Disentangling the black box around CEO and financial information-based accounting fraud detection: machine learning-based evidence from publicly listed U.S. firms

Schneider, Moritz; Brühl, Rolf Article — Published Version Disentangling the black box around CEO and financial informationbased accounting fraud detection: machine learning-based evidence from publicly listed U.S. firms Journal of Business Economics Provided in Cooperation with: Springer Nature Suggested Citation: Schneider, Moritz; Brühl, Rolf (2023) : Disentangling the black box around CEO and financial information-based accounting fraud detection: machine learning-based evidence from publicly listed U.S. firms, Journal of Business Economics, ISSN 1861-8928, Springer, Berlin, Heidelberg, Vol. 93, Iss. 9, pp. 1591-1628, https://doi.org/10.1007/s11573-023-01136-w This Version is available at: https://hdl.handle.net/10419/311070 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. 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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/ Vol.:(0123456789) Journal of Business Economics (2023) 93:1591–1628 https://doi.org/10.1007/s11573-023-01136-w 1 3 ORIGINAL PAPER Disentangling theblack box aroundCEO andfinancial information‑based accounting fraud detection: machine learning‑based evidence frompublicly listed U.S. firms MoritzSchneider1 · RolfBrühl1 Accepted: 28 December 2022 / Published online: 4 February 2023 © The Author(s) 2023 Abstract This study investigates the predictive power of CEO characteristics on accounting fraud utilizing a machine learning approach. Grounded in upper echelons theory, we show the predictive value of widely neglected CEO characteristics for machine learning-based accounting fraud detection in isolation and as part of a novel combination with raw financial data items. We employ five machine learning models well-established in the accounting fraud literature. Diverging from prior studies, we introduce novel model-agnostic techniques to the accounting fraud literature, opening further the black box around the predictive power of individual accounting fraud predictors. Specifically, we assess CEO predictors concerning their feature importance, functional association, marginal predictive power, and feature interactions. We find the isolated CEO and combined CEO and financial data models to outperform a no-skill benchmark and isolated approaches by large margins. Nonlinear models such as Random Forest and Extreme Gradient Boosting predominantly outperform linear ones, suggesting a more complex relationship between CEO characteristics, financial data, and accounting fraud. Further, we find CEO Network Size and CEO Age to contribute second and third strongest towards the best model’s predictive power, closely followed by CEO Duality. Our results indicate U-shaped, L-shaped, and weak L-shaped associations for CEO Age, CEO Network Size, CEO Tenure, and accounting fraud, consistent with our superior nonlinear models. Lastly, our empirical evidence suggests that older CEOs who are not simultaneously serving as chairman and CEOs with an extensive network and high inventory are more likely to be associated with accounting fraud. Keywords Accounting fraud· CEO characteristics· Corporate governance· Machine learning JEL Classification C63· K22· K42· M41· M48 * Moritz Schneider [email protected] Extended author information available on the last page of the article 1592 M.Schneider, R.Brühl 1 3 1 Introduction Accounting fraud cases are frequently and globally occurring events causing extensive financial and non-financial damage to employees, businesses, investors, and society.1 The Association of Certified Fraud Examiners (2020) estimates that fraud damages for organizations amount to 5% of total revenue or $4.5 trillion yearly, with financial statement fraud being the rarest but most costly fraud.2 Timely accounting fraud detection to mitigate the associated costs would be valuable to investors, regulators, and auditors (Bao etal. 2020).3 However, detecting accounting fraud is challenging (Bao etal. 2020). First, due to the severe class imbalance between detected fraud and non-fraud cases (Beneish 1999) and “partial observability of fraud" (Wang etal. 2010, p. 2256), there is a need for substantial sample sizes. Second, aggregated financial information does not fully reflect information asymmetry related to organizational behavior (Campbell and Shang 2022). While the vast majority of accounting fraud detection studies have mainly considered predictors based on financial information, scant empirical studies address non-financial information. Although the associations between non-financial characteristics and financial misconduct have been theoretically and empirically established (e.g., Beasley 1996; Dechow etal. 1996; Johnson etal. 2009; Troy etal. 2011; Wahid 2019; Zahra etal. 2005), only a few studies have considered such characteristics for machine learning-based accounting fraud detection (Bertomeu etal. 2021; Fanning and Cogger 1998; Kim etal. 2016; Wang etal. 2018, 2020). However, none of them primarily focus on CEO characteristics, whereas we aim at improving predictions by studying the joint predictive power of these predictors and raw financial data.4 We specifically investigate CEO-related data for three reasons. First, we look for alternative predictors, as aggregated financial information can be altered to disguise underlying firm-related manipulations (Lewis 2013). Second, while the CEO and CFO represent top managers likely to be associated with a firm’s accounting outcomes (e.g., Gupta etal. 2020; Troy etal. 2011), the literature typically considers the CEO as the most powerful character of a firm. Moreover, studies suggest that CEO power influences the interaction with CFOs, as they find a CEO to hold power over the CFO’s accounting behavior (e.g., Feng etal. 2011; Friedman 2014) and that pressure constitutes a primary cause for earnings management by CFOs (Dichev etal. 2013). Lastly, various CEO characteristics have been established concerning outcomes related to accounting fraud. Because upper echelons theory suggests that the top management team’s characteristics have predictive power on organizational 1 In this study, we use the terms “accounting fraud “ and “misstatement” synonymously, similar to previous literature (e.g., Bao etal. 2020). 2 This loss has been obtained by projecting an estimate of a 5% loss in revenue against 2019’s gross world product (GWP) of $90.52 trillion (Association of Certified Fraud Examiners 2020). 3 We follow prior literature (e.g., Bao etal. 2020) and use the terms “prediction” and “detection” interchangeably throughout our work. 4 We follow Bao etal.’s (2020) terminology and refer to “raw financial data items” as financial information that can be directly obtained from the financial statements rather than computed as human expertidentified financial ratios. 