Effects of the Minimum Wage (MW) on Income Inequality: Systematic Review and Analysis of the Spanish Case

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The article „Effects of the minimum wage (MW) …..” is a well-written research paper. The article discusses an important and up-to-date problem related to the impact of the increase in MW on the level of income of the active workforce (aged 16-64) based on a Spanish example.

The paper is interesting, its reasoning is clear, and the scientific quality is appropriate.

However, before publication, I suggest the following (minor) corrections:

1.       From my point of view, the title of the paper is a little misleading. The title suggests that the main subject of the article is the effect of the MW on income inequality. Although this holds for the theoretical part (the literature review), the main focus of the empirical part is on the impact of the MW increase on income level (p. 17). Furthermore, on p. 23 the authors write: “It is reasonable to assume that much of the reduction in inequality in Spain is attributable to the strong impact of the MW increase, although this causal relationship has not been explored in this study”. Therefore, the authors could consider the correction of the title of the paper to be more consistent with the content of the paper (its empirical analyses). Following this, the main goal of the paper could also be modified.

2.       The abstract of the paper is too long. Its optimal length should be 250-300 words.

3.       The description of the research methods (Abstract, Introductions) need to be corrected. The authors claim to use the DID approach; however, it was applied as a part of the regression analysis (OLS estimates). Information about the source of data and the research period should also be provided.

4.       When presenting the estimation results (Tables 4-6) information about statistical tests verifying the linearity of the relationship, the normality of residuals, etc. (announced on p. 17),  should also be presented.

5.       Some paragraphs are very general and their reasoning is confusing. These are:

-          p. 3, lines 124-144, for example, “Until the end of the 1980s, there was a scarcity of empirical studies in the field of economics, and they played a marginal role, dependent on theoretical studies” (in general or on a specific topic?);  “In fact, most of the empirical studies carried out in the field of economic sciences in recent decades have totally or partially refuted this traditional theory” (what theory exactly?)

-          p. 16, lines 643-649: for example, “To test this assumption, additional explanatory variables have been included in the modelling, and the results remain robust” (what the variables were?); “Furthermore, the standard error hardly changes, the standardised coefficients do not change significantly, and the R2 increases slightly” (where the results are presented in the paper?)

Author Response

See attached file or below:

Comments 1: The article „Effects of the minimum wage (MW) …..” is a well-written research paper. The article discusses an important and up-to-date problem related to the impact of the increase in MW on the level of income of the active workforce (aged 16-64) based on a Spanish example.

The paper is interesting, its reasoning is clear, and the scientific quality is appropriate.

Response 1: First of all, we would like to sincerely thank you for your time and work in reviewing and providing feedback on this paper. Your kind and clearly positive comments encourage us and help us to improve the text.

Comments 2: However, before publication, I suggest the following (minor) corrections:

From my point of view, the title of the paper is a little misleading. The title suggests that the main subject of the article is the effect of the MW on income inequality. Although this holds for the theoretical part (the literature review), the main focus of the empirical part is on the impact of the MW increase on income level (p. 17). Furthermore, on p. 23 the authors write: “It is reasonable to assume that much of the reduction in inequality in Spain is attributable to the strong impact of the MW increase, although this causal relationship has not been explored in this study”. Therefore, the authors could consider the correction of the title of the paper to be more consistent with the content of the paper (its empirical analyses). Following this, the main goal of the paper could also be modified.

 

Response 2: It is clear that the systematic review is broader than the empirical study. However, the empirical part also refers to income inequality since it analyses the increase in the income level of the lowest salaries in relation to the highest ones. Perhaps the solution is to clarify it better in the text as we have done. See lines 659-661. Additionally, because it causes confusion, we have removed lines 872-877.

 

Comments 3: The abstract of the paper is too long. Its optimal length should be 250-300 words.

Response 3: We agree so the abstract has been changed (see new abstract)

 

Comments 4: The description of the research methods (Abstract, Introductions) need to be corrected. The authors claim to use the DID approach; however, it was applied as a part of the regression analysis (OLS estimates). Information about the source of data and the research period should also be provided.

 

Response 4: The corresponding changes have been made to both the abstract and the introduction. See new abstract and introduction (lines 93-95).

