Statistical Analysis and Forecasting of the Number of Students, Teachers and Graduates in Romania’s Pre-University Education System

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

In the abstract, it is better to explain or mention what the three variables are, not just mention them on line 13. 

The manuscript is academically sound and makes a meaningful contribution. However, the manuscript may benefit from : 

1- improve the English language, for example, in the abstract, line number 18. The forecasting results confirm the continuation of the decline through 2027. Please go over the rest of the manuscript 

In conclusion, you can establish a link between empirical findings and policy recommendations by providing more concrete examples of how forecasts can inform resource allocation, curriculum reform, or teacher workforce planning.

Comments on the Quality of English Language

The English language can be improved.

Many sentences are long with multiple clauses, which may tire the reader. For instance, “The research is grounded in the premise of profound structural transformations within the Romanian educational system, driven by demographic decline, external migration, recurrent reforms, and shifts in resource allocation.”

Repetition of words like decline, forecast, and demographic factors, for example 

in line 58 
“…reflecting the continuous reduction of the school-age population and the restructuring of the educational network.”
“…The forecasting results confirm the continuation of the decline through 2027…”
“…suggesting that their dynamics are predominantly shaped by demographic and migratory factors.”

Teachers projected to fall to 178,700

Students projected to 2.78 million

Graduates declining until 2026, then stabilizing in 2027

These results are presented only in text form. You may consider presenting them in visual formats (tables, charts, graphs) to make results more accessible and impactful. They allow readers to see patterns, compare values, and understand forecasts at a glance.

The findings are coherent and linked to demographic decline, but the discussion is heavily focused on technical detail. Maybe the authors could balance with policy implications, and less repetition would strengthen it.

Author Response

We would like to thank you for the thorough and constructive feedback, which has greatly contributed to improving the quality and clarity of the manuscript. In the following lines, we will address your comments one by one, presenting the changes that we have introduced in the revised version of our manuscript. The revised text is marked with red in the manuscript

In the abstract, it is better to explain or mention what the three variables are, not just mention them on line 13. 

Thank you for your insightful comment. We have mentioned the variables (students, teaching staff and graduate) at lines 23-24

1- improve the English language, for example, in the abstract, line number 18. The forecasting results confirm the continuation of the decline through 2027. Please go over the rest of the manuscript 

Thank you for your insightful comment. We have proof read the entire manuscript and improved the quality of the English language.

In conclusion, you can establish a link between empirical findings and policy recommendations by providing more concrete examples of how forecasts can inform resource allocation, curriculum reform, or teacher workforce planning.

We thank you for this constructive suggestion. In response, we have expanded the Conclusions section by explicitly linking the empirical forecasting results to concrete education policy applications (lines 843-868). The revised text illustrates how the projections can inform school network planning and resource allocation, teacher workforce planning, and curriculum reform in the context of demographic decline. This addition strengthens the practical relevance and policy orientation of the study.

The English language can be improved.

Many sentences are long with multiple clauses, which may tire the reader. For instance, “The research is grounded in the premise of profound structural transformations within the Romanian educational system, driven by demographic decline, external migration, recurrent reforms, and shifts in resource allocation.”

Repetition of words like decline, forecast, and demographic factors, for example 

in line 58 
“…reflecting the continuous reduction of the school-age population and the restructuring of the educational network.”
“…The forecasting results confirm the continuation of the decline through 2027…”
“…suggesting that their dynamics are predominantly shaped by demographic and migratory factors.”

Thank you for your insightful comment. We have proof read the entire manuscript and improved the quality of the English language.

Teachers projected to fall to 178,700

Students projected to 2.78 million

Graduates declining until 2026, then stabilizing in 2027

These results are presented only in text form. You may consider presenting them in visual formats (tables, charts, graphs) to make results more accessible and impactful. They allow readers to see patterns, compare values, and understand forecasts at a glance.

Thank you for your valuable comment. We have to mention that the projections for teachers, students and graduates are presented in visual form in Figure 4 (teachers), Figure 6 (students) and Figure 8 (graduates)

The findings are coherent and linked to demographic decline, but the discussion is heavily focused on technical detail. Maybe the authors could balance with policy implications, and less repetition would strengthen it.