1593 1 3 Disentangling theblack box aroundCEO andfinancial… decisions (Hambrick and Mason 1984; Hambrick 2007), we consider CEO-related information. The latter is theoretically motivated and empirically associated with financial misconduct by previous literature (e.g., Ali and Zhang 2015; Bhandari etal. 2018; Dechow etal. 1996; Ho etal. 2015; Huang etal. 2012; Troy etal. 2011; Zahra etal. 2005). Moreover, prior machine learning-based detection studies focused on prediction improvements but lacked interpretability. While prediction and explanation are two distinct research goals (Shmueli 2010), understanding the drivers behind a model’s predictive power is paramount for financial applications (Sigrist and Hirnschall 2019). Consequently, we introduce state-of-the-art model-agnostic techniques to the accounting fraud detection literature, opening the black box surrounding model prediction. In particular, we rely on the permutation-based feature importance (Breiman 2001) and SHapley Additive exPlanation (SHAP) dependence plots (Lundberg and Lee 2017). We use five established machine learning algorithms to assess and disentangle the CEO characteristics’ out-of-sample predictive power for accounting fraud in isolation and a novel combination with raw financial data items. We expect that the inclusion of literature and theory-derived CEO characteristics captures and adds additional non-financial, and latent firm-related insights, resulting in models that outperform a no-skill benchmark and solely data-based financial models, respectively. Guided by Schnatterly etal. (2018) and the well-established fraud triangle framework (Cressey 1950), we derive CEO characteristics that reflect pressure, opportunity, and rationalization to commit fraud. Our reasoning is similar to recent literature that constitutes the additional value of complementing accounting with other firm-related information for predicting firm outcomes (e.g., Bertomeu etal. 2021; Cheynel and Levine 2020). Further, we specifically investigate the contribution of the variables toward the prediction, their marginal effects, functional form, and interactions to understand the drivers behind the predictive performance. Following prior literature (e.g., Bao etal. 2020; Beasley 1996; Brown etal. 2020; Cecchini etal. 2010; Dechow etal. 2011; Perols etal. 2017; Purda and Skillicorn 2015), we use material accounting misstatements published in the SEC’s Accounting and Auditing Enforcement Releases (AAERs) and provided by Dechow etal. (2011) as binary fraud measure. While established accounting fraud detection literature uses human expert-identified financial ratios to predict accounting fraud (e.g., Beneish 1999; Cecchini etal. 2010; Dechow etal. 2011), we instead incorporate their underlying raw financial data items directly. Thus, we follow recent empirical evidence of the predictive superiority of raw financial data items over financial ratios (Bao etal. 2020). Our sample covers publicly listed U.S. firms for 2000–2018 and contains matched financial and CEO data of 30,178 firm-years, including 198 fraudulent firm-years. Consistent with our expectations, we find empirical evidence that suggests a robust predictive performance of machine learning models based on CEO characteristics over a no-skill benchmark for accounting fraud detection. Further, we show the additional predictive value of CEO characteristics combined with raw financial predictors compared to isolated models across all classifiers. Interestingly, nonlinear models such as random forest (RF) and extreme gradient boosting (XGB) 1594 M.Schneider, R.Brühl 1 3 predominantly outperform their linear counterparts, suggesting more complex associations between CEO and financial data and accounting fraud. With CEO Network Size, CEO Age, and CEO Duality, we find half of the considered CEO characteristics included in the top 10 essential features. Consistent with our superior nonlinear models, our results indicate a U-shaped association between CEO Age, an L-shaped association for CEO Network Size, and a weak L-shaped relationship between CEO Tenure and accounting fraud. Lastly, we extend the literature’s knowledge by visualizing interactions between essential features. The results suggest that older CEOs not simultaneously serving as chairman and CEOs with a network of up to 2500 connections and high inventory are more likely to be associated with accounting fraud. This study complements previous accounting fraud detection literature in various aspects. First, to our knowledge, we are the first to focus on both CEO characteristics and assess the joint predictive power of CEO characteristics combined with raw financial data items in machine learning models for out-of-sample accounting fraud detection. Second, we address the shortage of empirical research investigating nonlinear relationships between corporate governance and financial misconduct (Velte 2021). Third, we follow the call by Doornenbal etal. (2021) that invoked research to incorporate more (interpretable) machine learning techniques to uncover currently hidden and more complex associations and allow for future theory advancements. Our results suggest future research’s potential to address more complex relationships between CEO Age, CEO Network Size, CEO Tenure, and accounting fraud. 2 Theoretical background andresearch questions development Our study draws on two literature streams. Firstly, our research relates to the substream of accounting fraud literature that develops out-of-sample accounting fraud detection models. Secondly, we draw on literature about fraud antecedents on the individual level of corporate governance—the CEO (Velte 2021). The first literature stream can be separated into explanatory and predictive approaches (Shmueli 2010). While many studies focused on investigating causal relationships between financial and non-financial firm-specific characteristics as antecedents of accounting fraud (e.g., Beasley 1996; Brazel etal. 2009; Dechow etal. 1996; Schrand and Zechman 2012), the rise of technological development initiated a transition towards more predictive approaches. Thus, having established associations of relevant antecedents for accounting fraud, many studies started to employ regression- or machine learning-based approaches to predict accounting fraud. Regression-based models appear to be the most frequently applied technique for accounting fraud detection within the accounting and information systems literature (Albizri etal. 2019). Among others, Beneish (1999) constructed a probit model to predict the likelihood of accounting fraud based on accounting variables. They showed that the model could identify about 50% of firm-years with manipulated earnings before public disclosure (Beneish 1999). Another well-known example is the study of a logit model developed by Dechow etal. (2011), which investigated financial information of about 16,000 firm-years including 2190 AAERs, and predicted misstating firms with an overall accuracy of 63.7% and a recall of 68.6%. This study is still considered a 1595 1 3 Disentangling theblack box aroundCEO andfinancial… competitive model and is used as a benchmark for more recent algorithms (Bao etal. 2020). While many studies have included regression-based models for accounting fraud detection (e.g., Bao etal. 2020; Bertomeu etal. 2021; Craja etal. 2020; Larcker and Zakolyukina 2012), a shift toward more advanced machine learning approaches has occurred along with technical developments. Thus, the majority of studies investigated the predictive power of random forests (RF) (e.g., Bertomeu etal. 2021; Craja etal. 2020; Wang etal. 2020; Whiting etal. 2012), support vector machines (SVM) (e.g., Bertomeu etal. 2021; Cecchini etal. 2010; Craja etal. 2020; Perols etal. 2017; Purda and Skillicorn 2015), and neural networks (NN) (e.g., Craja etal. 2020; Fanning and Cogger 1998; Green and Choi 1997; Ravisankar etal. 2011). Recently, ensemble methods like RUSBoost (Bao et al. 2020), extreme gradient boosting (XGB) (Craja etal. 2020), or gradient boosted regression tree (Bertomeu etal. 2021) have been introduced. Prior studies deployed financial ratios identified by experts and empirically shown to be associated with accounting fraud or material misstatements (e.g., Beneish 1997, 1999; Cecchini etal. 2010; Dechow etal. 2011). For instance, Beneish (1999, pp. 26–28) considered “Days’ sales in receivables index”, “Gross margin index”, “Asset quality index”, “Sales growth index”, “Depreciation index”, “Sales, general, and administrative expenses