Nonlinear Association Between Controlling Shareholders and Financial Reporting Integrity: An Explainable Optuna-Optimized Ensemble Learning Approach in Egypt and Saudi Arabia

Abstract

Financial reporting integrity (FRI) plays a critical role in capital market efficiency, yet its determinants remain difficult to model due to nonlinear relationships, heterogeneous firm characteristics, and institutional differences across emerging markets. Prior research largely relies on linear econometric approaches, which may overlook threshold effects and complex governance dynamics. This study develops an explainable Optuna-optimized Extremely randomized trees (ET) ensemble framework to examine the association between controlling shareholders and FRI in Egypt and Saudi Arabia. Using a panel dataset of 1746 firm-year observations over the period 2014–2022, the model incorporates advanced preprocessing and mutual information-based feature selection to enhance predictive accuracy and robustness. The proposed model significantly outperforms regularized linear models, standalone machine learning models, and alternative ensemble techniques, achieving R² values of 0.7935 in Egypt and 0.9231 in Saudi Arabia, alongside substantial reductions in RMSE and MAE. Diebold–Mariano tests confirm that these performance gains are statistically significant (p < 0.01). Explainability analysis using SHAP reveals that firm size and market share are the dominant drivers of FRI, while blockholder ownership exhibits a nonlinear and context-dependent association. Partial dependence results show a complex, non-monotonic relationship in Egypt—consistent with a monitoring–entrenchment trade-off—contrasted with a predominantly positive and monotonic association in Saudi Arabia. Importantly, these nonlinear patterns are not detected in conventional panel fixed effects models, highlighting the limitations of standard econometric specifications in capturing complex ownership dynamics. The findings highlight the importance of institutional context in shaping governance outcomes and demonstrate how explainable ensemble learning can uncover hidden nonlinearities in financial reporting behavior. This study contributes by identifying nonlinear thresholds and cross-country variation in ownership effects while integrating predictive performance with interpretability, offering a robust framework for analyzing corporate governance mechanisms in emerging markets and supporting more informed decision-making by investors, regulators, and policymakers.

1. Introduction

Financial reporting integrity (FRI) is a cornerstone of efficient capital markets, as it ensures that financial statements faithfully represent firms’ underlying economic performance and provide reliable information to investors and other stakeholders. High-quality financial reporting reduces information asymmetry, enhances investor confidence, and improves resource allocation decisions (P. Dechow et al., 2010). In contrast, weak reporting integrity can distort market valuations and undermine trust in financial disclosures, particularly in emerging markets where governance mechanisms and regulatory enforcement may be less developed.

A central determinant of financial reporting integrity is ownership structure, particularly the presence of controlling shareholders or blockholders. Corporate governance theory suggests that ownership concentration plays a dual role in shaping reporting outcomes. On one hand, large shareholders have strong incentives to monitor management due to their substantial financial stakes, thereby reducing managerial opportunism and improving reporting quality (Shleifer & Vishny, 1997). On the other hand, controlling shareholders may engage in opportunistic behavior by extracting private benefits of control at the expense of minority shareholders, potentially leading to lower transparency and increased earnings manipulation (Claessens et al., 2002). This duality creates an inherently complex and potentially nonlinear relationship between ownership concentration and financial reporting integrity.

Empirical evidence on this relationship remains mixed. Some studies find that ownership concentration enhances the informativeness of earnings and improves financial reporting quality (Fan & Wong, 2002), while others document higher levels of earnings management in firms with dominant shareholders, particularly in weak institutional environments (Leuz et al., 2003). More recent research suggests that these effects are nonlinear and context-dependent, varying across ownership levels, firm characteristics, and institutional settings (Alrobai et al., 2025; Attia et al., 2023). Such complexity highlights the limitations of traditional linear econometric approaches in capturing the true nature of ownership–reporting relationships. Despite extensive prior research, empirical findings on the relationship between ownership concentration and financial reporting integrity remain mixed. A key limitation is that most studies rely on linear econometric specifications that impose constant marginal effects and predefined functional forms. Such approaches are not well suited to capturing nonlinear governance mechanisms, including monitoring–entrenchment trade-offs, threshold effects, and interaction dynamics across ownership levels. As a result, existing evidence may overlook important variations in how controlling shareholders influence reporting outcomes across firms and institutional contexts.

These limitations are particularly relevant in emerging markets such as Egypt and Saudi Arabia. While both countries exhibit concentrated ownership structures, they differ markedly in regulatory quality, investor protection, and corporate governance reforms. Egypt is characterized by relatively weaker enforcement mechanisms and evolving governance practices, whereas Saudi Arabia has implemented substantial regulatory reforms aimed at enhancing transparency and market discipline (Aldoseri & Hussein, 2024; Ismail et al., 2024). These structural differences suggest that the association of controlling shareholders on financial reporting integrity is likely to vary across the two contexts.

This study addresses these limitations by explicitly modeling the ownership–reporting relationship as nonlinear and context-dependent. Rather than imposing a functional form, we use an explainable machine learning framework to uncover how the effect of blockholder ownership varies across its distribution and across institutional environments. This approach allows us to identify turning points, asymmetric effects, and cross-country differences that are difficult to detect using conventional econometric methods.

Specifically, this study employs an Optuna-optimized Extremely randomized trees (Extra Trees, ET) model capable of capturing nonlinearities and interaction effects in high-dimensional financial data (Gu et al., 2020). The model is trained using a comprehensive preprocessing pipeline—including mutual information-based feature selection—and evaluated using cross-validated metrics (coefficient of determination (R²), root mean square error (RMSE), and mean absolute error (MAE)), alongside the Diebold–Mariano (DM) test to assess statistical significance. To enhance interpretability, SHapley Additive exPlanations (SHAP) and Partial Dependence Plots (PDP) are utilized to uncover the marginal and nonlinear associations of ownership and firm characteristics (Lundberg & Lee, 2017).

Using a panel dataset of 1071 Egyptian and 675 Saudi firm-year observations over the period 2014–2022, this study proxies financial reporting integrity by the market-to-book ratio, reflecting investors’ perceptions of reporting credibility (Beaver & Ryan, 2000; Ismail et al., 2024). The empirical results show that ensemble learning models significantly outperform traditional statistical approaches, with the Optuna-tuned Extra Trees model achieving the highest predictive accuracy in both countries.

More importantly, the findings reveal pronounced nonlinear and country-specific associations of blockholder ownership. In Egypt, the relationship is complex and non-monotonic, characterized by declining valuation relationships at moderate-to-high ownership levels with partial recovery at extreme concentrations. In contrast, Saudi Arabia exhibits a largely positive and monotonic relationship, where higher ownership concentration is associated with higher firm valuation. These differences are further reinforced by feature importance and SHAP analyses, which highlight the dominant role of firm size and market share, alongside the heterogeneous contribution of ownership structure. Notably, the nonlinear patterns identified in this study main findings are not detected in conventional panel fixed effects models in robustness tests, underscoring the importance of flexible modeling approaches in uncovering complex governance relationships.

Building on these insights, this study contributes to literature along four main dimensions. First, it provides new evidence that the relationship between ownership concentration and financial reporting integrity is nonlinear and characterized by threshold effects, consistent with the monitoring–entrenchment trade-off. Second, it shows that this relationship is institutionally contingent, differing systematically between Egypt and Saudi Arabia, thereby highlighting the role of governance environments in shaping ownership effects. Third, it develops an explainable Optuna-optimized ensemble framework designed to capture the complex, high-dimensional, and nonlinear structure of corporate governance data, and systematically evaluates its performance against standalone machine learning models, and alternative ensemble techniques, demonstrating superior predictive accuracy and robustness. Fourth, it integrates SHAP-based interpretability and partial dependence analysis to identify the key drivers of financial reporting outcomes—including firm size, market share, and ownership structure—thereby offering deeper insights into the mechanisms through which governance influences reporting outcomes. Finally, it demonstrates that explainable machine learning methods can complement traditional econometric approaches by capturing complex, nonlinear, and cross-sectional patterns that are not identified in standard panel models. Collectively, the study advances the corporate governance and financial reporting literature by combining methodological rigor with economic interpretability in a unified, data-driven framework.

The remainder of the paper is structured as follows: Section 2 reviews the literature; Section 3 outlines the methodological framework; Section 4 presents the empirical results and discussion; Section 5 presents the robustness tests, and Section 6 concludes the study.

2. Literature Review

2.1. Financial Reporting Integrity and Its Measurement

Financial reporting integrity (FRI) refers to the extent to which financial statements faithfully represent a firm’s underlying economic performance and provide decision-useful information to investors and stakeholders. High FRI reduces information asymmetry, enhances transparency, and improves capital allocation efficiency in financial markets (P. Dechow et al., 2010). When financial information is perceived as credible, investors are better able to assess firm value, resulting in more accurate market pricing. Prior accounting research has employed several proxies for FRI, including earnings persistence, discretionary accruals, and financial restatements (Alrobai et al., 2025; P. Dechow et al., 2010; Francis et al., 2005; Nuhu et al., 2024).

Building on this literature, financial reporting integrity is fundamentally reflected in the quality of reported earnings. Earnings quality is widely used as an accounting-based proxy for FRI, as it captures the extent to which reported earnings faithfully represent firm performance and are free from managerial manipulation (P. Dechow et al., 2010; Francis et al., 2005). Consistent with this perspective, earnings quality serves as an accounting-based proxy for financial reporting integrity in the robustness analysis. Specifically, we construct a composite measure based on earnings persistence, earnings volatility, and earnings predictability, which together capture the extent to which reported earnings are stable, sustainable, and informative about future performance.

In contrast, earnings management reflects the intentional use of managerial discretion to misrepresent a firm’s underlying economic performance. Healy and Wahlen (1999) define earnings management as the manipulation of financial reporting to present a more favorable financial position than is warranted, often through the timing of revenue and expense recognition. Such practices can distort investors’ perceptions and lead to inefficient decision-making (McNichols & Stubben, 2008). While some forms, such as income smoothing, may reduce apparent volatility, more aggressive manipulation increases the risk of regulatory scrutiny and reputational damage (Abogun et al., 2021).

On the other hand, market-based measures provide an alternative perspective by capturing investors’ aggregate assessment of reporting credibility. The market-to-book ratio is one such measure, reflecting the extent to which market valuations incorporate reliable accounting information and growth expectations (Beaver & Ryan, 2000). Firms with higher perceived reporting integrity are expected to exhibit stronger market valuations relative to book value. Following Ismail et al. (2024), this study adopts the market-to-book ratio as a market-based proxy for financial reporting integrity in the main analysis.

Building on the “clean surplus” valuation framework established by Feltham and Ohlson (1995), the market-to-book ratio serves as a vital bridge between equity value and accounting transparency. According to their model, a company’s market worth is a product of its current book value and the anticipated abnormal earnings generated by its reported data. Since book value is a fundamental component of this calculation, the relationship between a firm’s market price and its recorded assets signals how much trust investors place in the underlying financial reports. Consequently, an elevated market-to-book ratio suggests that the market views the accounting information as both credible and predictive of future success, positioning the ratio as a valid market-based metric for financial reporting integrity.

Eugster and Wagner (2020) use a 10-year panel of Swiss firms to provide further support for the use of market-based measures in assessing financial reporting quality. Their study shows that firms with stronger reporting practices and more informative value reporting tend to achieve superior market valuations and better performance outcomes. This suggests that investors reward transparent and credible financial disclosures by assigning higher values to firms in the capital market. Accordingly, the market-to-book ratio can serve as an indirect proxy for financial reporting integrity, as higher ratios may reflect greater investor confidence in the quality and reliability of reported financial information.

