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Reliability and Accuracy of Alternative Default Prediction Models: Evidence from Slovakia

Int. J. Financial Stud. 2021, 9(4), 65; https://doi.org/10.3390/ijfs9040065

by Daniela Rybárová¹, Helena Majdúchová¹, Peter Štetka^1,*

and Darina Luščíková²

Reviewer 1: Anonymous

Reviewer 2: Anonymous

Reviewer 3:

Dagmar Čámská

Int. J. Financial Stud. 2021, 9(4), 65; https://doi.org/10.3390/ijfs9040065

Submission received: 31 August 2021 / Revised: 24 November 2021 / Accepted: 25 November 2021 / Published: 30 November 2021

(This article belongs to the Special Issue Alternative Models and Methods in Financial Economics)

Round 1

Reviewer 1 Report

Thank you for writing an in-depth and analytical research paper. I found it very interesting and enjoyable to read. There are a couple of minor edits that I propose to the paper before acceptance:

Could a summary table be utilised in the review of Literature to provide an overview of the previous research and areas that it has focused on? The literature review is fine, however it would aid the reader to have some sort of summary first with commentators below.
Could the materials and methods be moved to section 2? I found it quite confusing and kept having to read section 4 first before reading the results.
Minor typos - line 275 missing 'the' and line 552-555 minor formatting issues.

Author Response

Dear reviewer,

thank you for your detailed and comprehensive review. To correct deficiencies, enhance the manuscript and make it more valuable, we made following major changes and revisions.

We’ve changed the whole structure of the research paper:

Abstract

Introduction
Literature review
Research Design
Results

4.1 Testing prosperous businesses

4.2 Testing businesses in difficulty

4.3 Testing non-prosperous companies

4.4 General findings

Discussion
Conclusions

We’ve created a new version of Abstract:

“The aim of this paper is to assess the reliability of alternative default prediction models in local conditions, with subsequent comparison with other generally known and globally disseminated default prediction models. The comparison was carried out on a sample of 90 companies operating in the Slovak Republic over a period of 3 years (2016, 2017 and 2018) with a narrower focus on three sectors: construction, retail, and tourism. To verify the reliability of these models, tests of the significance of statistical hypotheses were used, such as type I and II error. According to research results, the highest reliability and accuracy was achieved by alternative default prediction models, originated in local conditions. Significant differences between sectors were identified.”

We’ve prepared a new version of Introduction:

In the current turbulently changing and uncertain economic environment, demand on the reliability and validity of the tools used to predict companies' financial health and financial distress is growing. Using default prediction models to assess companies' financial situation, and to separate prosperous from non-prosperous companies, or solvent from insolvent ones, has become a standard. Default prediction models are primarily based on the information provided by financial statements, transformed into ratios. Financial statements are the basic and sometimes the only available source of information. According to Zalai, et al. (2016), it is evident that the indicators of successful companies differ significantly from indicators of non-prosperous companies several years before bankruptcy, both as the absolute level and annual change. Default prediction models aim to classify companies as future prosperous (solvent) or non-prosperous (insolvent) companies (Zalai, et al., 2016).

To assess the financial health or financial distress of companies, several well-established default prediction models are being used on a global scale. These well-known models, such as Altman Z-score or Quick Test, are applied in different local conditions, regardless of the specifics of the environment in which they originated and the differences between the original business environment and the environment in which they are applied. Yet, several alternative models are emerging in different regions and localities, aiming to reflect the given market's specifics and thus increase the reliability and decrease the error rate of the company's financial health assessment. Authors of this research paper are focused on testing the reliability and error rate of such alternative models in local conditions and comparing this reliability with the reliability of the most used standard prediction models in specific local conditions. When selecting a locality, the criterion of a high concentration of alternative models in the given locality was applied, i.e., a high number of alternative prediction models compared to the size of the market in which they are being applied. From the spectrum of European national markets, the Czech and Slovak Republics were chosen. These countries could be characterized by many published models, and largely interconnected market with the presence of many similarities in the terms of market structure, corporate finance, business legislation, accounting, and reporting, etc. Eight alternative default prediction models were identified in Slovak market, while IN group models were taken from the Czech market and were tested on a sample of 90 companies from three different industries. The reliability and error rate of these models were evaluated and compared to the reliability and error rate of standard prediction models such as Altman’s Z-score, Quick Test, Binkert’s Model, Creditworthiness Index and Taffler's Model.

We’ve created a separate section 2. Literature review, which includes the original version of 1. Introduction, extended using additional literature sources, focused on testing default prediction models in other countries.

“The scientific literature provides a very wide range of default prediction models for assessing the financial health and financial distress of companies. The reliability of these models is the subject of research of many scientists. In the following section, the latest global scientific efforts to test the reliability of default prediction models are summarized. Given the main goal of this research, this paper is primarily focused on local models created in the Slovak and Czech Republic, which are not generally known. Subsequently, selected globally disseminated models are briefly described, the reliability of which was further compared with alternative default prediction models. At the end of this section, results of previous studies are summarized.

In CEE (Central and Eastern Europe) region, due to the geopolitical situation and the introduced economic system, the issue of default predictions started to be the subject of research starting in 90’s. Prusák and Blažej (2018) analyzed the level of advancement in these countries and came to conclusion that the most advanced research in this area is conducted in Visegrad countries (Czech Republic, Slovak Republic, Poland, Hungary), Estonia, and Russia. Kristóf and Virág (2020) conducted a comprehensive analysis based on 30 years of Hungarian empirical results and concluded that considering the validity of a key theoretical finding that no bankruptcy prediction model might function independently of time, space, and economic environment, it is not recommended to apply bankruptcy models on Hungarian companies that were developed on a foreign sample. This conclusion was confirmed by Singh and Mishra (2016), based on their research on a sample of Indian companies. An Estonian scientist Korol (2020) applied logistic regression and multilayer perceptron to predict bankruptcy using tax arrears’ information and came to conclusion that models created indicate that shortly before bankruptcy, tax arrears’ models outrun the financial ratio-based models in terms of accuracy. The accuracy reduces when further periods before bankruptcy declaration are considered. The highest accuracy is obtained by using tax arrears and financial ratios simultaneously.”

We’ve renamed Table 1. List of local default prediction models and Table 2. Parameters of local default prediction models. We’ve also made some adjustments in Table 1 and Table 2 to make the content of these tables clearer.

We’ve transferred 4. Materials and methods before 4. Results and renamed to 3. Research design. We’ve made some changes in the content of this section, including the main aim of the research paper.

comparison of the results of locally originated default prediction models with globally accepted models,
comparison of the explanatory value of these models among selected sectors,
evaluating the applicability of examined models for predicting companies' financial distress, considering the sector of economy.”

In this section, we’ve described the process of selecting the research sample in more details. We’ve specified the number of companies within each group (prosperous, non-prosperous companies and companies in difficulty). We’ve defined each category of companies, focusing primarily on companies in difficulty, which determines borders between these three categories. We’ve also described the process of selection of prosperous companies out of the major group of companies, using further criteria: 2^nd level liquidity and Return on Sales (ROS), as described in the revised version of manuscript.

“The explanatory value of selected default prediction models was tested on a specific sample of 90 companies over the period of 3 years (2016, 2017, 2018). The FinStat and Credit Bureau Slovakia databases were used to select a sample of companies. The essential selection of the sample was carried out according to precisely defined criteria:

SME’s (small and medium-sized companies) defined in terms of categorising business entities according to the size following the European Commission's recommendation 2003/361/EC effective from January 2005, (less than 250 employees, and turnover less than EUR 50 million);
companies accounting in the double-entry bookkeeping system following Act no. 431/2002 Coll. on Accounting and MEASURES of the Ministry of Finance of the Slovak Republic of 16^th December 2002 no. 23054/2002-92 specifying details of accounting procedures and a general chart of accounts for businesses accounting in the double-entry bookkeeping system;
companies with the legal form of a limited liability company.

Regarding the accuracy and purpose of the research, the first selection of sectors was conducted based on the general relevancy of the sector, especially the size of businesses operating in sector, employment, share of GDP, and a higher risk of insolvency and bankruptcy.

The final selection was based on the following criteria: number of enterprises in the sector, the average share of liabilities, and the survival rate (the share of companies operating in the sector at least for 5 years on the total number of entities established at the initial period). The highest number of enterprises was recorded in the services sector (46.10%), retail sector (19%) and construction sector (17%). The highest share of liabilities in 2018 was recorded in retail sector (65.16%), and construction sector (54.80%). The lowest survival rate (SBA, 2019) was recorded in construction sector (37.4%), and services sector (41.2%). Based on these results, three sectors were selected, namely construction sector, retail sector and services. Services sector contains a wide range of business activities. It was therefore necessary to reduce the internal heterogeneity by focusing on a narrower range of business activities. Out of the services sector, subset of companies operating in tourism was selected.