index”, “Leverage index”, and “Total accruals to total assets”. Similar categorizations have been established by Dechow etal. (2011). They categorized financial characteristics into “Accrual quality”, “Performance”, “Nonfinancial measures”, “Off-balance-sheet activities”, and “Market-related incentives” (Dechow etal. 2011, pp. 34–41). However, Bao etal. (2020) recently deviated from including the predominantly used financial ratios and empirically showed the superior performance of the underlying raw financial data items. In particular, they derived a combined set of 28 underlying raw financials from well-estab- lished financial ratios utilized by Cecchini etal. (2010) and Dechow etal. (2011). Among others, the variables included stock information, such as “Common Shares Outstanding” or “Price Close—Annual”, balance-sheet information like “Current Assets—Total”, “Account Payable—Trade” or “Cash and Short-Term Equivalents”, as well as income information, such as “Depreciation and Amortization” or “Net Income (Loss)” (Bao etal. 2020, p. 229).5 Robustness checks with different raw financials validated the predictive power of the identified 28 financials (Bao etal. 2020). Only a few machine learning-based studies employed prediction models using non-financial predictors. An exception is the sub-stream of literature that investigates text-based predictors either in isolation or in combination with financials (e.g., Brown etal. 2020; Craja etal. 2020; Hobson etal. 2012; Larcker and Zakolyukina 2012; Purda and Skillicorn 2015). However, besides this literature stream, hardly any study either combines financial and non-financial predictors, such as board characteristics (Fanning and Cogger 1998; Wang etal. 2020), executive compensation (Kim etal. 2016), governance, audit or business data (Bertomeu etal. 2021) or builds their model solely on non-financials, such as board data (Wang etal. 2018). 5 For a complete list of variable names see Table7 in Bao etal. (2020). 1596 M.Schneider, R.Brühl 1 3 Interestingly, several studies exist that investigate non-financial antecedents related to accounting fraud but are widely neglected by prior machine learning-based prediction approaches (e.g., Ali and Zhang 2015; Dechow etal. 1996; Huang etal. 2012; Troy etal. 2011; Schrand and Zechman 2012). The second literature stream we draw on focuses on accounting fraud-related antecedents at the CEO level, which has been widely neglected within machine learning-based accounting fraud studies. Inspired by Schnatterly etal. (2018), we consider six CEO characteristics derived from prior literature and categorize them within the well-established fraud triangle framework (Cressey 1950; Dorminey etal. 2012; Trompeter etal. 2013), common in the audit literature (Dorminey etal. 2012): pressure (CEO Tenure, CEO Network Size), opportunity (CEO Duality), and rationalization (CEO Age, CEO Gender, CEO MBA).6 According to the fraud triangle, these three interacting antecedent groups precede fraud, where higher interaction and manifestation of these elements result in higher fraud risk (Dorminey etal. 2012). Pressure (or Incentives). Pressure (or incentives) represents the perceived motivation that forces (incentivizes) the actor to behave fraudulently (Dorminey etal. 2012). CEOs’ perceived pressure (or incentives) to misbehave can originate from various sources, such as career concerns. Thus, Ali and Zhang (2015) argue that CEO and firm performance are linked (Fama 1980) and that the CEO has an interest in optimizing her future career perspectives, such as “compensation, reappointments or managerial autonomy” (Ali and Zhang 2015, p. 61). Therefore, the external labor market needs to perceive the CEO as a well-performer (e.g., Fama 1980). However, especially at the beginning of a CEO’s tenure at a firm, the market is likely uncertain about a CEO’s ability (Gibbons and Murphy 1992) due to a lack of historical CEO performance information (Ali and Zhang 2015). As unfavorable market valuations of the CEO’s ability could hamper her career perspectives, the CEO is incentivized to improve the market’s perception of her abilities in the early years (Ali and Zhang 2015). Consistent with this argumentation, Ali and Zhang (2015) find earnings overstatements to be greater in CEOs’ early years than in the later years of their tenure. However, the horizon problem7 suggests that departing CEOs have incentives to behave opportunistically in their final years of tenure to boost their short-term compensation (Dechow and Sloan 1991). Ali and Zhang (2015) consistently find that earnings are overstated in the CEO’s final years when controlling for early year overstatements. Similarly, social psychology suggests that human behavior is driven by social norms and the expected judgment of one’s behavior by others (Cialdini etal. 1991). 6 We also considered established compensation-related variables which were suggested to provide incentives for fraudulent action (e.g., Johnson etal. 2009; Zhang etal. 2008), such as CEO ownership and CEO options to compensation (Koch-Bayram and Wernicke 2018). However, following Cecchini etal. (2010), we removed them from the final sample because of missing values > 25%. 7 Following Smith and Watts (1982) we refer to the “horizon problem” as executives considering to leave the firm and focusing on short-term performance due to earnings-based compensation. 1597 1 3 Disentangling theblack box aroundCEO andfinancial… Corporate misconduct could result in reputational damages that mitigate future career prospects (Karpoff 2011). Thus, anticipated social capital losses may result in a disincentive to misbehave (Atanasov et al. 2012). Based on this reasoning, Bhandari etal. (2018) find the number of CEO connections negatively associated with earnings management and financial restatements. Opportunity. Opportunity describes the perceived possibility of the actor committing fraud without fearing detection or punishment (Dorminey etal. 2012). CEO power is typically considered the main characteristic of fraud opportunity on the CEO level (Schnatterly etal. 2018), commonly measured by CEO duality (Velte 2021). Particularly, Jensen (1993) theorizes that if a CEO simultaneously serves as chairman of the board, the oversight of the management is reduced. Based on this argument, Dechow etal. (1996) find firms with CEO duality to show a higher likelihood of receiving SEC AAERs, consistent with the prior expectations. Rationalization. Lastly, rationalization embodies the actor’s integrity to internally justify the fraudulent act as morally reasonable (Dorminey etal. 2012). According to Schnatterly etal. (2018), individuals try to resolve a moral trade-off between their fraudulent behavior and societal ethics (e.g., Cressey 1950; Trompeter etal. 2013). Thus, a CEO’s ethical socialization is likely important for rationalizing fraudulent behavior. CEO age, gender, and business education (MBA) may be associated with ethical processes and, in turn, fraudulent acts (Schnatterly etal. 2018). First, Troy etal. (2011) argue that prior literature suggests negative associations between age and unethical (e.g., Hunt and Chonko 1984; Kelley etal. 1990) or risktaking behavior (e.g., Brouthers etal. 2000; Hambrick and Mason 1984; Markóczy 1997). The authors further suggest that older individuals behave less risky, as they are more likely to adhere to organizational rules (Child 1974), are more morally developed (Kelley etal. 1990), construe a code of conduct more strictly (Serwinek 1992), and are less likely to succumb to external pressures (Daboub etal. 1995; Price and Norris 2009). Based on these findings, Troy etal. (2011) posit that older CEOs are less likely to rationalize the costs of the risk and the respective