2.2. Ownership Structure and Corporate Governance

From a theoretical standpoint, ownership structure represents a central corporate governance mechanism influencing financial reporting practices. Agency theory posits that the separation between ownership and control creates incentives for managerial opportunism (Jensen & Meckling, 1976). Concentrated ownership—particularly the presence of blockholders—can mitigate these agency conflicts by strengthening monitoring incentives (Shleifer & Vishny, 1997). However, ownership concentration also introduces principal–principal conflicts between controlling and minority shareholders (La Porta et al., 1999). When controlling shareholders possess significant voting power, they may engage in tunneling, related-party transactions, or manipulation of financial disclosures to extract private benefits (Claessens et al., 2002). Consequently, ownership concentration embodies a dual governance role: it can enhance monitoring while simultaneously enabling entrenchment. This duality suggests that the relationship between blockholder ownership and financial reporting integrity is unlikely to be strictly linear. Instead, it is likely to exhibit a nonlinear and potentially non-monotonic relationship, where the direction and magnitude of the effect vary across different ownership levels due to shifting dominance between monitoring and entrenchment incentives.

A substantial body of literature examines how ownership concentration influences financial reporting quality. Early studies emphasize the monitoring role of blockholders, arguing that large shareholders enhance oversight and improve the credibility of financial disclosures (Shleifer & Vishny, 1997). Empirical evidence supports this perspective. For example, Fan and Wong (2002) show that concentrated ownership increases the informativeness of accounting earnings. More recent studies reinforce this monitoring perspective. For instance, M. J. Ali et al. (2024) document that institutional ownership reduces discretionary accruals and real earnings manipulation, suggesting that sophisticated investors enhance reporting discipline. Similarly, Alrobai et al. (2025) provide evidence that ownership structures influence multiple dimensions of earnings quality, highlighting the active role of large shareholders in shaping reporting outcomes.

However, an alternative strand of literature highlights the entrenchment effect of controlling shareholders. Claessens et al. (2002) show that concentrated ownership may facilitate expropriation of minority shareholders, particularly in weak governance environments. Consistent with this view, Leuz et al. (2003) demonstrate that earnings management is more prevalent in countries with weaker investor protection, suggesting that controlling shareholders may reduce transparency when institutional constraints are limited. Recent research increasingly emphasizes that ownership–reporting relationships are complex and heterogeneous. Rather than exerting a uniform effect, different ownership structures—including families, institutions, and multiple blockholders—may produce varying governance outcomes (Edmans & Holderness, 2017; Jiang et al., 2020). For example, conflicts among multiple large shareholders may increase earnings manipulation, although external monitoring can mitigate such effects.

Importantly, emerging evidence suggests that ownership concentration may exhibit nonlinear effects on financial reporting quality. Alrobai et al. (2025) demonstrate that ownership structures in Egypt generate U-shaped and N-shaped relationships with earnings quality, indicating that the governance impact of ownership depends on both its level and interaction with firm characteristics. Similarly, Attia et al. (2023) identify a threshold effect, where low ownership levels are associated with entrenchment, while higher levels lead to improved monitoring and reduced earnings management. These findings challenge the linear assumptions embedded in traditional econometric models and suggest that ownership concentration operates through dynamic and context-dependent mechanisms.

The governance role of controlling shareholders is particularly sensitive to institutional environments. Egypt and Saudi Arabia provide a compelling comparative setting due to differences in regulatory development, investor protection, and governance reforms. In Egypt, ownership concentration is typically high, and governance mechanisms are still evolving. Empirical evidence suggests mixed effects of blockholders. While monitoring can improve reporting integrity, weak enforcement may allow entrenchment to dominate (Ismail et al., 2024; Samaha et al., 2012). Moreover, Alrobai et al. (2025) show that ownership effects in Egypt are inherently nonlinear and unstable, reflecting the coexistence of competing governance forces.

In contrast, Saudi Arabia has implemented significant corporate governance reforms, enhancing disclosure requirements and regulatory oversight. Evidence suggests that governance outcomes are more interaction-driven. Aldoseri and Hussein (2024) find that managerial ownership improves earnings quality, whereas ownership concentration exhibits weak or insignificant effects, indicating that governance effectiveness depends on complementary mechanisms such as board structure. These differences imply that ownership–reporting relationships are institutionally contingent, motivating cross-country analysis.

2.3. Explainable Machine Learning in Accounting

Despite extensive empirical evidence, the literature is dominated by linear econometric models, including panel regressions and generalized method of moments (GMM) estimations. While useful for causal inference, these methods impose restrictive functional forms and may fail to capture nonlinear governance relationships (Chemmaa & Ibrahimi, 2025). Recent advances in machine learning (ML) offer a powerful alternative. ML models can capture nonlinearities and complex interactions in high-dimensional data (Gu et al., 2020; Liaras et al., 2024; Ranta et al., 2023). Ensemble techniques such as Random Forest and Extremely Randomized Trees are widely recognized for their strong predictive performance in financial contexts due to their ability to model nonlinearities and complex variable interactions (Breiman, 2001; Geurts et al., 2006; Černevičienė & Kabašinskas, 2024). Their flexibility and robustness make them particularly suitable for high-dimensional financial datasets. Recent applications further demonstrate their effectiveness in financial performance prediction and valuation settings (e.g., G. M. Ali, 2026a). A recent paper by Wang et al. (2025) highlights the potential of ML to improve decision-making, foster trust among stakeholders, and ensure regulatory compliance.

Hezam et al. (2025) systematically reviewed 70 studies from 2013 to 2023 to investigate the application of ML techniques in predicting firm performance. The study reveals the potential of ML techniques to provide a more nuanced and accurate prediction of firm performance by integrating diverse data sources and attributes. P. Geertsema and Lu (2019) showed that machine learning models relying solely on historical accounting information produced a median absolute percentage error of 17.2% in firm valuation, surpassing the performance of both finance students and professional analysts. In a later study, P. Geertsema and Lu (2023) reported that decision-tree-based machine learning techniques lowered valuation errors by between 5.6 and 31.4 percentage points relative to conventional multiples-based valuation methods, while also identifying major value drivers consistent with discounted cash flow principles. In a similar vein, Koklev (2022) found that Gradient Boosting Decision Trees (GBDT) delivered strong explanatory performance (R² = 86.7%) in forecasting market capitalization, clearly outperforming standard econometric approaches. G. M. Ali (2026b) applies an explainable machine learning approach to Egyptian listed firms using a Super Learner ensemble with SHAP analysis to predict firm valuation. Their model outperforms traditional statistical and standalone ML approaches, achieving an R² of 0.572 compared to 0.19–0.47 for benchmark models, while also uncovering nonlinear effects of cash holdings and capital structure on firm value. Taken together, these studies indicate that machine learning can both improve valuation precision and generate richer insights into the factors influencing firm value.

However, interpretability remains a key concern. Explainable AI techniques, particularly SHAP (Lundberg & Lee, 2017), address this limitation by quantifying feature contributions and enabling visualization of nonlinear relationships through feature importance and partial dependence plots (PDPs). For example, D’Amato et al. (2024) incorporated ESG variables in their analysis of EuroStoxx 600 firms and employed PDPs to detect a nonlinear threshold effect at an ESG score of approximately 65 out of 100, with the highest predicted EBIT performance occurring within the 70–85 range.

Despite extensive research across these domains, limited studies integrate corporate governance theory with advanced explainable machine learning techniques to examine financial reporting outcomes. The accounting literature provides well-established measures of reporting quality (P. Dechow et al., 2010; Francis et al., 2005; Ball & Shivakumar, 2005), while the corporate governance literature highlights the complex and potentially nonlinear role of ownership concentration (Shleifer & Vishny, 1997; Claessens et al., 2002). However, these processes may not be adequately captured by the restrictive assumptions often imposed by traditional empirical methodologies. Recent developments in explainable machine learning offer a promising approach to addressing this limitation by enabling the identification of nonlinear and threshold-dependent relationships while preserving interpretability. By integrating governance theory with an explainable machine learning framework, this study contributes to these strands of literature and provides a more comprehensive understanding of how controlling shareholders influence financial reporting integrity across different institutional contexts.

2.4. Hypothesis Development

Extending the ownership–reporting quality literature, recent empirical evidence suggests that the relationship between ownership concentration and financial reporting outcomes is inherently nonlinear and context-dependent. For example, Alrobai et al. (2025) document complex nonlinear patterns—including U-shaped and N-shaped relationships—depending on ownership type and firm characteristics. Similarly, Attia et al. (2023) identify threshold effects in which the impact of ownership concentration shifts across different levels, reflecting changes in the dominance of entrenchment and monitoring incentives.

Consistent with this perspective, the effect of blockholder ownership is unlikely to follow a simple monotonic or symmetric pattern. At certain ownership levels, monitoring incentives may dominate, improving financial reporting integrity, while at other levels, entrenchment effects or coordination problems among large shareholders may reduce transparency. These dynamics can generate non-monotonic and asymmetric relationships, where the direction of the effect varies across ownership ranges rather than following a single functional form. Importantly, explainable machine learning techniques, such as SHAP-based partial dependence plots, enable the identification of such complex patterns by visualizing how predicted outcomes respond to changes in ownership concentration across its distribution. This allows for the detection of turning points, local minima, and varying marginal effects, which are often not captured by traditional linear models.

Building on agency theory, the relationship between ownership concentration and financial reporting integrity reflects a trade-off between monitoring and entrenchment effects. Alsultan and Hussainey (2024) show that ownership structure significantly shapes earnings quality outcomes, and that greater ownership power can intensify adverse reporting effects in certain contexts. At lower levels of ownership concentration, large shareholders have incentives to monitor management and enhance reporting quality. However, as ownership concentration increases, controlling shareholders may acquire sufficient power to extract private benefits, potentially reducing transparency. This dynamic suggests a nonlinear, threshold-dependent relationship. Accordingly, the following hypothesis is tested:

H1. 

The relationship between blockholder ownership and financial reporting integrity is nonlinear and follows an inverted U-shaped pattern. Specifically, increases in blockholder ownership initially improve financial reporting integrity due to enhanced monitoring incentives; however, beyond a certain threshold, further increases in ownership concentration reduce reporting integrity as entrenchment incentives dominate.

Institutional factors—including investor protection, regulatory enforcement, legal quality, and the overall effectiveness of governance systems—shape the relative balance between the monitoring and entrenchment effects of ownership concentration (La Porta et al., 1999; Leuz et al., 2003). In environments with stronger external governance systems, controlling shareholders are more likely to perform an effective monitoring role, as opportunistic behavior is constrained by legal frameworks, disclosure requirements, and market discipline. Conversely, in settings characterized by weaker enforcement mechanisms or ongoing governance reforms, concentrated ownership may increase the scope for the extraction of private benefits of control, thereby amplifying nonlinear and potentially unstable ownership effects.

Egypt provides an important example of the latter context. Prior studies and institutional assessments indicate that corporate governance enforcement and investor protection mechanisms are still evolving, which may allow entrenchment incentives to become more pronounced at higher ownership levels (European Bank for Reconstruction and Development, 2016; Samaha et al., 2012). Consistent with this view, Alrobai et al. (2025) document pronounced nonlinear ownership-related patterns in the Egyptian market.

