Enhancing credit risk assessments of SMEs with non-financial information

Wahlstrøm, Ranik Raaen; Becker, Linn-Kristin; Fornes, Trude Nonstad Article Enhancing credit risk assessments of SMEs with nonfinancial information Cogent Economics & Finance Provided in Cooperation with: Taylor & Francis Group Suggested Citation: Wahlstrøm, Ranik Raaen; Becker, Linn-Kristin; Fornes, Trude Nonstad (2024) : Enhancing credit risk assessments of SMEs with non-financial information, Cogent Economics & Finance, ISSN 2332-2039, Taylor & Francis, Abingdon, Vol. 12, Iss. 1, pp. 1-33, https://doi.org/10.1080/23322039.2024.2418910 This Version is available at: https://hdl.handle.net/10419/321640 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ Cogent Economics & Finance ISSN: 2332-2039 (Online) Journal homepage: www.tandfonline.com/journals/oaef20 Enhancing credit risk assessments of SMEs with non-financial information Ranik Raaen Wahlstrøm, Linn-Kristin Becker & Trude Nonstad Fornes To cite this article: Ranik Raaen Wahlstrøm, Linn-Kristin Becker & Trude Nonstad Fornes (2024) Enhancing credit risk assessments of SMEs with non-financial information, Cogent Economics & Finance, 12:1, 2418910, DOI: 10.1080/23322039.2024.2418910 To link to this article: https://doi.org/10.1080/23322039.2024.2418910 © 2024 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group View supplementary material Published online: 05 Nov 2024. Submit your article to this journal Article views: 1486 View related articles View Crossmark data Citing articles: 2 View citing articles Full Terms & Conditions of access and use can be found at https://www.tandfonline.com/action/journalInformation?journalCode=oaef20 ECONOMETRICS & DATA ANALYTICS | RESEARCH ARTICLE Enhancing credit risk assessments of SMEs with non-financial information Ranik Raaen Wahlstrøm , Linn-Kristin Becker and Trude Nonstad Fornes NTNU Business School, Norwegian University of Science and Technology, Trondheim, Norway ABSTRACT We investigate non-financial variables for predicting bankruptcy in small and mediumsized enterprises (SMEs). The variables encompass management, board and ownership structures and are sourced from universally accessible information, rendering them available to all stakeholders and allowing for the analysis of all SMEs within a market. Using a large and recent sample of SMEs, we empirically examine the variables that predict bankruptcy over time horizons of one, two and three years. Our analysis incorporates state-of-the-art discrete hazard models, the least absolute shrinkage and selection operator (LASSO), extreme gradient boosting (XGBoost), adaptive boosting (AdaBoost), bagging and random forest. We also test robustness using balanced datasets generated using the synthetic minority oversampling technique (SMOTE). We find that including non-financial variables enhances bankruptcy predictions compared to using financial variables alone. Moreover, our results show that among our variables, the most significant non-financial predictors of bankruptcy are the age of chief executive officers (CEOs), chairpersons and board members, as well as ownership share and place of the board members’residences. IMPACT STATEMENT This research highlights the critical role of integrating non-financial information with traditional financial variables to enhance the prediction of SME bankruptcy. While financial variables remain the most significant predictors, the inclusion of nonfinancial factors significantly improves the accuracy of the assessment of SMEs’financial health, benefiting investors, policymakers, and financial institutions by enabling better risk management and more effective support schemes. The findings underscore the importance of diverse board composition and local engagement in reducing bankruptcy risk, offering valuable insights for improving SME governance and stability. ARTICLE HISTORY Received 17 July 2024 Revised 2 October 2024 Accepted 15 October 2024 KEYWORDS Small and medium-sized enterprises (SMEs); bankruptcy prediction; corporate governance; non-financial predictors; LASSO JEL CLASSIFICATION CODES C25; C53; G17; G20; G33; M41 SUBJECTS Economics; Finance; Business, Management and Accounting 1. Introduction Improved assessments of the financial standing of small and medium-sized enterprises (SMEs) are important for many stakeholders. For example, better assessment helps SMEs access formal capital. This is crucial because SMEs exhibit a higher level of information asymmetry than larger corporations, making it more difficult for them to access formal capital, as they face challenges in conveying their standing to lenders and investors (Beck & Demirguc-Kunt, 2006; Beck et al., 2008; Berger & Udell, 1998,2002; Block et al., 2018; Masiak et al., 2019). This is particularly pressing now as they face challenges due to the war in Ukraine and being at the center of the economic shocks of the COVID-19 pandemic (G20 & OECD, 2015; Organisation for Economic Co-operation and Development, 2022). SMEs also benefit from an improved assessment of their financial standing when conveying credibility to customers and suppliers. Furthermore, banks and investors benefit from better assessments of SMEs’financial standing, as they improve risk management and reduce lending errors through more accurate evaluations of potential CONTACT Ranik Raaen Wahlstrøm [email protected] NTNU Business School, Norwegian University of Science and Technology, Trondheim, Norway Supplemental data for this article can be accessed online at https://doi.org/10.1080/23322039.2024.2418910. This article has been corrected with minor changes. These changes do not impact the academic content of the article. ß2024 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The terms on which this article has been published allow the posting of the Accepted Manuscript in a repository by the author(s) or with their consent. COGENT ECONOMICS & FINANCE 2024, VOL. 12, NO. 1, 2418910 https://doi.org/10.1080/23322039.2024.2418910 new borrowers and enhanced monitoring of existing borrowers. Additionally, better assessment enables a more precise determination of the risk-weighted value of loan portfolios. In summary, this may increase lending to SMEs, which significantly positively affects the profitability and diversification of loan portfolios (Altman & Sabato, 2007; Dietsch & Petey, 2004). Moreover, assessing SMEs’financial standing is important for regulators, who perform on-site supervision of banks by analyzing their loan portfolios. Similarly, enhanced assessments of SMEs’financial standing facilitate a better analysis of the financial standing of large populations of firms encompassing entire markets. This is crucial for investors in these markets and policymakers when designing support schemes for businesses or predicting losses in tax revenues resulting from bankruptcy. In summary, improved assessments of SMEs’financial standing benefit the economy as a whole, especially because SMEs make up a large proportion of the economy. 1 Firm’s standings are typically evaluated through credit risk modeling, which commonly relies on either historical accounting-based financial variables or securities market information (Altman et al., 2010). Early studies on credit risk modeling used only accounting-based financial variables (eg Altman, 1968; Beaver, 1966). However, using only accounting-based financial variables for credit risk modeling can be problematic for several reasons (Agarwal & Taffler, 2008; Hillegeist et al., 2004). First, because accounts represent the past, they may not be useful for predicting future credit risk. Second, the true value of firms’assets may differ from the book value because of accounting principles and conservatism. This may lead to an incorrect assessment of a firm’s standing. Third, accounts are subject to management manipulation. Finally, accounts are prepared on a going-concern basis and have limited utility in predicting bankruptcy. SMEs may be particularly exposed to these challenges because they usually have less detailed and transparent accounting-based financial data than larger corporations (Berger & Frame, 2007). Moreover, as SMEs have fewer obligations regarding accounting data disclosure, inherently smaller accounting figures and are more vulnerable to external events than larger companies, financial ratios may be weak predictors of SME bankruptcy (Ciampi, 2015; Ciampi et al., 2021). The limitations of using accounting-based financial variables can be overcome by using market-based variables. The literature has proven that such variables effectively increase the power of bankruptcy prediction models (Beaver et al., 2005; Chava & Jarrow, 2004; Hillegeist et al., 2004; Merton, 1974; Shumway, 2001; Tian et al., 2015). However, the market data for SMEs are unavailable. Thus, it is crucial to investigate non-financial variables to predict the bankruptcy of such companies (Altman et al., 2010; Ciampi et al., 2020,2021). This study investigates the non-financial predictors of bankruptcy in privately held SMEs. Soft non-financial information, context-dependent qualitative data that are not easily transferable, has been found to improve credit assessments (Corn ee, 2019; Grunert et al., 2005). However, such information is typically exclusively accessible to banks that acquire it through close relationships with borrowers (Corn ee, 2019; Liberti & Petersen, 2019). Moreover, soft non-financial information may be unsuitable for major decisions involving multiple decision-makers because of the challenges in transferring it from the collector to others and for minor decisions due to the high labor costs associated with its collection (Corn ee, 2019). However, hard non-financial information, which refers to quantitative, explicit and context-independent data, is usually documented as numbers or can be easily converted into a numerical form, ensuring that it can be communicated to others without any loss of detail. Related studies that use hard non-financial information to assess SME credit risk include Wilson and Altanlar (2014), who examined newly incorporated companies, including SMEs and other firms, and found that the board of directors’characteristics contribute to bankruptcy prediction. However, they do not consider financial variables because they focus solely on newly established firms with no prior accounts