 

Comments 5: When presenting the estimation results (Tables 4-6) information about statistical tests verifying the linearity of the relationship, the normality of residuals, etc. (announced on p. 17), should also be presented.

 

Response 5. The corresponding changes have been made. See lines 668-675.

Comments 6: Some paragraphs are very general and their reasoning is confusing. These are:

• 3, lines 124-144, for example, “Until the end of the 1980s, there was a scarcity of empirical studies in the field of economics, and they played a marginal role, dependent on theoretical studies” (in general or on a specific topic?); “In fact, most of the empirical studies carried out in the field of economic sciences in recent decades have totally or partially refuted this traditional theory” (what theory exactly?)
• 16, lines 643-649: for example, “To test this assumption, additional explanatory variables have been included in the modelling, and the results remain robust” (what the variables were?);

Response 6:

• Modified in the original text (line 132-134)
• The variables are on lines 699-700

Comments 7: “Furthermore, the standard error hardly changes, the standardised coefficients do not change significantly, and the R2 increases slightly” (where the results are presented in the paper?)

 

Response 7: R2 It is specified in tables 4-6

 

Finally, we want to reiterate our gratitude for your kind comments and suggestions for improvement that we have tried to incorporate into the text.

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

The topic discussed in this study is important and interesting. It is clearly presented in the Introdution, which provides a good background for the remaining of the paper.

The method used is adequate for the objective of the study.

The results are clear and useful for policy action.

For all these reasons, my opinion about the paper is very positive. I believe the paper has important merits.

I only have two concerns:

- the paper is too long;

- is is not clear to me the exact reason why the author opts to divide the period between a period pre and other after 2020. What is the advantage of this option? Please elaborate further on this question.

Author Response

Comments 1: The topic discussed in this study is important and interesting. It is clearly presented in the Introdution, which provides a good background for the remaining of the paper.

The method used is adequate for the objective of the study.

The results are clear and useful for policy action.

For all these reasons, my opinion about the paper is very positive. I believe the paper has important merits.

I only have two concerns:

Response 1: First of all, we would like to sincerely thank you for your time and work in reviewing and providing feedback on this paper. Your kind and clearly positive comments encourage us and help us to improve the text.

 

Comments 2: Tthe paper is too long;

Response 2: It is true that the paper is lengthy; however, this is due to its addressing two significant issues that necessitate such dimensions. The inclusion of a comprehensive systematic review requires a well-defined protocol (PRISMA), which additionally mandates a high degree of explicitness and transparency in its application. This entails the necessity of including appendices that may ultimately be converted in the final version to 'digitally available material,' a decision that will be determined by the journal's editorial team.

 

Comments 3:  Is is not clear to me the exact reason why the author opts to divide the period between a period pre and other after 2020. What is the advantage of this option? Please elaborate further on this question.

Response 3: Given that the reviews up to 2019 are sufficiently comprehensive, we have opted to conduct the systematic review starting from that year, as no such review has been undertaken since then (see lines 203 to 205).

Finally, we would like to reiterate our gratitude for your kind comments and suggestions for improvement, which we have endeavored to incorporate in order to enhance the manuscript.

Reviewer 3 Report

Comments and Suggestions for Authors

The paper titled: "Effects of the minimum wage (MW) on income inequality. Systematic review and analysis of the Spanish case" is an interesting study and addresses an important issue on minimum wages.

While the paper is generally lengthy, it may not a problem given that the focus of the study is twofold – to provide a comprehensive literature review and an empirical analysis on Spain as a case study. Based on the dual objective of the paper my comments will be set out accordingly, where I will denote the literature section as "Part 1" and empirical component as "Part 2"

Some suggestions and points strengthen the paper are as follows:

Abstract is lengthy and relatively unstructured. Present a more succinct abstract. You may rewrite in terms of the purpose of the study, focus of the paper, and approach you have taken, with key findings and implications.

 

Part 1

- the extensive reviews in this paper generally argue that increase in minimum wages reduces income inequality. Besides minimum wage, other factors also influence inequality, and this should be noted in the study.

 Part 2:

- The empirical study presents interesting results, supporting the notion that minimum wage increase reduces income inequality. Since the independent variables are dummy-type variables (0 or 1), and the independent variable (income) is expressed in natural log, then how can we explain the coefficient in terms of percent, because the right-hand side variable is not unit-free? Please revise this, and hence the subsequent discussion, and/or provide a clear approach you used to derive percentages.

a.    Indicate the level of significance in the table

b.    Provide DW-stat for all the models estimated.

c.     Include sample size in each table showing the estimated results.