In contrast, Saudi Arabia has implemented substantial governance and capital market reforms in recent years, including enhanced disclosure requirements, strengthened board governance standards, and increased regulatory oversight through the Capital Market Authority and related institutions. These developments may mitigate entrenchment risks and promote more stable governance outcomes. Supporting this interpretation, Aldoseri and Hussein (2024) report more conditional and interaction-based ownership effects in the Saudi context, rather than sharply unstable nonlinear patterns.

Taken together, these differences suggest that the relationship between ownership concentration and financial reporting integrity is institutionally contingent. The same ownership structure may yield different governance outcomes depending on the surrounding legal and regulatory environment. Accordingly, the following hypothesis is proposed:

H2. 

The nonlinear relationship between blockholder ownership and financial reporting integrity varies across institutional contexts. In weaker governance environments, entrenchment effects emerge at lower ownership levels, resulting in a steeper and more pronounced inverted U-shaped relationship. In stronger governance environments, regulatory enforcement constrains entrenchment, leading to a flatter and less pronounced relationship.

These hypotheses are examined using both explainable machine learning methods, which capture flexible nonlinear patterns in the main analysis, and panel regression specifications as robustness tests, which provide a more restrictive parametric benchmark.

3. Research Framework

3.1. General Context

The current study develops a nonlinear framework to examine the effect of controlling shareholders on financial reporting integrity using an Optuna-tuned Extra Trees model. The analysis is conducted in two stages: training and evaluation. As shown in Figure 1, data preprocessing includes handling missing values, encoding categorical variables, and preparing numerical features. Feature selection is performed using mutual information to retain the most relevant predictors. The core model is an Extra Trees algorithm, with hyperparameters optimized via Optuna to capture complex nonlinearities and interaction effects. Model performance is evaluated using RMSE, MAE, and R². To enhance interpretability, SHAP and partial dependence plots are employed to explain the model’s predictions and uncover the nonlinear impact of controlling shareholders.

It is crucial to make clear how ownership structure affects financial reporting integrity in order to connect the empirical model with the underlying economic mechanism (Figure 1). Controlling shareholders have two opposing ways of influencing reporting behavior from the standpoint of corporate governance. Higher ownership concentration, on the one hand, improves reporting quality, lessens managerial opportunism, and boosts monitoring incentives (Jensen & Meckling, 1976; Shleifer & Vishny, 1986). However, when ownership grows, controlling shareholders might have enough clout to demand personal gains, which would result in entrenchment and less openness. Ownership concentration and financial reporting integrity have intrinsically nonlinear and threshold-dependent interactions as a result of these conflicting forces. In particular, it is anticipated that the marginal impact of blockholder ownership will range among ownership levels and may shift in direction based on the predominance of entrenchment or monitoring effects.

3.2. Phase 1: Data Preparation

Step 1: Sample Selection and Data Collection:

This study investigates the nonlinear effect of controlling shareholders on financial reporting integrity using a panel dataset of listed non-financial firms from Egypt (119 firms) and Saudi Arabia (75 firms) over the period 2014–2022, yielding 1071 Egyptian and 675 Saudi firm-year observations. Ownership and financial data are obtained from Bloomberg. The selected timeframe captures recent developments in corporate governance practices and financial reporting standards in both markets, ensuring sufficient variation in ownership structures and reporting quality. The dependent variable is financial reporting integrity, while the key independent variable is the ownership stake of controlling shareholders. This study adopts a dual-measure approach to financial reporting outcomes, including market-based valuation (MTB) in the main analysis and accounting-based earnings quality proxies as robustness tests to capture both investor perceptions and underlying reporting quality. Additional firm-level controls are included to account for financial characteristics that may influence reporting quality. Financial firms are excluded due to their distinct regulatory environments and reporting requirements. The final panel structure supports robust estimation and enhances comparability across firms and over time.

Step 2: Data Preprocessing:

The variables used in the analysis are presented in

Table 1. Variables Measured.

Variable	Description
The Dependent Variable
Financial reporting Integrity (FRI)	A market-based proxy for reporting quality, proxied by the market-to-book (M/B) ratio, defined as the market price per share divided by the book value per share.
The Independent Variable
Controlling shareholders (Blockholder)	Blockholders’ ownership measured by the percentage of shares held by investors who own at least 5% of the total outstanding shares.
The Control Variables
Foreign ownership	The percentage of shares owned by foreign investors to the total number of shares.
Firm size	The natural logarithm of total assets
Firm Leverage	Total debts divided by the total assets
Firm Age	The number of years from the company’s establishment to the start of the fiscal year being analyzed.
Profitability	Net income divided by total assets
Market Share	The ratio of a firm’s total revenue to the overall revenue of its industry within the same year, calculated by dividing firm revenue by total industry-year revenue
Sales Growth	The change in a firm’s sales revenue divided by its revenue from the previous period
Year	Dummy variables included to control for time-related effects.
Industry	Dummy variables used to control for industry-specific effects, covering sectors such as Basic Materials, Consumer Discretionary, Consumer Staples, Energy, Health Care, Industrials, Real Estate, Technology, Telecommunications, and Utilities.

and include firm-level financial indicators, ownership measures, industry classification, and the dependent variable—financial reporting integrity. The preprocessing procedure follows a structured approach to ensure data quality and consistency across Egypt and Saudi Arabia. Data preprocessing is a crucial stage in machine learning, as real-world datasets often contain inconsistencies, inaccuracies, and missing values that can compromise model reliability.

To address these issues, missing values in numerical variables are imputed using the median, while categorical variables are completed using the mode. Industry and year variables are encoded using one-hot encoding, resulting in 10 industry dummies and 9 year dummies. All continuous independent variables are winsorized at the 5th and 95th percentiles to mitigate the influence of outliers. The dependent variable, Market-to-Book ratio, is log-transformed to address skewness and improve the distributional properties of the regression residuals. No log transformation is applied to independent variables, particularly because several are ratios that may take zero or negative values.

Step 3: Feature Validation and Selection:

In this phase, we compute a correlation matrix to evaluate the relationships between pairs of variables and to detect any potential problems with multicollinearity. Figure 1 and Figure 2 present the Pearson correlation matrices for Egypt and Saudi Arabia, respectively, with FRI as the dependent variable. For Egypt (Figure 2), FRI shows a positive and statistically significant correlation with firm size (SIZE; r = 0.36, p < 0.001), growth (GROWTH; r = 0.08, p < 0.05), profitability (Profit; r = 0.18, p < 0.001), and market share (MSHARE; r = 0.35, p < 0.001). A significant negative relationship is observed with foreign ownership (FOWN; r = −0.12, p < 0.001) and firm age (AGE; r = −0.11, p < 0.001). The association between FRI and blockholder ownership is negative but statistically insignificant (r = −0.04, p > 0.05), while leverage also shows no significant relationship with FRI (r = 0.03, p > 0.05).

For Saudi Arabia (Figure 3), FRI exhibits strong positive and statistically significant correlations with firm size (SIZE; r = 0.67, p < 0.001) and market share (MSHARE; r = 0.64, p < 0.001). Positive and significant relationships are also observed with blockholder ownership (Blockholder; r = 0.37, p < 0.001), leverage (LEVER; r = 0.11, p < 0.01), growth (GROWTH; r = 0.12, p < 0.01), and profitability (Profit; r = 0.17, p < 0.001). In contrast, firm age is negatively associated with FRI (AGE; r = −0.17, p < 0.001), while foreign ownership shows no statistically significant relationship (r = −0.05, p > 0.05).

Overall, the correlation patterns reveal notable differences between the two markets. In Egypt, ownership concentration does not exhibit a direct linear association with FRI, whereas in Saudi Arabia, blockholder ownership is positively and significantly correlated with firm valuation. Additionally, firm size and market share emerge as dominant correlates of FRI in both contexts, with stronger effects observed in Saudi Arabia. Across both countries, the pairwise correlations among independent variables remain below the conventional threshold of 0.80, indicating no evidence of severe multicollinearity.

To further assess the potential for multicollinearity in the regression models, a Variance Inflation Factor (VIF) diagnostic was conducted. As shown in Figure 4, the VIF values for all independent variables in both the Egyptian and Saudi Arabian models are well below the commonly accepted critical thresholds of 5 or 10. With all VIFs under 2.0, the analysis indicates that multicollinearity is not a concern, thus supporting the stability and reliability of the regression estimates.

Feature selection was conducted using a filter-based approach based on mutual information. Mutual information measures the dependency between each feature and the target variable, capturing both linear and nonlinear relationships. Unlike traditional correlation measures, it can detect any form of dependency between variables. Additionally, mutual information is a model-independent technique, meaning it can be applied prior to model training, making it computationally efficient and scalable for large datasets. This characteristic makes it particularly suitable for tabular financial data, where relationships between variables are often complex and not strictly linear. The top k features with the highest average mutual information scores were then selected for model development (Liu & Motani, 2025).

3.3. Phase 2: Model Development

Step 1: Specification of the Proposed Model:

This study adopts an ensemble learning approach to develop a predictive framework. The objective is to enhance predictive accuracy by identifying nonlinear patterns and relationships between ownership structure and financial reporting integrity. While the results provide valuable insights into the associations among these variables, they should not be interpreted as evidence of causal effects. Ensemble learning enhances supervised learning by combining multiple algorithms, where the aggregated predictions generally achieve higher accuracy and stability than those of individual models—an idea commonly referred to as the “wisdom of the crowd” (Kunapuli, 2023; Mohammed & Kora, 2023). Existing empirical evidence shows that ensemble techniques improve both predictive performance and model generalization (Bogaert & Delaere, 2023).

Ensemble methods can be broadly classified into homogeneous and heterogeneous approaches. Homogeneous ensembles are based on repeated applications of the same algorithm across different data samples. Bagging-based techniques, such as Random Forest (RF) and Extremely Randomized Trees (Extra Trees, ET), construct models in parallel and aggregate their outputs, while boosting methods—including Adaptive Boosting (AdaBoost), Gradient Boosting (GB), Light Gradient Boosting Machine (LightGBM), Categorical Boosting (CatBoost), and Extreme Gradient Boosting (XGBoost)—build models sequentially to minimize prediction errors (Mienye & Sun, 2022; Mohammed & Kora, 2023). In the current study, particular emphasis is placed on the Extra Trees algorithm due to its high randomness and ability to reduce variance, making it well-suited for handling complex and high-dimensional data. Additionally, several ensemble algorithms (e.g., RF, LightGBM, CatBoost, AdaBoost, ET) are implemented as benchmark models to enable a comprehensive comparison of performance across different ensemble techniques.

This section outlines the use of the Extra Trees algorithm alongside the Optuna-based hyperparameter optimization framework applied in the current study.

(a)

Extremely Randomized Trees (ET):

This study employs Extremely Randomized Trees (ET) as a core model within an ensemble learning framework. ET is an ensemble method that extends Random Forest by introducing additional randomness in both feature selection and split thresholds. It constructs multiple decision trees from randomly selected feature subsets, aggregating predictions through averaging for regression tasks (González et al., 2020; Schmid et al., 2023). This added randomness reduces variance, mitigates overfitting, and enhances the model’s ability to handle complex, high-dimensional financial data, making ET particularly suitable for financial applications.

The choice of the Extra Trees algorithm is motivated by its ability to capture complex nonlinear relationships and high-order interactions without requiring ex ante specification of functional form. This is particularly relevant in the ownership–governance context, where theoretical models predict threshold and non-monotonic effects that are difficult to approximate using standard linear or low-order polynomial panel regressions.