available. In contrast, we focus on improving credit assessments for all SMEs in an economy using all available bankruptcy predictors derived from both financial and non-financial information. Another study related to ours is that of Altman et al. (2023a,2023b), who found that models based on financial variables show improved predictive power when payment behavior, management-related and employee-related variables are incorporated. Moreover, Ciampi (2015) demonstrated that including management-related variables in existing models based on financial variables enhances the prediction of default among small enterprises. However, both of these studies use non-financial variables that are not readily available to all stakeholders and consequently analyze subsamples of the economy. For instance, employeerelated information about SMEs is typically only available internally within SMEs, whereas payment behavior variables are usually only accessible to banks that have long-standing customer relationships with the SMEs. Moreover, even for banks, payment behavior variables are not always available–for example, when assessing 2 R.R. WAHLSTRØM ET AL. loan applications from new borrowers. These limitations make such variables unsuitable for assessing large populations of SMEs, such as when investors want to assess the financial standing of SMEs in a larger population or when policymakers are designing business support schemes or forecasting losses in tax revenues resulting from bankruptcies. By contrast, we examine non-financial predictors derived from universally available information on all SMEs. These predictors enable stakeholders to assess the financial standing of SMEs across an entire economy. Thus, we contribute to the literature by investigating non-financial predictors of SME bankruptcy that not only assist banks in reducing lending errors and determining risk-weighted assets but also support other users of bankruptcy prediction models, including regulators involved in determining banks’capital requirements, policymakers, private and public investors and credit rating agencies (Altman et al., 2017; Rajan et al., 2015). Based on this, we derive the following research question: Can non-financial information available for all SMEs in an economy improve assessments of their collective financial standing? In general, by focusing on privately held SMEs, we address an important gap in the literature, as most existing research on credit risk assessment investigates large corporations (da Silva Mattos & Shasha, 2024; Kuizinien_ e et al., 2022; Matenda et al., 2022; Zhao et al., 2024). This focus is crucial given the economic significance of SMEs and their distinct financial frameworks and challenges compared with larger corporations. Overall, consistent with the future research avenue proposed by the existing literature on credit risk modeling (Ciampi et al., 2021; Habib et al., 2020), we make a valuable contribution by demonstrating how the integration of non-financial variables into bankruptcy prediction models mitigates the information asymmetry surrounding SMEs and enhances the ability of all stakeholders to evaluate their standing. We employ a new and unique sample of 818,927 SME financial statements from 2014 to 2019. For each financial statement, we derive the common financial variables found in Altman (1968), Altman and Sabato (2007) and Paraschiv et al. (2023) as benchmarks, as well as 20 non-financial variables representing management, board and ownership structures. We use these variables to predict SME bankruptcy over one, two and three years. We employ the least absolute shrinkage and selection operator (LASSO) method to explore the importance of the variables and select the most appropriate variable sets. This method is commonly used in finance literature (eg Calomiris & Mamaysky, 2019; Chae, 2024; Chinco et al., 2019; Coad & Srhoj, 2020; Hautsch et al., 2015; Ogneva et al., 2020; Tian et al., 2015); and is found by Paraschiv et al. (2023) to be superior to other methods for selecting corporate bankruptcy predictors. This method has also been used in recent literature on SME bankruptcy and default prediction (Altman et al., 2023; Paraschiv et al., 2023). We evaluate the selected variable sets inand out-of-sample when used in discrete hazard models with logistic regression (LR) (Shumway, 2001). Our empirical results show that financial variables are important predictors of SME bankruptcy. Furthermore, we find that both the in-sample fit and out-of-sample prediction performance improve when non-financial variables are included. Among these, the age of chief executive officers (CEOs), chairpersons and board members, along with the ownership share of board members and whether they reside in the same county as the SMEs’headquarters (HQs), are the most important non-financial bankruptcy predictors. However, we also find that bankruptcy prediction models consisting solely of non-financial variables do not achieve acceptable performance. This underscores the importance of financial variables and aligns with previous studies on predicting bankruptcy in larger companies (eg Liang et al., 2020). Our findings are robust across 18 permutations of three financial variable sets as benchmarks, two years as test populations (2018 and 2019) and three different horizons for predicting bankruptcy (one, two and three years). Furthermore, our results are robust to using balanced datasets generated with the synthetic minority oversampling technique (SMOTE). Finally, our findings are robust to employing the machine learning methods extreme gradient boosting (XGBoost), adaptive boosting (AdaBoost), bagging and random forest. These methods model nonlinear relationships that have been shown to substantially improve bankruptcy predictions (Lohmann et al., 2023; Lohmann & Ohliger, 2018). 2. Background The initial discussions on bankruptcy prediction in the literature focused on analyzing companies’ accounting figures (Smith & Winakor, 1930), while Beaver (1966) demonstrated how individual financial COGENT ECONOMICS & FINANCE 3 ratios can predict company bankruptcy in univariate models. Altman (1968) introduced the first multivariate bankruptcy prediction model, the Z-score model, which continues to be widely used by practitioners and academics (e.g, Bl€ ochlinger & Leippold, 2018; Campello et al., 2018; Chang et al., 2019; Chava & Jarrow, 2004; Tian et al., 2015). The model comprises five financial variables that are primary aspects of a company’s financial profile: liquidity, profitability, leverage, solvency (coverage) and activity. Altman’s(1968) model was initially designed to predict the bankruptcy of large listed companies and includes a variable derived in part from the market value of equity. However, it was later refined to target private firms by incorporating only financial variables derived exclusively from accounting values (Altman et al., 1977,2019). Edmister (1972) was the first to highlight that early bankruptcy prediction models largely ignored SMEs. Motivated by this, he developed a model to predict small business defaults. Altman and Sabato (2007) expand on Edmister’s(1972) work by developing a bankruptcy prediction model specifically for SMEs. Similar to the variable set in Altman (1968), the set of variables in Altman and Sabato (2007) consisted of five financial variables categorized as the main aspects of a company’s financial profile. Paraschiv et al. (2023) also considered SME bankruptcy prediction and employ the LASSO method to empirically identify the set of ten variables out of 155 financial variables that yield the best predictions. The authors further demonstrated that these variables improve credit risk assessments, resulting in significantly higher bank profits. The ten selected variables capture SMEs’leverage, liquidity, solvency (coverage), age and profitability. Moreover, financial variables have been applied to derive proxies for earnings management, which have been found to improve SME bankruptcy predictions (S everin & Veganzones, 2021). In the context of non-financial bankruptcy predictors, we differentiate between those derived from soft and hard non-financial information (Corn ee, 2019; Liberti & Petersen, 2019). Soft non-financial information refers to context-dependent qualitative information that is not easily transferable and is typically collected by banks about borrowers through close relationships. The literature suggests that such information is valuable for assessing the credit risk of small and opaque borrowers. For example, Berger and Udell (2002) argued that relationship lending, conditional on soft non-financial information, reduces information problems in small firms. Furthermore, Berger et al. (2005) found that smaller banks lend more to smaller firms because they have a comparative advantage in collecting and acting on soft nonfinancial information. Moreover, Stein (2002) suggested that consolidation in the banking industry leads to a decline in small business lending because soft information cannot be credibly transmitted within larger hierarchies. This is consistent with the findings of Rajan et al. (2015) that the models used for predicting the defaults of securitized subprime mortgages before the U.S. subprime mortgage crisis in 2007 severely underestimated the likelihood of default for opaque borrowers. Furthermore, using a sample of German SMEs, Grunert et al. (2005) found evidence suggesting that combining financial and soft nonfinancial variables leads to more accurate default predictions than using financial or soft non-financial variables. Corn ee (2019) replicated Grunert et al. (2005) using credit files from a social relational bank specializing in providing external debt funding to genuinely small and opaque firms that prioritize social over financial goals. Corn ee (2019) found that including soft non-financial variables yields better predictions than using only financial variables. However, compared to Grunert et al. (2005), he revealed that soft non-financial information tends to be more valuable than financial variables. He argued that this may be because he uses a smaller and more opaque sample of borrowers than that of Grunert et al. (2005). This suggests that the larger and more transparent the borrower, the lower the predictive value of soft non-financial information compared