To create a sample of companies, following criteria were applied:

Annual sales from 30 thousand up to 50 mil. EUR. The intention of setting the lower limit was to eliminate non-operating companies and very small companies. The upper limit represents the constraint for classifying a company as SME (small and medium-sized enterprise).
Type of ownership - private domestic.
Date of the business establishment no later than 31^st December 2014. The period considered in this research was 3 accounting periods (2016, 2017 and 2018), during which the stability of the company was assessed, by analysing continuous development of sales and economic results. Start-ups could report very specific results during the initial year. This factor could greatly distort the research results. Therefore, only companies operating more than 1 year were assessed. The other reason for setting this criterion is the definition of a company in difficulty (EC, 2014), according to which businesses that exist less than three years are excluded from this category. The research period (2016, 2017 and 2018) was not affected by the systematic risk, the source of which was the global pandemic.
Number of employees up to 250. This criterion represents an upper limit for classifying a company as SME.

Within the focus and needs of research, companies meeting the above criteria were divided into 3 groups, reflecting the local legislation, namely non-prosperous companies, companies in difficulty, and prosperous companies. It was crucial to properly define companies in difficulty. For this purpose, following legislation was applied: (EK, 2014) Communication from the Commission — Guidelines on State aid for rescuing and restructuring non-financial undertakings in difficulty (2014/C 249/01), and (EK, 2014) Commission Regulation (EU) No 651/2014 of 17 June 2014 declaring certain categories of aid compatible with the internal market in application of Articles 107 and 108 of the Treaty Text with EEA relevance. Based on this legislation, non-prosperous companies are companies with negative equity, companies in difficulty are companies with equity less than half of a share capital. Prosperous companies could be therefore defined as companies with the equity higher than a half of share capital. The structure of a sample gathered applying this criteria is presented in the following exhibit.”

Exhibit 1. Share of prosperous, non-prosperous companies, and companies in difficulty in selected sectors

Based on the above described procedure, we separated prosperous from nonprosperous companies. However, applying this procedure a homogeneous sample of prosperous companies has not being created yet. The lower limit of the interval for the 2^nd level liquidity was set to 1.0. The median ranged from 0.88 in Tourism sector to 1.32 in Construction sector. The Return on Sales (ROS) was applied as the secon selection criterion. The acceptance interval was chosen at the level of the upper quartile for each sector separately (3.78% in Tourism sector, 4.01% in Construction sector, and 9.22% in Retail sector).”

We’ve restructured the section 4. Results and created subsections 4.1 Testing prosperous businesses, 4.2 Testing businesses in difficulty, 4.3 Testing non-prosperous companies, and 4.4 General findings. We’ve corrected data included in Table 4. Results of testing prosperous businesses in construction sector. We’ve also corrected format of data presentation (dots instead of commas).

We’ve transferred the following part of 5. Discussion and included it in 4. Results:

“The assessed reliability of default prediction models enabled us to distinguish models with higher reliability from models with insufficient reliability. However, the models' success rate was set not only due to its high reliability but also due to its low error rate. The error rate was given as a type I error in the case of companies in bankruptcy, i.e., the number of non-prosperous companies incorrectly classified as healthy to all non-prosperous companies, and type II error in healthy companies, i.e., the number of prosperous companies incorrectly classified as unhealthy to the number of all prosperous companies. In the research, we also considered the middle category of average companies, and dealt with this category as with an auxiliary category for the final assessment purposes, based on type I and II errors and assigned it to healthy companies. It means that if a successful company was classified as an average company, it was appropriately classified. However, if an average company was classified as a company in bankruptcy, this was considered an incorrect result.

The high success rate determined the final selection of suitable models in the case of companies in bankruptcy, eliminating the type I error. The consequences of a type I error are more dangerous, because classifying a non-prosperous company as a healthy one brings many risks for the management, owners, investors, and creditors. The following table lists the models characterised by high reliability and low error rate.

Table 9. Error rate assessment

Model	Tourism		Construction		Retail
Model	Type I error	Type II error	Type I error	Type II error	Type I error	Type II error	Average	Rank
G-Index	.40	.00	.20	.00	.00	.00	.100	3
Model of Delina a Packova	.00	.10	.00	.10	.00	.00	.033	1
Model of Gulka	.60	.00	.10	.00	.00	.00	.117	4
Altman Z-score	.20	.10	.60	.00	.20	.00	.183	7
INDEX IN05	.00	.10	.20	.00	.10	.00	.067	2
Quick Test	1.00	.00	.00	.00	.00	.00	.167	6
Creditworthiness Index	.40	.00	.30	.00	.00	.00	.117	4

Source: Own table

Based on the overall average error rate, the order of successful models was set for all sectors. It is shown in the above table's last column. From the comparison between the sectors, the differences in the models’ error or success rates are apparent. It must be acknowledged that the cross-sectoral results could be distorted by the small number of companies within the sectors and that this claim should be verified on a larger sample of companies.”

We’ve deleted the final part of the original version of 5. Discussion, and we’ve transferred part of the original version of 6. Conclusion and included it in the revised version of 5. Discussion:

We’ve prepared a new version of 6. Conclusion:

Economist and statistician George P. E. Box (1987) said, ‘Basically, all models are incorrect, but some are useful’. This statement fits for models of predicting financial distress. The research results have shown that some models could be classified as unreliable because of their inablity to detect impending decline. This research identified also a group of models which were incorrectly penalizing healthy companies. Only few models were delivering reliable results, and could be used in real conditions to support qualified economic decisions. We consider results of this research to be directly applicable when selecting and choosing a suitable model for financial distress assessment.

Research has shown a higher reliability of alternative default prediction models, which were designed in local conditions, compared to globally disseminated default prediction models. This fact is evident from table no. 9, which presents the final evaluation of models included in testing. However, significant differences in reliability were identified across the spectrum of alternative default prediction models, but also across industries. It should be emphasized that a large group of unreliable models within the group of alternative default prediction models was identified. This subset of models was excluded from further testing.

This research confirmed doubts about the reliability of some models, which were proposed by several studies quoted in this paper, e.g. CH-index and Tafflers’ model. Different approaches applied by different scientists to defining a sample and methodology for evaluating the reliability resulted in a low degree of comparability of these studies. We consider the methodology proposed in this paper as a possible benchmark for further research.

This research has demonstrated a higher reliability of alternative default prediction models, which originated in local conditions. It is reasonable to assume similar findings in other local markets. Further research territorially targeting other markets is therefore necessary.

We’ve tried to fix all formal aspects that were brought up during the review (e.g. abbreviations, equations and the description of parameters, format, dots instead of commas, table labels, …).

We’ve excluded the term company in crisis and company in bankruptcy, and we’ve explained company in difficulty in the section 3. Research design.

In the Slovak Republic, where default prediction models where tested, the minimum amount of the share capital is set to € 5,000. We’ve excluded companies in the initial phase of their life cycle (the 1^st year). We’ve included Equity as an important criterion based on EC Directives, as stated in the revised version of the manuscript (section 3. Research design).

Due to the large number of models, the table was chosen as a suitable form of brief presentation of the models’ specifics. We haven’t described these specifics separately in the text bellow.

We’ve made corrections regarding quotations/references, incl. the section 3. Research design.

The selection of research period is described in the revised version of 3. Research design. The selection of local bankruptcy prediction models is not separately discussed. We’ve included all known local models, which originated in Slovak conditions.

Reviewer 2 Report

Dear authors, the approach used for testing bankruptcy prediction models for the case of Slovakian enterprises is really interesting, nevertheless, there are some conceptual as well as formal problems in the manuscript and these problems must be solved before the publication.

The abstract of the manuscript should be improved to represent clearly the main purpose of the research as well as the main results and their relevance both from a scientific and practical perspective.
It would be highly recommendable for the authors to think whether it is possible to situate their research in a broader (not only national) context because present results are important only for Slovakian scientists and practitioners.
It is also highly recommendable to expand the Literature review section and analyze much more scientific researches - not only Slovakian or regional ones. In the reviewer's opinion, the latest global scientific efforts must be analyzed and summarized.
The structure of the manuscript itself must be reorganized - it is usually expected the manuscript to have an introductory part (where the main goal and objectives, hypotheses, and methods are clearly stated), moreover, the research design (methodology) is usually discussed before results.
The authors must pay much more attention to the conclusions section because at the present form conclusions are not very well developed and lacks scientific and practical value. Suggestions / recommendations / implications for future research are also welcomed.
The selection of bankruptcy prediction models and research period must be discussed more clearly (argumentation is necessary).
Table 1 and Table 2 - the same title. There are other repetitions (titles of tables, titles of subsections, etc.).
English editing is necessary.

Taking everything into account, much more effort is necessary in order for this article could be published.

Good look at your researches.