(b)

Optuna Optimization:

The predictive performance of ET, like other machine learning models, is highly dependent on hyperparameter configuration. Traditional tuning methods, including Grid Search or algorithms like SGD and Adam, often become inefficient in high-dimensional settings. To address this, the study uses Optuna, a state-of-the-art hyperparameter optimization framework that employs adaptive sampling strategies to efficiently explore the hyperparameter space (Akiba et al., 2019). Optuna is particularly effective for tree-based models, including ET (Lai et al., 2024), and is designed to identify high-performing parameter combinations quickly while reducing computational overhead.

Optuna offers several advantages over conventional methods. It utilizes the Tree-structured Parzen Estimator (TPE) and Covariance Matrix Adaptation Evolution Strategy (CMA-ES) to focus the search on promising hyperparameter regions, reducing the number of unnecessary evaluations (Akiba et al., 2019; Hadianti & Kodri, 2023). Its pruning mechanism further improves efficiency by terminating poorly performing trials early (Srinivas & Katarya, 2022). Empirical studies demonstrate Optuna’s superior performance in diverse domains, including financial forecasting, and ICO return prediction, and DeFi Valuation, often outperforming traditional tuning approaches in combined algorithm selection and hyperparameter optimization (CASH) tasks (G. M. Ali, 2026a; Almarzooq & bin Waheed, 2024; Parekh et al., 2024; Shekhar et al., 2021).

The robustness and reliability of the research model are enhanced through the use of Optuna for hyperparameter optimization. Optuna employs adaptive search and pruning strategies to systematically identify optimal configurations, rather than relying on manually selected or grid-searched parameters. This approach improves predictive performance, enhances generalization, and reduces the risk of overfitting—addressing a common concern in flexible machine learning models. Overall, this systematic optimization ensures that model performance is driven more by the underlying data structure than by arbitrary parameter choices.

The Optuna optimization workflow, illustrated in Figure 5, comprises three primary stages (Priyadarshi & Kumar, 2024). First, the objective function is defined, where each trial trains the Extra Trees (ET) model on preprocessed corporate data using a sampled set of hyperparameters, such as the number of trees, maximum depth, minimum samples per leaf, and the number of features per split. Model performance is then evaluated using the R² metric, which is particularly suitable for capturing sensitivity to large deviations that are critical in financial valuation contexts. Second, an Optuna study is created, where the study object manages trials, records results, and directs the search toward promising hyperparameter configurations using the Tree-structured Parzen Estimator (TPE) sampler. Third, the optimization process is executed through the study.optimize() function, which iteratively explores the hyperparameter space using adaptive sampling and pruning techniques to terminate underperforming trials early. Over successive iterations, the optimization converges toward hyperparameter configurations that enhance predictive accuracy and model generalization.

The optimized parameters obtained via Optuna are summarized in

Table 2. Optimized hyperparameters of the Extra Trees.

Parameter	Definition	Egypt	Saudi Arabia
n_estimators	Total number of decision trees constructed in the ensemble.	166	454
max_depth	The maximum number of levels allowed in each decision tree.	26	48
min_samples_split	The minimum number of observations required to split an internal node.	2	2
min_samples_leaf	The minimum number of observations required at a terminal (leaf) node.	1	1
max_features	The number of features considered when searching for the best split.	sqrt	sqrt
bootstrap	Indicates whether bootstrap sampling is used when building the trees.	False	False

.

Step 2: Comparative Performance Analysis:

The performance of the proposed model was evaluated using 10-fold cross-validation and benchmarked against a range of machine learning and statistical models, including CatBoost, LightGBM, XGBoost, RF, K-Nearest Neighbors (KNN), Decision Tree, Multi-Layer Perceptron (MLP), Ridge Regression, Partial Least Squares (PLS) Regression, Elastic Net, and Least Absolute Shrinkage and Selection Operator (Lasso). Model performance was assessed using three key evaluation metrics: the R², RMSE, and MAE (Equations (1)–(3)) (Erdebilli & Devrim-İçtenbaş, 2022; Nguyen et al., 2021). RMSE measures the square root of the average squared differences between predicted and actual values, while MAE computes the average absolute deviations. R² evaluates the proportion of variance in the observed data explained by the model.

$${\mathrm{R}}^2=1-{\displaystyle \frac{{\sum }_{i=1}^n{\left(y_i-x_i\right)}^2}{{\sum }_{i=1}^n{\left(y_i-{\overline{x}}_i\right)}^2}}$$

(1)

$$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\sqrt{{\displaystyle {\sum }_{i=1}^n}{\displaystyle \frac{{\left(y_i-x_i\right)}^2}{n}}}$$

(2)

$$\mathrm{M}\mathrm{A}\mathrm{E}={\displaystyle \frac{{\sum }_{i=1}^n\left|y_i-x_i\right|}{n}}$$

(3)

In these equations, $x_i$ denotes the predicted value for the $i$th observation, ${\overline{x}}_i$ represents the mean of predicted values, $y_i$ is the actual observed value, and $n$ is the total number of observations. Higher R² values indicate a greater ability of the model to explain variability in the data and thus reflect better predictive performance (Erdebilli & Devrim-İçtenbaş, 2022). Collectively, these metrics provide a robust framework for evaluating and comparing the performance of statistical and machine learning models.

Step 3: Statistical Significance Test:

To assess the statistical significance of differences in predictive performance, this study employs the Diebold–Mariano (DM) test, a widely used method for comparing forecast accuracy between competing models (Diebold & Mariano, 1995). The DM test evaluates whether the difference in prediction errors between two models is statistically significant by analyzing the mean of the loss differential, typically based on squared errors. The test has been widely applied in forecasting and predictive modeling studies to compare model performance.

In the current study, the DM test is applied in two complementary ways. First, it is employed to assess the statistical significance of performance differences between the optimized ET model and a range of benchmark statistical and machine learning models, including Random Forest, Decision Tree, Ridge, Lasso, Elastic Net, KNN, PLS Regression, MLP, XGBoost, CatBoost, and LightGBM. Second, it is used to evaluate the incremental predictive contribution of the independent variable (i.e., blockholder ownership) by comparing Optuna-tuned Extra Trees models with and without this feature. Prediction errors are generated using 10-fold cross-validation to ensure robustness and comparability. For each model, errors are aggregated across folds, and the DM test is computed using squared error loss to derive the loss differential. The resulting DM statistic and corresponding p-value indicate whether observed differences in predictive accuracy are statistically significant.

Step 4: Model Explanation:

To improve model interpretability, this study employs both SHAP and PDP to explain the predictions of the Optuna-tuned Extra Trees model. SHAP analysis is implemented using the TreeExplainer, which is specifically designed for tree-based models, enabling the quantification of each feature’s contribution to predictions at both the global and individual levels. The final ET model, optimized using Optuna, is trained on the full dataset, and a representative holdout set is used to generate explanations. SHAP values are computed to capture the marginal contribution of each feature to the model’s output, allowing for a detailed understanding of feature importance and directional associations. These values are then used to produce global interpretations (e.g., feature importance rankings) as well as local explanations for individual predictions.

In addition, PDP are utilized to complement SHAP by illustrating the average marginal effect of selected features on the predicted outcome. PDPs provide a visual representation of how changes in a feature influence the model’s predictions while holding other variables constant, thereby offering further insight into nonlinear relationships captured by the ET model. Together, SHAP and PDP provide a comprehensive interpretability framework, enhancing transparency and supporting a deeper understanding of the drivers of model predictions in complex financial data (Lundberg et al., 2020).

3.4. Phase 3: Robustness Tests

As a robustness check, the analysis follows the same empirical design as the main specification, with two key modifications. First, all continuous predictors were scaled using a robust scaler to mitigate the influence of outliers. Second, robustness was assessed using alternative measures of financial reporting integrity based on an accounting-oriented earnings quality framework. Specifically, a composite earnings quality measure was constructed using a rolling window of five years (with a minimum of four observations) to enhance temporal stability and reduce measurement noise, which resulted in a reduced sample size to 974 observations. In addition, two of its underlying components—earnings persistence and earnings volatility—were employed as alternative dependent variables. This approach allows financial reporting integrity to be captured through both a composite indicator and its key dimensions, ensuring that the analysis is not dependent on a single proxy while preserving consistency with the underlying conceptual framework.

As an additional robustness check and to ensure comparability with conventional empirical approaches, the study employs panel econometric specifications alongside the machine learning framework. Specifically, firm-level fixed effects models with time (year) fixed effects are estimated to capture within-firm variation over time, with standard errors clustered at the firm level to account for serial correlation and heteroskedasticity. In parallel, to formally examine the hypothesized nonlinear relationship and cross-country heterogeneity, pooled panel models are estimated incorporating quadratic terms for blockholder ownership as well as interaction terms between ownership and a country indicator. These specifications allow for testing whether nonlinear effects can be approximated using low-order polynomial functions and whether such relationships differ systematically across institutional contexts. Together, these econometric benchmarks provide a structured comparison to the machine learning approach, enabling an assessment of whether the identified patterns persist under traditional linear and parametric modeling assumptions.

4. Experimental Results and Discussion

This section begins with a descriptive analysis of the study variables, followed by an evaluation of the predictive performance of several statistical and machine learning (ML) models. It further examines the contribution of key features to enhance decision-making, and concludes with the use of SHAP values and partial dependence plots to provide deeper insights into model interpretability.

4.1. Descriptive Analysis

Table 3. Descriptive Statistics—Egypt.

Variable	Mean	Median	Std. Dev.	Min	Max	Skewness	Kurtosis
FRI	640.654	105.556	1084.470	0.858	3920.543	2.011	2.917
Blockholder	64.819	68.000	18.540	26.000	91.000	−0.557	−0.574
FOWN	7.169	0.000	17.084	0.000	65.000	2.591	5.535
LEVER	0.165	0.117	0.174	0.000	0.558	0.883	−0.363
SIZE	6.007	5.981	0.748	4.793	7.449	0.155	−0.841
GROWTH	0.137	0.095	0.395	−0.586	1.113	0.613	0.552
Profit	0.044	0.038	0.075	−0.107	0.205	0.216	−0.106
AGE	34.706	32.000	16.162	13.000	72.000	0.739	−0.332
MSHARE	0.031	0.006	0.055	0.000	0.209	2.301	4.177

and

Table 4. Descriptive Statistics—Saudi Arabia.

Variable	Mean	Median	Std. Dev.	Min	Max	Skewness	Kurtosis
FRI	953.106	250.172	1562.458	36.667	5797.937	2.168	3.504
Blockholder	40.733	40.000	21.292	9.000	75.000	0.085	−1.293
FOWN	2.403	0.000	7.233	0.000	28.000	2.908	6.937
LEVER	0.250	0.244	0.182	0.000	0.570	0.142	−1.196
SIZE	6.646	6.519	0.599	5.759	7.958	0.657	−0.460
GROWTH	0.037	0.022	0.222	−0.337	0.597	0.711	0.552
Profit	0.041	0.031	0.069	−0.082	0.196	0.454	−0.113
AGE	27.884	27.000	12.835	9.000	54.000	0.284	−0.862
MSHARE	0.056	0.017	0.101	0.001	0.435	2.881	7.665

present the descriptive statistics for Egypt and Saudi Arabia. The financial reporting integrity (FRI), proxied by market-to-book ratio, exhibits substantial dispersion in both markets, with a mean of 640.65 in Egypt and 953.11 in Saudi Arabia, accompanied by large standard deviations (1084.47 and 1562.46, respectively). The distributions are highly right-skewed (2.01 in Egypt; 2.17 in Saudi Arabia), indicating the presence of a small number of firms with exceptionally high market valuations. Regarding the key independent variable, Blockholder ownership is considerably higher in Egypt, with an average of 64.82%, compared to 40.73% in Saudi Arabia. This suggests a more concentrated ownership structure in Egyptian firms. Foreign ownership remains relatively low in both contexts (mean of 7.17% in Egypt and 2.40% in Saudi Arabia) but is highly skewed, reflecting its concentration among a limited number of firms.