We thank you for this constructive suggestion. In response, we have expanded the Conclusions section by explicitly linking the empirical forecasting results to concrete education policy applications (lines 843-868). At the same time, we have improved the quality of the English language throughout the manuscript and eliminated repetitions.

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

Title: Statistical analysis and forecasting of the number of students, 2 teachers and graduates in Romania's pre-university education 3 system

Comments:

1. In the introduction, authors provide a long background of the study. I suggest to make it shorter. Keep the main focus only.
2. In page 2: authors mentioned, “At the same time, researchers acknowledge the need to complement ARIMA 52 forecasts with qualitative insights and scenario analyses.” Please add supporting references.
3. I suggest to bring section 2: Literature review before section 1: Introduction. So, please follow this steps to present: A. Introduction: - Background, - Literature review, B. Novelty of the study – Significance of the study – Hypothesis. C. Methods, D. Results, E. Discussion, ...
4. In the materials and method sections: Please add who are the participants, what are their demographic informations, how did you get the data, how did you process the data, how did you analyze the data. And then create a subsection where you will present all your models.
5. Please add a statement of your data availability and please provide all the links. Example: You mentioned the results in Figs. 1, 2, how did you get all these data?
6. Please provide data source of Fig. 3?
7. You have used ARIMA for forecasting, how did you consider the quality of your prediction? Your RMSE values are extremely large. Did you try any other model to compare your results? Why don’t you use LSTM and compare the findings with ARIMA?
8. I suggest to separate your Results section and Discussion section.
9. Also, please separate your conclusion section, limitation section, future research direction section.

Thanks

Author Response

We would like to thank you for the thorough and constructive feedback, which has greatly contributed to improving the quality and clarity of the manuscript. In the following lines, we will address your comments one by one, presenting the changes that we have introduced in the revised version of our manuscript. The revised text is marked with red in the manuscript

1. In the introduction, authors provide a long background of the study. I suggest to make it shorter. Keep the main focus only.

Thank you for your insightful comment. We have shortened the introduction, eliminating the lines related to the “National Recovery and Resilience Plan (NRRP), as well as the technical information related to ARIMA.

1. In page 2: authors mentioned, “At the same time, researchers acknowledge the need to complement ARIMA 52 forecasts with qualitative insights and scenario analyses.” Please add supporting references.

Thank you for your valuable feedback. We have added the citation (Zellner et al., 2021) in text line 64 and in the reference list (lines 1027-1028)

1. I suggest to bring section 2: Literature review before section 1: Introduction. So, please follow this steps to present: A. Introduction: - Background, - Literature review, B. Novelty of the study – Significance of the study – Hypothesis. C. Methods, D. Results, E. Discussion, ...

We thank the reviewer for this constructive structural suggestion. After careful consideration, we respectfully propose to retain the current organization of the manuscript, as it aligns with both the journal’s conventions and the analytical logic of the study.

In the revised manuscript, the Introduction is intentionally designed to provide a concise contextual background, clearly state the research motivation, articulate the novelty and significance of the study, and formulate the research hypotheses. This structure allows readers to immediately understand the purpose, contribution, and empirical focus of the research before engaging with the more detailed synthesis of prior studies.

The Literature Review is therefore presented as a standalone section following the Introduction, where previous empirical and methodological contributions are systematically analyzed and positioned in relation to the present study. This separation improves conceptual clarity by avoiding excessive fragmentation of the Introduction and allows the literature to be discussed in greater depth without interrupting the narrative flow of the research objectives and hypotheses.

Furthermore, the current structure—Introduction, Literature Review, Materials and Methods, Results and Discussion (combined), and Conclusions—is consistent with the standard format commonly adopted in empirical, quantitatively oriented articles published in Education Sciences and other MDPI journals. In particular, the combined Results and Discussion section reflects the integrated interpretation of empirical findings, which is appropriate for time-series forecasting studies where methodological outputs and their implications are closely intertwined.

For these reasons, we believe that the existing structure offers a clear, logical, and reader-friendly progression from research motivation to empirical evidence and policy-relevant interpretation, and we therefore respectfully maintain the current organization of the manuscript.

