Review Reports - Government Subsidies and Industrial Productivity in South Africa: A Focus on the Channels

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The paper "Government Subsidies and Industrial Productivity in South Africa: A Focus on the Channels" investigates the effect of government subsidies on productivity via technologic change and (in-)efficiency in South Africa. The paper employs a stochastic frontier analysis

The paper is nicely motivated and well written. In its current state, there are some points that require further attention before the paper is ready for publication. The following comments provide some pointers:

Introduction
-l.135 and 139: How do the authors envision the government "to carefully consider the design and structure of ist subsidy programmes"? How does this align with the sentence in l.132-134 where it is concluded that the empirical results of the paper suggest "that government interventions considerably stifle technological progress that is essential for long-term economic growth and global competitiveness"?

Review of the Literature
-l.169-174: Missing reference(s)
-l.183-197: f(), x, and t should be defined more explicitly in the text to make the summary of the concepts self-contained
-l.212: define u(t) explictly in the text
-l.214-215: Shouldn't it be "increase/decrease" and "(in-)efficiency" here?
-Fig.3: Using the notation f(x_1, t) and f(x_2, t) might be more sensible here, as the inputs differ (if the production functions are identical; otherwise f_1() and f_2() should be used). According to the text, technology may differ?! This should also be clarified by (for example) collecting and explaining the assumptions in a particular subsection of the text. Collecting the assumptions in one position (the classical assumptions typically imposed in the literature) also makes it easier to highlight in which aspects your paper differs.

Materials and Methods
-Will the data and code be made publicly available so that other researchers can replicate the results?
-Is it sensible here to pool the goods sector and the services sector? Can these sectors be considered to have the same or at least similar production functions?
-Which software packages were used to generate the results? For the stochastic frontier analysis the references seem to indicate that Stata functions were employed. This should be clarified in the text.
-l.349-350 "reflecting the main criticism of the specification of being susceptible to curvature problems": references should be provided here.
-Equation(2): Why is the "it" index in the equation given outside of the parentheses; also, is it really the logarithm with base 10 that was used here or the natural logarithm? Both is fine, but less common, so this comment is just for clarification.
-l.401: based on Equation (3), it should be x'_{yit} here!? Also, the transpose could be omitted.
-l.496: include reference to Arellano and Bond (1991) paper.
-For the dynamic panel data models, which software packages were used for estimation? This should be clarified in the text. For example, there are a number of popular Stata and R routines for estimation of dynamic panel data models such as xtabond2 (Roodman, 2009b), xtdpdgmm (Kripfganz, 2019) (both Stata) and plm (Croissant and Millo, 2018; Croissant and Millo, 2008) and pdynmc (Fritsch, Pua, and Schnurbus, 2021) (both R). As the time series dimension is relatively large, was the instrument set reduced in any way (see Roodman, 2009a)? Additionally, it is not entirely clear how the estmation results obtained for the dynamic panel data models feed into the analysis from the current version of the manuscript.

Results and Discussion
-l.597-598: as this refers to the significance level alpha employed in the test (see table notes), this should also be stated explicitly in the text.
-Fig.5 and 6: presenting both figures on the same scale makes them better comparable.

Minor comments
-not all journal names are capitalized in the References

Some typos
l.46, l.272, l.370, l.374, l.404,
l.846, l.855, l.870, l.908

References

Arellano, M., & Bond, S. (1991). Some tests of specification for panel data: Monte Carlo evidence and an application to employment equations. The Review of Economic Studies, 58(2), 277-297. https://doi.org/10.2307/2297968

Croissant, Y., & Millo, G. (2008). Panel Data Econometrics in R: The plm Package. Journal of Statistical Software, 27(2), 1–43. https://doi.org/10.18637/jss.v027.i02

Croissant Y, Millo G (2018). Panel Data Econometrics with R. Wiley. https://doi.org/10.1002/9781119504641

Fritsch, M., Yu Pua, A. A., & Schnurbus, J. (2021). Pdynmc: a package for estimating linear dynamic panel data models based on nonlinear moment conditions. The R Journal, 13(1), 218-231. https://journal.r-project.org/articles/RJ-2021-035/RJ-2021-035.pdf

Kripfganz, S. (2019). Generalized method of moments estimation of linear dynamic panel data models. Proceedings of the 2019 London Stata Conference. https://www.stata.com/meeting/uk19/slides/uk19_kripfganz.pdf

Roodman, D. (2009a). A note on the theme of too many instruments. Oxford Bulletin of Economics and Statistics, 71(1), 135-158.