Leverage is higher in Saudi Arabia (mean = 0.250) than in Egypt (mean = 0.165), indicating greater reliance on debt financing in the Saudi context. Firm size is also larger on average in Saudi Arabia (mean log size = 6.646) compared to Egypt (6.007). In contrast, Egyptian firms tend to be older (mean age = 34.71 years) than Saudi firms (27.88 years) and exhibit higher growth rates (mean = 0.137 vs. 0.037). Market share remains relatively low in both samples but is slightly higher in Saudi Arabia (0.056) compared to Egypt (0.031).

Collectively, the pronounced skewness and kurtosis observed across key variables—particularly FRI, foreign ownership, and market share—indicate substantial departures from normality and the presence of outliers. These distributional characteristics justify the use of robust, non-parametric ensemble methods such as the Extra Trees model, which can effectively capture nonlinear relationships and are less sensitive to extreme values. These cross-country differences in distributions—particularly in ownership concentration, firm size, leverage, and market valuation—have important implications for comparability. While the same model architecture is applied to both samples, the models are estimated separately, and therefore capture country-specific data-generating processes. As a result, subsequent analyses focus on within-country relationships, and comparisons across countries should be interpreted in terms of differences in patterns rather than direct equivalence in marginal effects.

4.2. Performance Comparison of Various Statistical and ML Models

This section compares the predictive performance of the proposed Optuna-tuned Extra Trees model with linear regression models, individual ML algorithms, and other ensemble techniques in estimating FRI for Egypt and Saudi Arabia, as shown in Figure 6.

Table 5. Cross-validation results of the Proposed Model compared to statistical, individual ML, and other ensemble techniques—Egypt.

	Model	R2 (±SD)	RMSE	MAE	DM Stat (Sig.)
Ensemble Models	Optuna Extra Trees	0.7935 ± 0.0321	0.9884	0.6788	___
	CatBoost	0.7697 ± 0.0298	1.0448	0.7421	−3.3437 ***
	LightGBM	0.7312 ± 0.0297	1.1277	0.8027	−5.8500 ***
	XGBoost	0.7250 ± 0.0525	1.1381	0.7996	−5.5192 ***
	Random Forest	0.7120 ± 0.0426	1.1681	0.8092	−7.6679 ***
Individual ML Models	KNN	0.3971 ± 0.1033	1.6848	1.2708	−13.8470 ***
	Decision Tree	0.3949 ± 0.1378	1.6876	0.9857	−9.3096 ***
	MLP	0.3557 ± 0.0850	1.7430	1.3940	−19.0501 ***
Statistical Models	Ridge	0.2452 ± 0.0546	1.8908	1.5626	−22.5508 ***
	PLS Regression	0.2451 ± 0.0515	1.8909	1.5516	−22.6626 ***
	ElasticNet	0.0451 ± 0.0271	2.1286	1.8067	−26.5610 ***
	Lasso	0.0247 ± 0.0250	2.1512	1.8248	−26.6730 ***

Note: (***) indicates statistical significance at the 0.1% level (p < 0.001).

and

Table 6. Cross-validation results of the Proposed Model compared to statistical, individual ML, other ensemble techniques—Saudi Arabia.

	Model	R2 (±SD)	RMSE	MAE	DM Stat (Sig.)
Ensemble Models	Optuna Extra Trees	0.9231 (±0.0267)	0.3892	0.2908	___
	CatBoost	0.9125 (±0.0316)	0.4148	0.3087	−3.4429 ***
	Random Forest	0.8982 (±0.0392)	0.4487	0.3192	−3.7900 ***
	XGBoost	0.8980 (±0.0373)	0.4484	0.3275	−4.2384 ***
	LightGBM	0.8933 (±0.0401)	0.4588	0.3359	−4.8522 ***
Individual ML Models	Decision Tree	0.8303 (±0.0607)	0.5804	0.4034	−7.4350 ***
	MLP	0.6983 (±0.0695)	0.7840	0.6103	−12.8027 ***
	KNN	0.6334 (±0.1368)	0.8567	0.6350	−10.5028 ***
Statistical Models	Ridge	0.7559 (±0.0679)	0.7013	0.5353	−10.8798 ***
	PLS Regression	0.7292 (±0.0614)	0.7413	0.5757	−13.5602 ***
	ElasticNet	0.2022 (±0.0604)	1.2855	1.0609	−20.2302 ***
	Lasso	0.1540 (±0.0579)	1.3237	1.0974	−20.9125 ***

Note: (***) indicates statistical significance at the 0.1% level (p < 0.001).

display model performance evaluated using cross-validated R², RMSE, MAE, and the DM test to assess statistical differences in predictive accuracy. Across both countries, ensemble tree-based models show higher predictive accuracy than linear and regularized regression models. These comparisons relate to predictive performance and should not be interpreted as evidence of superiority for causal inference. The proposed Optuna-tuned Extra Trees model achieves the highest predictive accuracy in both contexts, with a mean R² of 0.7935 (Std. = 0.0321) in Egypt and 0.9231 (Std. = 0.0267) in Saudi Arabia, alongside the lowest prediction errors (RMSE = 0.9884 and 0.3892; MAE = 0.6788 and 0.2908, respectively). These results confirm the robustness and superior predictive power of the proposed model.

In Egypt, CatBoost ranks second with a mean R² of 0.7697, followed by LightGBM (0.7312) and XGBoost (0.7250), while Random Forest achieves 0.7120. A similar pattern is observed in Saudi Arabia, where CatBoost (0.9125), Random Forest (0.8982), and XGBoost (0.8980) demonstrate strong predictive performance, although still below the proposed model. The relatively small standard deviations across top-performing models indicate stable cross-validation performance. The Diebold–Mariano test results further confirm the statistical superior predictive power of the proposed model. For all competing models, the DM statistics are negative and statistically significant (p < 0.01), indicating that their forecast errors are significantly larger than those of the Extra Trees model. For example, in Egypt, CatBoost (DM = −3.3437, p = 0.0009) and LightGBM (DM = −5.8500, p < 0.001) perform significantly worse than the proposed model.

Similar results are observed in Saudi Arabia, where CatBoost (DM = −3.4429, p = 0.0006) and Random Forest (DM = −3.7900, p = 0.0002) show statistically inferior predictive accuracy. These findings suggest that the performance gains of the proposed model are not only economically meaningful but also statistically significant. Lower-performing models further highlight the advantages of ensemble learning. In Egypt, KNN (R² = 0.3971) and Decision Tree (0.3949) show limited predictive capability, while neural networks (MLP: 0.3557) and linear models such as Ridge (0.2452) and PLS (0.2451) perform substantially worse. The weakest results are observed for ElasticNet (0.0451) and Lasso (0.0247), indicating that linear and regularized models fail to capture the underlying complexity of the data. A similar trend is evident in Saudi Arabia, although overall performance levels are higher, with even weaker models such as KNN (0.6334) and MLP (0.6983) outperforming their counterparts in Egypt.

Importantly, the Saudi data consistently yields higher out-of-sample R² values and lower prediction errors across all models compared to Egypt. This suggests that the relationships between explanatory variables and FRI are more stable, structured, and predictable in the Saudi market. In contrast, the lower predictive performance and higher variability observed in Egypt indicate greater complexity, noise, or heterogeneity in the underlying data-generating process. In sum, the findings demonstrate that the proposed Extra Trees model is the most robust and accurate approach for predicting financial reporting integrity in both countries. The significant performance gap between ensemble methods and traditional models highlights the importance of capturing nonlinear relationships and interaction associations, which are particularly relevant in corporate governance and financial reporting contexts.

4.3. Feature Importance Analysis Using Optuna-Optimized Extra Trees

The Optuna-Optimized Extra Trees feature importance results reveal notable cross-country differences in the determinants of perceived reporting integrity between Egypt and Saudi Arabia, highlighting the role of institutional and market structure. For Egypt (Figure 7), the results indicate that perceived reporting integrity is driven by a relatively balanced set of firm characteristics rather than a single dominant factor. Firm size (SIZE) and market share (MSHARE) emerge as the most influential variables, each contributing 17.2% to the model’s predictive power, followed by firm age (AGE) at 14.0%. These findings underscore the importance of firm maturity and competitive positioning in shaping valuation. Blockholder ownership ranks next (12.1%), confirming its economically meaningful role in influencing perceived reporting credibility, consistent with the study’s focus on ownership structure. Leverage (LEVER) and profitability (Profit) also contribute substantially (11.4% and 10.8%, respectively), while foreign ownership (FOWN) and industry effects play comparatively smaller roles.

However, the Saudi Arabian results (Figure 8) exhibit a more concentrated structure, with firm size (SIZE) overwhelmingly dominating the model, contributing 39.8% of total importance. This suggests that valuation in Saudi Arabia is heavily scale-driven, reflecting stronger market emphasis on firm magnitude and market visibility. Market share (MSHARE) follows at 18.9%, reinforcing the importance of competitive positioning. Profitability (Profit) and blockholder ownership contribute 8.7% and 8.3%, respectively, indicating that while ownership concentration remains relevant, its influence is more moderate compared to Egypt. Firm age (AGE) and industrial sector exposure (IND_Industrials) each contribute 6.0%, while leverage (LEVER), consumer discretionary sector exposure, growth (GROWTH), and foreign ownership (FOWN) exhibit relatively smaller associations.

Collectively, the findings suggest a clear contrast between the two markets. Egypt displays a more diversified importance structure, where valuation is influenced by a broad combination of firm characteristics, ownership, and financial factors. In contrast, Saudi Arabia shows a more concentrated pattern, with firm size acting as the primary driver of valuation. Importantly, blockholder ownership remains a consistently relevant factor in both contexts, supporting its role in explaining perceived reporting integrity, although its relative importance is stronger in Egypt. These results align with the theoretical expectation that ownership structure interacts with market characteristics, potentially shaping the monitoring and entrenchment effects examined in this study.

4.4. Model Explanation with SHapley Additive Explanations

Since financial reporting integrity is proxied by the market-to-book ratio, the SHAP results should be interpreted as reflecting how firm characteristics and ownership structure are associated with market valuation incorporating perceptions of reporting credibility, rather than direct measures of underlying reporting quality. Given the differences in variable distributions across Egypt and Saudi Arabia, SHAP values should be interpreted as reflecting relative importance and marginal associations within each country, rather than directly comparable effect sizes across countries. Differences in SHAP magnitudes may partly reflect underlying data structure, scale, and variability, in addition to economic relationships.

The SHAP summary plot (Figure 9) for Egypt indicates that firm size (SIZE) has the strongest and most consistent influence on the perceived reporting credibility, with higher values generally associated with higher model predictions. Market share (MSHARE) also exhibits a substantial positive association, although with noticeable dispersion across observations. The industry indicator for real estate (IND_Real Estate) shows a pronounced positive contribution when present, suggesting higher valuations in this sector. Firm age (AGE) shows variable contributions to the model’s predictions, alternating between positive and negative associations across observations. Leverage (LEVER) tends to have a negative association at higher levels, indicating that more highly leveraged firms are associated with lower predicted valuations. Profitability (Profit) contributes positively, as higher profit levels are generally linked to higher market-to-book ratios.

