefully revise the writing style of the whole manuscript, which should be improved.

All the best.

Author Response

We would like to thank the Reviewers and Editor for their detailed comments and suggestions for the manuscript.

We believe that the comments have identified important areas which required improvement.

After completion of the suggested edits, the revised manuscript has benefitted from an improvement in the overall presentation and clarity.

Below, you will find a point by point description of how each comment was addressed in the manuscript; original reviewer comments in black color and responses in red color.

Point 1

Reviewer

Dear Authors,

Your complex paper "Social Housing and affordable rent. The effectiveness of legal thresholds of rents in two Italian metropolitan cities" is supported by a coherent and reliable argumentation and it is based on extensive literature review.

Authors

Thank you for your positive comments.

Point 2

Reviewer

The weak point is the methodology. Even if it is clearly explained and extensively exemplified by the case studies, important parts are copy-pasted from theory which is a major weakness, leading to suspicion of plagiarism. The disparate sections of the methodology should form a unitary whole.

Authors

We have modified the methods section.

Point 3

Reviewer

- Introduction should be shorter, the first section can be split into two parts, the second one with the title "Social Housing in the EU and United Kingdom" for instance;

Authors

We followed your suggestion and split the first section into two parts.

Point 4

Reviewer

- It is necessary to eliminate minor grammar errors, e.g.:

Authors

We revised the text.

Point 5

Reviewer

"it worth mentioning" -> "it is worth mentioning", title of Chart 1, "social housin" -> "social housing", "In the literature, there are many studies dealings" -> "... dealing", "Zona3-Peripheral" -> Zone 3, "however there are numerous areas or municipalities where they are strong or very strong dissimilarity" -> "... where there are strong or very strong dissimilarities".

Authors

Thanks for reporting them. We corrected the errors.

Point 6

Reviewer

 - "In fact, in 2019, around three tenths (30.2%) of the EU-27 population lived in rented dwellings, although this share ranged from 4.2% in Romania up to 58.4% in Switzerland". Some comments are needed here, for instance not all rentals are transposed into legal leases, especially in countries where tax evasion is high.

It should also be mentioned that there is no direct correlation between the percentage of social housing in the stock of residential properties and the percentage of the population at risk of poverty in the total population.

Authors

It may happen that not all rentals are transposed into legal leases in some countries, but according to the housing statistics by Eurostat [21], the range of population lived in rented dwellings mainly depends on the distribution of tenure status between landlords and tenants. For instance, in Romania there is a high percentage of homeowners (95.8%), even though it is associated with a high rate of overcrowding (46.3%), especially for the population at risk of poverty (56.4%). We included this explanation in the text.

Thanks for your consideration, we included it in the text.

Point 7

Reviewer

- Source of Table 1 is missing.

Authors

The data source was added.

Point 8

Reviewer

- "In each zone, rents have been divided into 3 levels, i.e. sub 1, sub 2 and sub 3, concerning the characteristics of the dwelling, for an overall total of 314 agreed rents" - my question is: have you divided rents into three categories or is it an official classification?

Authors

The subdivision into three sub-zones (1,2 and 3) based on the real estate characteristics was taken over by the NUUTA agreed rent, it is an official classification.

Point 9

Reviewer

- "By cluster analysis we mean a multivariate statistical technique, through which it is possible to obtain a groups structure from a certain population of data, that is, by grouping several similar units together in a certain number of groups". Please reformulate: cluster analysis is a multivariate statistical technique. Instead of "population of data", population data.

Authors

We have modified the text based on your suggestions.

Point 10

Reviewer

- "Homogeneity (heterogeneity) and heterogeneity (diversity)"

-> Homogeneity (uniformity), not Homogeneity (heterogeneity).

Authors

We have modified the text based on your suggestions. It was a typo, thank you for reporting it.