Roodman, D. (2009b). How to do Xtabond2: An Introduction to Difference and System GMM in Stata. The Stata Journal, 9(1), 86-136. https://doi.org/10.1177/1536867X0900900106

Author Response

Dear editor,

I would like to sincerely thank the reviewers for their careful reading, insightful comments, and constructive suggestions on my manuscript. I am grateful for the time and effort the reviewers have taken to evaluate my work. Their feedback has been invaluable in helping me improve the quality and clarity of the manuscript.

I have carefully considered all the comments raised. While I agree with many of the suggestions and have made the necessary revisions, there are also some points where I respectfully disagree. I have provided detailed responses to each comment below, indicating the revisions made or explaining the reasons for my disagreement. For ease of reference, my responses are highlighted in yellow both in this response letter and in the revised manuscript.

Reviewer One

Thank you for your insightful observation regarding the alignment of our statements on government interventions and subsidy program design. The empirical results suggest that government subsidies, may stifle technological progress. The paragraph you correctly cited inappropriately used the word “intervention” which is too broad. The correct term should have been subsidies. I have replaced “interventions” with subsidies so that the statements won’t appear contradictory. The word I was trying to put across in the subsequent lines is that the negative effect of subsidies observed in the study could be mitigated by a number of factors such as increased accountability, close monitoring and ensuring that the subsidies have an R&D incentive. This is indicated in yellow in the revised manuscript.

Review of the Literature
-l.169-174: Missing reference(s)

I have corrected this. The corrections are highlighted in yellow.

-l.183-197: f(), x, and t should be defined more explicitly in the text to make the summary of the concepts self-contained

Thank you for noting this. I have explicitly defined t and t+1, x, f and y.

-l.212: define u(t) explictly in the text

The term has been defined. Thank you.

-l.214-215: Shouldn't it be "increase/decrease" and "(in-)efficiency" here?

True. It was a typo. The correct paraphrased wording should be that an increase in production arises from technical changes and an increase in efficiency. I have corrected this accordingly.

-Fig.3: Using the notation f(x_1, t) and f(x_2, t) might be more sensible here, as the inputs differ (if the production functions are identical; otherwise f_1() and f_2() should be used). According to the text, technology may differ?! This should also be clarified by (for example) collecting and explaining the assumptions in a particular subsection of the text. Collecting the assumptions in one position (the classical assumptions typically imposed in the literature) also makes it easier to highlight in which aspects your paper differs.

This is true. I have corrected the graph to explicitly distinguish between the initial frontier and the second frontier. The initial frontier now has y1=f(x1t) while the second frontier has y2=f(x2t). Regarding the assumption, I have clarified as indicated in yellow that the shift in the frontier from the initial to the higher frontier reflects technical change.

Materials and Methods
-Will the data and code be made publicly available so that other researchers can replicate the results?

Yes, I actually submitted the data to the journal during the submission process, but I am happy to share with anyone interested. I am also happy to share the codes. The code is the xtsfkk command by Karakaplan (2022). Noteworthy, however, as the manuscript explains in the methodology, I had to first transform the variables using the within-transformation to get rid of unobserved heterogeneity. The within-transformation of frontier inputs is done using the command: egen X_mean = mean(X), by(id) where X is the frontier variable. This is followed by the command: gen X_within = X - X_mean.

-Is it sensible here to pool the goods sector and the services sector? Can these sectors be considered to have the same or at least similar production functions?

Intuitively you are right. it is more sensible to separate the two sectors. However, secondary regressions did not yield any significant difference in the frontier estimates (which is key to determining the efficiency scores). I had to balance between presenting additional separate regressions with similar findings and only presenting one set of results. I did not feel the need to present these results especially given the word count which was now exceeding 11k and the desire to retain more degrees of freedom. If you strongly feel however that I need to add these results and if the editor agrees, I am more than happy to expand the paper with this set of new results.

-Which software packages were used to generate the results? For the stochastic frontier analysis the references seem to indicate that Stata functions were employed. This should be clarified in the text.