Author Response

Dear reviewer,

thank you for your detailed and comprehensive review. To correct deficiencies, enhance the manuscript and make it more valuable, we made following major changes and revisions.

We’ve changed the whole structure of the research paper:

Abstract

Introduction
Literature review
Research Design
Results

4.1 Testing prosperous businesses

4.2 Testing businesses in difficulty

4.3 Testing non-prosperous companies

4.4 General findings

Discussion
Conclusions

We’ve created a new version of Abstract:

We’ve prepared a new version of Introduction:

comparison of the results of locally originated default prediction models with globally accepted models,
comparison of the explanatory value of these models among selected sectors,
evaluating the applicability of examined models for predicting companies' financial distress, considering the sector of economy.”

SME’s (small and medium-sized companies) defined in terms of categorising business entities according to the size following the European Commission's recommendation 2003/361/EC effective from January 2005, (less than 250 employees, and turnover less than EUR 50 million);
companies accounting in the double-entry bookkeeping system following Act no. 431/2002 Coll. on Accounting and MEASURES of the Ministry of Finance of the Slovak Republic of 16^th December 2002 no. 23054/2002-92 specifying details of accounting procedures and a general chart of accounts for businesses accounting in the double-entry bookkeeping system;
companies with the legal form of a limited liability company.

To create a sample of companies, following criteria were applied:

Annual sales from 30 thousand up to 50 mil. EUR. The intention of setting the lower limit was to eliminate non-operating companies and very small companies. The upper limit represents the constraint for classifying a company as SME (small and medium-sized enterprise).
Type of ownership - private domestic.
Date of the business establishment no later than 31^st December 2014. The period considered in this research was 3 accounting periods (2016, 2017 and 2018), during which the stability of the company was assessed, by analysing continuous development of sales and economic results. Start-ups could report very specific results during the initial year. This factor could greatly distort the research results. Therefore, only companies operating more than 1 year were assessed. The other reason for setting this criterion is the definition of a company in difficulty (EC, 2014), according to which businesses that exist less than three years are excluded from this category. The research period (2016, 2017 and 2018) was not affected by the systematic risk, the source of which was the global pandemic.
Number of employees up to 250. This criterion represents an upper limit for classifying a company as SME.

Exhibit 1. Share of prosperous, non-prosperous companies, and companies in difficulty in selected sectors

We’ve transferred the following part of 5. Discussion and included it in 4. Results:

Table 9. Error rate assessment

Model	Tourism		Construction		Retail
Model	Type I error	Type II error	Type I error	Type II error	Type I error	Type II error	Average	Rank
G-Index	.40	.00	.20	.00	.00	.00	.100	3
Model of Delina a Packova	.00	.10	.00	.10	.00	.00	.033	1
Model of Gulka	.60	.00	.10	.00	.00	.00	.117	4
Altman Z-score	.20	.10	.60	.00	.20	.00	.183	7
INDEX IN05	.00	.10	.20	.00	.10	.00	.067	2
Quick Test	1.00	.00	.00	.00	.00	.00	.167	6
Creditworthiness Index	.40	.00	.30	.00	.00	.00	.117	4

Source: Own table

We’ve prepared a new version of 6. Conclusion:

We’ve excluded the term company in crisis and company in bankruptcy, and we’ve explained company in difficulty in the section 3. Research design.

Due to the large number of models, the table was chosen as a suitable form of brief presentation of the models’ specifics. We haven’t described these specifics separately in the text bellow.

We’ve made corrections regarding quotations/references, incl. the section 3. Research design.

Reviewer 3 Report

The paper has many limitations and weaknesses which are described below. These issues can be corrected and therefore the final version of paper can be significantly improved. The structure of the paper is difficult for the readers when methods, materials are described and explained after results and discussion. The structure of the paper is not presented in advance. Formulas of some applied models are not clear and therefore they do not allow replication of research. The selection of companies is not described step by step and therefore the replication of research is not possible. Specific areas focused on research issues, grammar issues or formal issues are discussed below. Author/s should follow the recommendations because the reader should be oriented and provided by clearly stated information.

Research issues

Sample structure is not clear. Number of healthy and unhealthy enterprises is not specified for each sector. Line 560 mentions 90 companies in total but the structure should be specified.
Methods applied are not described before the results are presented. Chapter 4 is dedicated to methods and materials but this chapter is after Results and Discussion. Introduction could contain the description of paper structure which would guide the reader through the paper. The followed structure is not typical.
Line 256 – companies with negative equity are discussed but it is not clear why this kind of companies is important.
Chapter 2 – results are presented for 3 subsamples (prosperous companies, businesses in difficulty and non-prosperous companies). Chapter 4 is dedicated to methods and materials but this chapter is after Results and Discussion. Introduction could contain the description of paper structure which would guide the reader through the paper. The followed structure is not typical. It is extremely difficult for the reader to be orientated.
Line 431 – what is meant by CR sector? Abbreviations should be explained or not used when it is not necessary.
Part Discussion focuses on error rate and accuracy rate although they were not explained yet. Chapter 4 is dedicated to methods and materials but this chapter is after Results and Discussion. Introduction could contain the description of paper structure which would guide the reader through the paper. The followed structure is not typical. It is extremely difficult for the reader to be orientated.
Table 9 should be a part of results and not discussion.
End of discussion just looks as notes and not finalized version.
Discussion should take more attention to the differences between selected industrial sectors which could influence the testing.
The term company in difficulty according to the legislation is not explained. The same is valid for company in crisis and company in bankruptcy (lines 550 and 529).
Line 584 – the company with negative equity - the weakness of this indicator should be discussed, especially in the case of legal form limited liability company. Companies can be set up with almost no equity.
It is not clear how prosperous companies have been selected.
Liquidity of the 2^nd degree should be defined and recommended ranges are very sensitive according to the industry sector.
Lines 508 and 509 mention type II error but according to the context type I error is meant.
Conclusion is very short, seems unfinished, next ways of research are not mentioned, clear recommendations for practise are not provided because especially the belonging to industry should be highlighted and general working of models (only probabilistic roots).
Applied methods – F1 score, sensitivity, specificity, type II error, type I error are not based on the literature review.
Specifics of applied models are not discussed – CH index and G index were constructed for agriculture and therefore it is not a surprising results that these models do not reach high accuracy in the case of other sectors.

Tables

Table 1

Sector's description in the case of Model of Hurtošová is unclear.
Sector's description in the case of M-model is missing.

Table 2

The title is written separately on the previous page.
The numbers should use decimal points instead of decimal commas.
Some equations are difficult to read because there are overlaps of the text.
Liquidity 3^rd is not defined.
HGN2 model – prosperous and non-prosperous criteria seem to be switched.
Formulas should checked because some parts seem to be incorrect, unfinished, not fully defined.
Formulas should be fully clear otherwise they do not allow research to be replicated by others. Attention should be taken to the issues such as profit or loss (which kind of profit?), minus 1 (part of fraction or not?), inventory turnover/salesx365 (it seems as double turnover), economic activity and financial activity (clear definitions of areas), definition of share capital or total output, HGN2 model – should net profit + depreciation be in bracket?, M-model almost in each indicator missing brackets, what does VH mean?, Model of Gulka – what do total financial accounts and BITDA mean?

Table 3

The title is written separately on the previous page.
The numbers should use decimal points instead of decimal commas.

Table 4

The numbers should use decimal points instead of decimal commas.
The table is divided into two pages.

Table 5

The numbers should use decimal points instead of decimal commas.
The table is incorrect because it is the same table as for the construction industry and therefore the text does not reflect the data displayed in the table.

Table 6

The numbers should use decimal points instead of decimal commas.
The table is divided into two pages.

Table 7

The numbers should use decimal points instead of decimal commas.

Table 8

The numbers should use decimal points instead of decimal commas.
The table is divided into two pages.

Grammar issues

Line 18 - The paper contains several informal collocations such as on the other hand.
Line 51 – Following table is presenting – simple tense would be more appropriate.
Line 58 – The sentence should be finished.
Oxford comma is missing repeatedly in the text – line 63, line 66, line 143
Line 497 – dis issue - unclear

References

Line 70 – When was the Altman paper published? In 2002 or 2012? The text does not match with the reference list.
Line 75 – the source Neumaierová and Neumaier is not included in the reference list.
Line 101 - the source Machek is not included in the reference list.
The names of authors should be written fully and not only partially corrected such as Čámská, Klečka, Režňáková, Gavurová etc.
Line 258 – The year of Gurský source is not mentioned in the text.
Line 711, 712 – The source details are not written in the original language but they are translated.