Point 11

Reviewer

- You should pay attention to sources, a whole part of the methodology is copy-pasted from the following links

http://www.math.le.ac.uk/people/ag153/homepage/KmeansKmedoids/Kmeans_Kmedoids.html

Authors

The section of the methods related to the cluster analysis has been modified, all the text has been rewritten and for further information on the topic we have referred to the literature, since any explanation of the mathematical notation of the algorithm is likely to be judged a plagiarism.

Thank you for reporting it.

Point 12

Reviewer

"k-medoids is also a partitioning technique of clustering that clusters the data set of objects into k clusters with k known a priori. A useful tool for determining k is the silhouette.

It could be more robust to noise and outliers as compared to k-means because it minimizes a sum of general pairwise dissimilarities instead of a sum of squared Euclidean distances. The possible choice of the dissimilarity function is very rich, the most used is the Euclidean distance.

A medoid of a finite dataset is a data point from this set, whose average dissimilarity to all the data points is minimal i.e. it is the most centrally located point in the set.

The most common realisation of k-medoid clustering is the Partitioning Around Medoids (PAM) algorithm and is as follows:

1. Initialize: randomly select k of the n data points as the medoid.
2. Assignment step: Associate each data point to the closest medoid.
3. Update step: For each medoid m and each data point o associated to m swap m and o and compute the total cost of the configuration (that is, the average dissimilarity of o to all the data points associated to m). Select the medoid o with the lowest cost of the configuration".

https://www.ncss.com/software/ncss/clustering-in-ncss/

"In the second phase, possible alternatives to the k objects selected in phase one are considered in an iterative manner. At each step, the algorithm searches the unselected objects for the one that if exchanged with one of the k selected objects will lower the objective function the most. The exchange is made, and the step is repeated. These iterations continue until no exchanges can be found that will lower the objective function.

Note that all potential swaps are considered, and that the algorithm does not depend on the order of the objects on the database".

Repeat alternating steps 2 and 3 until there is no change in the assignments".

You can synthesize the methodology as it is supposed to be well known by scholars and formulate it synthetically in your own words.

Authors

The section of the methods related to the cluster analysis has been modified, all the text has been rewritten and for further information on the topic we have referred to the literature, since any explanation of the mathematical notation of the algorithm is likely to be judged a plagiarism.

Thank you for reporting it.

Point 13

Reviewer

- The SC has to be defined the first time it is mentioned, at page 15, it is not enough the description "The maximum average silhouette across all values of k are denoted by SC".

Authors

The meaning of the acronym SC has been defined in the previous version of the paper at line five in the page 15, in this version revised at line nineteenth in the page15.

Point 14

Reviewer

PAM (Partition Around Medoids) acronym is detailed four times.

Authors

Now the acronym is detailed only once.

Point 15

Reviewer

In Tables 4 and 5, you have to explain how you selected the 13/269 elements for Milan and 12/45 elements for Bari and as Table notes, the .... meaning that the rest of data are not included due to lack of space or other reasons.

Authors

We decided to report only a part of the tables for the two databases, for reasons of space.

In order to clarify this choice, we have included in the text an in-depth analysis of this issue, in the period preceding Tables 4 and 5.

Thank you for reporting it.

Point 16

Reviewer

- For the following:

Figure 19b shows the distance of the agreed rent considered with the centroid or reference agreed rent for cluster 2, i.e. with Bitonto and sub-zone 2.

Figure 19c shows the distance of the agreed rent considered with the centroid or reference agreed rent for cluster 2, i.e. with Bitonto and sub-zone 3.

Figure 19d shows the distance of the agreed rent considered with the centroid or reference agreed rent for cluster 2, i.e. with Bitonto and sub-zone 4.

Figure 19e shows the distance of the agreed rent considered with the centroid or reference agreed rent for cluster 2, i.e. with Bitonto and sub-zone 5.

Figure 19f shows the distance of the agreed rent considered with the centroid or reference agreed rent for cluster 2, i.e. with Bitonto and sub-zones 6-7-8-9 that characterize only in the municipality of Bari.

are needed some explanations, even if concise and brief.