You may have missed it in the submitted manuscript which is understandable since the manuscript is long. It is contained on line 527, the last paragraph of the methodology section.

-l.349-350 "reflecting the main criticism of the specification of being susceptible to curvature problems": references should be provided here.

The reference has been added and highlighted in yellow.

-Equation(2): Why is the "it" index in the equation given outside of the parentheses; also, is it really the logarithm with base 10 that was used here or the natural logarithm? Both is fine, but less common, so this comment is just for clarification.

Thank you for the comment. My response is that putting subscripts “it” inside or outside the brackets has no material effect since the brackets themselves have no operation. Regarding the logarithm, it is clarified just below equation 2 that it is base 10 and not base e.

-l.401: based on Equation (3), it should be x'_{yit} here!? Also, the transpose could be omitted.

Thank you for raising this. x_{yit} needed a further clarification that it can be broken into exogenous and endogenous frontier variables. I have however simplified matters by removing y since I am treating all frontier variables as endogenous. I have also removed the transpose. Thank you.

-l.496: include reference to Arellano and Bond (1991) paper.

I have added the reference.

-For the dynamic panel data models, which software packages were used for estimation? This should be clarified in the text. For example, there are a number of popular Stata and R routines for estimation of dynamic panel data models such as xtabond2 (Roodman, 2009b), xtdpdgmm (Kripfganz, 2019) (both Stata) and plm (Croissant and Millo, 2018; Croissant and Millo, 2008) and pdynmc (Fritsch, Pua, and Schnurbus, 2021) (both R). As the time series dimension is relatively large, was the instrument set reduced in any way (see Roodman, 2009a)? Additionally, it is not entirely clear how the estimation results obtained for the dynamic panel data models feed into the analysis from the current version of the manuscript.

The innovation of the paper is to use the control function procedure within the SFA framework. As you are aware, the control function procedure involves running an auxiliary regression (with instruments) from which the residuals will be generated and plugged into the main equation. The point raised in the paper is that using the traditional fixed effects approach in the auxiliary regression will invite the famous dynamic panel bias. To avoid this, the LSDV approach was used. This approach uses the bias approximations in Bruno (2005). The bias correction can be initialized using either the Anderson-Hsiao, the Arellano-Bond, the Blundell-Bond or one’s own initial values. The methodology of this paper is therefore essentially stating that the Arrellano-Bond was used to initialize the bias-correction. Lastly, Roodman (2009a) applies to the system and difference GMM, not in the bias-adjusted LSDV approach.

Results and Discussion
-l.597-598: as this refers to the significance level alpha employed in the test (see table notes), this should also be stated explicitly in the text.

I am sorry if I misunderstood this comment. I have put the *** in the table so that it corresponds to what is in the text. The *** are highlighted in yellow.

-Fig.5 and 6: presenting both figures on the same scale makes them better comparable.

I am of the view that lumping the two graphs may be slightly confusing to the reader especially given that the two graphs include four difference industries.

Minor comments
-not all journal names are capitalized in the References

I am counting on editorial work (at some cost) from the journal should the manuscript be accepted.

Some typos
l.46, l.272, l.370, l.374, l.404,
l.846, l.855, l.870, l.908

I am counting on editorial work (at some cost) from the journal should the manuscript be accepted.

Thank you for suggesting this. I will make a request for the journal’s editorial services should the manuscript be accepted.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript investigates the relationship between government subsidies and industrial productivity, with a particular focus on the channels of influence. The topic is of significant value. Building on an analysis of existing literature regarding the relationship between government subsidies and productivity growth in South Africa, the manuscript constructs a panel stochastic frontier model, incorporating true fixed effects and control functions to examine unobserved heterogeneity and idiosyncratic endogeneity. This approach allows for a detailed analysis of the channels through which government subsidies affect efficiency and technological change in South Africa's productivity. The empirical analysis yields some meaningful conclusions. However, there is room for improvement in the manuscript:

1. Abstract: The abstract consists of three main parts: a brief research background, the main approach, and the conclusions. The abstract should elaborate on the research approach in more detail and present the conclusions more clearly.