- Please provide (a)-(c) in the appendix as well. What does beta-1, beta-2 and beta-3 refer to, in the results provided in the Appendix.

- On line 643-646, the study mentions the use of additional explanatory variables. What are those? Please mention in the paper for clarity.

- In Table 3, please check the number column. Does number mean sample size? And please note that 2.344 is not the same as 2344 for total sample. Also, same goes for treatment group 3, where 1.297 is a decimal number, which does not accurately indicate the sample size.

- Line 701: what other explanatory variables does X4 takes? Please be specific.

- For clarity, in lines 721-734, specify the analysis in three cases. E.g., Case I, Case II and Case II, and then structure your discussions based on these cases.

- Your data is from 2018-2019. You rightly mentioned that your study did not account for macro factors. You also need to note that your study also did not account for structural factor, especially COVID-19, which is likely to affect employment opportunities, and wage rates.

- Moreover, your study did not look at the implication of minimum wages on employment. Please note studies like Card and Krueger (1995) which find the effect of minimum wages on employment. Additionally, other factors like the pension system, market structure and environmental taxes, (please refer to theoretical discussions on income inequality and minimum wages).

Other comments to address:

-       Rewrite lines 398-407. What does the alphabets ‘(a), (b, j)’ etc. indicate?

-       Rewrite lines 426-429 for clarity.

-       Lines 450-453: negative correlation between with two variables? Please clarify.

-       Please rephrase lines 598-601.

-       Paper needs proof reading (see for e.g., lines 80, 280, 392). In the discussion, what does it mean to say that ‘… results obtained can be considered solid…’. How do you measure ‘solid’?

-       In the Practical Implication section, the paper mentions that ‘The results of this study demonstrate that the measure is effective in achieving the desired outcomes, namely reducing inequality and poverty by ensuring that more people receive a fair minimum wage for their work.’ How was the study related to poverty? What measure of poverty was used to examine the impact of minimum wages on poverty?

-       Additionally, in line 931, the study mentions that: ‘the measure has been shown to have minimal impact on employment.’ – how was employment analyzed in the model and estimations?

 Some references:

-       Time-series minimum-wage studies: a meta-analysis. The American Economic Review, 85(2), 238-243.

-       Why the increase in the retirement age will lead to more inequality and poverty? An ignored fairness problem. Panoeconomicus, 70(1), 29-46.

-       Environmental Injustice: The Effects of Environmental Taxes on Income Distribution in an Oligopolistic General Equilibrium Model. Sustainability, 16(10), 4142.

 

-       Economic and social sustainability: The influence of oligopolies on inequality and growth. Sustainability, 12(22), 9378.

 

Comments on the Quality of English Language

A moderate level of proof-reading is recommended.

Author Response

First of all, we would like to sincerely thank you for your time and work in reviewing and providing feedback on this paper. Your kind comments encourage us and help us to improve the text.

Comment 1: The paper titled: "Effects of the minimum wage (MW) on income inequality. Systematic review and analysis of the Spanish case" is an interesting study and addresses an important issue on minimum wages.

While the paper is generally lengthy, it may not a problem given that the focus of the study is twofold – to provide a comprehensive literature review and an empirical analysis on Spain as a case study. Based on the dual objective of the paper my comments will be set out accordingly, where I will denote the literature section as "Part 1" and empirical component as "Part 2"

Some suggestions and points strengthen the paper are as follows:

Abstract is lengthy and relatively unstructured. Present a more succinct abstract. You may rewrite in terms of the purpose of the study, focus of the paper, and approach you have taken, with key findings and implications.

Response 1: We agree, so the abstract has been changed (see new abstract)

Comment 2: The extensive reviews in this paper generally argue that increase in minimum wages reduces income inequality. Besides minimum wage, other factors also influence inequality, and this should be noted in the study.

Response 2: It should be noted that the objective of the study is the MW and its effect on income inequality and not the other way around. We do not intend to study all the factors that affect inequality, but only whether the MW meets one of its objectives, which is to reduce inequality and working poverty. For this reason, we have not considered other possible factors that influence inequality discussed in other works, such as those recommended by the evaluator below.