consequences of being discovered than their younger counterparts. Consistently, the literature finds CEO age negatively related to accounting fraud (Huang etal. 2012; Troy etal. 2011). Second, different socializations between genders contribute towards diverging individual ethical values (e.g., Mason and Mudrack 1996; Weeks etal. 1999), which can result in more ethical decision-making at work (Dawson 1995). In particular, female practitioners are more ethically sensitive and risk-averse than their male counterparts (e.g., Weeks etal. 1999). Following these studies, Ho etal. (2015) find female CEOs positively associated with accounting conservatism. Building on this, Schnatterly etal. (2018) propose an association between CEO gender and financial misconduct. Lastly, Troy etal. (2011) draw on prior literature that indicates positive associations between education and moral development (Freeman and Gilbert 1988; Rest and Thoma 1985), information processing (Wiersema and Bantel 1992), and better decision-making (e.g., Fiske and Taylor 1991). The authors follow the 1598 M.Schneider, R.Brühl 1 3 “preponderance of literature” (Troy etal. 2011, p. 265) and Barker and Mueller (2002), who suggest that business education establishes analytical skills that avoid negative business consequences. Based on this argumentation, Troy etal. (2011) argue that the findings on education levels can be extended to business education, which establishes fundamental knowledge of accounting and the potential negative consequences of misbehavior. This is, in turn, expected to result in CEOs being less likely to rationalize accounting fraud (Troy etal. 2011). Consistent with this reasoning, Troy etal. (2011) find significant negative associations between firms with CEOs holding business degrees and accounting fraud. Grounded in upper echelons theory (Hambrick and Mason 1984) and the proposed individual predictive value of the CEO characteristics on accounting fraud, we argue that the combination of CEO characteristics could reveal a large share of a CEO’s underlying values and cognitive processes linked to accounting fraud behavior. Therefore, we explore if machine learning models based on these characteristics perform better in separating fraudulent from non-fraudulent firm-years than a random guessing threshold. Hence, the first research question can be stated as follows: RQ1a Do machine learning models for accounting fraud detection based on CEO characteristics achieve a predictive performance superior to random guessing? Bao etal. (2020) suggest that although most accounting fraud detection literature relies on human expert-identified financial ratios, raw financial data items capture a superior predictive value compared to financial ratios. However, following the argumentation of Campbell and Shang (2022), aggregated financial information only partially reflects the company’s inner workings, including behavioral patterns and values, which are likely associated with misconduct. Similarly, Bertomeu etal. (2021) propose that accounting variables add predictive value to their accounting fraud detection model, primarily through their complementary effect with other information sources. Following this line of reasoning, we fit in the scant but growing accounting fraud prediction literature, which suggests that complementing accounting information with non-financial data (e.g., business, text, corporate governance data) leads to superior predictive models (e.g., Bertomeu etal. 2021; Craja etal. 2020; Wang etal. 2020).8 We argue to incorporate additional latent firm-specific information associated with accounting fraud and neglected by financial predictors. This information increase likely results in higher predictive performance for accounting fraud detection, which is essential to detect and reduce costs on time. Following this reasoning, in combination with raw financial data items, we posit that CEO characteristics deliver superior predictive performance than financial and CEO models in isolation. Hence, the second research question can be stated as follows9: 8 Many studies investigate non-financial information and their associations with accounting fraud (e.g., Dechow etal. 1996). While we follow this stream and believe the disclosed information to capture valuable latent information, we acknowledge its potentially decreased reliability due to a lack of external auditing of reports that include this information. We thank an anonymous reviewer for raising this point. 9 See Online Appendix A for a visual presentation of the main research framework, including RQ1a and b. 1605 1 3 Disentangling theblack box aroundCEO andfinancial… descriptive result of accounting fraud firms in Koch-Bayram and Wernicke (2018). The higher rate of male CEOs in fraudulent firm-years is in line with prior literature suggesting more conservative accounting behavior by firms led by female CEOs (Ho etal. 2015). 4.2 Research design This study performs a research design similar to Craja etal. (2020) and Doornenbal etal. (2021). Thus, consistent with Craja etal. (2020), we apply five distinct classification models to detect accounting fraud out-of-sample. We perform various models to establish robustness across multiple prediction approaches and allow for potential insights into the complexity of the association. This argumentation is similar to Doornenbal etal. (2021), who employ a linear and more complex RF model to assess the degree of nonlinearity within the leadership-trait paradigm. Specifically, the models considered within this study are LR, SVM, RF, XGB, and a NN. Following Craja etal. (2020), we train and test the selected models incorporating different groups of variables.21 While we only consider CEO-related variables within the Table 1 Sample selection overview Bold values indicates the important values Compustat firm-years BoardEx firm-years AAER firm-years Initial Sample from Compustat (2000–2018) 202,529 Initial Sample from AAER (2000– 2018) 1055 Less: missing CIK −22,865 −93 Less: duplicates −21,878 −4 Sample Merged Compustat-AAER (2000–2018) 157,786 838 Initial CEO Sample from BoardEx (2000–2018) 120,261 Less: non-matching identifiers (ISIN) −25,496 Less: non-US headquarters −12,577 Less: duplicates −14,070 Sample BoardEx 68,118 Less: non-matching identifiers & years −103,143 −471 Sample Merged Compustat—BoardEx 54,643 367 Less: financial industry (SIC 6000–6999) −12,873 −61 Less: missing values −11,592 −108 Final Sample (firm-years 2000–2018) 30,178 198 21 Consequently, we follow Craja etal.’s (2020) depiction of the variable groups and similarly refer to them as CEO, FIN, and CEO + FIN. 1606 M.Schneider, R.Brühl 1 3 selected models to answer RQ1a, we perform the detection models on the isolated CEO (CEO) and financial variables (FIN) as well as on the combined set of features (CEO + FIN) to answer RQ1b. Referring to prior studies, we perform permutation-based feature importance (e.g., Doornenbal etal. 2021) to rank the features by importance for model building and introduce the novel SHAP dependence plots by Lundberg and Lee (2017) on the best performing model. We assess the feature ranking, the direction of the association, functional form, and main and interaction effects to investigate RQ2a to RQ2c. Following previous literature, we mainly use the AUC to evaluate the models’ capability to separate fraudulent and non-fraud- ulent firm-years correctly (e.g., Bao etal. 2020; Bertomeu etal. 2021; Craja etal. 2020). Model Development. This study conducts an extensive model development process, including data pre-processing, hyperparameter tuning, and resampling. To address Table 2 Descriptive statistics for CEO-characteristics Panel A represents key summary statistics of the CEO