to financial variables. In contrast, hard non-financial information is quantitative, explicit and context-independent. It is typically recorded as or can be easily reduced to numbers, making it easy to convey to others without losing information. Variables derived from such information include payment behavior variables, that is, indicators of late payments to creditors, which previous studies found to increase bankruptcy prediction accuracy compared to using only financial variables (eg Altman et al., 2023; Back, 2005; Laitinen, 1999; Wilson et al., 2000). Furthermore, the variables derived from hard non-financial information include management-related variables, which are indicators based on the characteristics of the management and board of directors. For example, Wilson and Altanlar (2014) reported that the board of directors’characteristics contribute to predicting the bankruptcy of newly incorporated companies with limited publicly available 4 R.R. WAHLSTRØM ET AL. data, including SMEs and other firms. Moreover, Ciampi (2015) found that default predictions among small enterprises improve when management-related variables are included in existing models based on financial variables. Altman et al. (2023a,2023b) developed an SME default predictor by considering financial variables in combination with payment behavior, management-related and employee-related variables and found that the predictive power of models based on financial variables improves when introducing these additional variables. Other hard non-financial variables used to assess SME credit risk are derived from the local banking market (Arcuri & Levratto, 2020), published legal judgments (Yin et al., 2020) and bag-of-words models applied to content scraped from corporate websites (Crosato et al., 2023). Additional hard non-financial factors that may help convey the credit risk include receiving government grants. Srhoj et al. (2021a,2021b) showed that receiving such grants can have a certification effect, increasing the likelihood of obtaining a long-term bank loan by being ‘certified’by the government. Moreover, Lohmann and Ohliger (2020) argued that including qualitative information from firms’annual reports, such as structural and linguistic characteristics, enhances the discriminatory power of bankruptcy prediction models based on financial variables. Integrating non-financial predictors can also introduce ethical challenges that must be carefully considered as they can perpetuate or exacerbate discrimination. For instance, Fuster et al. (2022) highlighted that machine learning techniques exhibit improved accuracy in predicting mortgage defaults when considering borrowers’ethnicity, leading to adverse consequences for specific borrower groups. The legal implications are also significant. Reliance on non-financial predictors could expose stakeholders to legal challenges if they lead to discriminatory practices in lending or investment decisions. Therefore, we argue that the non-financial variables used in our study should be employed to assess the collective financial standing of all firms in a larger population and should be used with caution when applied to decision support at the individual level. We further mitigate the bias in the non-financial variables by not considering them in isolation but with other financial and non-financial variables. 3. Variables We investigate the 20 non-financial bankruptcy predictors presented in Table 1, both individually and in conjunction with the benchmark sets of accounting-based financial predictors in Altman (1968), Altman and Sabato (2007) and Paraschiv et al. (2023), as presented in Table 2. The 20 non-financial variables listed in Table 1 are divided into three categories. First, they include management structure variables indicating the characteristics of SMEs’CEOs. Second, they constitute board structure variables indicating board characteristics that can significantly impact firm performance by supporting, controlling and evaluating management (Krause et al., 2016; Withers & Fitza, 2017). Finally, Table 1 includes ownership structure variables. Our non-financial variables indicate the ages of the CEOs, chairpersons and board members. These are included because previous literature argues that persons of higher and lower ages in these roles can result in lower bankruptcy probabilities (Platt & Platt, 2012). On the one hand, older age may mean greater experience, which can help avoid bankruptcy. However, as older age may bring about conservatism, younger CEOs and board members may help avoid bankruptcy by being more willing to try new ideas and adapt to changing business environments. Platt and Platt (2012) found that firms that went bankrupt had, on average, younger CEOs and board members than those that did not go bankrupt. Furthermore, Antulov-Fantulin et al. (2021) investigated the predictability of municipal bankruptcy and found that the age of council members is one of the most important predictors. Furthermore, we hypothesize that SME governance improves if its management and board are rooted in the same local community. Thus, we include in Table 1 variables that indicate whether CEOs, chairpersons and board members reside in the same county as the SME HQs. This is consistent with Wilson and Altanlar (2014), which found that bankruptcy was associated with fewer board members living in the same county as the company’s registered address. Table 1 also includes variables that indicate the genders of CEOs, chairpersons and board members. We include this, as previous literature suggests that women tend to be more risk-averse than men (eg Borghans et al., 2009; Charness & Gneezy, 2012; Dwyer et al., 2002; Jianakoplos & Bernasek, 1998). The literature on bankruptcy prediction confirms this assumption by suggesting that more women among COGENT ECONOMICS & FINANCE 5 the management and board members yield lower probabilities of bankruptcy. For example, Cho et al. (2021) found that among Chinese firms during 2005–2016, the likelihood of bankruptcy was negatively associated with the proportion of female executives. C. J. Garc ıa and Herrero (2021) found that the likelihood of bankruptcy among EU firms during 2002–2019 is negatively associated with greater board gender diversity. Wilson and Altanlar (2014) found that bankrupt companies have fewer female board members. Moreover, Antulov-Fantulin et al. (2021) show that the gender of council members is among the most important variables for predicting default in municipalities. Moreover, we include in Table 1 variables indicating whether the CEO sits on the board, whether the SME has two CEOs and whether a single individual serves as the SME’s CEO and chairperson, referred to as CEO duality (Krause et al., 2014). The existing literature highlights the potential advantages and disadvantages of CEO duality. On the one hand, it may be unfortunate because it reduces the independence between the board and management, reducing the board’s ability to control the management (Jensen, Table 1. Non-financial variables. Variable name Description Management structure CEO age The natural logarithm of the age of the CEO CEO woman Dummy; one if the CEO is a woman CEO duality Dummy for CEO duality; one if a single individual serves as both the CEO and chairperson of the board CEO on board Dummy; one if the CEO sits on the board CEO county Dummy; one if the CEO resides in the same county as the SME’s headquarters (HQs) Two CEOs Dummy; one if the company has two CEOs Board structure Chairperson age The natural logarithm of the age of the chairperson of the board Chairperson woman Dummy; one if the chairperson of the board is a woman Chairperson county Dummy; one if the chairperson of the board resides in the same county as the SME’s headquarters (HQs) Board size The natural logarithm of the number of board members Board age avg The natural logarithm of the average age among all board members Board age std Standard deviation of age among board members Board women Proportion of board members who are women Board county Proportion of board members who resides in the same county as the SME’s headquarters (HQs) Board non-owners Proportion of board members who are not shareholders Ownership structure Ownership concentration 1 Average holdings of shareholders Ownership concentration 2 Standard deviation of shareholders’holdings Ownership CEO Ownership share with the CEO Ownership chairperson Ownership share with the chairperson of the board Ownership board Ownership share with the board members Note: The 20 non-financial variables of interest divided into categories representing the management, board and ownership structures. Table 2. Benchmark financial variable sets. Variable name Category Altman (1968) EBIT/total assets Coverage Retained earnings/total assets Profitability Sales/total assets Activity Total equity/total liabilities Leverage Working capital/total assets Liquidity Altman and Sabato (2007) Current liabilities/total equity Leverage EBITDA/interest expense Activity EBITDA/total assets Profitability Retained earnings/total assets Coverage Short-term liquidity/total assets Liquidity Paraschiv et al. (2023) (Current liabilities - short-term liquidity)/total assets Leverage Accounts payable/total assets Liquidity Dummy; one if paid-in equity is less than total equity Solvency Dummy; one if total liability exceeds total assets Leverage Interest expenses/total assets Solvency Inventory/current assets Liquidity Log(age in years) Age Net income/total assets Profitability Public taxes payable/total assets Liquidity Short-term liquidity/current assets Liquidity Notes: The benchmark variable sets of accounting-based financial variables are those of Altman (1968), Altman and Sabato (2007) and Paraschiv et al. (2023). The variables are sorted alphabetically. 