2. Introduction: The introduction should provide an appropriate evaluation of the existing literature. Although the second section of the manuscript is dedicated to a literature review, the content appears to conflate literature evaluation with the theoretical analysis of the manuscript. In the research process, literature evaluation involves summarizing and critiquing the work of others, while theoretical analysis pertains to the fundamental theories or perspectives of the current study. Theoretical analysis forms the basis for subsequent model construction. Therefore, it is recommended that the author adds literature evaluation content to the second section and, based on this evaluation, elaborates on the marginal contributions of this study. Additionally, methodological literature should be included in the literature evaluation, such as:
(1) Mamta Keswani, Uttam Khedlekar. 2024: Optimizing pricing and promotions for sustained profitability in declining markets: A Green-Centric inventory model, Data Science in Finance and Economics, 4(1): 83-131. doi: 10.3934/DSFE.2024004

3. Second Section: Currently titled "Literature Review," the second section lacks theoretical analysis for model design. It is recommended that the author adds theoretical analysis for this study, modifying the existing content of the second section to focus on theoretical analysis. This theoretical analysis should serve as the basis for model construction, rather than an exposition of others' research.

4. Third Section: The third section elaborates on the model and methodology. The exposition should first describe the model, then the variables within the model, and finally how these variables are measured. The manuscript currently discusses the data before the model, which does not conform to normative research practices and should be revised. Additionally, since the research topic involves micro-level behavioral mechanisms, peer effects among micro-enterprises could also be considered, such as:
(2) Li, Z.; Guo, F.; Du, Z.Learning from Peers: How Peer Effects Reshape the Digital Value Chain in China? J. Theor. Appl. Electron. Commer.Res. 2025, 20, 41. https://doi.org/10.3390/jtaer20010041

5. It is recommended to provide concise conclusions following each chart or table. Conclusions derived from the charts or tables should be presented immediately after them, followed by an explanation of these conclusions, including statistical measures, economic significance analysis, and the relationship between these analyses and the conclusions.

6. It is advised that the author proofreads the entire manuscript to make appropriate textual revisions.

Comments on the Quality of English Language

The language of the manuscript requires appropriate refinement to ensure it fully conveys the research content.

Author Response

Dear editor,

Reviewer Two

Abstract: The abstract consists of three main parts: a brief research background, the main approach, and the conclusions. The abstract should elaborate on the research approach in more detail and present the conclusions more clearly.

Thank you for suggesting this. I was following the template of the journal. I have tried to illustrate below how I formulated my abstract without putting headlines following the template. Unfortunately, this abstract is 199 words. The template encourages only a maximum of 200 words which makes it difficult to elaborate further.

Journal Template

Abstract: A single paragraph of about 200 words maximum. For research articles, abstracts should give a pertinent overview of the work. We strongly encourage authors to use the following style of structured abstracts, but without headings: (1) Background: Place the question addressed in a broad context and highlight the purpose of the study; (2) Methods: briefly describe the main methods or treatments applied; (3) Results: summarize the article’s main findings; (4) Conclusions: indicate the main conclusions or interpretations. The abstract should be an objective representation of the article and it must not contain results that are not presented and substantiated in the main text and should not exaggerate the main conclusions.

Manuscript

This article estimates the impact of government subsidies on productivity growth in South Africa, joining the ongoing debate among economists regarding the effectiveness of subsidies as a driver of industrial productivity. While some argue that subsidies address market failures, facilitate R&D, and improve efficiency, others criticise the attendant dependence, which reduces the incentive for industries to operate efficiently. This article contributes by examining the specific channels – efficiency, and technical changes – through which subsidies affect productivity in South Africa. The analysis is based on a panel dataset comprising 64 three-digit industries observed between 1993 and 2023. Estimation is done through an endogeneity robust panel stochastic frontier model, which treats subsidies as both an inefficiency driver and a technology variable. An additional estimation approach is proposed integrating the true-fixed effects with a control function in a bid to account for both unobserved heterogeneity and idiosyncratic endogeneity. The results show that subsidies are detrimental to productivity, particularly through stifling technological progress. This result supports the view that subsidies reduce the incentive for beneficiaries to innovate. This evidence calls for a reevaluation and a possible restructuring of subsidy programmes in South Africa in a bid to mitigate their adverse effects on industrial productivity.