characteristics for the full sample. Panel B depicts the means, standard deviations (SD), and p values for these variables between the fraudulent and nonfraudulent firm-year groups. All results are rounded to two decimals except for the p values, which are rounded to three decimals. The superscripts *, **, and *** represent the standard statistical significance levels of 10, 5, and 1% of a two-tailed students t test or Welch’s test Boldvalues indicates the significance values Panel A full sample Mean SD Median Min Max CEO Age 53.89 7.66 54.00 27.00 86.00 CEO Network Size 1310.67 1463.59 829.00 5.00 17,168.00 CEO Tenure 3.94 5.28 2.10 0.00 54.90 CEO Duality 0.46 0.50 0.00 0.00 1.00 CEO MBA 0.36 0.48 0.00 0.00 1.00 CEO Gender 0.96 0.19 1.00 0.00 1.00 n = 30,178 Panel B By fraud status Fraudulent firm-years Non-fraudulent firm-years Mean SD Mean SD t test p-value Welch’s test p value CEO Age 50.83 8.45 53.91 7.65 < 0.001*** < 0.001*** CEO Network Size 977.14 1036.86 1312.88 1465.76 0.001*** < 0.001*** CEO Tenure 3.24 3.89 3.94 5.29 0.062* 0.012** CEO Duality 0.58 0.50 0.46 0.50 0.002*** 0.002*** CEO MBA 0.36 0.48 0.36 0.48 0.869 0.869 CEO Gender 0.97 0.16 0.96 0.19 0.359 0.269 n198 29,980 1607 1 3 Disentangling theblack box aroundCEO andfinancial… the potential spurious effects of outliers which could significantly influence outliersensitive models (LR, NN), we follow previous studies and winsorize financial variables at the 1% and 99% levels (Beneish 1999; Bertomeu etal. 2021; Dechow etal. 2011; Green and Choi 1997).22 Consistent with Craja etal. (2020), we perform a random and stratified sample split to keep a constant fraud-to-nonfraud ratio across training and test samples.23 Following common machine learning practice, we split the data to reach a training set of 70% (21,124, incl. 139 fraud-years) and a hold-out test set of 30% (9054, incl. 59 fraud-years) of the total firm-year observations. We normalize the data sets to address potential scaling biases across LR, SVM, and NN features. As tree-based methods are insensitive to different scales, we follow Sigrist and Hirnschall (2019) and do not scale the RF and XGB models. To prevent our models from potentially misidentifying fraud years caused by an imbalanced data bias, we follow recent literature (e.g., Bao etal. 2020; Craja etal. 2020) and address the severely imbalanced data using random under sampling (RUS). RUS randomly removes majority class observations (i.e., nonfraud) to reach a targeted nonfraud- to-fraud ratio. While this approach could result in a biased majority class sample,24 van Hulse etal. (2007) demonstrate the improved predictive performance of resampled models, with RUS performing best in most experimental settings, including settings relying on the AUC. As our data constitute a similar absolute fraud number to Craja etal. (2020), we follow them and target a nonfraud-to-fraud ratio of 4:1.25 This reduces the severe imbalance and keeps a reasonable training size that allows for proper model training while still acknowledging non-fraudulent observations as the majority class (Craja etal. 2020).26 We apply all models to the isolated (CEO, FIN) and combined feature sets (CEO + FIN). Because different models are based on various meta-parameters that can be tuned to optimize their predictive power on out-of-sample testing, we apply the well-established grid-search algorithm to find each model’s optimal values. The algorithm utilizes fivefold cross-validation to establish robustness in predictive performance over five varying training and validation set combinations to prevent the trained model from overfitting. Overall, the algorithm repeatedly runs through a grid of specified parameter values to train and validate the model on all potential combinations of parameters and identifies the parameter combination that results in the best AUC averaged over the five left-out validation sets. Following this procedure for the CEO + FIN data, we find the optimal parameters for the SVM to incorporate a complexity parameter C = 10 and polynomial degree 22 Analyses without winsorization show qualitatively similar results, which are available upon request. 23 Following previous literature (e.g., Bao etal. 2020) and common machine learning practice, we set a random seed equaling zero to allow for random number generations that enable replications of our results for any random element. 24 We thank an anonymous reviewer for raising this point. 25 Acknowledging that the precise determination of a nonfraud-to-fraud ratio can hardly be supported by theoretical arguments or empirical evidence, we also compute our out-of-sample performance comparison with the adjacent ratios of 3:1 and 5:1. The untabulated analyses show qualitatively similar results, suggesting our findings to be robust. 26 Specifically, we apply the outlined normalization and RUS approaches within grid-search and crossvalidation to adapt to repeatedly changing training and validation sets. 1608 M.Schneider, R.Brühl 1 3 d = 2. For the RF model, we find the number of trees M = 100, the maximum number of features m = 2, and tree depth T = ∞ .27 We find the final XGB model to include M = 500 boosting iterations, a maximum depth T = 10, and a learning rate v = 0.1, and the NN consists of h = 100, a = “relu”, s = “adam”, and l2 = 0.05. Following prior literature (e.g., Bao etal. 2020; Perols 2011), the LR has not been tuned. We follow an equivalent approach for the isolated (CEO, FIN) models. See Appendix A for details on the selection of the tuning parameters.28 An overview of the model development and testing process is visualized in Fig.1. 5 Results 5.1 Performance evaluation RQ1a Do machine learning models for accounting fraud detection based on CEO characteristics achieve a predictive performance superior to random guessing? Having found optimal hyperparameters, we assess the predictive power of these models on unseen test data. We follow prior literature and use the AUC to evaluate the models’ predictive power. Model comparison primarily relies on the AUC differences in magnitude rather than statistical differences (e.g., Bao etal. 2020; Bertomeu etal. 2021; Cecchini etal. 2010; Craja etal. 2020). Table3 Panel A displays the prediction results for the final models based solely on CEO data (CEO). Our results indicate that all models exceed the benchmark Fig. 1 Overview of model development and testing process 27 We draw on Sigrist and Hirnschall (2019) in denoting the parameters. Thus, ∞ represents a tree’s indefinite depth. 28 Our results are based on computations in Python. Specifically, we draw on the scikit-learn (Pedregosa etal. 2011), SHAP (Lundberg and Lee 2017), Alibi (Klaise etal. 2021), and imblearn (Lemaître etal. 2017) packages. 