Comment 3: The empirical study presents interesting results, supporting the notion that minimum wage increase reduces income inequality. Since the independent variables are dummy-type variables (0 or 1), and the independent variable (income) is expressed in natural log, then how can we explain the coefficient in terms of percent, because the right-hand side variable is not unit-free? Please revise this, and hence the subsequent discussion, and/or provide a clear approach you used to derive percentages.

Response 3: We have reviewed what you tell us, and the Response is that we used logarithms and not natural logs. When using logarithms, changes in variables are interpreted as percentage changes. See lines 693.

Comment 4: Indicate the level of significance in the table.

Response 4: It has been included (see tables 4 to 6).

Comment 5: Provide DW-stat for all the models estimated.

Response 5: It has been included in tables 4 to 6.

Comment 6: Include sample size in each table showing the estimated results.

Response 6: Yes, agreed. It has been included in tables 4 to 6

Comment 7: Please provide (a)-(c) in the appendix as well. What does beta-1, beta-2 and beta-3 refer to, in the results provided in the Appendix.

Response 7: Yes, agreed. It has been included in Appendix C.

Comment 8: On line 643-646, the study mentions the use of additional explanatory variables. What are those? Please mention in the paper for clarity.

Response 8: Done. See lines 699-700.

Comment 9: In Table 3, please check the number column. Does number mean sample size? And please note that 2.344 is not the same as 2344 for total sample. Also, same goes for treatment group 3, where 1.297 is a decimal number, which does not accurately indicate the sample size.

Response 9: Done. See table 3.

Comment 10: Line 701: what other explanatory variables does X4 takes? Please be specific.

Response 10: These variables are gender, mode of cohabitation and tertiary education. They are specified in lines 699-700 and lines 727-733.

Comment 11: For clarity, in lines 721-734, specify the analysis in three cases. E.g., Case I, Case II and Case II, and then structure your discussions based on these cases.

Response 11: Done, see lines 714 and following.

Comment 12: Your data is from 2018-2019. You rightly mentioned that your study did not account for macro factors. You also need to note that your study also did not account for structural factor, especially COVID-19, which is likely to affect employment opportunities, and wage rates.

Response 12: Yes, agreed. We changed it in the text, see lines 584-585.

Comment 13: Moreover, your study did not look at the implication of minimum wages on employment. Please note studies like Card and Krueger (1995) which find the effect of minimum wages on employment. Additionally, other factors like the pension system, market structure and environmental taxes, (please refer to theoretical discussions on income inequality and minimum wages).

Response 13: The study, as rightly said, does not address the issue of employment, nor other aspects such as the pension system or environmental taxes that have been the subject of other studies. The aim of this article is to analyse the relationship between MW and income inequality, and more specifically in the empirical part, the influence of MW on workers' income and their differences.

Other comments to address:

Comment 14: Rewrite lines 398-407. What does the alphabets ‘(a), (b, j)’ etc. indicate?

Response 14: Yes, you are right, these are typos. They have been changed in the text (see lines 393-397).

Comment 15: Rewrite lines 426-429 for clarity.

Response 15: Done. See lines 417-421.

Comment 16: Lines 450-453: negative correlation between with two variables? Please clarify.

Response 16: Done. See lines 441-442.

Comment 17: Please rephrase lines 598-601.

Response 17: Done. See lines 589-592.

Comment 18: Paper needs proof reading (see for e.g., lines 80, 280, 392). In the discussion, what does it mean to say that ‘… results obtained can be considered solid…’. How do you measure ‘solid’?

Response 18: one. See lines 68, 264 et seq., 382 and 387.

“Solid” (or robust) refers in the statistical literature to the results of the different sensitivity analyses that guarantee the validity and reliability of the results. Given that in our study the different sensitivity analyses have been very satisfactory, we can affirm that the results are “solid”.

Comment 19: In the Practical Implication section, the paper mentions that ‘The results of this study demonstrate that the measure is effective in achieving the desired outcomes, namely reducing inequality and poverty by ensuring that more people receive a fair minimum wage for their work.’ How was the study related to poverty? What measure of poverty was used to examine the impact of minimum wages on poverty?