Formal issues

It should be checked if the journal's template enables footnotes. It is generally recommended to include the text written in footnotes into the main text.
Subchapters of chapter 2 are chosen vaguely. Testing of prosperous companies should contain other 3 subchapters and the same is valid for testing businesses in difficulty and for testing non-prosperous companies.
Some subchapters starts directly with the table without any introduction text.
Line 416 – there is a double space before Gulka.
Line 427 and further – these sentences should not be a part of Retail sector because they are valid generally.
Line 619 – empty line

Author Response

Dear reviewer,

thank you for your detailed and comprehensive review. To correct deficiencies, enhance the manuscript and make it more valuable, we made following major changes and revisions.

We’ve changed the whole structure of the research paper:

Abstract

Introduction
Literature review
Research Design
Results

4.1 Testing prosperous businesses

4.2 Testing businesses in difficulty

4.3 Testing non-prosperous companies

4.4 General findings

Discussion
Conclusions

We’ve created a new version of Abstract:

We’ve prepared a new version of Introduction:

comparison of the results of locally originated default prediction models with globally accepted models,
comparison of the explanatory value of these models among selected sectors,
evaluating the applicability of examined models for predicting companies' financial distress, considering the sector of economy.”

SME’s (small and medium-sized companies) defined in terms of categorising business entities according to the size following the European Commission's recommendation 2003/361/EC effective from January 2005, (less than 250 employees, and turnover less than EUR 50 million);
companies accounting in the double-entry bookkeeping system following Act no. 431/2002 Coll. on Accounting and MEASURES of the Ministry of Finance of the Slovak Republic of 16^th December 2002 no. 23054/2002-92 specifying details of accounting procedures and a general chart of accounts for businesses accounting in the double-entry bookkeeping system;
companies with the legal form of a limited liability company.

To create a sample of companies, following criteria were applied:

Annual sales from 30 thousand up to 50 mil. EUR. The intention of setting the lower limit was to eliminate non-operating companies and very small companies. The upper limit represents the constraint for classifying a company as SME (small and medium-sized enterprise).
Type of ownership - private domestic.
Date of the business establishment no later than 31^st December 2014. The period considered in this research was 3 accounting periods (2016, 2017 and 2018), during which the stability of the company was assessed, by analysing continuous development of sales and economic results. Start-ups could report very specific results during the initial year. This factor could greatly distort the research results. Therefore, only companies operating more than 1 year were assessed. The other reason for setting this criterion is the definition of a company in difficulty (EC, 2014), according to which businesses that exist less than three years are excluded from this category. The research period (2016, 2017 and 2018) was not affected by the systematic risk, the source of which was the global pandemic.
Number of employees up to 250. This criterion represents an upper limit for classifying a company as SME.

Exhibit 1. Share of prosperous, non-prosperous companies, and companies in difficulty in selected sectors

We’ve transferred the following part of 5. Discussion and included it in 4. Results:

Table 9. Error rate assessment

Model	Tourism		Construction		Retail
Model	Type I error	Type II error	Type I error	Type II error	Type I error	Type II error	Average	Rank
G-Index	.40	.00	.20	.00	.00	.00	.100	3
Model of Delina a Packova	.00	.10	.00	.10	.00	.00	.033	1
Model of Gulka	.60	.00	.10	.00	.00	.00	.117	4
Altman Z-score	.20	.10	.60	.00	.20	.00	.183	7
INDEX IN05	.00	.10	.20	.00	.10	.00	.067	2
Quick Test	1.00	.00	.00	.00	.00	.00	.167	6
Creditworthiness Index	.40	.00	.30	.00	.00	.00	.117	4

Source: Own table

We’ve prepared a new version of 6. Conclusion:

We’ve excluded the term company in crisis and company in bankruptcy, and we’ve explained company in difficulty in the section 3. Research design.

Due to the large number of models, the table was chosen as a suitable form of brief presentation of the models’ specifics. We haven’t described these specifics separately in the text bellow.

We’ve made corrections regarding quotations/references, incl. the section 3. Research design.

Round 2

Reviewer 2 Report

The authors have implemented significant changes. Thus, in the present form, the paper deserves to be published.

Author Response

Thank you for your valuable recommendations, comments and notes during the revision process.

Reviewer 3 Report

The paper has been significantly improved especially in the case of the paper structure. Many limitations and weaknesses have remained although they were highlighted in the previous review and some new flaws have occurred in the current version. The paper keeps its potential and therefore the reviewer will provide the detailed description of improvements. The reviewer is very benevolent because most of the work should have been done by the authors before the manuscript submission. The structure of the paper is not presented in advance. The structure could be presented at the end of introduction and therefore it would be introduced to the reader in advance before reading the full paper. The selection of companies is not described step by step and therefore the replication of research is not possible. Specific areas focused on research issues, grammar issues or formal issues are discussed below. Author/s should follow the recommendations because the reader should be oriented and provided by clearly stated information.

Research issues

Abstract seems very short. The importance of the solved topic should be highlighted. Specific models applied could be mentioned.
Sample size is extremely small because 10 companies belong to the group of prosperous companies, 10 to companies in difficulty, and 10 to non-prosperous companies. The total sample consists of 90 companies because there are 3 sectors analysed. 10 companies in each category is very low number for reliable scientific results.
Chapter 3 describes as the research methods accuracy rate, accuracy adj., F1 score, sensitivity specificity. Results are based only on the correct and incorrect classification of the analysed business entities. Paper should focus only on the methods which are applied and not describe additional methods which were not employed herein. Line 664 contains the statement that results are based on these methods. Repetition of this statement is on the line 707. Any numbers and results of these methods have not been presented in the paper.
Methods described in the chapter 3 - F1 score, sensitivity, specificity, type II error, type I error are not based on the literature review any previous recommendations and experience.
Discussion should take more attention to the differences between selected industrial sectors which could influence the testing. Discussion should focus only on the original industry areas of the tested models.
The company with negative equity - the weakness of this indicator should be discussed, especially in the case of legal form limited liability company. Companies can be set up with almost no equity.
It is not clear how prosperous companies have been selected. Criteria are provided in the text what the companies should fulfil but exhibit 1 shows that the number of companies in the affected sectors of all three types (prosperous companies, companies in difficulty, and 10 to on-prosperous companies) is much higher than the final number 10. Exhibit 1 proves that more options/combinations of 10 companies in each subcategory are possible.
Exhibit 1 – it is not clear for which year the numbers are valid and the data source is not mentioned.
Line 319 - Liquidity of the 2^nd level should be defined. What is the liquidity of the 2^nd level?
Conclusion has been extended but limitations of the current paper should be highlighted and presented more clearly. Recommendations for practise are essential and especially the belonging to industry should be highlighted. General working of models is based on the probabilistic roots and verification on the sample of 10 companies seems to be not reliable.
Specifics of applied models are not discussed – CH index and G index were constructed for agriculture and therefore it is not a surprising results that these models do not reach high accuracy in the case of other sectors.
Table 2 and Equation 1 display formulas of the specific models applied in the paper. Formulas such as Altman Z-Score, Quick test, Creditworthiness Index and Model of Taffler are missing and the original references are not mentioned at all. The authors even highlight that there are more versions of some models and they are not sure themselves which versions were applied in previous research works but they repeat the same steps.
Line 356 – The explanation of random match Pe is not provided.
Lines 320-324 – the authors decided some values of criteria liquidity and ROS. This decision is not based on anything. This is not any scientific approach to the solved issue.
Lines 362 and 363 should be checked if the provided formulas are correct because their current version does not seem consistent with the research aim.
The sample covers the years 2016, 2017, and 2018. It is not clear how it is worked with these three different years. Are the financial data valid for 2016, 2017, or 2018?
The research is based on three subsamples but only results for 60 companies are clearly presented – for prosperous and non-prosperous companies. The companies in difficulty are left aside in the part of results and they came back in the part of general findings.
Line 616 – what is the average company? How is this company defined? Such kind has been not mentioned yet. Is this expression used for companies in difficulty how lines 708-710 write?
Lines 618-621 are difficult to understand because it is written of average company which has not been explained yet. This company is classified as a successful company and decision is done. This company is classified as a company in bankruptcy and decision is done. Who has decided which decision is correct and which is incorrect? This decision is not based on anything. This paper should be an example of research scientific paper.
Line 676 – unclear sentence – how are the models mentioned in the bracket connected with Siekelová and IN05 presented in the previous sentence?

Tables

Table 1

Sector's description in the case of Model of Hurtošová should be mentioned with the small letter as in the case of other models.

Table 2

Table 2 covers almost two full pages and therefore it could be organised as an appendix and not in the main text.
The numbers should use decimal points instead of decimal commas but 0 should be included in the formulas as well. The number 0.37 should not be written as .37. 0 omitting is unclear for readers. This note is connected with all models presented. The same is valid for IN05 model displayed on the line 109.
Model of Binkert - Liquidity 3^rd is not defined. What does st. stand for?
Model of Binkert – the first, second, third year are not defined and therefore the work replication is impossible.
Under the formula of Binkert model unclear sentence is located because of the used language.
HGN2 model – criteria for prosperous and non-prosperous seem to be switched.
Formulas should checked because some parts seem to be incorrect, unfinished, not fully defined.
Formulas should be fully clear otherwise they do not allow research to be replicated by others. Attention should be taken to the issues such as costs of operations, EBAT, share capital, prevádzkové náklady, working capital, production).
Formulas of individual indicators sometimes contains extra space/s.
Formulas included in the table contain different multiplying signs, sometimes no multiplying signs were used. The style should be unified.