Ownership concentration (Blockholder) shows a significant but mixed influence, though higher concentration is more frequently associated with negative relationships. The industry indicator for consumer staples (IND_Consumer Staples) exhibits a modest and somewhat negative contribution, while foreign ownership (FOWN) has a relatively smaller and mixed relationship overall. Finally, the industry indicator for health care (IND_Health Care) appears to have the least influence, with SHAP values tightly clustered around zero. In sum, the SHAP results emphasize SIZE, MSHARE, AGE, LEVER, Profit, and Blockholder as the most influential drivers of firm valuation in Egypt.

The SHAP summary plot (Figure 10) for Saudi Arabia highlights firm size (SIZE) as the most dominant determinant of perceived reporting credibility, with higher SIZE values consistently associated with strong positive relations on model predictions. Market share (MSHARE) ranks as the second most influential variable, generally exhibiting a positive relationship, although with some variability across observations. The industry indicator for industrials (IND_Industrials) shows a noticeable but mixed contribution, with associations distributed on both sides of zero. Profitability (Profit) exerts a clear positive influence, as higher profit levels are associated with higher predicted valuations. Ownership concentration (Blockholder) also indicates a meaningful association, though its predictive relationship appears more balanced between positive and negative contributions.

Firm age (AGE) has a relatively modest and mixed predictive effect on the model output. Foreign ownership (FOWN) shows limited influence overall, with SHAP values clustered near zero. Similarly, the industry indicator for consumer discretionary (IND_Consumer Discretionary) exhibits a small and somewhat dispersed contribution. Leverage (LEVER) plays a minor role and is more frequently associated with negative relationships at higher levels. Sales growth (GROWTH) appears to have the least influence, with values tightly concentrated around zero. Collectively, the SHAP results indicate that firm valuation in Saudi Arabia is primarily driven by SIZE and MSHARE, with Profit and Blockholder serving as secondary contributors, while the remaining variables have comparatively limited explanatory power.

4.5. Partial Dependency Plots

The SHAP partial dependence plots (Figure 11) for blockholder ownership reveal pronounced nonlinear and country-specific relationships between ownership concentration and the predicted perceived reporting integrity, supporting the hypothesis that the governance role of controlling shareholders varies across institutional contexts. It is noteworthy that partial dependence plots and SHAP values offer descriptive interpretations of model behavior. They do not prove causation, but they do show how expected results change when input variables are changed while keeping other parameters constant. As a result, associations rather than causal effects should be seen in the data.

For Egypt, the relationship exhibits a clear nonlinear and predominantly negative pattern beyond moderate ownership levels. The predicted value is relatively high when blockholder ownership is around 25–35%, after which it declines steadily as ownership concentration increases toward approximately 60%, indicating a weakening contribution to valuation. Around this mid-range, the relationship stabilizes briefly, followed by a further decline at high ownership levels (above ~75–85%), where the predicted value reaches its lowest point. A sharp recovery is observed at very high ownership levels (above ~90%), suggesting a possible threshold relationship. This pattern implies that while moderate ownership supports effective monitoring, increasing concentration may give rise to entrenchment effects and minority shareholder concerns, associated with lower market valuation, potentially reflecting investor concerns about entrenchment and reduced transparency. The rebound at extreme ownership levels may reflect situations where dominant shareholders exert strong strategic control or signal long-term commitment, partially restoring market confidence.

Importantly, the partial dependence results identify a critical ownership interval—approximately between 60% and 85%—characterized by relative stabilization followed by a renewed decline in predicted reporting integrity. This pattern suggests a transition zone in which the benefits of monitoring weaken while entrenchment incentives begin to intensify, albeit in a non-monotonic manner. Within this range, controlling shareholders appear to possess sufficient influence to affect reporting outcomes without fully internalizing the associated economic costs, increasing the risk of opportunistic behavior. From a governance perspective, this finding has direct regulatory implications. Firms within this ownership range may require enhanced oversight mechanisms, including stricter disclosure requirements, stronger enforcement of minority shareholder protections, and closer monitoring of related-party transactions. These measures are particularly relevant in emerging market contexts, where institutional enforcement mechanisms may be evolving and ownership concentration plays a central governance role (La Porta et al., 1999; Leuz et al., 2003). Accordingly, a more targeted, threshold-based approach to corporate governance regulation may be more effective than uniform policies applied across all ownership structures.

The sharp rebound observed at very high ownership levels (above approximately 90%) can be interpreted through an alignment-based perspective. When ownership becomes highly concentrated, controlling shareholders internalize a substantially larger proportion of the firm’s economic outcomes, which may reduce incentives for opportunistic behavior and improve the perceived credibility of financial reporting. In such settings, the classic agency conflict between controlling and minority shareholders becomes less pronounced, as the relative importance of minority interests declines. This interpretation is consistent with the view that extremely high ownership concentrations can mitigate certain agency problems by aligning incentives more closely with long-term firm value (Shleifer & Vishny, 1997; Morck et al., 1988). Consequently, the observed recovery in predicted reporting integrity at near-full ownership levels likely reflects a transition from entrenchment-driven behavior to incentive alignment and stronger strategic commitment.

In contrast, the pattern for Saudi Arabia is predominantly positive and more monotonic. The predicted market-to-book ratio increases steadily as blockholder ownership rises, particularly from low levels up to approximately 40–50%, indicating that ownership is associated with higher market valuation, consistent with stronger perceived monitoring and governance quality. Beyond this range, the relationship flattens slightly with minor fluctuations, indicating diminishing marginal associations but no reversal. At very high ownership levels (above ~70–75%), the predicted value increases again, reaching its highest levels. This pattern suggests that higher ownership concentration in Saudi Arabia is consistently perceived as beneficial, likely reflecting stronger monitoring, better alignment between owners and managers, and enhanced investor confidence in controlling shareholders.

In sum, the comparison highlights substantial institutional heterogeneity in the governance role of blockholders. Egypt displays a nonlinear relationship consistent with a monitoring–entrenchment trade-off, where the benefits of ownership concentration diminish and potentially reverse at higher levels before recovering at extreme concentrations. In contrast, Saudi Arabia exhibits a largely positive relationship, indicating that ownership concentration is more uniformly associated with improved perceived reporting credibility. These findings reinforce the view that the association between controlling shareholders and financial reporting outcomes and firm valuation is highly context-dependent, shaped by differences in governance structures, investor protection, and market dynamics. Importantly, these results demonstrate the value of explainable machine learning techniques in corporate governance research. Unlike traditional econometric models that impose restrictive functional forms, SHAP partial dependence plots allow for the visualization of nonlinearities, threshold relationships, and cross-country heterogeneity, providing deeper insights into the complex role of ownership structure.

The SHAP partial dependence plots (Figure 12) for firm size (SIZE) reveal differing valuation sensitivities between Egypt and Saudi Arabia. In Egypt, SIZE exhibits a generally positive relationship with the market-to-book ratio, but the increase is gradual at lower levels and becomes more pronounced after a log-size of around 6.0. Below this point, the slope is relatively modest, indicating limited incremental valuation associations for smaller firms. Beyond 6.0, the relationship steepens, with predicted valuations rising more quickly until approximately 6.7–7.2, after which the curve begins to level off, suggesting diminishing marginal associations for the largest firms.

In Saudi Arabia, the SIZE association is stronger and more consistently increasing across the distribution. The relationship appears nearly monotonic, with a steady upward trend starting around 6.0 and continuing through the upper range. The slope becomes particularly pronounced beyond 6.8–7.0, indicating that larger firms contribute substantially more to predicted valuations. Unlike Egypt, there is little evidence of a clear plateau, although the curve shows slight smoothing at the extreme upper end, implying only mild diminishing associations. The histograms indicate that Egyptian firms are more concentrated in the lower size range (approximately 5.0–6.5), whereas Saudi firms are generally larger, with more observations in the higher size intervals. This distributional difference helps explain the stronger and more sustained valuation sensitivity to size in Saudi Arabia. Overall, while firm size positively influences perceived reporting credibility in both countries, the association in Egypt is more threshold-based and tapers off at higher levels, whereas in Saudi Arabia it remains consistently strong across the size spectrum.

The partial dependence plots (Figure 13) indicate a generally positive relationship between market share (MSHARE) and the perceived reporting credibility in both Egypt and Saudi Arabia, with higher market shares associated with higher valuations. In Egypt, the relationship shows a modest nonlinear pattern at very low levels of market share, followed by a gradual and steady increase as MSHARE rises, becoming more pronounced beyond roughly 0.10. In Saudi Arabia, the pattern is more distinctly nonlinear, with a noticeable upward shift beginning at relatively low market share levels (around 0.05–0.10), after which the relationship continues to increase steadily, eventually flattening slightly at the highest observed values. The histograms suggest that most firms in both countries are concentrated at relatively low market share levels, particularly below 0.10. However, Saudi Arabia exhibits a wider distribution, with some firms reaching substantially higher market shares (above 0.40), whereas Egypt’s distribution is more tightly clustered. This implies that the stronger valuation associations at higher levels of market share are influenced by a relatively small number of firms, especially in Saudi Arabia.

It is important to emphasize that these patterns reflect how the market incorporates ownership structure into firm valuation (i.e., market perception of reporting quality), rather than providing direct evidence on underlying financial reporting quality. The nonlinear relationships identified in the SHAP partial dependence plots therefore capture investor responses to ownership concentration, which may embed expectations about monitoring effectiveness, entrenchment risks, and reporting credibility. This interpretation is consistent with the use of the market-to-book ratio as a forward-looking, perception-based measure. To address this distinction, the study further examines accounting-based earnings quality measures in the robustness analysis, providing a complementary perspective on reporting integrity.

4.6. Performance Comparison of the Proposed Model with and Without Blockholder Ownership

The comparison of cross-validated R² scores using the Optuna-Optimized Extra Trees model (

Table 7. The role of Blockholder on Predictive Performance (Optuna Extra Trees).

	Egypt		Saudi Arabia
Model Specification	R2 (±SD)	DM Statistic	R2 (±SD)	DM Statistic
With Blockholder	0.7935 (±0.0321)	−6.0013 ***	0.9231 (± 0.0267)	−2.9914 ***
Without Blockholder	0.7507 (±0.0234)		0.9173 (± 0.0307)

Note: (***) indicates statistical significance at the 0.1% level (p < 0.001).

and Figure 14) provides clear evidence on the role of ownership concentration (Blockholder) in enhancing predictive performance across both countries. In Egypt, the inclusion of the Blockholder variable is associated with a noticeable improvement in model performance, with the average R² increasing from 0.7507 (±0.0234) to 0.7935 (±0.0321). This improvement is also visually supported by the boxplot, where the distribution of R² values shifts upward when Blockholder is included. The DM test further suggests that this gain is statistically significant (DM = −6.0013, p < 0.01), indicating that the model with Blockholder consistently outperforms the specification without it.

In Saudi Arabia, the model already demonstrates a high level of predictive accuracy even without Blockholder. Nevertheless, including this variable still results in a modest improvement, with R² increasing from 0.9173 (±0.0307) to 0.9231 (±0.0267). The boxplot shows a slight upward shift and reduced dispersion in performance when Blockholder is incorporated. The DM test suggests that this difference is also statistically significant (DM = −2.9914, p < 0.01), suggesting that even small gains are consistent and meaningful. Collectively, the results indicate that Blockholder plays a more substantial role in improving predictive performance in Egypt, where the relative gain is larger and more pronounced. However, while the improvement in Saudi Arabia is smaller in magnitude, it remains statistically significant, highlighting the variable’s incremental value even in a high-performing model.