Response 19: In fact, no empirical analysis has been carried out linking MW with poverty for the Spanish case. What is indicated here comes from the literature review especially for the case of Brazil and South Africa. It has been removed from the text to avoid confusion (see line 918 et seq.

Comment 20: Additionally, in line 931, the study mentions that: ‘the measure has been shown to have minimal impact on employment.’ – how was employment analyzed in the model and estimations?

Response 20: This analysis you mention has not been carried out. It has been removed from the text to avoid confusion (see lines 918 et seq).

Comment 21: Some references:

- Time-series minimum-wage studies: a meta-analysis. The American Economic Review, 85(2), 238-243.

Response 21: We are aware of and have considered the work of Card and Kruger, as can be seen in the bibliography. However, this specific paper is not cited because it has not been expressly used, in accordance with the journal's rules.

Comment 22: Some references:

- Why the increase in the retirement age will lead to more inequality and poverty? An ignored fairness problem. Panoeconomicus, 70(1), 29-46.

- Environmental Injustice: The Effects of Environmental Taxes on Income Distribution in an Oligopolistic General Equilibrium Model. Sustainability, 16(10), 4142.

- Economic and social sustainability: The influence of oligopolies on inequality and growth. Sustainability, 12(22), 9378.

Response 22: We have carefully reviewed these three articles by authors Peter J. Stauvermann and Ronald R. Kumar that you recommend and have noted their great interest. However, although the topic is related to inequality, the aspects with which it is related: retirement age, environmental issues and oligopolies are quite far from our topic that refers to MW. Therefore, following the rules of the journal, we cannot cite them.

Comment 23: Comments on the Quality of English Language: A moderate level of proof-reading is recommended.

Response 23: We have proceeded to revise the text in this regard.

Finally, we would like to reiterate our gratitude for your kind comments and suggestions for improvement that we have tried to incorporate to improve it.

Author Response File: Author Response.docx

Round 2

Reviewer 3 Report

Comments and Suggestions for Authors

Dear Authors,

I can see that you have addressed some of my comments, and provided justifications quoting journal polict on others. 

However, there is still some confusion regarding comment #3, which can create some serious issues on the outcomes of the empirical analysis:

----

Comment 3: The empirical study presents interesting results, supporting the notion that minimum wage increase reduces income inequality. Since the independent variables are dummy-type variables (0 or 1), and the independent variable (income) is expressed in natural log, then how can we explain the coefficient in terms of percent, because the right-hand side variable is not unit-free? Please revise this, and hence the subsequent discussion, and/or provide a clear approach you used to derive percentages.

Your Response 3: We have reviewed what you tell us, and the Response is that we used logarithms and not natural logs. When using logarithms, changes in variables are interpreted as percentage changes. See lines 693.

---

Do note that using log or natural log of the dependent variable will not alter the outcome. You can use either/or.

Based on your model framework, you are using a semi-log equation. The issue is on the independent variables. Since all your independent variables are dummy type (0 or 1), then the estmated coefficients of the dependent variable cannot imply percentage change, but in fact a form of assymetric effect. We can only consider percentage change if we have a log-log model (making all variables unit-free). 

Please review these papers for more insights and make necessary adjustments.

Derrick, F. W. (1984). Interpretation of dummy variables in semilogarithmic equations: Small sample implications. Southern Economic Journal, 1185-1188.

Jan van Garderen, K., & Shah, C. (2002). Exact interpretation of dummy variables in semilogarithmic equations. The Econometrics Journal, 5(1), 149-159.

Giles, D. E. (2011). Interpreting dummy variables in semi-logarithmic regression models: Exact distributional results. University of Victoria Department of Economics Working Paper EWP, 1101, 1-24.

All the best.

Author Response

First of all, we would like to thank you for your comments. Your suggestions have been extremely helpful and constructive. We sincerely regret that we missed the errors in the data during our initial review. We deeply appreciate your attention to detail and your dedication to helping us improve the quality of our work.

Indeed, as you point out, in a semilogarithmic model, the coefficients cannot be directly interpreted as percentage changes. Dichotomous variables indicate the presence or absence of a characteristic (for example, belonging to a treatment group, a specific year, or the interaction between year and treatment). The coefficients associated with these variables reflect the change in the logarithm of income when the dichotomous variable changes from 0 to 1. In practical terms, this means that these coefficients show the effect of "activating" or "deactivating" that particular characteristic.