Table 3

This table has incorrect numbering because the current version contains the number 10 instead of 3. This should change the numbering of all following tables. Further Table 3 is the Table 4 etc.

Tables displaying research results

Accuracy rates and Misclassifications rates are displayed without zeros. The number 0.3 should not be written as .3. 0 omitting is unclear for readers.

Current table 9 called Error rate assessment

This table is inconsistent with the previous tables presenting results and if it is included in general findings the reader would expect that it is based on already presented results which are now provided in different form.
It is unclear how the average was counted.
Which data are included in the table? Which subsample of companies is taken into account?
It seems impossible that general findings are based on this table when this table is inconsistent with previous tables providing results for prosperous and non-prosperous companies belonging to different sectors.

Grammar issues

Line 5, 7, 9, 11 – affilation – Faculty should be written with the large letter because it is the name of affilation.
Lines 17, 290, and 297 – Oxford comma is needed before and 2018.
Line 57 – Oxford comma before and Taffler's Models.
Line 88 – The sentence should be finished with . and not with :.
Line 179 - Oxford comma before and IN05.
Line 276 and 277 when only two sectors are described then the Oxford comma should not be written.
Line 279 - Oxford comma before and services.
Line 318 – non-prosperous companies should be written.
Line 321 – second instead of secon should be written.
Line 353 – Oxford comma before and false negative cases.

References

Line 79 – the scientist Korol is not Estonian but Polish focusing especially on Polish data.
The names of authors should be written fully and not only partially corrected such as Čámská, Klečka, Režňáková, Gavurová etc. Attention to special alphabet does not have to be taken at all but when the specific signs are used then all specific signs of one particular name should be applied.
Line 445 – the source Řezbová is not included in the reference list.
Line 785, 844 – The source details are not written in the original language but they are translated into the other local language. The references should be written fully in original – titles, place publisher etc.
Line 821 – what does 2. vydanie stand for in the case of English reference?

Formal issues

Lines 67 and 84 – the spaces between paragraphs seem bigger.

Author Response

Dear reviewer,

thank you again for reviewing the proposed research paper/article and providing us with valuable insights. Following your instructions, comments, and suggestions, we’ve made following changes.

The importance of the solved topic was highlighted in Abstract. It also includes the list of models applied.

“In the current volatile and interconnected economic environment, comprehensive synthetic approaches to financial health assessment came to the forefront of interest, represented by default prediction models. In recent decades, scientists and researchers have been intensively searching for the ideal default prediction model, both at the international level and at the national level, considering the specifics of domestic economies. The aim of this paper is to assess the reliability of alternative default prediction models in local conditions, with subsequent comparison with other generally known and globally disseminated default prediction models, such as Altman’s Z-score, Quick Test, Binkert’s Model, Creditworthiness Index, and Taffler's Model. The comparison was carried out on a sample of 90 companies operating in the Slovak Republic over a period of 3 years (2016, 2017, and 2018) with a narrower focus on three sectors: construction, retail, and tourism, using alternative default prediction models, such as CH-index, G-index, Binkert’s Model, HGN2 Model, M-model, Gulka’s Model Hurtošová’s Model, and Model of Delina and Packová. To verify the reliability of these models, tests of the significance of statistical hypotheses were used, such as type I and II error. According to research results, the highest reliability and accuracy was achieved by alternative default prediction models, originated in local conditions. Significant differences between sectors were identified.”

The structure of the research paper is presented in advance, included at the end of introduction, to introduce the structure to the reader before reading the full paper.

“The following section focuses on a literature review, especially in relation to default prediction models, which are the subject of reliability and accuracy assessment. Due to the limited scope of this research paper, the construction and parameters of alternative default prediction models (Appendix A) and globally disseminated models (Appendix B) were included in the appendices. The literature review continues with an overview of previous research in the field of evaluating the reliability of these models. The next section is dedicated to research design, where the research goals, methods and procedures applied in this research are described. The main research results are presented in section 4, separately for testing prosperous companies, companies in difficulty, and non-prosperous companies. Given the purpose of assessed models, the emphasis is placed mainly on testing non-prosperous companies. The research results are supplemented by general findings. The reported results are supported by partial analytical results listed in appendices (Appendix C, …, Appendix I). These results are further discussed in the section 5. Discussion and summarized in the section 6. Conclusion, which also includes the limitations related to the research presented.”

The selection of companies is described step by step to allow the replication of research. We adjusted mainly the text below the Exhibit 1.

“Based on the above described procedure, prosperous from non-prosperous companies were separated, as shown in Exhibit 1. However, applying this procedure a homogeneous sample of prosperous companies has not being created yet. We do not consider defining prosperous companies as companies with equity higher than a half of their share capital as sufficient. According to Brealey, Myers, and Allen (2016), liquidity and profitability are the two basic financial goals of a company, which in mutual interaction demonstrate the solvency and the ability to achieve financial results. Therefore, the 2^nd level liquidity as the first indicator was selected. This indicator is calculated as the sum of financial accounts and short-term receivables divided by short-term liabilities. This indicator is also known as quick liquidity. It expresses the ability to cover short-term liabilities of the company with financial accounts and short-term receivables (Zalai et al., 2016). The median of this indicator ranged in 2018 from 0.88 in Tourism sector to 1.32 in Construction sector. The lower limit of the interval for the 2^nd level liquidity was therefore set to 1.0. As the profitability indicator, the Return on Sales (ROS) was applied, calculated as EBIT divided by total sales. The acceptance interval was chosen at the level of the upper quartile for each sector separately (3.78% in Tourism sector, 4.01% in Construction sector, and 9.22% in Retail sector). A random sample was made from such a narrowed sample of prosperous companies.

From the processed data of a total sample of 11,168 small and medium-sized enterprises operating in the tourism, construction, and retail sector, which were active in 2018 (reported sales higher than 30,000 EUR), up to 23.13% of companies reported negative equity. Most companies with negative equity occurred in 20118 in the tourism sector - up to 35.07%. The construction sector reported the lowest share of companies with negative equity – up to 15.70%. The finding of such a high share of companies with negative equity operating in these sectors is alarming. This finding emphasizes the need for reliable and accurate default prediction models that could be applied in local conditions. The research design respects the fact that companies, especialy limited liability company, can be set up with almost no equity. The selected sample of non-prosperous companies includes only those companies, which reported positive equity in 2016 and 2017, but the declining trend in the value of this indicator resulted in negative equity in 2018. The fact that only those companies that were established by the end of 2014 at the latest were selected is not affected. A random sample was applied from such a narrowed sample of non-prosperous companies.”

Further, we included the following text, which deals with the sample size.

“Selecting a proper sample of companies by applying above stated selection criteria, thus ensuring a homogeneous sample within the category and significant differences between categories, was a prior interest. Resulting sample may not be considered large, but it ensures the internal consistency of presented research. ”

We also included in conclusion limitations related to the sample size.

“The research sample size could be considered as another limitation of this research. However, it should be noted that this sample consists of companies, which passed the selection criteria described in the methodology. It could be therefore defined as a homogeneous sample, which ensures internal consistency of each category and differences between categories. Though, for the further research, it would be appropriate to expand the sample.”

We didn’t realize that it was not clear from the previous version of the manuscript that results are based also on measures such as F1 score, sensitivity, and specificity. Therefore, we included appendices (Appendix C, …, Appendix I), which include all the relevant partial analysis results. We are quoting these appendices in the main text of the manuscript.

We also included and quoted literature sources related to the methods described in the chapter 3, such as F1 score, sensitivity, specificity, type II error, type I error, etc.

We added to the discussion following text, to highlight the aspect of sector-specifity of selected models.

“It must be acknowledged that this research deserves a larger sample of companies focusing on more sectors to determine which model is the most suitable for each sector. According to research results, the Model of Delina and Packová appears to be the most reliable generally applicable model. It was able to reliably identify companies that are prosperous and non-prosperous within all considered sectors. Other models show some differences in reliability between sectors. Gulka’s Model, due to its type I error, is unsuitable for the Tourism sector, while in the other two sectors, it achieved reliable results. Altman’s Z-score showed a high error rate in the construction sector. It’s important to mention that while some default prediction models, such as the Model of Delina and Packová and M-model, were constructed for the general use, regardless of the economy sector, some other tested models were specifically designed for a particular sector of economy, such as CH-Index and G-Index, which were meant to predict the financial health or financial distress in the sector of agriculture. There’s also a group of default prediction models, which were designed for broader applications, such as the Model of Binkert and HGN2 model, but still contain partial sector-specificity. When interpreting the research results presented in this article, it is highly recommended to consider the primary sector for which the model was constructed.”