1609 1 3 Disentangling theblack box aroundCEO andfinancial… AUC for no-skill models of 0.5 by a large margin. Even the weakest model, the LR, outperforms the random benchmark by about 11%-points. The strongest predictive model, the XGB, even outperforms the benchmark by 31%-points, closely followed by the RF with 29%-points. These results suggest robust empirical evidence of CEO characteristics’ joint predictive power toward firm-year accounting fraud detection across various prediction models. Interestingly, we also find superior tree-based models, suggesting a nonlinear relationship between CEO characteristics and accounting fraud. We find the XGB as the most sensitive model when considering the other metrics. It correctly identifies TPs out of all investigated firms (TP, FP) in about 85% of firm-years. However, compared to the RF model, the XGB performs weaker in correctly identifying nonfraudulent firm-years (TN) out of all non-fraudulent firm-years (0.6819), also resulting in lower accuracy (0.6830). The LR and especially the SVM models appear to have difficulties achieving high sensitivity. RQ1b Do machine learning models for accounting fraud detection based on a combination of raw financial and CEO information (CEO + FIN) outperform isolated approaches (CEO, FIN)? In addition to assessing CEO-based models, we compare the models for CEO data combined with raw financial data items drawn from Bao et al. (2020) and expect superior predictive performance. Table3 Panel C shows the results for the combined model (CEO + FIN). We find that the RF outperforms the other models with a test AUC (sensitivity) of 0.9285 (0.8644), followed by the XGB with a score of 0.9018 (0.7458). The weakest prediction model, the LR, achieves an AUC score (sensitivity) of 0.7590 (0.6610). Thus, the strongest model outperforms the weakest by a large AUC margin of about 17%-points. Related to specificity (0.8987) and accuracy (0.8977), the XGB outperforms all other models. Again, the tree-based models strongly exceed the performance of the other models when considering the AUC. This is consistent with Craja etal. (2020), who found that the RF and XGB models outperformed the LR, SVM, and NN models for finance data. Again, this provides empirical evidence for a potential nonlinear relationship between these predictors and accounting fraud. Further, Panel B of Table3 presents the results of the isolated financial (FIN) models for comparison. When comparing the results of the combined models (CEO + FIN) with equivalent models on the isolated data (CEO, FIN), we find the combined data models to outperform these separated approaches across all models. While the AUC deltas are higher for the isolated CEO models than the isolated FIN models, we still find relevant increases in prediction results for the combined models over the FIN models. Thus, especially among the weaker performing models (LR, NN, SVM), the added predictive power of the combined models on out-of-sample data reaches an increase of 7%-points for the LR, 6%-points for the NN, and about 5%-points for the 1610 M.Schneider, R.Brühl 1 3 SVM. While the added predictive value appears smaller for the RF and XGB models (about 2%-points each), this still represents an economically significant improvement, as prior studies find similar improvement ranges. The most similar study by Craja etal. (2020) finds the combination of financial and textual models to outperform models based on a combination of financial and linguistic data by 2%-points of AUC for RF and 3% for XGB.29 Despite more diverging data pre-processing, models, and testing approaches, Bao etal. (2020) show the combination of the novel RUSBoost model and raw data to outperform the financial ratio-based LR model by Dechow etal. (2011) by 5.3%-points as measured by an average AUC score on unseen test data. They also show a predictive improvement of the LR and RUSBoost Table 3 Out-of-sample performance comparison of different feature models This table’s presentation is inspired by Craja etal. (2020). The scores of all metrics are rounded to 4 decimals. The Delta AUC scores rely on the rounded 4-decimal AUC scores Bold values indicates the important values Panel A CEO data (CEO) Model AUC Sensitivity Specificity Accuracy Delta AUC (No skill) LR 0.6148 0.5593 0.6804 0.6796 0.1148 SVM 0.6252 0.3729 0.8316 0.8286 0.1252 RF 0.7919 0.6610 0.8744 0.8744 0.2919 XGB 0.8089 0.8475 0.6819 0.6830 0.3089 NN 0.7073 0.6949 0.6784 0.6785 0.2073 Panel B finance data (FIN) Model AUC Sensitivity Specificity Accuracy Delta AUC (CEO) LR 0.6884 0.4576 0.8822 0.8794 0.0736 SVM 0.7209 0.5593 0.8328 0.8310 0.0957 RF 0.9133 0.8983 0.8327 0.8331 0.1214 XGB 0.8849 0.9322 0.6854 0.6870 0.0760 NN 0.7936 0.7458 0.7675 0.7674 0.0863 Panel C CEO and finance data (CEO + FIN) Model AUC Sensitivity Specificity Accuracy Delta AUC (FIN) Delta AUC (CEO) LR 0.7590 0.6610 0.7676 0.7670 0.0706 0.1442 SVM 0.7748 0.5763 0.8888 0.8868 0.0539 0.1496 RF 0.9285 0.8644 0.8743 0.8742 0.0152 0.1366 XGB 0.9018 0.7458 0.8987 0.8977 0.0169 0.0929 NN 0.8581 0.7458 0.8410 0.8404 0.0645 0.1508 29 We note that Craja etal. (2020) diverge from our study in their use of different financial data and other aspects, such as imputing missing values. Consequently, these studies’ results can only be compared with caution. 1611 1 3 Disentangling theblack box aroundCEO andfinancial… models by 2%-points and 6%-points for changing from 14 financial ratios to 28 raw financials (Bao etal. 2020). Overall, the results suggest the added predictive power by combining CEO and raw financial data items compared to equivalent models based on their isolated predictors (CEO, FIN). The results appear to be robust across all tested prediction models.30 5.2 Model interpretability RQ2a How influential are individual CEO characteristics for accounting fraud detection within the best CEO + FIN model? Interpretability is relevant to identifying the main drivers behind an algorithm classifying firm-years into fraudulent and non-fraudulent. Consequently, many featureimportance techniques have been proposed (see Molnar (2022) for an introduction). We follow recent literature (e.g., Doornenbal etal. 2021) and apply the permutation-based feature importance to our best performing CEO + FIN model, the RF.31 We do so rather than following prior accounting fraud literature (Bao etal. 2020; Bertomeu etal. 2021) since Strobl etal. (2007) showed empirical evidence for the superiority of the permutation-based approach. According to Strobl etal. (2007), impurity-based feature importance can lead to more unreliable feature importance estimates than permutation-based ones. Specifically, as the importance of impuritybased features systematically discriminates against lower-cardinality features (Strobl etal. 2007), we would expect the impurity-based feature importance to strongly bias the importance against the low-cardinality variables CEO Duality, CEO MBA, and CEO Gender. While this would limit the accurate interpretation of the variables’ importance,32 applying the permutation-based approach mitigates this potential bias. Permutation-based feature importance was developed by Breiman (2001) to provide a relative ranking of the contributions of a model’s features toward its prediction. The technique shows the total feature importance, including main and secondorder effects (Molnar 2022). The idea is to introduce noise by permuting a feature’s values, keeping the other features constant, and measuring the increase in the model’s prediction error (Molnar 2022). The higher the difference in prediction error after permutation, the more the model depends on this (permuted) feature and vice versa (Molnar 2022). However, we would like to point out that the ranking is not linked to the variables’ statistical significance (Shmueli 2010). Features that are not 30 Robustness tests comparing equal variable models support the models’ increased predictive performance by complementing FIN with CEO characteristics. See Online Appendix E for detailed results. 31 See https:// scikitlearn. org/ stable/ modul es/ permu tation_ impor tance. html for a more detailed explanation of the function and a computational example. 32 To validate this expectation, we also estimated the impurity-based feature importance ranking on the best performing CEO + FIN RF model and found strong evidence of lower cardinality variables being discriminated, whereas CEO Age (1) and CEO Network Size (7) retained a top 10 rank. The untabulated results are available upon request. 