4.7. Discussion of Main Results

The findings of this study suggest that the relationship between blockholder ownership and FRI is nonlinear, data-driven, and highly context-dependent. By employing an Optuna-optimized Extra Trees model combined with SHAP-based interpretability techniques, the analysis uncovers complex patterns that extend beyond the scope of traditional econometric approaches. Consistent with agency theory, ownership concentration reflects both monitoring and entrenchment effects (Claessens et al., 2002; Shleifer & Vishny, 1997). However, the results demonstrate that these associations vary significantly across ownership levels and institutional settings. The SHAP partial dependence plots reveal clear nonlinearities and threshold associations, supporting recent literature that emphasizes the dynamic nature of ownership–reporting relationships (Attia et al., 2023).

In Egypt, the relationship between blockholder ownership and FRI is highly nonlinear and unstable. The results show that valuation is relatively high at moderate ownership levels (approximately 25–35%) but declines as ownership concentration increases toward mid-to-high levels, indicating the dominance of entrenchment effects. At very high ownership levels (above 90%), a recovery in predicted valuation is observed, suggesting a potential threshold behavior. This complex pattern aligns with prior evidence from emerging markets, where weak governance structures allow controlling shareholders to extract private benefits, thereby reducing transparency (Ismail et al., 2024; Leuz et al., 2003). In contrast, Saudi Arabia exhibits a more stable and predominantly positive relationship between ownership concentration and FRI. The partial dependence results show a monotonic increase in valuation with higher ownership levels, with only mild flattening at intermediate ranges and renewed increases at high ownership levels. This suggests that monitoring and alignment effects dominate in the Saudi context, consistent with stronger regulatory frameworks and governance reforms (Aldoseri & Hussein, 2024; La Porta et al., 1999). This difference may be attributed to the relatively inefficient nature of the Egyptian market, where standard theoretical assumptions and conventional governance mechanisms may not fully apply (Kamel & Shahwan, 2014; Mousa et al., 2022). The market is characterized by structural imbalances and limited competitive dynamics, which can weaken the effectiveness of ownership structure as a disciplinary mechanism and contribute to the observed nonlinear and unstable relationship with financial reporting integrity.

Beyond ownership concentration, the results highlight the importance of firm characteristics. Feature importance and SHAP analyses show that firm size and market share are the primary drivers of valuation in both countries, with a particularly dominant role in Saudi Arabia. In Egypt, the importance structure is more diversified, with size, market share, age, and ownership contributing more evenly. These findings indicate that valuation dynamics are influenced by a combination of firm fundamentals and governance factors, with ownership playing a complementary but meaningful role. The model performance analysis further reinforces these insights. The Optuna-tuned Extra Trees model significantly outperforms all benchmark models across both countries, achieving R² values of 0.7935 in Egypt and 0.9231 in Saudi Arabia, with statistically significant improvements confirmed by the Diebold–Mariano test. The higher predictive accuracy observed in Saudi Arabia suggests a more structured and predictable relationship between firm characteristics and valuation, whereas the lower performance in Egypt reflects greater heterogeneity and complexity.

Importantly, the incremental contribution of blockholder ownership to predictive performance is more pronounced in Egypt, where its inclusion is associated with a substantial improvement in model accuracy. In Saudi Arabia, although the improvement is smaller, it remains statistically significant, confirming the relevance of ownership concentration even in a highly predictive environment.

Overall, the findings provide partial and method-dependent support for the proposed hypotheses. The explainable machine learning results reveal clear nonlinear and context-dependent associations between blockholder ownership and financial reporting integrity, consistent with H1 and H2. However, these patterns are not statistically supported in the panel fixed-effects models in the robustness tests, suggesting that the identified relationships are primarily driven by cross-sectional variation and nonlinear interactions rather than within-firm changes over time. This divergence highlights an important methodological insight. While machine learning models capture complex nonlinearities and interaction effects across firms, conventional panel models impose restrictive functional forms and rely on within-firm variation, which may obscure such relationships. Accordingly, the results should be interpreted as evidence of predictive and structural associations rather than causal effects.

Importantly, cross-country comparisons should be interpreted with caution. The Egyptian and Saudi samples differ substantially in ownership concentration, firm size, leverage, and market structure, which may influence both model performance and the shape of estimated relationships. While the use of a consistent modeling framework ensures methodological comparability, the resulting SHAP patterns primarily reflect within-country dynamics. Therefore, the observed differences—such as the stronger non-monotonic relationship in Egypt and the more stable pattern in Saudi Arabia—should be understood as context-specific rather than directly comparable in magnitude. These findings are further supported by pooled panel models with country interaction terms in the robustness tests, which confirm cross-country heterogeneity, although they do not fully capture the nonlinear patterns identified by the machine learning approach.

5. Robustness and Complementary Econometric Analysis

5.1. Accounting-Based Measures of Financial Reporting Integrity

Financial reporting integrity (FRI) is fundamentally reflected in the quality of reported earnings. Following prior literature, we adopt earnings quality as the accounting-based representation of reporting integrity, as it captures the extent to which reported earnings faithfully reflect firm performance and are free from managerial manipulation (P. Dechow et al., 2010; Francis et al., 2004; P. M. Dechow et al., 1995). In line with this approach, earnings quality is measured using a composite index that incorporates earnings persistence, predictability, and volatility, which are widely used dimensions capturing the stability, reliability, and informational content of earnings (Francis et al., 2004; P. Dechow et al., 2010). Higher persistence and predictability, combined with lower volatility, indicate higher reporting quality. To ensure robustness, we estimate all models using (i) the composite earnings quality measure, as well as (ii) its individual components—earnings persistence and earnings volatility—as alternative dependent variables.

The components of the earnings quality measure were derived from firm-level time-series properties of earnings using a rolling-window framework. Earnings persistence was estimated by regressing current earnings on lagged earnings within each rolling window, where the estimated coefficient on lagged earnings captures the degree to which current performance is sustained over time, with higher coefficients indicating greater persistence. Earnings volatility was measured as the standard deviation of earnings over the same rolling window, reflecting the extent of fluctuations in firm performance, with higher volatility indicating lower earnings quality. Earnings predictability was captured by the variability of the residuals from the persistence regression, typically measured as the standard deviation of the regression errors, where lower residual variance indicates higher predictability of earnings. These components were subsequently standardized and combined to construct the composite earnings quality index, ensuring comparability across firms and over time while capturing multiple dimensions of financial reporting quality.

While the main analysis also considers the market-to-book ratio as a broader, market-based proxy capturing how financial information is incorporated into firm valuation, the accounting-based measures provide a direct test of reporting integrity and address potential construct validity concerns. All candidate models were systematically evaluated during the model selection stage. However, for clarity and parsimony, only the top-performing models are presented in the main tables, while the full set of results is available upon request.

As shown in

Table 8. Machine Learning Performance Using Alternative Earnings Quality Measures.

Country	Measure	Extra Trees R2	Random Forest R2	ΔR2
Egypt	Earnings Quality	0.460	0.387	+0.073
	Persistence	0.222	0.171	+0.051
	Volatility	0.598	0.549	+0.049
Saudi	Earnings Quality	0.414	0.360	+0.054
	Persistence	0.180	0.151	+0.029
	Volatility	0.520	0.373	+0.147

, the results confirm that the machine learning specification remains robust across all alternative measures. In particular, the Extra Trees model consistently outperforms benchmark models, including Random Forest (the second-best performing model), in both Egypt and Saudi Arabia, with notable improvements in explanatory power across all specifications. For Egypt, the Extra Trees model achieves an R² of 0.460 for the composite earnings quality measure, compared to 0.387 for Random Forest, representing an improvement of 0.073. Similar gains are observed for persistence (R² = 0.222 vs. 0.171, Δ = 0.051) and volatility (R² = 0.598 vs. 0.549, Δ = 0.049).

For Saudi Arabia, the pattern is consistent, with Extra Trees yielding an R² of 0.414 for earnings quality compared to 0.360 for Random Forest (Δ = 0.054), and 0.180 versus 0.151 for persistence (Δ = 0.029). The largest improvement is observed for volatility, where the Extra Trees model achieves an R² of 0.520 compared to 0.373 for Random Forest, corresponding to a substantial increase of 0.147. Overall, these results demonstrate that the superior performance of the Extra Trees model is not driven by a specific earnings quality proxy, but rather reflects a consistent advantage across different dimensions of earnings quality and across both country samples.

As shown in

Table 9. Diebold–Mariano Test (Optuna Extra Trees vs. Random Forest).

Country	Measure	DM Stat	p-Value
Egypt	Earnings Quality	−2.0489	0.0405
Saudi	Earnings Quality	−2.3420	0.0192

, Diebold–Mariano tests further indicate that these performance differences are statistically significant, especially for Egypt, confirming the superiority of the Optuna-optimized Extra trees in capturing complex reporting dynamics.

Importantly, the role of blockholder ownership remains economically meaningful but varies across institutional contexts as shown in

Table 10. Blockholder Contribution to Model Performance.

Country	R2 With	R2 Without	ΔR2	DM Stat	p-Value
Egypt	0.4787	0.4223	+0.0563	−3.0855	0.0020
Saudi	0.4412	0.4412	0	-	-

. In Egypt, blockholder ownership is consistently ranked among the most important predictors in the earnings quality model and significantly improves predictive accuracy (ΔR² = +0.056, DM p < 0.01). In contrast, its contribution in Saudi Arabia is weaker and not consistently selected among the top predictors.

1.

Feature Importance Analysis:

Feature importance analysis (Figure 15 and Figure 16) reveals consistent patterns across countries. In both Egypt and Saudi Arabia, firm size, Age, leverage, and profitability dominate predictive performance. However, blockholder ownership ranks among the top five predictors in Egypt (≈11.5%), whereas it does not appear among the most influential variables in Saudi Arabia. This divergence suggests that ownership concentration plays a more prominent role in shaping reporting outcomes in environments with weaker governance structures.

2.

Partial dependence analysis:

Partial dependence analysis (Figure 17) provides further insight into the nature of the ownership effect. In Egypt, the relationship between blockholder ownership and earnings quality is distinctly nonlinear, following an inverted U-shaped pattern. Earnings quality initially improves as ownership increases, consistent with enhanced monitoring incentives, but declines beyond higher ownership thresholds, suggesting the emergence of entrenchment effects. This pattern aligns with the monitoring–entrenchment framework discussed in the literature. In contrast, the corresponding plot for Saudi Arabia is effectively flat, indicating that blockholder ownership does not exert a systematic marginal effect on earnings quality. This suggests that ownership concentration is less informative for predicting reporting outcomes in the Saudi context.

Overall, the results across accounting-based and market-based measures reveal a nuanced and context-dependent pattern rather than uniform consistency. In Egypt, blockholder ownership exhibits a significant and nonlinear relationship with both market-based valuation and accounting-based earnings quality, indicating that ownership concentration affects both underlying reporting behavior and investor perception. This pattern is consistent with a monitoring–entrenchment trade-off, where the effects of ownership vary across different concentration levels. In contrast, in Saudi Arabia, the influence of blockholder ownership is primarily reflected in market-based measures, while its impact on accounting-based earnings quality is limited. This divergence suggests that the market-to-book results in Saudi Arabia may partly capture valuation dynamics, such as investor expectations or signaling effects, rather than underlying reporting integrity.