We also highlighted this issue in conclusion – research limitations.

“When interpreting the research results, the sector-specificity of assessed models must be considered. The subjects of testing were also default prediction models, which were designed for specific industries, e.g. agriculture. These models were included in the testing in order to verify their reliability for other sectors.”

Regarding the negative equity issue, and the fact that companies can be set up with almost no equity, during the research, we were trying to minimize the impact of this issue and took special measures. Therefore, we included the following text.

“The research design respects the fact that companies, especially limited liability company, can be set up with almost no equity. The selected sample of non-prosperous companies includes only those companies, which reported positive equity in 2016 and 2017, but the declining trend in the value of this indicator resulted in negative equity in 2018. The fact that only those companies that were established by the end of 2014 at the latest were selected is not affected.”

We understand that the exhibit 1 shows that the number of companies in the affected sectors of all three types (prosperous companies, companies in difficulty, and non-prosperous companies) is much higher than the final number included in the sample. But this exhibit shows the initial volume, considering only the classification included in legislation: Communication from the Commission — Guidelines on State aid for rescuing and restructuring non-financial undertakings in difficulty (2014/C 249/01), and (EK, 2014) Commission Regulation (EU) No 651/2014 of 17 June 2014 declaring certain categories of aid compatible with the internal market in application of Articles 107 and 108 of the Treaty Text with EEA relevance. But this was only the starting point and further measures were taken. Therefore, we included the following text, describing the procedure, in the manuscript:

From the processed data of a total sample of 11,168 small and medium-sized enterprises operating in the tourism, construction, and retail sector, which were active in 2018 (reported sales higher than 30,000 EUR), up to 23.13% of companies reported negative equity. Most companies with negative equity occurred in 20118 in the tourism sector - up to 35.07%. The construction sector reported the lowest share of companies with negative equity – up to 15.70%. The finding of such a high share of companies with negative equity operating in these sectors is alarming. This finding emphasizes the need for reliable and accurate default prediction models that could be applied in local conditions. The research design respects the fact that companies, especially limited liability company, can be set up with almost no equity. The selected sample of non-prosperous companies includes only those companies, which reported positive equity in 2016 and 2017, but the declining trend in the value of this indicator resulted in negative equity in 2018. The fact that only those companies that were established by the end of 2014 at the latest were selected is not affected. A random sample was applied from such a narrowed sample of non-prosperous companies.

Selecting a proper sample of companies by applying above stated selection criteria, thus ensuring a homogeneous sample within the category and significant differences between categories, was a prior interest. Resulting sample may not be considered large, but it ensures the internal consistency of presented research.”

We also included the size of a sample as a significant factor in the research limitations, stated in the conclusion.

We also stated in the revised version of the manuscript that Exhibit 1 shows data for 2018 year, and we included the source of data (FinStat).

Line 319 – we defined the liquidity of the 2^nd level: “This indicator is calculated as the sum of financial accounts and short-term receivables divided by short-term liabilities. This indicator is also known as quick liquidity. It expresses the ability to cover short-term liabilities of the company with financial accounts and short-term receivables (Zalai et al., 2016).”

We include and highlighted the limitations of the current paper in Conclusion: “It shoul be noted that this research has some limitations. When interpreting the research results, the sector-specificity of assessed models must be considered. The subject of testing were also default prediction models, which were designed for specific industries, e.g. agriculture. These models were included in the testing in order to verify their reliability for other sectors. The research sample size could be considered as another limitation of this research. However, it should be noted that this sample consists of companies, which passed the selection criteria described in the methodology. It could be therefore defined as a homogeneous sample, which ensures internal consistency of each category and differences between categories. Though, for the further research, it would be appropriate to expand the sample. It is also necessary to realize that the tested models do not reflect systematic risk and the occurance of extraordinary events, such as the COVID-19 pandemic and the related structural changes in economy. The research was therefore conducted in a pre-pandemic period (2016, 2017, and 2018).”

We also included in the Conclusion following recommendation with a focus on practice: “When choosing a proper model to predict the financial distress in real conditions, based on above presented research results, three factors should be considered, i.e., the sector-specificity of a selected model, whether to rely on the overall Rank (I, II) or to prefere the type I error rate, and the target period as the distance of time for which the model should be reliable.”

We included in the discussion the aspect of sector-specificity: “It’s important to mention that while some default prediction models, such as the Model of Delina and Packová and M-model, were constructed for the general use, regardless of the economy sector, some other tested models were specifically designed for a particular sector of economy, such as CH-Index and G-Index, which were meant to predict the financial health or financial distress in the sector of agriculture. There’s also a group of default prediction models, which were designed for broader applications, such as the Model of Binkert and HGN2 model, but still contain partial sector-specificity. When interpreting the research results presented in this article, it is highly recommended to consider the primary sector for which the model was constructed.”

In the original Table 2 (currently Appendix A - Table A1) formulas such as Altman Z-Score, Quick test, Creditworthiness Index, etc. were missing. Therefore, we’ve prepared a new table, containing these formulas, which was attached as the Appendix B (Table A2).

Line 356 – The explanation of random match Pe is now provided: “, where (Cohen, 1968) Pe is the probability of a chance detection for the given data set. Pe can be interpreted as normalizing the accuracy from the range [0,1] to [p_chance 1], where p_chance is the accuracy expected by random guess given a test subset (i.e. 1 M in an M-class classifier). Pe (Berthold et al., 2020) is the probability of the raters to agree by chance … formulas provided in the manuscript …., when n is the number of instances in the data set.”

Lines 320-324 – the authors decided some values of criteria liquidity and ROS. We have provided in the manuscript the following reasoning for these criteria: “Based on the above described procedure, prosperous from non-prosperous companies were separated, as shown in Exhibit 1. However, applying this procedure a homogeneous sample of prosperous companies has not being created yet. We do not consider defining prosperous companies as companies with equity higher than a half of their share capital as sufficient. According to Brealey, Myers, and Allen (2016), liquidity and profitability are the two basic financial goals of a company, which in mutual interaction demonstrate the solvency and the ability to achieve financial results. Therefore, the 2^nd level liquidity as the first indicator was selected. This indicator is calculated as the sum of financial accounts and short-term receivables divided by short-term liabilities. This indicator is also known as quick liquidity. It expresses the ability to cover short-term liabilities of the company with financial accounts and short-term receivables (Zalai et al., 2016). The median of this indicator ranged in 2018 from 0.88 in Tourism sector to 1.32 in Construction sector. The lower limit of the interval for the 2^nd level liquidity was therefore set to 1.0. As the profitability indicator, the Return on Sales (ROS) was applied, calculated as EBIT divided by total sales. The acceptance interval was chosen at the level of the upper quartile for each sector separately (3.78% in Tourism sector, 4.01% in Construction sector, and 9.22% in Retail sector).”

The research design also includes statement related to the selected research period (years 2016, 2017, and 2018): “Because of the models’ inability to consider the systematic risk and the occurrence of extraordinary events, such as the COVID-19 pandemic and the related structural changes in economy, pre-pandemic research period was selected. No significant deviations were observed during the period considered.”

Originally, it could seem that companies in difficulty were left aside in the part of results and then came back in the part of general findings. We’ve enhanced this part by preparing appendices (Appendix A, …, Appendix I), which are directly quoted in the text of the manuscript.

Originally, we were mentioning an “average company” in the text. We’ve checked and cleared the text and now we are clearly presenting two approaches to classification: the classification applied by default prediction models (1) healthy, grey zone, and unhealthy companies; and classification applied in testing these models (2) prosperous companies, companies in difficulty, and non-prosperous companies.

We’ve adjusted the general findings (including the Table 9) and made it clearer. We included before the table 9 the following text: “The following table lists the models characterised by high reliability and low error rate, and presents synthesized results obtained in 2018. Data included in this table were transferred from Appendix E, Appendix F, and Appendix G.” And after this table, “Considering the importance of type I error, the above stated table presents two rankings. Rank (I, II) is based on Average (I, II), which represents an overall average of type I and type II errors, while Rank (I) is based on Average (I), which represents the average of type I errors only. Comparing these two rankings, we can conclude the impact of type I and type II errors on overall ranking of a specific model.”

Line 676 – there was an unclear sentence – how are the models mentioned in the bracket connected with Siekelová and IN05 presented in the previous sentence. We cleared this sentence: “Siekelová, et al. (2018) evaluated it as the most successful model, compared to Model of Jakubík and Teplý, Hurtošová’s Model, Gulka’s Model, in 2018 on a sample of 500 companies.”