Introduction: The introduction should provide an appropriate evaluation of the existing literature. Although the second section of the manuscript is dedicated to a literature review, the content appears to conflate literature evaluation with the theoretical analysis of the manuscript. In the research process, literature evaluation involves summarizing and critiquing the work of others, while theoretical analysis pertains to the fundamental theories or perspectives of the current study. Theoretical analysis forms the basis for subsequent model construction. Therefore, it is recommended that the author adds literature evaluation content to the second section and, based on this evaluation, elaborates on the marginal contributions of this study. Additionally, methodological literature should be included in the literature evaluation, such as:
(1) Mamta Keswani, Uttam Khedlekar. 2024: Optimizing pricing and promotions for sustained profitability in declining markets: A Green-Centric inventory model, Data Science in Finance and Economics, 4(1): 83-131. doi: 10.3934/DSFE.2024004

Thank you for this suggestion. Firstly, I think lines 24-50 address the first concern of evaluating literature in the introduction. Secondly, I have separated theoretical literature from empirical literature. I would have loved to add the suggested reference, but I struggled to relate it to my empirical analysis. I am also constrained by the word count which is well above 11,500 otherwise I would have added the suggested section on methodological evaluation. The journal would need a strong justification or permission from the editor if the manuscript exceeds 12,000 words from what I read on the website.

Second Section: Currently titled "Literature Review," the second section lacks theoretical analysis for model design. It is recommended that the author adds theoretical analysis for this study, modifying the existing content of the second section to focus on theoretical analysis. This theoretical analysis should serve as the basis for model construction, rather than an exposition of others' research.

Thank you for raising this, I have added a theoretical section that also includes theoretical equations from which the empirical model is derived. This is highlighted in yellow at the end of the theoretical literature section. I resisted the temptation to make these derivations as they are well-established from seminal papers.

Third Section: The third section elaborates on the model and methodology. The exposition should first describe the model, then the variables within the model, and finally how these variables are measured. The manuscript currently discusses the data before the model, which does not conform to normative research practices and should be revised. Additionally, since the research topic involves micro-level behavioral mechanisms, peer effects among micro-enterprises could also be considered, such as:
(2) Li, Z.; Guo, F.; Du, Z.Learning from Peers: How Peer Effects Reshape the Digital Value Chain in China? J. Theor. Appl. Electron. Commer.Res. 2025, 20, 41. https://doi.org/10.3390/jtaer20010041

Thank you for your feedback regarding the structure of the methodology section. However, I respectfully argue that presenting the data before specifying the model is a more logical and reader-friendly approach, particularly in the context of a panel data study.

I am of the view that an empirical analysis should first establish an understanding of the dataset, including its panel dimensions (i.e., cross-sectional units and time periods), before introducing the model specification. This sequencing ensures that when the model is introduced, the subscripts, variables, and panel structure are already familiar to the reader which reduces ambiguity.

I must add, however, that while some research papers follow the convention of presenting the model first, there is no strict normative rule mandating this order. I think the structure should primarily be guided by clarity and logical flow of the methodology. The approach in the manuscript of introducing the data first aligns with studies that emphasize the importance of understanding the dataset before engaging with the model's technical details. Therefore, I respectfully prefer to maintain the current structure as I believe it enhances readability and comprehension.

Lastly, I am of the view that addressing peer effects would constitute a paper on its own. I will surely consider this in my next paper. Thank you, however, for this suggestion.

It is recommended to provide concise conclusions following each chart or table. Conclusions derived from the charts or tables should be presented immediately after them, followed by an explanation of these conclusions, including statistical measures, economic significance analysis, and the relationship between these analyses and the conclusions.

Thank you for your suggestion regarding the placement of conclusions following each chart or table. However, the current structure of the manuscript follows the template and formatting guidelines of the journal, which systematically groups results, discussion, and conclusions into distinct sections. The journal's template is designed to ensure a structured and cohesive presentation of findings, where results are first introduced, followed by an in-depth discussion and then consolidated conclusions.

It is advised that the author proofreads the entire manuscript to make appropriate textual revisions.

Thank you for suggesting this. I will make a request for the journal’s editorial services should the manuscript be accepted.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The adjustments made by the author resolve the points raised by my previous comments. From my perspective the paper is ready for publication (after correcting a few typos and capitalizing some journal names in the references).