6 R.R. WAHLSTRØM ET AL. 1993). However, CEO duality may also be beneficial if it leads to a more flexible leadership, which improves company efficiency (Combs et al., 2007; Dowell et al., 2011). The empirical evidence on how CEO duality affects the probability of bankruptcy is inconclusive. For instance, Ciampi (2015) found that CEO duality reduces the risk of default. Duru et al. (2016) found that CEO duality negatively affects firm performance when independent board members account for a small proportion of the board. However, this negative effect is mitigated as the proportion of independent board members increases. Eventually, the authors found that the impact becomes positive when the proportion of independent board members increases even more. By contrast, Platt and Platt (2012) and Manzaneque et al. (2016) found no significant effect of CEO duality on the likelihood of company bankruptcy. We also include non-financial variables that measure board size and the proportion of board members who are not shareholders. Having more board members results in greater diversity and access to information, thereby increasing the board’s efficiency and independence by boosting its ability to control management and direct the company in the right direction (Dalton et al., 1999; Manzaneque et al., 2016; Pearce & Zahra, 1992). However, board efficiency can decrease with more members if this results in a poorer flow of information (Guest, 2009). Platt and Platt (2012) and Manzaneque et al. (2016) found a negative relationship between the size of a company’s board and the likelihood of bankruptcy. By contrast, Ciampi (2015) reported that board size did not significantly help predict defaults. Furthermore, we include two non-financial variables that measure ownership concentration. 2 Theoretically, high ownership concentration has pros and cons (Ciampi, 2015). On the one hand, larger shareholders can benefit firm performance because they typically have more expertise relevant to the firm than smaller shareholders. They also have greater incentives to monitor management and boards effectively. However, they may also promote firm inefficiency if they exercise their control rights for private benefits. Ciampi (2015) found that a higher ownership concentration, where a single shareholder has the majority of shares, reduces the probability of an SME default. Tang et al. (2020) and Liang et al. (2020) revealed that the ownership stake of the majority of stakeholders helps predict corporate bankruptcy. In contrast, Manzaneque et al. (2016) suggested that ownership concentration does not significantly impact financial distress. Finally, Table 1 presents three non-financial variables indicating the proportion of ownership by CEOs, chairpersons and board members. We include these variables because we hypothesize that the probability of bankruptcy is negatively associated with the ownership share of SMEs’key personnel; higher ownership should provide greater incentives to avoid bankruptcy. This corresponds with Lilienfeld-Toal and Ruenzi (2014), who found that CEO ownership increases the performance of listed firms. 4. Data Our data consist of all unconsolidated annual financial statements of privately held Norwegian limitedliability SMEs for the accounting years 2014–2019. Although related studies also focus on data from only one economy and time period, 3 we recognize the limitations of the generalizability of our analyses, specifically on Norwegian SMEs. However, we consider Norway over 2014–2019 to be a feasible test environment for several reasons. During our sample years, Norway experienced stable economic conditions and a lack of significant business cycle fluctuations, falling between the aftermath of the European debt crisis and the onset of the financial shock caused by the coronavirus crisis. Moreover, Norway is integrated with the European internal market as part of the European Economic Area (EEA) and is considered a high-income European country. 4 Additionally, 99% of all Norwegian firms are SMEs, comparable to other European countries, employing 56% of the workforce. 5 The annual financial statements for our data were provided by the Norwegian government agency Brønnøysund Register Centre (BRC). 6 It is mandatory for all Norwegian limited liability companies to report their annual financial statements to the authorities, and these are subsequently stored with the BRC. Additionally, the BRC has provided us with the industry classification of the firms when reporting their annual financial statements by the Norwegian Standard Industrial Classification (SIC2007). 7 Moreover, the BRC has supplied us with the dates of bankruptcy filings for all firms in our data that have filed for bankruptcy. Furthermore, information on firms’CEOs, chairpersons, board members, and owners used to derive our non-financial variables was provided by Enin AS. 8 COGENT ECONOMICS & FINANCE 7 given the large data sample size and the memory-intensive and computationally complex nature of these methods, they are impractical without significant computational resources that are not available to us. Moreover, we do not derive coefficient estimates and their statistical significance from the LASSO method but merely use it to select variables that are later used in LR models for which we derive coefficient estimates and their statistical significance. However, we correct the standard errors used to derive z-scores by clustering them at the firm level. 5.3. Machine learning methods We also test the robustness of our results by predicting bankruptcy using machine learning methods instead of LASSO and LR, otherwise applying the same test setting (see Section 5.1). Specifically, following da Silva Mattos and Shasha (2024), we employ four machine learning methods within three classes of ensemble methods: boosting (XGBoost and AdaBoost), bagging and random forest. Indeed, these three classes of ensemble methods have been found to outperform other methods for bankruptcy prediction (Barboza et al., 2017). XGBoost (Chen & Guestrin, 2016), which was also used to test the robustness in Altman et al. (2023a) and AdaBoost (Freund & Schapire, 1997) build ensembles of decision trees sequentially, where each tree corrects the errors of the previous ones. Furthermore, bagging, or bootstrap aggregating (Breiman, 1996), trains multiple decision tree classifiers on subsets of the training data selected randomly with replacement and then aggregates their predictions to improve stability and accuracy. Finally, random forest (Breiman, 2001) trains multiple independent decision trees with randomly selected subsets of variables and outputs the mode of the classes for classification. For each machine learning method, we tune the hyperparameters using a grid search with a cross-validation scheme. 12 To avoid data leakage, tuning is performed on the training data. For further description of the machine learning methods, we refer to their descriptions in the bankruptcy prediction studies by Barboza et al. (2017) and Radovanovic and Haas (2023). 5.4. Evaluation metrics We evaluate our bankruptcy prediction models using several evaluation metrics. First, we evaluate them using average precision (AP) and the area under the receiver operating characteristic curve (AUC), which are widely used for binary classification problems, including bankruptcy prediction (eg Altman et al., 2023a; Paraschiv et al., 2023; Tian et al., 2015). The AUC is the area under the plot of the false positive rate against the true positive rate across all observations when varying the discrimination threshold across the two limit values of 0 and 1 (Hosmer et al., 2013). AP is calculated similarly, but based on the plot of precision against recall and is recommended over AUC for evaluating model performance with imbalanced datasets (Saito & Rehmsmeier, 2015). Higher AUC and AP values indicate a better-performing model. As suggested by Paraschiv et al. (2023), we follow Hosmer et al. (2013) by considering AUC 2 ½0:7, 0:8Þacceptable, AUC 2½0:8, 0:9Þexcellent and AUC 0:9 outstanding. Furthermore, they were evaluated based on the accuracy ratio (AR), a performance metric derived from the cumulative accuracy profile (CAP) curve (Engelmann et al., 2003; Mai et al., 2019). It is calculated as the ratio of the area between the CAP curve of the model and the random model to the area between the CAP curve of the perfect model and the random model. Moreover, we use the Kolmogorov-Smirnov (KS) statistic (Hodges, 1958), a non-parametric test to compare the distributions of two samples by the maximum difference between their cumulative distribution functions. In the context of bankruptcy prediction model evaluation, the KS statistic can be used to compare the predicted probabilities for bankrupt and non-bankrupt classes. Higher AR and KS statistics indicate better model performance, reflecting a greater ability to distinguish between bankrupt and non-bankrupt cases. Additionally, we evaluate them based on Hinge loss (Crammer & Singer, 2001), measuring the distance between the predicted and actual classifications encoded as −1 and 1, as well as the logistic loss (Log loss), which is the value of the log-likelihood function shown in Equation (2), divided by the number of observations. Moreover, following Tian et al. (2015) and Paraschiv et al. (2023), we use the Akaike (1974) Information Criterion (AIC), evaluating the goodness of fit of the model similarly to the log loss but penalized for the number of parameters to prevent overfitting, balancing model complexity and fit. 14 R.R. WAHLSTRØM ET AL. We also use the Bayesian Information Criterion (BIC), which is similar to the AIC but introduces a stronger penalty for the number of parameters. Additionally, we assess the models using Brier (1950) score, which quantifies the mean-squared difference between the actual and predicted bankruptcy probabilities. Lower Hinge loss, Log loss, AIC, BIC and Brier scores indicate better models. We also report the Brier Skill Score (BSS), which compares the Brier score of a predictive model with that of a reference model (Roulston, 2007). As a reference model, we use a model that always predicts the average of y2f0,1gN, which is the bankruptcy frequency, in the training data. Furthermore, we follow bankruptcy prediction literature (eg Campbell et al., 2008; Paraschiv et al., 2023; Tian et al., 2015)by evaluating the in-sample fit of LR models using McFadden’s(1974) pseudo-R squared R2¼1− lðb,b0Þ lðb0Þ2 ½0, 1where the denominator is the log-likelihood of a model containing only the intercept coefficient b0:Higher BSS and R2values indicate better models. Finally, following the bankruptcy prediction literature (eg Chava & Jarrow, 2004; Paraschiv et al., 2023; Shumway, 2001; Tian et al., 2015), we evaluate them based on decile rankings. When applying this method, the observations are divided into deciles based on their predicted probability of bankruptcy provided by the model, and the proportion of actual bankruptcies within each decile is then reported. This method allows a clear assessment of the model’s discriminatory power by showing how well bankrupt and non-bankrupt firms can be distinguished across different risk levels. 