Table 1

Sector's description in the case of Model of Hurtošová is now mentioned with the small letter as in the case of other models.

Table 2

Table 2 was transferred to appendices and is now labelled as Table.A1 in Appendix A. Numbers use decimal points instead of decimal commas and 0 is included in the formulas as well.

Model of Binkert - Liquidity 3^rd was not defined. Therefore, we included the formula “current assets / current liabilities” instead.

Model of Binkert – the first, second, third year were not defined and therefore the work replication was impossible. Under the formula of Binkert model was included unclear sentence because of the used language. We’ve translated the sentence and included the translation instead of the original text: “where: superscript represents the year of reporting, subscript identifies the indicator in the initial set of indicators (its order)”. We also changed e.g. (the 1^st year) to (indicators reported in the 1^st year).

HGN2 model – criteria for prosperous and non-prosperous seem to be switched. We know it seems that way. It was also an objection on a scientific conference, where these authors presented their model. But the formula is correct – we’ve used the same formula as the original formula proposed by the authors of this model. To present it more clearly, we’ve included “HGN2=…”.

We’ve checked also other formulas. We made adjustments regarding some parameters, such as operating costs instead of costs of operations, EBIT instead of EBAT, operating costs instead of prevádzkové náklady, current assets – current liabilities instead of working capital, total sales instead of sales of goods and production. We did not change the term share capital, but we included “share capital as the amount of money invested by its owners in exchange for shares of ownership”. The reason of leaving the term unchanged is that share capital can have different forms depending on the legal form of entity, e.g. common stocks, preferred stock, etc.

We cleared extra space/s included in formulas of individual indicators.

We unified and used the same multiplying sign for every formula included in tables.

Table 3

We changed the numbering of tables.

Tables displaying research results

Accuracy rates and Misclassification rates are now displayed with zeros.

Current table 9 called Error rate assessment

Based on your comments, we’ve adjusted this table and included two rankings: Rank (I, II) and Rank (I). We’ve also described the data entry: “The following table lists the models characterised by high reliability and low error rate, and presents synthesized results obtained in 2018. Data included in this table were transferred from Appendix E, Appendix F, and Appendix G.” Now it should be consistent with these tables, presenting all the necessary partial analytical results. All appendices are quoted in the manuscript. To make it even clearer, we’ve included the following text bellow the table: “Considering the importance of type I error, the above stated table presents two rankings. Rank (I, II) is based on Average (I, II), which represents an overall average of type I and type II errors, while Rank (I) is based on Average (I), which represents the average of type I errors only. Comparing these two rankings, we can conclude the impact of type I and type II errors on overall ranking of a specific model.”

Grammar issues

The faculty is now written with the large letter.

Lines 17, 290, and 297 – Oxford comma was included before and 2018.

Line 57 – Oxford comma was included before and Taffler's Models.

Line 88 – The sentence is now finished with “.”

Line 179 - Oxford comma was included before and IN05.

Line 276 and 277- Oxford comma is not written.

Line 279 - Oxford comma was included before and services.

Line 318 – non-prosperous companies are written.

Line 321 – second instead of secon is written.

Line 353 – Oxford comma was included before and false negative cases.

References

Line 79 – we incorrectly stated that the scientist Korol is an Estonian scientist. It was corrected.

We checked and corrected the names of authors (Čámská, Klečka, Režňáková, Gavurová, Kopta).

Line 445 – the source Řezbová was included to the reference list.

Line 785, 844 – The source details were checked and rewritten back to the original language.

Line 821 – “2. Vydanie” was corrected to “2^nd edition”

We’ve included additional literature sources related to adjustments described above.

Formal issues

Lines 67 and 84 – the spaces between paragraphs were reduced.

Round 3

Reviewer 3 Report

The paper has been significantly improved and it currently provides clear scientific results. Many limitations and paper weaknesses have been reduced. The author team have still not become cautious and many mistakes are repeated. More emphasis should be placed on the paper structure. Number of additional appendices should be reduced. These semi-results are not of readers' interest and they are only generally commented in the main text. These additional appendices cover the range of pages 26-38. The selection of companies is not clearly described and the research hides itself behind a homogenous sample which cannot be attained by the described steps. The list of references is again not complete and contains mistakes. Specific areas focused on research issues, grammar issues or formal issues are discussed below.

Research issues

Abstract has been rewritten but it should contain the names of models which reached the highest accuracy (conclusions). More attention should be paid to the list of models because Binkert's Model belongs to the group of alternative models as well as to the group of traditional worldwide models.
Sample size is extremely small because 10 companies belong to the group of prosperous companies, 10 to companies in difficulty, and 10 to non-prosperous companies. The total sample consists of 90 companies because there are 3 sectors analysed. 10 companies in each category is very low number for reliable scientific results. The scientific paper hides the small sample size behind the sample homogeneity. The sample cannot be called homogenous because the business model of companies, their customers, suppliers etc. were not described and taken into consideration. According to the text, the companies were selected randomly.
It is not clear how prosperous companies have been selected. Criteria are provided in the text what the companies should fulfil but exhibit 1 shows that the number of companies in the affected sectors of all three types (prosperous companies, companies in difficulty, and 10 to on-prosperous companies) is much higher than the final number 10. Exhibit 1 proves that more options/combinations of 10 companies in each subcategory are possible. The paper should specify how many companies fulfilled the defined criteria (subsample) because the random sample is based on this subgroup which is not described.
Formulas such as Altman Z-Score, Quick test, Creditworthiness Index and Model of Taffler have been added to the table located in appendices. The source of the table is incorrect. Reference list does not contain the original sources of each model.
Model of Binkert – the first, second, third year are not defined and therefore the work replication is impossible. Is the year (1^st or 3^rd) connected with the oldest data or with the most current data?
Table 9, line 847 It seems very questionable that alternative models achieved better results because this table also contains quick test, index IN05 which finished with very high ranking.

Grammar issues

Line 343 – the noun we is too subjective and does not belong to the scientific paper. The sentence should be rewritten.
Line 57 – There should not be a comma before and largely.
Line 23-24 – The comma is missing between models Gulka and Hurtošová.
Line 71 – There should be a comma before and procedures.
Oxford commas – Line 671 (and HGN2), line 603 (and the Gulka's Model), and other places
Line 548 – Tourism is written with a large letter although there is no need.
Line 423 – p nes and p neg should be probably the same.

References

Line 92 – The source mentioned is not written by Prusák and Blažej but by the professor called Blažej Prusak.
References needed for the preparation of Appendix B.

Formal issues

Text of abstract is not changed in the journal system and therefore the current paper version contains different abstract than the system.
Page 15 is empty.

Author Response

Dear reviewer. Thank you again for reviewing the revised version of the proposed manuscript and for your valuable recommendations, notes and comments.

We have reduced the number of additional appendices by excluding some partial results, which are not of readers' interest, but still ensure the replicability of presented research.

We’ve also checked the list of references, compared it with quotes included in text, corrected some mistakes and adjusted it to the journal format.

We’ve also adjusted the abstract and included the names of models which reached the highest accuracy and related conclusions. More attention was paid to the list of models, especially to Binkert's Model as it belongs to both, the group of alternative models and the group of well disseminated models. The new version of abstract is following:

“In the current volatile and interconnected economic environment, comprehensive synthetic approaches to financial health assessment came to the forefront of interest, represented by default prediction models. In recent decades, scientists and researchers have been intensively searching for the ideal default prediction model, both at the international level and at the national level, considering the specifics of domestic economies. The aim of this paper is to assess the reliability of alternative default prediction models in local conditions, with subsequent comparison with other generally known and globally disseminated default prediction models, such as Altman’s Z-score, Quick Test, Creditworthiness Index, and Taffler's Model. The comparison was carried out on a sample of 90 companies operating in the Slovak Republic over a period of 3 years (2016, 2017, and 2018) with a narrower focus on three sectors: construction, retail, and tourism, using alternative default prediction models, such as CH-index, G-index, Binkert’s Model, HGN2 Model, M-model, Gulka’s Model, Hurtošová’s Model, and Model of Delina and Packová. The research includes also Binkert’s Model, which originated in local conditions but can be considered as globally disseminated model. To verify the reliability of these models, tests of the significance of statistical hypotheses were used, such as type I and type II error. According to research results, the highest reliability and accuracy was achieved by an alternative local Model of Delina and Packová. The least reliable results within the final list of models were reported by the most globally disseminated model Altman’s Z-score. In contrast, the Quick Test, as one of globally well disseminated models, achieved high ranking as it reported low error rates, both type I and type II errors. While Index IN05, one of the most applied models in Slovak Republic, showed its ability to correctly classify non-prosperous companies, the overall rating of this model was low as it reported high type II error rate. Significant differences between sectors were identified.”