In this sense, indeed, the change in the dependent variable is not symmetrical because it shifts from one condition (0) to another (1). This change does not represent a continuous percentage change but a change of state.

In summary, we cannot say that the coefficients of the independent variables directly indicate a percentage change in income. It is necessary to convert these coefficients to interpret the percentage effect. The conversion would be:

Percentage change =

The following table reflects the coefficient (β) and the percentage change it represents, according to the above formula

	Case 1	Case 2	Case 3
Variable “Year”
Model (1)	0.021à2.1%	0.03à3%	0.041à4.1%
Model (2)	0.020à2.0%	0.031à3.1%	0.039à4%
Variable Treatment
Model (1)	-1.062à-65.5%	-0.982à-62.6%	-0.782à-54.3%
Model (2)	-1.024à-64.1%	-0.954à-61.5%	-0.731à-51.9%
Variable Treatment*year
Model (1)	0.187à20.5%	0.036à3.7%	0.019à1.9%
Model (2)	0.188à20.7%	0.037à3.8%	0.018à1.8%

 

Indeed, the effect that the 2019 MW increase has had on the income of individuals in treatment group 1 is not 18% but 20%.

We have made the changes in the full text. See lines: 743-750; 772-779; 798-803; 823 and 834.

Author Response File: Author Response.pdf

Round 3

Reviewer 3 Report

Comments and Suggestions for Authors

I appreciate you putting effort to realise and understand your error in computation and interpretation. The analysis and discussion remains incomplete, if we consider all explanatory variables (like gender, living as couple, education). Please update them.

Include the table provided in the cover letter (including gender, couple, education) in the appendix for reference.

Methodology need to be updated to include the updated computation methods with respective citations. This will also help readers understand your results.

Your conclusion should capture the nuances of gender, couple and education effects on wage.

All the best.

Author Response

Comments 1: I appreciate you putting effort to realise and understand your error in computation and interpretation. The analysis and discussion remains incomplete, if we consider all explanatory variables (like gender, living as couple, education). Please update them.

Response 1: First of all, thank you again for your comments. We hope that the following response and the changes introduced in the text will fully comply with your observations.

Although the study of differences by gender, type of cohabitation, or level of education is not the primary focus of this research, the results indicate significant differences that warrant further investigation in subsequent studies. Nevertheless, we have introduced several modifications.

Lines 784-788; 837-841; 856; 867; 912-914; 927-929 and 931-933 can be consulted.

See also Table B Appendix C.

Comments 2: Include the table provided in the cover letter (including gender, couple, education) in the appendix for reference.

Response 2: See Table B in the Appendix C reproduced below

Table B. The coefficient (β) and the percentage change it represents, according to Halvorsen and Palmsquist (1980) y Kennedy (1982).
	Case 1	Case 2	Case 3
Variable “Year”
Model (1)	0.021à2.12%                (2.11%)	0.031à3.15%                 (3.14%)	0.041à4.19%                (4.17%)
Model (2)	0.020à2.01%                (2.02%)	0.03à3.05%              (3.04%)	0.039à3.98%                (3.97%)
Variable “Treatment”
Model (1)	-1.062à-65.42%               (-65.44%)	-0.982à-62.54%  (-62.55%)	-0.786à-54.43%               (-54.44%)
Model (2)	-1.024à-64.08%                 (-64.10%)	-0.954à-61.48%               (-61.49%)	-0.731à-51.86%            (-51.86)
Variable “Treatment*Year”
Model (1)	0.187à20.56%              (20.54%)	0.036à3.67%              (3.65%)	0.019à1.92%              (1.90%)
Model (2)	0.188à20.68%              (20.66%)	0.037à3.77%           (3.76)	0.018à1.82%                (1.80%)
Variable “Gender”
Model (2)	-0.023à-2.27%               (-2.28%)	-0.019à-1.88%               (-1.89%)	-0.063à-6.11%               (-6.11%)
Var. “Living as a couple”
Model (2)	-0.035à-3.44%               (-3.45%)	-0.024à-2.37%               (-2.38%)	-0.034à-3.34%               (-3.35%)
Variable  “Education”
Model (2)	0.062à6.40%              (6.39%)	0.052à5.34%              (5.33%)	0.182à19.96%              (19.96%)
Note: The value obtained by applying the Kennedy (1981) and Giles (1982) formula appears in parentheses.