1. In the materials and method sections: Please add who are the participants, what are their demographic informations, how did you get the data, how did you process the data, how did you analyze the data. And then create a subsection where you will present all your models.

Thank you for this constructive comment. In the material and methods (lines 313-318) have added a paragraph explaining the source of our data (the National Institute of Statistics of Romania), as well as the software that we have used to process and analyze the data (SPSS and Eviews).

1. Please add a statement of your data availability and please provide all the links. Example: You mentioned the results in Figs. 1, 2, how did you get all these data?

We have added the source of our data for every figure (National Institute of Statistics of Romania, 2025)

1. Please provide data source of Fig. 3?

We have added the source of our data for every figure (National Institute of Statistics of Romania, 2025)

1. You have used ARIMA for forecasting, how did you consider the quality of your prediction? Your RMSE values are extremely large. Did you try any other model to compare your results? Why don’t you use LSTM and compare the findings with ARIMA?

The forecasting quality was assessed using accuracy indicators such as RMSE and MAPE, as well as model selection criteria including AIC and SC. The RMSE values are relatively high due to the large absolute magnitude of the analysed data (e.g., number of students and graduates). In contrast, the MAPE values are low—6.8%, 4.7%, and 7.3%, respectively—each below the 10% threshold, which indicates an excellent level of forecasting accuracy. Given that the data exhibit a predominantly linear trend, the ARIMA approach was selected. While LSTM models are capable of capturing complex, nonlinear structures, long-term dynamics, and long-range dependencies, such characteristics are not present in this dataset. ARIMA performs effectively when the dataset is relatively small and the forecast horizon is short, whereas LSTM models require substantially larger datasets to generalise adequately and are typically suited to longer forecast horizons. Furthermore, ARIMA offers greater interpretability—particularly for readers unfamiliar with advanced machine-learning techniques—as its AR, I, and MA coefficients have clear statistical meaning. In contrast, LSTM models operate as “black boxes,” making it difficult to understand or justify the underlying mechanisms that generate their predictions.

1. I suggest to separate your Results section and Discussion section.

We thank the reviewer for this valuable structural suggestion. After careful consideration, we respectfully propose to retain the combined Results and Discussion section in the current manuscript.

The decision to integrate results and discussion is deliberate and reflects the analytical nature of the study. The research relies on time-series econometric modeling and forecasting (ARIMA), where empirical outputs—such as diagnostic tests, model selection criteria, and forecasts—are closely linked to their interpretation and implications. Presenting results alongside their discussion allows for a clearer, more coherent explanation of how statistical findings translate into substantive insights regarding demographic dynamics and educational system adjustments.

Moreover, this integrated structure is commonly adopted in quantitative and forecasting-oriented studies published in Education Sciences and other MDPI journals, particularly when results require immediate contextual interpretation rather than post-hoc discussion. Separating the sections in this case would likely lead to repetition and fragmentation of the narrative, without substantially improving clarity.

Finally, combining the Results and Discussion sections enhances readability by guiding the reader through the empirical evidence and its interpretation in a single, continuous analytical flow, which is especially appropriate for policy-oriented studies where findings and implications are tightly interwoven. For these reasons, we respectfully maintain the current structure of the manuscript.

1. Also, please separate your conclusion section, limitation section, future research direction section.

Thank you for this insightful comment. We have divided the conclusion section in 3 parts: general conclusions, limitations, future research directions

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Thank you for addressing all of the comments 

Author Response

We would like to thank you for the thorough and constructive feedback, which has greatly contributed to improving the quality and clarity of the manuscript. In the following lines, we will address your comments one by one, presenting the changes that we have introduced in the second revised version of our manuscript. The revised text is marked with red in the manuscript.

1. Thank you for addressing all of the comments.

Thank you for your valuable feedback.