We’ve paid special attention to the sample size. The paper now also specifies how many companies fulfilled the defined criteria (subsample). This part is now discussed in broader extend. The methodology now includes following:

“The structure of total sample gathered applying this criteria for the 2018 year is presented in the following table.

Table 2. Share of prosperous and non-prosperous companies in selected sectors in 2018

Economy sectors	Business categories	Initial categorization (legislative criteria) in 2018 [n]	Final categorization (passing additional criteria) in 2018 [n]
Tourism sector	Non-prosperous companies	955	158
	Companies in difficulty	158	158
	Prosperous companies	1 610	399
Construction sector	Non-prosperous companies	758	165
	Companies in difficulty	154	154
	Prosperous companies	3 917	881
Retail sector	Non-prosperous companies	870	45
	Companies in difficulty	85	85
	Prosperous companies	2 661	496
Total	Non-prosperous companies	2 583	368
	Companies in difficulty	397	397
	Prosperous companies	8 188	1 776

Source: Own processing; based on data extracted from the FinStat database

Selecting a proper sample of companies by applying above stated selection criteria, thus ensuring consistent sample within the category and significant differences between categories, was a prior interest. Resulting sample may not be large and therefore could be considered as a research limitation. 270 observations (90 companies x 3 years) were applied, resulting in 3 510 estimations (13 models x 270 observations).

The research methodology offers various ways of compiling a sample (Tomšík 2017). A multistage selection was applied, based on a hierarchical description of the elements of the base set. These elements were specified by gradual selections through higher selection units. Gradual selections were compiled using cluster selection. Clusters were designed to be homogeneous within and heterogeneous between groups in relation to testing the reliability and accuracy of default prediction models. The generalizability of research results is linked to this deliberate sample.

Based on the success rate of each defalut prediction model to correctly classify non-prosperous companies within the applied sample (1 minus type I Error rate), the confidence interval of the model for the base set was determined. If significance tests are available for general values of a parameter, then confidence intervals can be constructed by including in the 100p% confidence region all those points for which the significance test of the null hypothesis that the true value is the given value is not rejected at a significance level of (1 − p) (Cox and Hinkley 1974).”

We’ve calculated the confidence interval as presented in the general findings section:

“Because of the sample limitations, the confidence interval was further estimated, based on the classification of non-prosperous companies. The population was set to 368 non-prosperous companies, which represents the gathered sample of all non-prosperous companies within all three sectors of economy passing the selection criteria. The sample applied was set to 30 non-prosperous companies and the confidence level was set to 95%. The results of confidence level estimation are presented in the following table.

Table 11. Confidence interval of classifying non-prosperous companies

Model	The success rate of classifying non-prosperous companies	Confidence interval	Interpretation	Range
Model		Confidence interval	Interpretation	Range
G-Index	80.00%	13.74	In 95% of cases, the model correctly classifies non-prosperous companies with the success rate interval from 93.74% to 66.26%.	0.94 - 0.66
Model of Delina and Packová	100.00%	3.42	In 95% of cases, the model correctly classifies non-prosperous companies with the success rate interval from 100% to 96.58%.	1 - 0.97
Model of Gulka	76.67%	14.45	In 95% of cases, the model correctly classifies non-prosperous companies with the success rate interval from 91.12 % to 62.22%.	0.91 - 0.62
Altman Z-score	66.67%	16.15	In 95% of cases, the model correctly classifies non-prosperous companies with the success rate interval from 82.82% to 50.52%.	0.83 - 0.51
Index IN05	90.00%	10.3	In 95% of cases, the model correctly classifies non-prosperous companies with the success rate interval from 100 % to 79.70%.	1.00 - 0.80
Quick Test	96.67%	5.86	In 95% of cases, the model correctly classifies non-prosperous companies with the success rate interval from 100% to 90.81%.	1.00 - 0.91
Creditworthiness Index	76.67%	14.45	In 95% of cases, the model correctly classifies non-prosperous companies with the success rate interval from 91.12 % to 62.22%	0.91 - 0.62

Source: Own table

The above stated confidence interval of each model corresponds with the success rate of classifying non-prosperous companies (1 minus type I Error rate). The narrowest range was estimated for the Model of Delina and Packová, followed by Quick Test. The broadest range was estimated for the Altman Z-score, followed by Creditworthiness Index and model of Gulka.”

We’ve included original literature sources related to formulas such as Altman Z-Score, Quick test, Creditworthiness Index, and Model of Taffler, which have been added to the table located in appendices. These sources are included also in the reference list.

Model of Binkert – the first, second, third year are defined now, using t sign for the most current years and defining the distance in time, e.g. t-1 and t-2 as further described in the paper.

Research results presented in the original Table 9 (currently Table 10) weren’t consistent with the statement that alternative models achieved better results. We’ve therefore adjusted our interpretation of these results, as currently presented in the discussion and conclusion. E.g., conclusion includes following: “Based on the research results, it can not be generally stated that a higher reliability and accuracy was achieved by alternative default prediction models, which originated in local conditions, compared to globally disseminated default prediction models. The highest overall ranking was achieved by the local alternative model and the least reliable results were recorded by the most globally disseminated model. But the score between these two models provides ambiguous results when comparing these two categories of default prediction models. It is reasonable to assume similar findings in other local markets. Further research territorially targeting other markets is therefore necessary.” Further adjustments were made in discussion.

Line 343 – we’ve changed the sentence, not to include the noun we as it was too subjective.

Line 57 – there is no comma before and largely anymore.

Line 23-24 – we’ve included comma between models Gulka and Hurtošová.

Line 71 – we’ve included comma before and procedures.

Oxford commas – we’ve checked and included all necessary Oxford commas, incl. the line 671 (and HGN2), line 603 (and the Gulka's Model), and other places.

Line 548 – Tourism was rewritten to small letter

Line 423 –p neg was corrected to p nes.

Line 92 – The source Prusák and Blažej was corrected to Prusák.

References were included in Appendix B.

The empty space on page 15 was corrected.

The text of abstract in the journal system will be changed by editorial team after accepting the final version of the manuscript.

Round 4

Reviewer 3 Report

The paper has been significantly improved and it currently provides clear scientific results. Many limitations and paper weaknesses have been reduced. Number of additional appendices has been reduced but still these semi-results cover the range of pages 25-33. The paper could be accepted after minor revision. The following lines contain possible recommendations leading to the higher paper value. The current paper structure is very difficult to understand (original paper, first revision, second revision etc.) therefore the author/s should take attention to proofreading. All parts should be consistent and coherent.

Research issues

Sample size is extremely small because 10 companies belong to the group of prosperous companies, 10 to companies in difficulty, and 10 to non-prosperous companies. The total sample consists of 90 companies because there are 3 sectors analysed. 10 companies in each category is very low number for reliable scientific results.
It seems very controversial to calculate confidence intervals when the sample size is so extremely limited. It is not clear when the paper mentions the population of 368 non-prosperous companies but the sample contains only 30 non-prosperous companies for quantifying confidence intervals.

Grammar issues

Tourism sector is sometimes written with a large letter and sometimes written with a small letter. These issues should be unified and respecting also other two sectors analysed – construction and retail.

Formal issues

Text of abstract is not changed in the journal system and therefore the current paper version contains different abstract than the system.
Page 20 seems not to be used fully for the paper text.
Lines 678 – 687 – The text seems to be written in italics and there is no need for.

Author Response

Dear reviewer,

thank you for your recommendations. We’ve tried to follow your instructions.

We do recognize limitations related to the sample size. That is the reason why we’ve included these limitations in the paper and estimated the confidence interval. We’ve adjusted the text explaining the confidence interval and related issues. The reason of these changes is to clearly present the difference between the population of 368 non-prosperous companies and the sample applied (30 non-prosperous companies). The current version states:

„The population was set to 368 non-prosperous companies, which represents the base set of all non-prosperous companies within all three sectors of economy passing the selection criteria, which were specified and further described in the methodology section. The sample applied was set to 30 non-prosperous companies, based on which the research was conducted. The confidence level was set to 95%. The results of confidence interval estimation are presented in the following table. …Table 11…“

We’ve considered applying the bootstrapping. But we concluded that bootstrapping is not a suitable method for this kind of research and will not enhance the reliability of presented results and therefore the confidence interval was applied instead.

In the revised version of manuscript, we are using small letters when mentioning tourism, construction, or retail sector, except when the sector is the first word in the sentence or in the cell of a table.

We were instructed by the Editor/Assistant Editor that the text of abstract will be changed in the journal system by the editorial team after the final revised version of manuscript is accepted.

Page 20 is fully used for the paper text.

Because of the official template used, sometimes the text is automatically transferred in italics. We’ve checked this issue again, and in the version currently uploaded all italics have been corrected to standard format.

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Reliability and Accuracy of Alternative Default Prediction Models: Evidence from Slovakia

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