Authors

We have integrated information on Figures 19b,19c, 19d, 19e and 19f.

Point 17

Reviewer

- In the section of Conclusions

"Public administrations must set a rule to limit SH rents that is easy to apply but also flexible and updatable. In the case of Italian law, these limits are based on local territorial agreements between landlord and tenant associations. These agreed rents have the advantage of being renewed every year and of being diversified by city and area, although they are not mandatory and do not exist for all Italian municipalities".

Which kind of limitation? As value? Please reformulate.

This section has to be more detailed.

Authors

According to Housing Policy the SH rents have to be lower than market rents. To achieve this goal the Italian legislation set a limitation that was presented in sub-section 2.4: “The Italian legislation, taking into account the different conditions of the real estate market in Italian cities and the need for continuous updates, has established that the reduced rents of Social Housing cannot be higher than the agreed rents set by annual Local Agreements between Landlords and Tenants Associations”.

However, we agree with you that it is better to rephrase the issue more clearly in the conclusions.

Point 18

Reviewer

- Which are the limitations of your research?

Authors

We added some consideration of the limitations of our study in the conclusion section.

Point 19

Reviewer

- You mention in text Appendix 1, 2 and 3, but you present only Appendix A.

Authors

Thank you for reporting it. We corrected the references. We called them Appendix A, B and C.

Thank you very much for your attention

Sincerely yours,

Authors

Reviewer 3 Report

The presented paper is very interesting.

The “current research” section is elaborated in great detail and thoroughly. The whole article is accompanied by a number of graphs and pictures, which suitably complement the text (even though some Figures are not referenced correctly – Figure 3/4 on page 5, for example). I see serious flaws in the methodology section, however. The chapter 4.3 describes the theoretical background of the cluster analysis thoroughly,  authors do not explain why they chose particular methods, though. In more detail:

• Why did you chose the cluster analysis? Have you considered other options? Which ones? And why did you choose cluster analysis?

• The k-medoids algorithm is described in detail and compared to k-means algorithm. However, there is no reason why this particular method was used.

• As mentioned by authors, there is a number of metrics that can be used to measure the distance of objects. They list their properties and name the most frequently used metrics – Euclidean distance. But again, they do not explain why this distance was used (except to mention that it is “the most used” distance measure). Explain why you used this metrics, whether it is a suitable metrics and, most importantly, whether both datasets meet the criteria for using it.

• Please, supply the results of the maximum average silhouette calculations. Based on these calculations, optimal number of clusters (3) was determined for both datasets. However, no such results are presented in the paper. Unless you provide results that confirm that the optimal number of clusters is 3, the "results" chapter cannot be presented correctly.

To sum it up: Chapter 4.3 describes the methodology, however, there is no justification as to why particular methods were chosen, nor is there confirmation of the correctness of selected methods.

Just some small fixes: In formula (1), please supply the matrix in usual format – in parentheses. Also I wonder why you write: “This is example 1 of an equation”. In my opinion, this is not an example, this is a definition. Also the formula (3) is not written correctly, I am afraid.

Once the methodological procedures will be supplemented and justified, it will be possible to further verify the results presented in Chapter 5.

Author Response

We would like to thank the Reviewers and Editor for their detailed comments and suggestions for the manuscript.

We believe that the comments have identified important areas which required improvement.

After completion of the suggested edits, the revised manuscript has benefitted from an improvement in the overall presentation and clarity.

Below, you will find a point by point description of how each comment was addressed in the manuscript; original reviewer comments in black color and responses in red color.

Point 1

Reviewer

The presented paper is very interesting.

Authors

Thank you for your positive comments.

Point 2

Reviewer

The “current research” section is elaborated in great detail and thoroughly. The whole article is accompanied by a number of graphs and pictures, which suitably complement the text (even though some Figures are not referenced correctly – Figure 3/4 on page 5, for example).

Authors

Thank you for your positive comments.

Figure 3 is now correctly referred. The correspondence between the text and the Figure 4 has been improved.