1612 M.Schneider, R.Brühl 1 3 significantly associated with the target might still be necessary for the out-of-sample predictive performance of a model (Gow etal. 2016). We follow Doornenbal etal. (2021) and employ the permutation-based feature importance with 200 feature permutations on the test set. However, while Doornenbal etal. (2021) based their feature importance method on the regression-based root mean squared error (RMSE), we consider the decrease in AUC for our imbalanced classification setting. This seems reasonable, as the AUC is used to find the best model. Panel A of Table4 visualizes the permutation feature importance and the respective mean AUC decrease. Columns 1 and 3 of Panel B of Table4 compare our RF model’s top 10 most essential features on CEO + FIN and Bao etal. (2020). Following Bao etal. (2020), we investigate the 10 most essential features. For the best performing RF model on the test sample, our results suggest Inventories—Total, CEO Network Size, CEO Age, Receivables—Total, Investment and Advances—Other, Liabilities—Total, Property, Plant, and Equipment—Total (Gross), Cash and Short-Term Investments, CEO Duality and Interest and Related Expense—Total as the essential features, ranked from highest to lowest.33 Interestingly, this implies two of the three most important features to be CEO characteristics. Mainly, CEO Network Size contributes second most towards the predictions, followed by CEO Age. When permuting the most critical variables, CEO Network Size and CEO Age decrease the mean AUC by about 1.8 and 1.2%-points. Additionally, with CEO Duality, a third CEO variable ranks within the top 10 most essential features. Thus, half of the CEO variables enter the top 10 despite their strong numerical inferiority compared to the incorporated raw financials. This suggests the strong predictive power of some CEO characteristics in the novel combination with raw financials for accounting fraud detection. However, the remaining CEO characteristics only rank 19 (CEO Tenure), 21 (CEO MBA), and 30 (CEO Gender). This result suggests the rather mediocre importance of CEO Tenure and CEO MBA and the weak contribution of CEO Gender towards the model’s predictive power. Especially when introducing noise to CEO Gender while keeping the other variables’ values constant, it has nearly no effect on the AUC. Consistent with similar literature (e.g., Bertomeu etal. 2021), our relatively low mean AUC decreases indicate that the final model heavily draws on the combinations of variables rather than a few strongly predictive ones.34 Inspired by Bao etal. (2020), we relate those findings to prior literature. For CEO Network Size, Bhandari etal. (2018) suggest a negative association between CEO connections and accounting fraud. Concerning the importance of CEO Age for accounting fraud, Troy etal. (2011) argue and empirically show that younger 33 As stated by Bertomeu etal. (2021), the results of this feature importance ranking should be interpreted with caution. Thus, correlations between variables can bias the results, as is typical for multivariate descriptive analyses (Bertomeu etal. 2021). However, when testing our results by comparing the RF and XGB feature rankings, we find a large overlap (7/10, incl. CEO Network Size, CEO Age and CEO Duality) in the top 10 features, suggesting that our results are robust. The results are presented in Sect.5.2, Table4 Panel B, and verbally in Sect.5.3. 34 This explanation is consistent with our untabulated impurity-based feature importance analysis. Thus, most features show a relative importance of about 3%, indicating the essentiality of variable combination. 1613 1 3 Disentangling theblack box aroundCEO andfinancial… Table 4 Feature importance of the best performing RF Model on CEO + FIN test data Panel A Permutation feature importance Rank Predictor Mean AUC decrease 1 Inventories—Total 0,018402 2 CEO Network Size 0,017624 3 CEO Age 0,011711 4 Receivables—Total 0,011329 5 Investment and Advances—Other 0,009656 6 Liabilities—Total 0,009263 7 Property, Plant, and Equipment—Total (Gross) 0,009229 8 Cash and Short-Term Investments 0,008977 9 CEO Duality 0,008436 10 Interest and Related Expense—Total 0,008409 11 Sale of Common and Preferred Stock 0,006927 12 Long-Term Debt—Total 0,006790 13 Income Taxes Payable 0,006324 14 Common Shares Outstanding 0,004984 15 Debt in Current Liabilities—Total 0,004929 16 Current Assets—Total 0,004559 17 Long-Term Debt—Issuance 0,004486 18 Common/Ordinary Equity—Total 0,004325 19 CEO Tenure 0,003247 20 Retained Earnings 0,003063 21 CEO MBA 0,002446 22 Income Before Extraordinary Items 0,001946 23 Price Close—Annual—Fiscal 0,001849 24 Depreciation and Amortization 0,001669 25 Income Taxes—Total 0,001589 26 Preferred/Preference Stock (Capital)—Total 0,001420 27 Current Liabilities—Total 0,001022 28 Net Income (Loss) 0,000587 29 Assets—Total 0,000231 30 CEO Gender 0,000042 31 Accounts Payable—Trade −0,000436 32 Cost of Goods Sold −0,000554 33 Short-Term Investments—Total −0,002645 34 Sales/Tturnover (Net) −0,004064 Panel B Top 10 feature importance—test comparisons CEO + FIN Bao etal. (2020) Rank RF XGB RUSBoost 1Inventories—Total Common/Ordinary Equity— Total Common Shares Outstanding 2CEO Network Size CEO Network Size Current Assets, Total 1614 M.Schneider, R.Brühl 1 3 CEOs rationalize accounting fraud significantly stronger than older CEOs. Similarly, Huang etal. (2012) investigate financial reporting quality and CEO Age and found a positive association. Considering the association between CEO Duality and accounting fraud, we assume this variable to be important as the power of the CEO strongly increases when also serving as chairman of the board, which in turn results in higher earnings management and financial misconduct (e.g., Dechow etal. 1996; Yang etal. 2017). Consequently, this literature suggests a positive relationship between CEO Duality and accounting fraud. However, further empirical evidence in this study’s setting would be required to validate this expectation. While these CEO characteristics are suggested to contribute significantly to the model’s overall prediction, we also find that some characteristics appear relatively irrelevant. Interestingly, CEO Gender shows a neglectable contribution to the prediction despite previously found empirical evidence for a significant association between gender and accounting fraud (e.g., Gupta etal. 2020; Ho etal. 2015; Wahid 2019). We assume that the small absolute and relative number of female CEOs in our data set partially explains this finding. Only 1135 (3.8%) of the included firm-years represent observations with female CEOs. Panel A represents the permutation-based feature importance ranking, and the respective mean AUC decreases after permutation for the best CEO + FIN model, RF. Panel B displays our top 10 most important features and compares them with the top 10 features by Bao etal. (2020) as a benchmark. We note, however, that the comparison with Bao etal. (2020) requires caution, as we use permutation-feature importance instead of impurity-based feature importance. Variables with asterisks signify CEO characteristics that were not included in Bao etal. (2020). Variables within the top 10 feature importance rankings of RF and XGB are bold. Variables in the RF/XGB and Bao etal.’s (2020) RUSBoost are written in italics Table 4 (continued) Panel B Top 10 feature importance—test comparisons CEO + FIN Bao etal. (2020) Rank RF XGB RUSBoost 3CEO Age CEO Age Sale of Common and Preferred Stock 4Receivables—Total Receivables—Total Property, Plant, and Equipment, Total 5Investment and Advances— Other Investment and Advances— Other Account Payable, Trade 6 Liabilities—Total Inventories—Total Cash and Short-Term Investments 7Property, Plant, and Equipment—Total (Gross) CEO Duality Price Close, Annual, Fiscal 8Cash and Short-Term Investments property, Plant, and Equipment—Total (Gross) Retained Earnings 9CEO Duality Sale of Common and Preferred Stock