6. Results 6.1. Main results Tables 6,7and 8present the estimation results of the LR models when predicting bankruptcy over horizons of one, two and three years, respectively, using variable sets selected by the LASSO method from the population of non-financial variables in Table 1 and the set of financial variables in Altman (1968), Altman and Sabato (2007) and Paraschiv et al. (2023) (see Table 2). Additionally, we report the results using all the financial statements from 2018 and 2019, respectively, as out-of-sample test samples. First, we use the accounting year 2018 as our test sample and let the LASSO method use all the financial statements from the four previous years to select the best variable set among the population of 25 variables, consisting of the five financial variables in Altman (1968) (see Table 2) and the 20 non-financial variables in Table 1. The selected variables and the estimation results when used in LR models are presented in the first columns of Tables 6,7and 8. Next, we repeat the procedure using the 2019 accounting year as our test sample and report the results in the second column. We then repeat the procedure with the variables in Altman and Sabato (2007) instead of those in Altman (1968) and show the results in the third and fourth columns. Finally, the procedure is repeated with a population of 30 variables, including those in Paraschiv et al. (2023) and the 20 non-financial variables in Table 1. The results are presented in the last two columns of Tables 6,7and 8. In each table, Panel A presents the variables selected by the LASSO method and their LR coefficient estimates and z-scores in parentheses. Panels B and C report the in-sample fit and out-of-sample prediction performance, respectively, when using the variable sets selected by the LASSO method, as shown in Panel A, in the top rows, and when using exclusively financial variables in the bottom rows. 6.1.1. The importance of financial variables The tables show that financial variables are undoubtedly important because the LASSO method selects most financial variables across all variable sets, prediction horizons and accounting years as our test sample. Furthermore, the selected financial variables are consistent across all settings. Specifically, the same financial variables are selected in all settings, except for ‘interest expenses / total assets’which is selected when using the financial variable set of Paraschiv et al. (2023) only when 2019 is the test period and when predicting bankruptcy over a horizon of three years (see Panel A of Table 8). The importance of the financial variables is further confirmed by the associated LASSO path plots. Figures IA.1, IA.2 and IA.3 in the Internet Appendix present the LASSO path plots of the variables selected among the non-financial variables and those in Altman (1968), Altman and Sabato (2007) and Paraschiv et al. (2023), respectively, when predicting bankruptcy over a horizon of one year. Panels A COGENT ECONOMICS & FINANCE 15 Table 6. Estimation results when predicting bankruptcy over a horizon of one year. Panel A. Variables selected using the LASSO method and their LR coefficient estimates when predicting bankruptcy over a horizon of one year. Altman (1968) Altman and Sabato (2007) Paraschiv et al. (2023) 2018 2019 2018 2019 2018 2019 CEO age −0.65(−5.18) −0.57(−4.31) −0.84(−6.26) −0.78(−6.03) −0.35(−2.73) −0.35(−2.65) Chairperson age −0.78(−6.30) −0.48(−2.74) −0.84(−4.84) −0.54(−3.19) −0.40(−3.13) −0.23(−1.32) Board age avg −0.56(−2.81) −0.21(−1.07) −0.74(−3.85) −0.40(−1.97) Board county −0.82(−14.97) −0.92(−17.46) −0.87(−15.83) −0.97(−18.33) −0.78(−14.16) −0.88(−16.77) Board non-owners −0.29(−2.88) −0.40(−3.92) −0.30(−2.93) Ownership board 0.72(13.50) 0.50(4.96) 0.95(18.04) 0.66(6.56) 0.60(11.31) 0.41(4.02) EBIT / total assets −1.72(−21.24) −1.78(−22.87) Retained earnings / total assets −0.38(−9.75) −0.33(−8.97) −0.70(−22.88) −0.66(−22.71) Sales / total assets 0.14(15.07) 0.15(16.59) Working capital / total assets −0.77(−13.80) −0.78(−14.57) EBITDA / total assets −1.99(−23.86) −2.07(−25.82) Short-term liquidity / total assets −1.77(−15.06) −1.75(−15.53) (Current liabilities - shortterm liquidity) / total assets 0.12(1.76) 0.20(3.06) Accounts payable / total assets 1.27(12.77) 1.18(12.31) Dummy; one if paid-in equity is less than total equity −0.69(−9.44) −0.78(−10.84) Dummy; one if total liability exceeds total assets 0.65(9.03) 0.59(8.42) Inventory / current assets 0.43(5.66) 0.44(6.02) Log(age in years) −0.20(−8.93) −0.19(−8.57) Net income / total assets −1.08(−13.71) −1.10(−14.71) Public taxes payable / total assets 4.12(22.33) 4.03(22.84) Short-term liquidity / current assets −1.49(−13.69) −1.37(−13.25) Intercept −0.04(−0.10) 0.87(2.20) 2.23(5.62) 3.34(8.75) −2.28(−5.30) −1.06(−2.48) Panel B: In-sample fit when predicting bankruptcy over a horizon of one year. Altman (1968) Altman and Sabato (2007) Paraschiv et al. (2023) 2018 2019 2018 2019 2018 2019 Financial and non-financial variables R20.137 0.151 0.129 0.141 0.197 0.209 AUC 0.834 0.846 0.827 0.838 0.876 0.885 AP 0.036 0.042 0.031 0.035 0.057 0.062 AR 0.664 0.690 0.650 0.672 0.749 0.767 KS statistic 0.536 0.558 0.511 0.527 0.612 0.631 Hinge loss 1.004 1.004 1.004 1.004 1.004 1.004 Log loss 0.023 0.023 0.023 0.023 0.021 0.021 AIC 24,345 25,113 24,573 25,421 22,684 23,415 BIC 24,446 25,237 24,673 25,533 22,841 23,595 Brier score 0.004 0.004 0.004 0.004 0.004 0.004 BSS 0.012 0.014 0.011 0.012 0.028 0.030 Decile 1 0.578 0.592 0.548 0.571 0.672 0.690 Decile 2 0.156 0.160 0.154 0.150 0.137 0.136 Decile 3 0.074 0.081 0.097 0.090 0.065 0.055 Decile 4 0.048 0.045 0.052 0.052 0.035 0.038 Decile 5 0.042 0.035 0.046 0.043 0.028 0.025 Decile 6-10 0.103 0.088 0.104 0.095 0.064 0.055 Exclusively financial variables R20.118 0.127 0.099 0.104 0.185 0.193 AUC 0.816 0.826 0.794 0.800 0.868 0.874 AP 0.031 0.034 0.024 0.025 0.050 0.053 AR 0.628 0.649 0.585 0.597 0.733 0.745 KS statistic 0.514 0.530 0.470 0.486 0.603 0.607 Hinge loss 1.004 1.004 1.004 1.004 1.004 1.004 Log loss 0.024 0.024 0.024 0.024 0.022 0.022 AIC 24,892 25,815 25,411 26,503 22,999 23,866 (continued) 16 R.R. WAHLSTRØM ET AL. and B in each figure present the plots using 2018 and 2019 as the out-of-sample test samples. In summary, Figures IA.1, IA.2 and IA.3 have six panels presenting the LASSO path plots for the six modeling permutations shown in the six columns of Table 6. Similarly, the six panels of Figures IA.5, IA.6 and IA.7 in the Internet Appendix present the LASSO path plots for the six modeling permutations shown in the Panel C. Out-of-sample prediction performance when predicting bankruptcy over a horizon of one year. Altman (1968) Altman and Sabato (2007) Paraschiv et al. (2023) 2018 2019 2018 2019 2018 2019 Financial and non-financial variables AUC 0.855 0.830 0.842 0.804 0.889 0.860 AP 0.043 0.025 0.035 0.022 0.064 0.041 AR 0.707 0.657 0.680 0.607 0.775 0.718 KS statistic 0.587 0.519 0.536 0.466 0.632 0.600 Hinge loss 1.004 1.004 1.004 1.004 1.004 1.003 Log loss 0.024 0.017 0.024 0.018 0.022 0.017 AIC 6866 5166 6976 5274 6398 4922 BIC 6955 5275 7065 5373 6537 5080 Brier score 0.004 0.003 0.004 0.003 0.004 0.003 BSS 0.015 −0.005 0.011 −0.001 0.032 0.011 Decile 1 0.586 0.563 0.575 0.505 0.683 0.617 Decile 2 0.192 0.150 0.152 0.148 0.143 0.150 Decile 3 0.070 0.089 0.081 0.103 0.063 0.099 Decile 4 0.049 0.070 0.062 0.056 0.046 0.023 Decile 5 0.029 0.021 0.041 0.056 0.017 0.031 Decile 6-10 0.075 0.106 0.089 0.131 0.048 0.080 Exclusively financial variables AUC 0.833 0.835 0.786 0.787 0.876 0.860 AP 0.035 0.022 0.026 0.016 0.055 0.037 AR 0.664 0.668 0.570 0.572 0.749 0.718 KS statistic 0.538 0.541 0.486 0.435 0.601 0.583 Hinge loss 1.004 1.004 1.004 1.004 1.004 1.004 Log loss 0.025 0.018 0.026 0.018 0.023 0.017 AIC 7078 5234 7443 5408 6543 4953 BIC 7137 5293 7502 5468 6651 5062 Brier score 0.004 0.003 0.004 0.003 0.004 0.003 BSS 0.009 −0.011 0.005 −0.005 0.027 0.008 Decile 1 0.560 0.577 0.573 0.500 0.667 0.608 Decile 2 0.167 0.157 0.102 0.129 0.125 0.169 Decile 3 0.097 0.082 0.049 0.080 0.084 0.082 Decile 4 0.051 0.052 0.065 0.092 0.041 0.040 Decile 5 0.032 0.038 0.060 0.061 0.024 0.023 Decile 6-10 0.094 0.094 0.151 0.138 0.059 0.077 Notes: Estimation results of LR models that predict bankruptcy over a one-year horizon, using variable sets selected by the LASSO method from a population of non-financial variables in Table 1 and a set of financial variables. The columns display the results of permutations using all financial statements from 2018 and 2019 as out-of-sample test samples and the variables in Altman (1968), Altman and Sabato (2007) and Paraschiv et al. (2023), presented in Table 2, as the set of financial variables. Panel A presents the variables selected using the LASSO method, along with their coefficient estimates and z-scores in parentheses, derived from standard errors clustered at the firm level. Panels B and C report the in-sample fit and out-of-sample prediction performance, respectively, using R2, AUC, AP, AR, KS statistic, Hinge loss, Log loss, AIC, BIC, Brier score, BSS and decile rankings. The first rows in Panels B and C report metric values when using the variable sets selected by the LASSO method, shown in Panel A, from the population of both non-financial and financial variables. The bottom rows show the metric values when the financial variables are used exclusively per benchmark set, as shown in 2. To train the models, a four-year rolling window approach was followed in which the models were trained on all financial statements from the four accounting years preceding the test populations. These data are presented in 3. Table 6 Continued. Altman (1968) Altman and Sabato (2007) Paraschiv et al. (2023) 2018 2019 2018 2019 2018 2019 BIC 24,959 25,882 25,478 26,570 23,122 23,990 Brier score 0.004 0.004 0.004 0.004 0.004 0.004 BSS 0.009 0.011 0.007 0.008 0.024 0.026 Decile 1 0.546 0.562 0.549 0.560 0.647 0.660 Decile 2 0.157 0.160 0.116 0.117 0.150 0.142 Decile 3 0.095 0.089 0.065 0.064 0.068 0.071 Decile 4 0.046 0.048 0.068 