Point 3

Reviewer

I see serious flaws in the methodology section, however. The chapter 4.3 describes the theoretical background of the cluster analysis thoroughly, authors do not explain why they chose particular methods, though. In more detail:

• Why did you choose the cluster analysis? Have you considered other options? Which ones? And why did you choose cluster analysis?
• The k-medoids algorithm is described in detail and compared to k-means algorithm. However, there is no reason why this particular method was used.
• As mentioned by authors, there is a number of metrics that can be used to measure the distance of objects. They list their properties and name the most frequently used metrics – Euclidean distance. But again, they do not explain why this distance was used (except to mention that it is “the most used” distance measure). Explain why you used this metrics, whether it is a suitable metrics and, most importantly, whether both datasets meet the criteria for using it.

Authors

We have integrated a new paragraph in section 4. We hope that this paragraph will help to better explain the reasons behind our choices.

Point 5

Reviewer

• Please, supply the results of the maximum average silhouette calculations. Based on these calculations, optimal number of clusters (3) was determined for both datasets. However, no such results are presented in the paper. Unless you provide results that confirm that the optimal number of clusters is 3, the "results" chapter cannot be presented correctly.

Authors

The values of the maximum average silhouette calculations SC for the cluster analysis with k-medoid was already present in the previous version of the paper on page 18 (Milan) and 23 (Bari) and, that in the new version we highlighted in red to help you locate it on page 19 for the metropolitan city of Milan, and page 24 for the metropolitan city of Bari.

Point 6

Reviewer

• Based on these calculations, optimal number of clusters (3) was determined for both datasets. However, no such results are presented in the paper. Unless you provide results that confirm that the optimal number of clusters is 3, the "results" chapter cannot be presented correctly.

Authors

The results reported in the previous version of paper 18 (Milan) and page 23 (Bari) highlight three clusters for both metropolitan cities, for which we also highlight the number of elements.

In the case of the metropolitan city of Milan the value of SC for this classification (Cluster 1) is 0,88, which according to the values proposed for it by Kaufman and Rousseeuw [38] identifies a strong structure.

In the case of the metropolitan city of Bari the value of SC for this classification is 0,84, which according to the values proposed for it by Kaufman and Rousseeuw identifies a strong structure.

The results reported in the new version of paper 19 (Milan) and page 24 (Bari) show three clusters for both metropolitan cities, in order to supported in the understanding of the results the text is now highlighted in red. In this section to improve the level of understanding of the results we have modified the text and added a small paragraph for both the metropolitan city of Milan and Bari.

Point 7

Reviewer

To sum it up: Chapter 4.3 describes the methodology, however, there is no justification as to why particular methods were chosen, nor is there confirmation of the correctness of selected methods.

Authors

We have integrated a paragraph to facilitate a better understanding of the analysis choices made by us in this study.

Point 8

Reviewer

Just some small fixes: In formula (1), please supply the matrix in usual format – in parentheses. Also I wonder why you write: “This is example 1 of an equation”. In my opinion, this is not an example, this is a definition. Also the formula (3) is not written correctly, I am afraid.

Yes, you are right, there were typing errors in the formulas, however now on the advice of another reviewer, any mathematical representation of the cluster analysis has been eliminated.

Authors

Point 9

Reviewer

Once the methodological procedures will be supplemented and justified, it will be possible to further verify the results presented in Chapter 5.

We hope that based on the changes made to our paper, it will now be easier to check the results we have achieved.

Thank you very much for your attention

Sincerely yours,

Authors

Round 2

Reviewer 2 Report

Dear Authors,

Congratulations for the revised manuscript.

I have only one additional suggestion. As section 4 comprises only one subsection (“4.1”), it is advisable to delete “4.1” and leave the title 4. Case studies: two Italian metropolitan cities

All the best!

Reviewer 3 Report

I would like to thank the author for all the corrections. All my questions have been answered, and content editing requests have been made and are included in the new version of the article. I think that the article is interesting, well-edited.