Inventories, Total 10 Interest and Related Expense— Total Common Shares Outstanding Common/Ordinary Equity— Total 1621 1 3 Disentangling theblack box aroundCEO andfinancial… accounting behavior (e.g., Feng etal. 2011; Friedman 2014). Various CEO characteristics have been established concerning outcomes related to accounting fraud. Consistent with this line of argumentation, we find all isolated CEO models to outperform random guesses by a large AUC margin. For all combined data models (CEO + FIN), we find them to outperform the isolated models by large margins, with RF performing the best. These results suggest the complementary predictive value of CEO characteristics within machine learning-based accounting fraud detection. We confirm prior empirical evidence by Craja etal. (2020) that showed the superiority of tree-based models, suggesting nonlinear relationships between financial predictors and accounting fraud, and extend it to CEO characteristics. While we rely on research design elements of similar studies (Bao etal. 2020; Craja et al. 2020), we diverge from these studies in various ways. Thus, to our knowledge, we are the first to focus on the predictive power of CEO characteristics in isolation and combination with raw financials for machine learning-based accounting fraud detection. Additionally, diverging from most prior literature, we address the typical issue of black-box models and introduce model-agnostic techniques to gain feature-related insights. Thus, we disentangle the novel combination models’ predictive performance drivers utilizing permutation-feature importance and introduce SHAP dependence plots to the accounting fraud detection literature. Our results suggest that CEO Network Size, CEO Age, and CEO Duality are among the top 10 most substantial contributors to the model’s predictions. Robustness checks confirm these results. We are also the first to extend these findings and show the L-shaped, U-shaped, and L-shaped main effects of CEO Network Size, CEO Age, and CEO Tenure within machine learning models, respectively. We suggest strong, weak, and neglectable main effects for CEO Duality, CEO MBA, and CEO Gender. Moreover, we indicate complex interactions between CEO Duality and CEO Age and CEO Network Size and Inventories—Total. Thus, older CEOs not serving as the chairman and CEOs with a network of up to 2500 and high inventory are more likely to be associated with accounting fraud. Our study extends current knowledge of CEO characteristics and accounting fraud detection in multiple ways. First, we indicate that CEO characteristics effectively detect accounting fraud within machine learning models in isolation and complement raw financial data items. Second, opening the black box, we find empirical evidence for nonlinear relationships between nonbinary CEO characteristics and accounting fraud and complex interactions, suggesting future research potential to advance theories and develop novel hypotheses. Our research also has practical implications. Stakeholders interested in detecting accounting fraud, such as auditors and authorities, might incorporate or improve predictive models, including CEO characteristics, to reduce detection time. CEO- based models could also be used for widely excluded firms (e.g., the financial industry) with diverging financial statement requirements. Incorporating SHAP also allows for explaining predictions, which is essential for applying such models in practice. Novel insights into CEO characteristics’ functional form and interactions on accounting fraud likelihood might provide ground for new policy directions or research theories. 1622 M.Schneider, R.Brühl 1 3 Appendix A Tuning parameter selection Following prior literature (e.g., Bao etal. 2020; Perols 2011; Wang etal. 2020), we do not tune the LR model. For the SVM, we follow previous studies (e.g., Perols 2011; Shin etal. 2005) and tune the complexity parameter C ∈ {1, 10, 50, 75, 100} and Perols (2011) in tuning the polynomial kernel-based SVM concerning its degree d ∈ {0.5, 1, 2, 5, 10}. After searching the parameter combinations to optimize the cross-validation AUC, we yield a final model with C = 10 and d = 2 for the combined feature model. For tuning the RF, we follow Sigrist and Hirnschall (2019) and consider the number of decision trees M, the maximum depth of each base tree T, and the maximum number of randomly chosen features for decision tree splits m to be tuned. We consider M ∈ {100, 500, 1000, 1500, 2000, 2500, 3000, 3500} and T ∈ {3, 5, 10, ∞ }.42 Following standard machine learning practices (e.g., James etal. 2021), we investigate values around m ≈ √p .43 Specifically, we consider lower values of m leading to higher decorrelation of the individually grown decision trees, primarily used data sets with potentially correlated predictors (James etal. 2021). Thus, we consider m ∈ {1, 2, 3, 4, 5, 6} for the combined CEO + FIN model. We find optimal parameters for the number of trees M = 100, the maximum number of features m = 2, and tree depth T = ∞ . Following Sigrist and Hirnschall (2019) for tuning boosted trees, the XGB is tuned concerning the number of boosting iterations M, maximum depth of each decision tree T, and the learning rate v.44 We consider parameter combinations of M ∈{ 100, 500, 1000, 1500, 2000, 2500, 3000, 3500}, T ∈ {3, 5, 10, ∞ } and v ∈ {0.01, 0.1, 0.001}. Further, we set early stopping rounds to 10 to speed up the computing process. The final XGB model includes M = 500 boosting iterations, a maximum depth T = 10, and a learning rate v = 0.1. For the hyperparameter tuning of the NN, we find the best model by searching through the parameter combinations of hidden layer sizes h ∈{ 10, 50, 100, 200, 300, 400, 500}, the activation functions a ∈ {hyperbolic tan function, rectified linear unit function}, solver functions s ∈{ “sgd”, “adam”} and the l2 penalty l2 ∈{ 0.0001, 0.05}. Validating these parameter combinations, we find the optimal model to consist of h = 100, a = “relu”, s = “adam,” and l2 = 0.05. The tuning parameter selection for FIN and CEO are visualized in Table5. 42 Following Sigrist and Hirnschall (2019), we denote an indefinite maximum tree depth as ∞ . 43 As p represents to total number of predictors, m represents a subsample as its square root, here √34 = 6. 44 James etal. (2021) also highlight the importance of tuning these meta-parameters for boosting algorithms. 1623 1 3 Disentangling theblack box aroundCEO andfinancial… Table 5 Hyperparameter tuning finance (FIN) and CEO (CEO) models Method Hyperparameter Grid range Final value CEO Final value FIN Final value CEO + FIN LR – – – – – SVM C Polynomial Degree 1, 10, 50, 75, 100 0.5, 1, 2, 5, 10 10 5 50 2 10 2 RF # Estimators Max. Depth Max. Features 100, 500, 1000, 1500, 2000, 2500, 3000, 3500 3, 5, 10, ∞ 1, 2, 3, 4, 5, 6 500 ∞ 1 500 ∞ 1 100 ∞ 2 XGB Learning Rate Max. Depth # Estimators Early Stopping 0.001, 0.01, 0.1 3, 5, 10, ∞ 100, 500, 1000, 1500, 2000, 2500, 3000, 3500 10 0.01 ∞ 2500 10 0.1 10 100 10 0.1 10 500 10 NN Hidden Layer Size Activation Learning Rate Solver 10, 50, 100, 200, 300, 400, 500 “tanh”, “relu” 0.0001, 0.05 “sgd”, “adam” 500 “relu” 0.0001 “adam” 100 “relu” 0.0001 “adam” 100 “relu” 0.05 “adam” 1624 M.Schneider, R.Brühl 1 3 Supplementary Information The online version contains supplementary material available at https:// doi. org/ 10. 1007/ s11573- 023- 01136-w. Funding Open Access funding enabled and organized by Projekt DEAL. Data availability The datasets analyzed for the current study are available from the corresponding author upon reasonable request. Declarations Conflict of interest The authors have no relevant financial or non-financial interests to disclose. 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