0.062 0.041 0.038 Decile 5 0.035 0.033 0.055 0.050 0.024 0.025 Decile 6-10 0.121 0.109 0.148 0.147 0.070 0.063 COGENT ECONOMICS & FINANCE 17 Table 7. Estimation results when predicting bankruptcy over a horizon of two years. Panel A. Variables selected using the LASSO method and their LR coefficient estimates when predicting bankruptcy over a horizon of two years. Altman (1968) Altman and Sabato (2007) Paraschiv et al. (2023) 2018 2019 2018 2019 2018 2019 CEO age −0.58(−6.96) −0.62(−7.79) −0.78(−9.42) −0.88(−10.93) −0.36(−4.30) Chairperson age −0.65(−5.95) −0.77(−7.39) −0.73(−6.92) −0.69(−6.62) −0.35(−3.17) −0.34(−3.10) Board age avg −0.70(−5.66) −0.69(−5.84) −0.83(−6.97) −0.77(−6.51) −0.60(−5.10) −0.38(−3.01) Board county −0.92(−27.23) −0.71(−22.61) −0.97(−28.66) −0.92(−28.12) −0.88(−25.92) −0.83(−25.41) Board non-owners −0.38(−6.04) −0.51(−15.89) Ownership board 0.62(19.15) 0.84(25.83) 0.42(6.62) 0.56(17.03) EBIT / total assets −1.24(−24.63) −1.17(−24.15) Retained earnings / total assets −0.37(−14.53) −0.28(−11.81) −0.68(−34.59) −0.65(−35.15) Sales / total assets 0.15(26.36) 0.17(29.56) Working capital / total assets −0.73(−20.57) −0.76(−22.36) EBITDA / total assets −1.42(−27.13) −1.36(−27.02) Short-term liquidity / total assets −1.54(−22.57) −1.46(−22.51) (Current liabilities - short-term liquidity) / total assets 0.24(5.39) 0.20(4.57) Accounts payable / total assets 1.44(22.63) 1.46(23.44) Dummy; one if paid-in equity is less than total equity −0.57(−13.77) −0.60(−15.00) Dummy; one if total liability exceeds total assets 0.35(8.03) 0.36(8.41) Inventory / current assets 0.53(11.24) 0.45(9.73) Log(age in years) −0.34(−26.40) −0.32(−24.94) Net income / total assets −0.63(−11.94) −0.61(−12.13) Public taxes payable / total assets 4.33(36.71) 4.17(36.60) Short-term liquidity / current assets −1.37(−20.74) −1.36(−21.44) Intercept 3.00(12.10) 3.74(15.76) 5.16(21.56) 5.50(23.36) −0.19(−0.72) 0.84(3.24) Panel B: In-sample fit when predicting bankruptcy over a horizon of two years. Altman (1968) Altman and Sabato (2007) Paraschiv et al. (2023) 2018 2019 2018 2019 2018 2019 Financial and non-financial variables R20.126 0.119 0.117 0.112 0.195 0.189 AUC 0.814 0.810 0.802 0.797 0.867 0.862 AP 0.063 0.059 0.055 0.054 0.098 0.095 AR 0.622 0.612 0.597 0.587 0.725 0.717 KS statistic 0.479 0.475 0.459 0.451 0.583 0.571 Hinge loss 1.010 1.010 1.010 1.010 1.010 1.010 Log loss 0.053 0.054 0.054 0.055 0.049 0.050 AIC 56,248 59,217 56,875 59,691 51,846 54,557 BIC 56,359 59,318 56,976 59,803 52,003 54,726 Brier score 0.011 0.011 0.011 0.011 0.010 0.011 BSS 0.020 0.018 0.019 0.019 0.045 0.043 Decile 1 0.485 0.467 0.457 0.455 0.603 0.591 Decile 2 0.178 0.182 0.182 0.174 0.171 0.174 Decile 3 0.106 0.118 0.115 0.113 0.083 0.089 Decile 4 0.077 0.074 0.075 0.081 0.054 0.053 Decile 5 0.051 0.053 0.060 0.056 0.032 0.034 Decile 6-10 0.102 0.106 0.112 0.120 0.057 0.061 Exclusively financial variables R20.097 0.096 0.076 0.073 0.179 0.174 AUC 0.789 0.790 0.756 0.754 0.858 0.855 AP 0.051 0.051 0.040 0.039 0.085 0.083 AR 0.572 0.573 0.507 0.503 0.709 0.702 KS statistic 0.458 0.461 0.387 0.380 0.564 0.558 Hinge loss 1.010 1.010 1.011 1.011 1.010 1.010 Log loss 0.055 0.056 0.056 0.057 0.050 0.051 AIC 58,131 60,759 59,500 62,369 52,833 55,530 BIC 58,198 60,827 59,567 62,437 52,956 55,653 Brier score 0.011 0.011 0.011 0.011 0.011 0.011 BSS 0.013 0.012 0.010 0.009 0.037 0.035 Decile 1 0.430 0.432 0.427 0.421 0.576 0.568 Decile 2 0.197 0.195 0.145 0.145 0.176 0.179 Decile 3 0.125 0.128 0.109 0.109 0.093 0.096 Decile 4 0.073 0.071 0.082 0.087 0.058 0.056 Decile 5 0.046 0.044 0.062 0.063 0.037 0.038 Decile 6-10 0.129 0.130 0.175 0.175 0.061 0.064 18 R.R. WAHLSTRØM ET AL. six columns of Table 7. Moreover, the six panels of Figures IA.9, IA.10 and IA.11 show the LASSO path plots for the six modeling permutations shown in the six columns of Table 8. As explained in Section 5.2, the LASSO path plots are generated by repeatedly minimizing Equation (3) with varying kvalues. Initially, kis set high enough that the term kjjbjj1dominates, causing all estimated coefficients to be zero. This can be observed on the far-left side of the plots. As kgradually decreases, moving to the right on the plots, more coefficients become non-zero and enter the model. Variables that become non-zero at higher kvalues (further to the left in the plots) have stronger predictive power and thus greater importance compared to variables that become non-zero at lower kvalues (further to the right in the plots). We observe that the LASSO method selects financial variables before non-financial ones, as financial variables become non-zero at higher kvalues (further to the left in the plots). Moreover, in most cases, the financial variables are selected at much higher kvalues than the non-financial variables, further indicating their relative importance. We also observe that the coefficient signs of all financial variables in Tables 6,7and 8follow the expected directions. 13 The only exception being the positive sign of ‘sales / total assets’for the variable set in Altman (1968). However, this variable is excluded from the revised versions of Altman’s(1968) Panel C. Out-of-sample prediction performance when predicting bankruptcy over a horizon of two years. Altman (1968) Altman and Sabato (2007) Paraschiv et al. (2023) 2018 2019 2018 2019 2018 2019 Financial and non-financial variables AUC 0.797 0.799 0.776 0.782 0.847 0.852 AP 0.056 0.035 0.045 0.029 0.086 0.056 AR 0.587 0.593 0.545 0.561 0.686 0.700 KS statistic 0.455 0.467 0.414 0.430 0.546 0.554 Hinge loss 1.010 1.010 1.010 1.010 1.009 1.009 Log loss 0.055 0.038 0.056 0.038 0.051 0.035 AIC 15,771 11,270 16,075 11,388 14,740 10,484 BIC 15,870 11,359 16,164 11,487 14,878 10,633 Brier score 0.011 0.007 0.011 0.007 0.011 0.007 BSS 0.013 −0.011 0.010 −0.007 0.036 0.009 Decile 1 0.450 0.448 0.405 0.415 0.548 0.555 Decile 2 0.187 0.193 0.182 0.192 0.182 0.186 Decile 3 0.102 0.116 0.117 0.112 0.091 0.094 Decile 4 0.078 0.078 0.086 0.079 0.063 0.070 Decile 5 0.060 0.055 0.068 0.065 0.043 0.029 Decile 6-10 0.122 0.110 0.142 0.137 0.073 0.065 Exclusively financial variables AUC 0.797 0.792 0.751 0.749 0.846 0.850 AP 0.049 0.033 0.038 0.024 0.078 0.054 AR 0.588 0.579 0.497 0.494 0.684 0.696 KS statistic 0.478 0.474 0.386 0.368 0.544 0.541 Hinge loss 1.011 1.011 1.010 1.011 1.010 1.010 Log loss 0.056 0.039 0.060 0.040 0.051 0.036 AIC 16,021 11,474 17,368 11,797 14,823 10,579 BIC 16,080 11,533 17,428 11,856 14,931 10,688 Brier score 0.011 0.007 0.011 0.007 0.011 0.007 BSS 0.007 −0.015 0.004 −0.008 0.030 0.005 Decile 1 0.439 0.450 0.417 0.427 0.543 0.553 Decile 2 0.194 0.188 0.150 0.125 0.189 0.173 Decile 3 0.138 0.126 0.114 0.105 0.099 0.103 Decile 4 0.073 0.067 0.088 0.089 0.056 0.067 Decile 5 0.037 0.041 0.065 0.072 0.041 0.038 Decile 6-10 0.119 0.127 0.167 0.182 0.073 0.066 Notes: Estimation results of LR models that predict bankruptcy over a two-year horizon, using variable sets selected by the LASSO method from a population of non-financial variables in Table 1 and a set of financial variables. The columns display the results of permutations using all financial statements from 2018 and 2019 as out-of-sample test samples and the variables in Altman (1968), Altman and Sabato (2007) and Paraschiv et al. (2023), presented in Table 2, as the set of financial variables. Panel A presents the variables selected using the LASSO method, along with their coefficient estimates and z-scores in parentheses, derived from standard errors clustered at the firm level. Panels B and C report the in-sample fit and out-of-sample prediction performance, respectively, using R2, AUC, AP, AR, KS statistic, Hinge loss, Log loss, AIC, BIC, Brier score, BSS and decile rankings. The first rows in Panels B and C report metric values when using the variable sets selected by the LASSO method, shown in Panel A, from the population of both non-financial and financial variables. The bottom rows show the metric values when the financial variables are used exclusively per benchmark set, as shown in 2. To train the models, a four-year rolling window approach was followed in which the models were trained on all financial statements from the four accounting years preceding the test populations. These data are presented in 3. COGENT ECONOMICS & FINANCE 19 model, which targets private companies across all industries, because it is highly industry-sensitive (Altman, 2018; Altman et al., 2019). Moreover, Panels B and C of Tables 6,7and 8show that among the three financial variable sets, the one in Paraschiv et al. (2023) yields the highest in-sample fit and out-of-sample prediction performance across all prediction horizons, years as our test sample and whether using financial variables exclusively or enriching them with non-financial variables. This is expected because Paraschiv et al. (2023) selected their variable set with a sample similar in many respects to that we use in our study. 