Reviewer 2 Report

Comments and Suggestions for Authors

Authors addressed most of the comments. And I agreed with authors response. But, I am not happy with the ARIMA model performance. Authors should consider another model for prediction and should make a comparison with the present one.  Example; RMSE ≈ 45,968. Authors should justify how such big RMSE value is acceptable for any kind of data analysis? I suggest authors to provide supporting references to justify this reason. Otherwise, authors need to remove the prediction part. Thanks 

Author Response

We would like to thank you for the thorough and constructive feedback, which has greatly contributed to improving the quality and clarity of the manuscript. In the following lines, we will address your comments one by one, presenting the changes that we have introduced in the second revised version of our manuscript. The revised text is marked with red in the manuscript

1.Authors addressed most of the comments. And I agreed with authors response.

Thank you for your valuable feedback.

2.Authors should consider another model for prediction and should make a comparison with the present one. 

I have previously answered this question.

3. Example; RMSE ≈ 45,968. Authors should justify how such big RMSE value is acceptable for any kind of data analysis? I suggest authors to provide supporting references to justify this reason.

The forecast accuracy of the selected ARIMA models was assessed using both absolute and relative error measures. To ensure scale-independent evaluation, relative RMSE values were computed by normalizing the RMSE with respect to the mean of each series. For the teaching staff series (TEACH), the ARIMA(1,1,1) model yielded a relative RMSE of approximately 8.9%. In the case of pre-university students (STUD), the ARIMA(4,1,3) specification achieved a relative RMSE of about 5.2%, indicating high predictive accuracy despite the large absolute error values. For pre-university graduates (GRAD), the ARIMA(3,1,5) model produced a relative RMSE of approximately 9.2%.

These findings confirm that the magnitude of absolute RMSE values is primarily driven by the scale of the data rather than by poor model performance. Consequently, RMSE should be interpreted in conjunction with scale-independent accuracy measures. In this respect, the Mean Absolute Percentage Error (MAPE) values—below 10% for all selected models—support a high degree of predictive accuracy.

As noted by Hyndman and Athanasopoulos (2021), RMSE can be misleading when the scale of the data is large, whereas relative measures such as MAPE provide a more meaningful assessment of forecast accuracy. Moreover, all models satisfy standard diagnostic requirements, including the absence of residual autocorrelation and conditional heteroskedasticity, thereby reinforcing their statistical adequacy. Model adequacy is primarily judged by residual diagnostics rather than solely by forecast error magnitude (Gujarati and Porter, 2009).

Large absolute forecast errors are common in long-term demographic (see Box, Jenkins et al., 2015) and educational time series due to structural changes, policy reforms, and population dynamics. Therefore, the obtained RMSE values are consistent with findings reported in similar empirical studies and do not undermine the validity of the selected ARIMA specifications.

The previous text was inserted in the conclusions section (lines 833-856).

References:

Hyndman, R.J., & Athanasopoulos, G. (2021) Forecasting: principles and practice, 3rd edition, OTexts: Melbourne, Australia. OTexts.com/fpp3.

Box, G. E. P., Jenkins, G. M., Reinsel, G. C., & Ljung, G. M. (2015). Time Series Analysis: Forecasting and Control. Wiley.

Gujarati, D.N. and Porter, D.C. (2009). Basic Econometrics. 5th Edition, McGraw Hill Inc., New York.

These papers were inserted in the references section.

Hyndman & Athanasopoulos (2021):

„RMSE can be misleading when the scale of the data is large; relative measures such as MAPE provide a more meaningful assessment of forecast accuracy.”

Box, Jenkins & Reinsel (2015):

„Large forecast errors are expected in long-term demographic series due to unmodelled structural changes.”

Gujarati & Porter (2009):

„Model adequacy is primarily judged by residual diagnostics, not solely by forecast error magnitude.”

Round 3

Reviewer 2 Report

Comments and Suggestions for Authors

I suggest authors to show relative RMSE throughout the manuscript. Thanks

Author Response

We would like to thank you for your constructive comments and feedback, which greatly improved the quality and clarity of the manuscript. In the following lines, we will address your comments one by one, presenting the changes we have introduced in the third revised version of our manuscript. The revised text is marked in red in the manuscript.

1. I suggest authors to show relative RMSE throughout the manuscript.

I have included the relative value of RMSE, denoted rRMSE, wherever RMSE appears in the paper.

Lines 418-419; 577; 635; 709