Comments 3: Methodology need to be updated to include the updated computation methods with respective citations. This will also help readers understand your results.

Response 3: Lines 713-746 can be consulted.

In a semilogarithmic model with dichotomous variables, such as the one we are concerned with here, the coefficients of the independent variables are not interpreted as continuous percentage changes, but as changes in state. Dichotomous variables indicate the presence or absence of a specific characteristic, such as membership in a certain treatment group, a specific year, or the interaction between year and membership in the treatment group, represented, in our study, by the coefficients β1, β2 y β3, respectively. Consequently, the coefficients associated with these dichotomous independent variables reflect the change in the logarithm of annual income when the dichotomous variables change from 0 to 1.

To interpret the percentage effect, we mainly follow the conversions proposed by Halvorsen and Palmquist (1980), Kennedy (1981), and Giles (1982). Halvorsen and Palmquist (1980) provide a solid theoretical basis for the interpretation of coefficients of dichotomous variables in semilogarithmic models. The formula is as follows:

Percentage change =

Where β is the coefficient of the corresponding dichotomous variable.

Kennedy (1981) expands on Halvorsen and Palmquist's interpretation by noting that this interpretation is correct only under certain conditions and proposes an additional adjustment that takes into account the variance of the coefficient estimator, improving the precision of the interpretation. Thus, Kennedy’s correction (1981) includes an additional term to account for this omission. The corrected formula (introducing the variance) is as follows:

here β is the coefficient of the corresponding dichotomous variable and σ2 is the variance of the β estimator.

Giles (1982) provides an unbiased estimation of the percentage effect of the dummy variables. He adjusts the formulation of Halvorsen and Palmquist (1980) but with a different approach to ensure that the estimation is unbiased. The validation is performed through Monte Carlo simulations. Although Kennedy and Giles address the same problem, Giles' formula is distinguished by its focus on bias correction and validation through simulations, providing a more accurate and unbiased estimation of the effect of dummy variables in semilogarithmic models.

In our case, the variations between both approaches are minimal, as can be seen in Table B of Appendix C.

Comments 4: Your conclusion should capture the nuances of gender, couple and education effects on wage.

Response 4: We have made the changes. See lines: 1069-1075:

Although it is not the specific object of this work, the inclusion of complementary explanatory variables in the models allows us to observe significant differences in terms of the impact in the case of gender, the form of cohabitation or the level of tertiary education. The study shows that income is higher for men than for women, that it is lower when living alone than with a partner and that it is higher in the case of having tertiary education. However, to study the impact on these groups a more specific analyse is necessary, which will be addressed in future studies.

 

Bibliography included:

Halvorsen, R. & Palmquist, R. (1980), The Interpretation of Dummy Variables in Semilogarithmic Equations, American Economic Review, 70, issue 3, p. 474-75. https://EconPapers.repec.org/RePEc:aea:aecrev:v:70:y:1980:i:3:p:474-75.

Kennedy, Peter, (1981), Estimation with Correctly Interpreted Dummy Variables in Semilogarithmic Equations, American Economic Review, 71, issue 4,p. 801 https://EconPapers.repec.org/RePEc:aea:aecrev:v:71:y:1981:i:4:p:801.

Giles, David E.A. (1982): The interpretation of dummy variables in semilogarithmic equations: Unbiased estimation. Economics Letters, Volume 10, Issues 1–2, 77-79. https://doi.org/10.1016/0165-1765(82)90119-7.

Van Garderen, K. J., & Shah, C. (2002). Exact interpretation of dummy variables in semilogarithmic equations. The Econometrics Journal, 5(1), 149–159. http://www.jstor.org/stable/23114086.

We believe that this is all, we reiterate our thanks for your interest.

Author Response File: Author Response.docx

Round 4

Reviewer 3 Report

Comments and Suggestions for Authors

Thanks for addressing the comments in the paper, and bearing with me in the process. The paper looks much better than where we started from. I appreciate the additional information added in Appendix B, which will support your future work and the paper has potential to be used as references for future studies.   

All the best.

Comments on the Quality of English Language

Just a minor comment that if the editorial team could support with proof-reading.