6.1.2. Enhancing models with non-financial variables Furthermore, we observe that enriching financial variables with non-financial ones improves bankruptcy prediction models. Specifically, as shown in Panels B and C of Tables 6,7and 8, using variable sets containing both financial and non-financial variables (top rows in the panels) results in a better in-sample fit and out-of-sample prediction performance across all evaluation metrics compared with using exclusively financial variables (bottom rows of the panel). The improved model performance is due to the six non-financial variables selected by the LASSO method. Specifically, the LASSO method consistently selects ‘chairperson age’across all 18 permutations of the financial variable sets, years used as the test sample and prediction horizons. Additionally, ‘CEO age’and ‘board age avg’are selected in all except one and two, respectively, cases. In all cases, we observe a negative coefficient for these variables, indicating that an older age results in a lower probability of bankruptcy. This finding is consistent with Platt and Platt (2012) finding that older CEOs and board members are associated with less bankruptcy. Furthermore, the LASSO method consistently selects the variable ‘board county’in all cases, which indicates whether board members reside in the same county as the SMEs’HQs. The coefficients of this variable are negative in all cases, indicating a lower probability of bankruptcy if board members reside in the same county as the SME. Finally, in most cases, the LASSO method selects the variables ‘board non-owners’and ‘ownership board’. The estimated coefficients of these variables consistently have negative and positive signs, respectively. This finding indicates that a higher proportion of board members who are not shareholders decreases the SME’s likelihood of bankruptcy, and a lower share of ownership by board members also decreases the likelihood of bankruptcy. This may be because boards with a lower ownership share have more outsiders among board members, which can strengthen the board by providing more diversity than boards with high ownership in the SME. 6.1.3. Only non-financial variables Next, we test the performance of variable sets consisting only of non-financial variables. Such variable sets are useful for assessing, for example, newly established firms without their first financial statement. We create these variable sets by allowing the LASSO method to consider only the 20 non-financial variables in Table 1.Table 9, Panel A shows the selected variables and estimation results when they are used in LR models using 2018 and 2019 as test samples and when predicting bankruptcy over horizons of one, two and three years. Panel B presents the in-sample fit and out-of-sample prediction performance. While Panel B of Table 9 indicates a better prediction than random when exclusively using non-financial variables; specifically, AUC >0:5, the prediction performance is not considered acceptable as AUC <0:7 (see Section 5.4). Furthermore, we observe that across all evaluation metrics, the in-sample fit and out-of-sample prediction performance are higher when using variable sets consisting exclusively of financial variables or financial and non-financial variables combined (see Panels B and C of Tables 6,7 and 8) than when using only non-financial variables (see Panel B of Table 9). This further proves the importance of financial variables for bankruptcy prediction, while non-financial variables should be used only in combination with financial variables. Furthermore, the importance of the non-financial variables in Tables 6,7and 8is supported as all these variables are present in Table 9 with the same sign for the estimated coefficient values. The only exception is ‘board non-owners’, which has another sign for the estimated coefficient in some cases in Table 9 compared with Tables 6,7and 8. However, the estimated coefficients are not statistically significant in these cases. Moreover, we observe in Figures IA.4, IA.8 and IA.12 in the Internet Appendix, which 20 R.R. WAHLSTRØM ET AL. Table 8. Estimation results when predicting bankruptcy over a horizon of three years. Panel A. Variables selected using the LASSO method and their LR coefficient estimates when predicting bankruptcy over a horizon of three years. Altman (1968) Altman and Sabato (2007) Paraschiv et al. (2023) 2018 2019 2018 2019 2018 2019 CEO age −0.70(−8.56) −0.72(−8.57) −0.92(−11.19) −0.91(−10.99) −0.45(−5.29) −0.45(−5.30) Chairperson age −0.93(−8.82) −0.69(−6.27) −0.86(−8.09) −0.75(−6.92) −0.51(−4.67) −0.42(−3.74) Board age avg −0.34(−2.89) −0.40(−3.20) −0.38(−3.14) −0.54(−4.34) −0.06(−0.47) −0.18(−1.41) Board county −0.74(−23.24) −0.80(−23.77) −0.97(−28.85) −0.85(−25.04) −0.88(−26.25) −0.77(−22.86) Board non-owners −0.47(−14.49) −0.33(−5.19) −0.65(−20.20) −0.28(−4.41) −0.50(−15.33) Ownership board 0.42(6.57) 0.27(4.19) EBIT / total assets −0.88(−17.33) −0.84(−16.61) Retained earnings / total assets −0.31(−12.14) −0.32(−12.54) −0.62(−31.11) −0.59(−30.05) Sales / total assets 0.15(25.77) 0.14(23.26) Working capital / total assets −0.60(−16.67) −0.63(−17.41) EBITDA / total assets −0.95(−17.96) −0.90(−16.85) Short-term liquidity / total assets −1.34(−20.57) −1.36(−20.71) (Current liabilities - short-term liquidity) / total assets 0.29(6.40) 0.29(6.60) Accounts payable / total assets 1.20(18.33) 1.21(18.46) Dummy; one if paid-in equity is less than total equity −0.53(−13.53) −0.52(−12.89) Dummy; one if total liability exceeds total assets 0.17(3.93) 0.21(4.59) Interest expenses / total assets 1.99(6.44) Inventory / current assets 0.48(10.16) 0.35(7.37) Log(age in years) −0.29(−22.49) −0.31(−23.55) Net income / total assets −0.39(−7.15) −0.27(−4.89) Public taxes payable / total assets 3.34(27.74) 3.08(25.52) Short-term liquidity / current assets −1.13(−18.11) −1.10(−17.72) Intercept 3.43(13.89) 3.04(12.48) 4.81(19.60) 5.20(22.21) 0.48(1.76) 0.76(2.84) Panel B. In-sample fit when predicting bankruptcy over a horizon of three years. Altman (1968) Altman and Sabato (2007) Paraschiv et al. (2023) 2018 2019 2018 2019 2018 2019 Financial and non-financial variables R20.088 0.088 0.085 0.081 0.137 0.133 AUC 0.777 0.777 0.767 0.764 0.826 0.825 AP 0.041 0.040 0.040 0.035 0.060 0.055 AR 0.548 0.549 0.528 0.522 0.644 0.643 KS statistic 0.410 0.416 0.398 0.391 0.505 0.500 Hinge loss 1.010 1.010 1.010 1.010 1.010 1.010 Log loss 0.056 0.052 0.056 0.053 0.053 0.050 AIC 58,635 57,231 58,773 57,678 55,455 54,415 BIC 58,736 57,343 58,885 57,779 55,634 54,594 Brier score 0.011 0.010 0.011 0.010 0.011 0.010 BSS 0.010 0.010 0.012 0.010 0.023 0.021 Decile 1 0.393 0.405 0.397 0.383 0.499 0.488 Decile 2 0.189 0.188 0.175 0.182 0.192 0.195 Decile 3 0.122 0.114 0.121 0.119 0.105 0.109 Decile 4 0.091 0.092 0.086 0.095 0.071 0.075 Decile 5 0.073 0.064 0.070 0.068 0.046 0.049 Decile 6-10 0.132 0.137 0.151 0.153 0.088 0.084 Exclusively financial variables R 2 0.066 0.064 0.050 0.048 0.122 0.119 AUC 0.758 0.753 0.723 0.719 0.814 0.813 AP 0.035 0.033 0.028 0.026 0.052 0.048 AR 0.509 0.502 0.441 0.434 0.621 0.620 KS statistic 0.400 0.394 0.325 0.317 0.486 0.484 Hinge loss 1.011 1.010 1.011 1.010 1.010 1.010 Log loss 0.057 0.054 0.058 0.055 0.054 0.051 AIC 60,037 58,707 61,014 59,739 56,434 55,286 BIC 60,104 58,774 61,081 59,806 56,557 55,409 Brier score 0.011 0.010 0.011 0.010 0.011 0.010 BSS 0.006 0.006 0.005 0.004 0.018 0.017 Decile 1 0.348 0.351 0.331 0.328 0.463 0.452 Decile 2 0.205 0.195 0.162 0.154 0.197 0.203 Decile 3 0.139 0.140 0.125 0.122 0.119 0.123 Decile 4 0.092 0.093 0.100 0.106 0.073 0.076 Decile 5 0.062 0.061 0.082 0.086 0.052 0.053 Decile 6-10 0.153 0.160 0.201 0.204 0.096 0.093 COGENT ECONOMICS & FINANCE 21 present the LASSO path plots for six modeling permutations shown in the six columns of Table 9, that ‘board non-owners’is among the last chosen by the LASSO method, that is, at low kvalues. 6.2. Robustness tests 6.2.1. Robustness using balanced datasets As with any bankruptcy prediction dataset, our sample is highly imbalanced; the rate of financial statements categorized as bankrupt is much lower than those categorized as non-bankrupt (Beaver et al., 2010). We acknowledge that sampling to create a balanced training dataset would distort the capabilities of a bankruptcy prediction model because the ratio of non-bankrupt to bankrupt observations in the data used for development deviates from the real-world population (Zmijewski, 1984). However, in this section, we investigate the robustness of our main results when using balanced datasets because this approach has been shown to improve classification accuracy significantly (J. Garcia, 2022). Specifically, we use SMOTE (Fernandez et al., 2018) to generate synthetic samples for the minority class by interpolating between existing minority class samples. SMOTE selects a minority class sample, identifies its k-nearest neighbors and creates new synthetic samples along the line segments joining the Panel C. Out-of-sample prediction performance when predicting bankruptcy over a horizon of three years. Altman (1968) Altman and Sabato (2007) Paraschiv et al. (2023) 2018 2019 2018 2019 2018 2019 Financial and non-financial variables AUC 0.752 0.785 0.741 0.770 0.810 0.840 AP 0.025 0.009 0.023 0.008 0.035 0.015 AR 0.499 0.569 0.479 0.538 0.615 0.679 KS statistic 0.375 0.436 0.358 0.406 0.487 0.531 Hinge loss 1.010 1.010 1.010 1.009 1.010 1.009 Log loss 0.043 0.017 0.043 0.017 0.040 0.016 AIC 12,270 5,058 12,326 5,064 11,679 4,780 BIC 12,359 5,157 12,425 5,153 11,837 4,939 Brier score 0.008 0.002 0.008 0.002 0.008 0.002 BSS −0.007 −0.119 −0.006 −0.093 0.000 −0.117 Decile 1 0.342 0.445 0.348 0.415 0.440 0.570 Decile 2 0.182 0.166 0.174 0.147 0.208 0.155 Decile 3 0.138 0.117 0.127 0.125 0.129 0.091 Decile 4 0.106 0.083 0.102 0.102 0.072 0.072 Decile 5 0.073 0.057 0.068 0.087 0.058 0.045 Decile 6-10 0.158 0.132 0.182 0.125 0.092 0.068 Exclusively financial variables AUC 0.741 0.768 0.700 0.726 0.809 0.840 AP 0.024 0.007 0.019 0.005 0.036 0.013 AR 0.479 0.536 0.396 0.451 0.613 0.679 KS statistic 0.380 0.426 0.305 0.328 0.475 0.539 Hinge loss 1.011 1.010 1.010 1.010 1.010 1.010 Log loss 0.043 0.018 0.046 0.018 0.041 0.017 AIC 12,427 5,290 13,248 5,392 11,718 4,950 BIC 12,486 5,349 13,307 5,451 11,827 5,059 Brier score 0.008 0.002 0.008 0.002 0.008 0.002 BSS −0.007 −0.124 −0.005 −0.086 0.003 −0.127 Decile 1 0.348 0.411 0.335 0.351 0.430 0.551 Decile 2 0.179 0.192 0.133 0.162 0.206 0.185 Decile 3 0.148 0.109 0.124 0.098 0.131 0.087 Decile 4 0.083 0.083 0.099 0.109 0.082 0.060 Decile 5 0.068 0.045 0.100 0.068 0.057 0.026 Decile 6-10 0.174 0.158 0.209 0.211 0.093 0.091 Notes: Estimation results of LR models that predict bankruptcy over a three-year horizon, using variable sets selected by the LASSO method from a population of non-financial variables in Table 1 and a set of financial variables. The columns display the results of permutations using all financial statements from 2018 and 2019 as out-of-sample test samples, and the variables in Altman (1968), Altman and Sabato (2007) and Paraschiv et al. (2023), presented in Table 2, as the set of financial variables. Panel A presents the variables selected using the LASSO method, along with their coefficient estimates and z-scores in parentheses, derived from standard errors clustered at the firm level. Panels B and C report the in-sample fit and out-of-sample prediction performance, respectively, using R2, AUC, AP, AR, KS statistic, Hinge loss, Log loss, AIC, BIC, Brier score, BSS and decile rankings. The first rows in Panels B and C report metric values when using the variable sets selected by the LASSO method, shown in Panel A, from the population of both non-financial and financial variables. The bottom rows show the metric values when the financial variables are used exclusively per benchmark set, as shown in 2. To train the models, a four-year rolling window approach was followed in which the models were trained on all financial statements from the four accounting years preceding the test populations. These data are presented in 3. 22 R.R. WAHLSTRØM ET AL. selected sample and its neighbors. This approach helps balance the class distribution without duplicating the existing minority class samples. We use this approach on the data for each accounting year thrice, depending on whether we categorize bankruptcy over one, two, or three-year horizons, resulting in three datasets with 1,631,396, 1,620,862 and 1,623,426 financial statements, respectively, each with 50% of observations categorized as bankrupt per accounting year. Tables IA.1, IA.2 and IA.3 in Internet Appendix IA.4 present the model performance when using balanced datasets in predicting bankruptcy over horizons of one year, two years and three years, respectively. In each table, Panels A and B exhibit the in-sample fit and out-of-sample prediction performance, respectively. As before, we let the LASSO method select variables from a population of non-financial variables in Table 1 and a set of financial variables, and we measure the performance of using the selected models in LR models. The performance of these models is displayed in the tables’top rows. The bottom rows show the metric values when using exclusively the financial variables per benchmark set. The tables’columns display the results of permutations, using all financial statements from 2018 and 2019 as out-of-sample test samples and the variables in Altman (1968), Altman and Sabato (2007) and Paraschiv et al. (2023) as the set of financial variables. We also follow the same four-year rolling window approach. In summary, Tables IA.1, IA.2 and IA.3 are comparable to Tables 6,7and 8, but for when using balanced datasets. We observe that Tables IA.1, IA.2 and IA.3 confirm our findings. Specifically, across all metrics and test settings, variable sets that include financial and non-financial variables (top rows of panels) yield superior in-sample fit and out-of-sample prediction performance compared to sets that use only the financial variables (bottom rows of panels). We also note that among the three financial variable sets, the one in Paraschiv et al. (2023) consistently yields the highest in-sample fit and out-of-sample prediction performance. Additionally, we observe that while the AUC is at the same level as when not employing a balanced dataset (see Tables 6,7and 8), the AP is higher when using balanced datasets. This is expected because in the context of highly imbalanced datasets, it is common to observe that the AP is significantly lower than the AUC. This discrepancy arises from the different sensitivities of these metrics to class imbalances. The AUC evaluates the model’s ability to distinguish between classes by considering both true positive and false positive rates, which can result in deceptively high values owing to the large number of true negatives. In contrast, AP focuses on the precision-recall trade-off, directly reflecting the model’s performance on the minority class. Consequently, the AP is more sensitive to the model’s ability to correctly identify the minority class, often resulting in lower values in imbalanced datasets. Furthermore, Table IA.4 in the Internet Appendix displays the model performance when considering exclusively non-financial variables and using the balanced datasets. As with not using a balanced dataset (see Table 9), the in-sample fit and out-of-sample prediction performance is overall higher across all evaluation metrics when using variable sets of exclusively financial variables or combined financial and non-financial variables (see Tables IA.1, IA.2 and IA.3), compared with using only non-financial variables (see Table IA.4). Figures IA.13, IA.14 and IA.15 in Internet Appendix IA.4 present the associated LASSO path plots, when using the balanced datasets, of the variables selected among the non-financial ones and those in Altman (1968), Altman and Sabato (2007) and Paraschiv et al. (2023), respectively, when predicting bankruptcy over a horizon of one year. In each figure, Panels A and B present the plots using 2018 and 2019 as out-of-sample test samples. Furthermore, Figures IA.17, IA.18 and IA.19 present the same but for predicting bankruptcy over a horizon of two years, whereas Figures IA.21, IA.22 and IA.23 present the same but for predicting bankruptcy over a horizon of three years. Moreover, Figures IA.16, IA.20 and IA.24 present the LASSO path plots of the variables selected among only the non-financial variables when using a balanced dataset and predicting bankruptcy over horizons of one year, two years and three years, respectively. As with not using balanced datasets, we observe from the LASSO path plots that financial variables are selected before non-financial ones, as financial variables become non-zero at higher kvalues (further to the left in the plots), and that in most cases, the financial variables are selected at much higher k values. Thus, the LASSO path plots also confirm the importance of the financial variables when the balanced datasets were used. 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Financial statements Number of companies Bankruptcy frequency Industry level 1 Industry level 2 One-year horizon Two-year horizon Three-year horizon Agriculture, forestry and fishing Crop and animal production, hunting 4765 1084 0.36% 0.78% 0.61% Forestry and logging 2461 570 0.33% 0.61% 0.37% Fishing and aquaculture 12,989 3155 0.14% 0.32% 0.43% Mining and quarrying Mining of coal and lignite 14 3 0.00% 0.00% 0.00% Extraction of oil and natural gas 633 147 0.16% 0.16% 0.16% Mining of metal ores 75 15 0.00% 0.00% 0.00% Other mining and quarrying 2709 538 0.11% 0.33% 0.41% Mining support service activities 2769 617 0.14% 0.43% 0.54% M anufacturing Food products 9188 2007 0.52% 1.40% 1.09% Beverages 1103 285 0.54% 1.45% 1.18% Textiles 1353 283 0.00% 0.59% 0.30% Wearing apparel 809 197 0.37% 2.35% 1.73% Leather and leather products 98 22 0.00% 0.00% 0.00% Wood and wood products 5177 1079 0.31% 0.89% 0.83% Paper and paper products 340 67 0.29% 0.59% 0.29% Printing and reproduction 3156 669 0.29% 0.92% 0.92% Refined petroleum products 55 15 0.00% 1.82% 0.00% Chemicals, chemical products 925 197 0.32% 0.97% 0.97% Pharmaceuticals 201 51 0.50% 0.50% 0.00% Rubber and plastic products 1860 374 0.27% 0.75% 0.59% Other non-metal mineral products 2818 573 0.00% 0.75% 0.53% Basic metals 548 114 0.18% 1.28% 0.55% Fabricated metal prod. 8944 1885 0.48% 1.20% 0.91% Electronic and optical products 1372 293 0.29% 0.44% 0.36% Electrical equipment 1641 353 0.43% 0.98% 1.04% Machinery and equipment 4308 892 0.42% 0.79% 0.56% Motor vehicles etc. 758 143 0.40% 1.06% 0.92% Other transport equipment 2043 456 0.64% 1.52% 1.37% Furniture 2143 467 0.84% 1.49% 1.12% Other manufacturing 2500 558 0.16% 0.76% 0.68% Repair, installation of machinery 6870 1573 0.28% 0.89% 0.74% Construction Construction of buildings 96,658 23,772 0.46% 1.26% 1.05% Civil engineering 3956 878 0.46% 1.11% 1.21% Specialised construction activities 76,835 17,755 0.50% 1.45% 1.20% Domestic trade, car repair shop Motor vehicles, trade and repair 30,129 6786 0.42% 1.17% 1.05% Wholesale trade 70,096 15,636 0.37% 0.99% 0.89% Retail trade 87,311 20,031 0.73% 1.80% 1.45% Transportation and storage Land transport, pipeline transport 20,653 4685 0.49% 1.51% 1.35% Water transport 10,675 2447 0.10% 0.43% 0.36% Air transport 544 113 0.18% 0.37% 0.37% Support act. for transportation 10,401 2167 0.12% 0.50% 0.46% Postal and courier activities 1121 321 1.52% 4.10% 2.59% Accommodation, food service Accommodation 11,848 2534 0.28% 0.86% 0.74% Food and beverage service act. 26,109 6949 1.12% 2.95% 2.28% Information and communication Publishing activities 8021 1701 0.20% 0.49% 0.45% Motion picture, TV, music prod. 4532 1190 0.22% 0.46% 0.44% Programming, broadcasting act. 295 78 0.00% 0.68% 0.34% (continued) 32 R.R. WAHLSTRØM ET AL. Table A1. Continued. Financial statements Number of companies Bankruptcy frequency Industry level 1 Industry level 2 One-year horizon Two-year horizon Three-year horizon Telecommunications 2405 575 0.17% 0.54% 0.71% Computer programming, consultancy 26,886 7062 0.22% 0.53% 0.49% Information service activities 2927 738 0.10% 0.48% 0.38% Profess., scientific, tech. act. Legal and accounting activities 20,103 4350 0.05% 0.17% 0.20% Head offices, management consult. 37,651 9148 0.18% 0.29% 0.27% Architecture, engineering act. 43,187 10,557 0.20% 0.44% 0.42% Scientific research and development 3030 765 0.10% 0.40% 0.40% Advertising and market research 6291 1571 0.17% 0.87% 0.92% Other prof., scientific, techn. act. 12,268 3187 0.37% 0.82% 0.71% Veterinary activities 2216 494 0.09% 0.05% 0.05% Administrative, support service Rental and leasing activities 11,403 2667 0.30% 0.73% 0.66% Employment activities 6701 1718 0.70% 1.63% 1.49% Travel agency, tour operators 5355 1378 0.35% 0.88% 0.90% Security, investigation activities 1045 253 0.48% 1.91% 1.72% Buildings, landscape service act. 9082 2221 0.53% 1.21% 0.87% Business support activities 8924 2066 0.18% 0.52% 0.44% Education Education 10,236 2548 0.20% 0.51% 0.52% Human health, social work Human health activities 26,538 6115 0.08% 0.14% 0.15% Residential care activities 704 152 0.00% 0.43% 0.43% Social work without accommodation 9066 1951 0.08% 0.19% 0.17% Arts, entertainment and recreation Arts and entertainment activities 5023 1309 0.24% 0.48% 0.40% Libraries, museums, other culture 436 85 0.00% 0.00% 0.00% Gambling and betting activities 778 165 0.13% 0.64% 0.77% Sports, amusement, recreation 9288 2160 0.23% 0.54% 0.55% Other service activities Membership organisations 516 120 0.00% 0.00% 0.19% Repair, personal, household goods 1037 256 0.87% 1.83% 1.35% Other personal service activities 12,022 2782 0.23% 0.62% 0.57% Total 818,927 192,118 0.39% 1.04% 0.88% Notes: Our sample of SMEs’financial statements, the number of unique companies and bankruptcy frequency over different time horizons per industry at the oneand two-digit levels, in accordance with the Norwegian Standard Industrial Classification (SIC2007) based on the UN’s ISIC Rev. 4 and EU’s NACE Rev. 2. COGENT ECONOMICS & FINANCE 33