Collectively, these findings indicate that ownership concentration operates through distinct channels across institutional environments: in weaker governance settings such as Egypt, it shapes both reporting quality and valuation, whereas in more regulated environments such as Saudi Arabia, its role is more closely related to market perception than to actual reporting outcomes. This distinction underscores the importance of jointly considering valuation-based and accounting-based measures when assessing financial reporting integrity.

5.2. Panel Econometric Benchmark

To address concerns regarding comparability with conventional econometric approaches, we estimate panel fixed effects models including firm and year effects. These models capture within-firm variation over time and are estimated with clustered standard errors.

Table 11. Panel Fixed Effects Results.

Variables	Egypt (EQ)	Saudi (EQ)	Egypt (MTB)	Saudi (MTB)
Blockholder	0.103	—	0.0001	0.0021
	(0.088)		(0.0044)	(0.0036)
SIZE	0.266	0.454	0.469	−1.029 ***
	(0.448)	(0.394)	(0.323)	(0.383)
LEVER	−0.083 ***	0.250 *	−0.236	0.749 **
	(0.020)	(0.150)	(0.421)	(0.345)
MSHARE	−0.013	0.001	2.467	5.016 ***
	(0.017)	(0.068)	(3.675)	(1.613)
AGE	0.522	1.328	−0.069 **	0.023
	(1.251)	(0.936)	(0.034)	(0.020)
Profit	−0.007	0.031	0.200	2.510 ***
	(0.056)	(0.041)	(0.696)	(0.457)
FOWN	−0.000	−0.011 **	−0.008	−0.012
	(0.002)	(0.005)	(0.006)	(0.016)
GROWTH	—	—	0.001	—
			(0.067)
Observations	599	375	1071	675
R2 (Within)	0.004	−0.006	0.068	0.196
Firm FE	Yes	Yes	Yes	Yes
Year FE	Yes	Yes	Yes	Yes

Notes: Standard errors in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.10. All models include firm and year fixed effects with clustered standard errors.

reports firm and year fixed-effects panel regressions for Egypt and Saudi Arabia using earnings quality (EQ) and the market-to-book ratio (MTB) as dependent variables. The results indicate relatively low within-firm R² values, particularly for earnings quality, suggesting limited explanatory power from within-firm variation. For the market-to-book ratio (MTB), the within-firm R² is higher, especially in the Saudi sample, indicating that valuation is more responsive to time-varying firm characteristics. Across all specifications, blockholder ownership is not statistically significant. In contrast, variables such as market share, profitability, and leverage exhibit more consistent associations with MTB. These findings differ from the machine learning results, where blockholder ownership contributes to predictive performance. This difference reflects the distinct nature of the two approaches: fixed effects models rely on within-firm variation and impose linear functional forms, whereas machine learning models capture nonlinearities and cross-sectional variation. Accordingly, the two approaches should be viewed as complementary rather than competing.

5.3. Nonlinearity and Cross-Country Effects

To test the hypothesized nonlinear relationship (H1) and cross-country differences (H2), we estimate pooled panel models including quadratic terms for blockholder ownership and interaction terms with a country indicator. As shown in

Table 12. Pooled Fixed Effects with Nonlinear Interaction.

Variables	Market_to_Book	Earnings Quality
Blockholder	−0.0037	0.0515
	(0.0165)	(0.1071)
Blockholder2	0.0000	−0.0390
	(0.0001)	(0.0696)
Blockholder × Country	0.0124	0.2075
	(0.0193)	(0.3259)
Blockholder2 × Country	−0.0002	−0.1961
	(0.0002)	(0.2634)
SIZE	0.2496	0.4529
	(0.2909)	(0.3205)
MSHARE	4.2821 *	−0.0126
	(2.2820)	(0.0199)
LEVER	0.0008	−0.0613 **
	(0.2842)	(0.0252)
AGE	−0.0566 **	1.0885
	(0.0281)	(0.7570)
FOWN	−0.0079	−0.0010
	(0.0059)	(0.0021)
Profit	1.1129 **	−0.0067
	(0.5202)	(0.0498)
Observations	1746	974
Firm FE	Yes	Yes
Year FE	Yes	Yes
R2 (Within)	0.0112	−0.0222

Notes: Robust standard errors clustered at firm level in parentheses. * p < 0.10, ** p < 0.05.

, the results do not provide strong statistical evidence of nonlinear effects or cross-country differences. Neither the linear nor quadratic terms are statistically significant, and the interaction terms are also insignificant across both valuation and earnings quality specifications.

While the estimated coefficients for earnings quality are directionally consistent with an inverted U-shaped relationship, they are not precisely estimated. This suggests that low-order polynomial specifications may not adequately capture the complexity of the ownership–reporting relationship. These findings contrast with the explainable machine learning results, which reveal nonlinear patterns in the data. Accordingly, the results highlight the limitations of conventional panel models in detecting complex relationships, rather than providing definitive evidence against nonlinearity.

Taken together, the robustness analyses provide a more nuanced interpretation of the main findings. The machine learning results remain stable across alternative accounting-based measures of financial reporting integrity, particularly in Egypt, where a clear nonlinear (inverted U-shaped) relationship is observed. However, the absence of consistent effects in Saudi Arabia and the lack of statistical significance in fixed-effects models suggest that the ownership–reporting relationship is not uniform across contexts or methodologies. Instead, it appears to be driven by complex, cross-sectional, and potentially nonlinear patterns that are not well captured by traditional econometric specifications.

The divergence between the panel fixed effects results and the explainable machine learning findings reflects fundamental differences in methodological assumptions and the nature of the ownership–reporting relationship. Fixed effects models impose a linear functional form and rely primarily on within-firm variation over time, which may be limited in settings where ownership structures are relatively stable. More importantly, when the underlying relationship is nonlinear and non-monotonic—as predicted by agency theory—linear estimators tend to capture only an average effect, which may be statistically insignificant due to offsetting positive and negative marginal effects across different ownership levels. In contrast, machine learning models do not impose ex ante functional form restrictions and are better suited to capturing nonlinearities, interaction effects, and heterogeneous responses across the distribution of ownership concentration (Athey & Imbens, 2019).

The SHAP-based partial dependence analysis further reveals turning points and varying marginal effects that are consistent with an inverted U-shaped relationship, which conventional low-order polynomial specifications may fail to detect. This limitation of parametric models in identifying complex relationships is well documented in the literature (e.g., Varian, 2014). Accordingly, the contrasting results should be interpreted as complementary: while fixed effects models provide a conservative benchmark under restrictive assumptions, the explainable machine learning framework uncovers richer structural patterns that align more closely with the theoretical prediction of competing monitoring and entrenchment effects.

6. Conclusions

This study examines the relationship between controlling shareholders and financial reporting integrity using an explainable machine learning framework applied to firms in Egypt and Saudi Arabia. By employing an Optuna-optimized Extra Trees model and SHAP-based interpretability techniques, the study provides new insights into the nonlinear and context-dependent nature of ownership–reporting dynamics.

Overall, the findings provide conditional support for the proposed hypotheses, depending on the empirical approach and measurement of financial reporting integrity. Specifically, the machine learning results demonstrate that ownership concentration has a substantial but heterogeneous association with financial reporting integrity. In Egypt, the relationship is nonlinear and consistent with a monitoring–entrenchment trade-off, while in Saudi Arabia it is more stable and predominantly positive. However, these patterns are not replicated in the panel fixed-effects models, where ownership variables are not statistically significant. This suggests that the identified relationships are primarily cross-sectional and nonlinear in nature, rather than driven by within-firm dynamics over time. The robustness analysis using accounting-based earnings quality measures further refines these conclusions. While nonlinear effects persist in Egypt, they are weak or absent in Saudi Arabia, indicating that ownership concentration may influence both reporting behavior and market valuation in weaker governance environments, but plays a more limited role in shaping underlying reporting quality in stronger institutional settings.

The findings also highlight the dominant role of firm size and market share in explaining valuation, particularly in Saudi Arabia, where these factors account for a large proportion of predictive power. In Egypt, the determinants of financial reporting integrity are more diversified, reflecting greater structural complexity. The superior predictive performance of the Optuna-tuned Extra Trees model, confirmed through cross-validation and Diebold–Mariano tests, underscores the importance of capturing nonlinear relationships and interaction effects in financial data.

From a policy perspective, the results suggest that the effectiveness of ownership concentration as a governance mechanism depends critically on the institutional environment. In weaker governance settings such as Egypt, stronger regulatory enforcement and investor protection may be required to mitigate entrenchment risks. In more developed frameworks such as Saudi Arabia, ownership concentration appears to enhance monitoring and investor confidence, contributing positively to firm valuation. Methodologically, this study demonstrates the value of combining advanced machine learning techniques with explainability tools to bridge the gap between predictive accuracy and theoretical interpretation. By uncovering nonlinearities, threshold effects, and cross-country heterogeneity, the approach offers a more comprehensive understanding of corporate governance dynamics.

Despite its contributions, the study is subject to limitations. The analysis focuses on two emerging markets, which may limit generalizability. Future research could extend this framework to additional countries, incorporate alternative measures of financial reporting integrity, and explore interactions between ownership structure and other governance mechanisms using advanced machine learning models. Collectively, this study provides robust evidence on the complex role of controlling shareholders and highlights the potential of explainable machine learning to advance research in financial reporting and corporate governance.

Practical and Policy Implications

The study’s results have important implications for regulatory policy and corporate governance. These implications are derived from predictive and associational patterns identified using explainable machine learning techniques. First, the findings indicate that ownership concentration exhibits different associations across ownership levels. Moderate blockholder ownership is associated with higher firm valuation and improved financial reporting outcomes, consistent with monitoring incentives. However, at higher ownership levels, the association weakens or becomes negative—particularly in weaker institutional environments—consistent with potential entrenchment effects. These patterns should be interpreted as associational evidence reflecting both market-based valuation and accounting-based reporting quality, rather than direct causal effects.

From a managerial perspective, the results suggest that ownership concentration is associated with both potential benefits and risks. While moderate ownership levels are linked to more favorable reporting and valuation outcomes, higher concentration may coincide with patterns consistent with entrenchment. Accordingly, firms with highly concentrated ownership structures may benefit from complementary governance mechanisms, such as stronger board independence, audit oversight, and enhanced disclosure practices, to mitigate potential agency concerns.

The findings also suggest that a “one-size-fits-all” approach to ownership regulation may be ineffective. Instead, governance frameworks should account for institutional context. In environments with relatively weaker enforcement mechanisms—such as those characterized by evolving governance systems—the results indicate more pronounced nonlinear and potentially adverse associations at higher ownership levels. In such contexts, policies aimed at strengthening disclosure requirements, minority shareholder protection, and monitoring of related-party transactions may help mitigate these risks.

In contrast, in stronger regulatory environments, ownership concentration is more consistently associated with positive valuation and reporting outcomes, suggesting that monitoring incentives may be more effectively supported by external governance mechanisms. In these settings, policy efforts may be better directed toward enhancing transparency, market discipline, and enforcement, rather than imposing strict ownership constraints.

Overall, the results highlight the importance of both ownership structure and institutional quality in shaping financial reporting outcomes. By combining market-based (valuation) and accounting-based (earnings quality) measures, the findings suggest that the role of ownership concentration extends beyond valuation effects to broader reporting-related dynamics. These insights support the development of more context-sensitive corporate governance frameworks that reflect the nonlinear and institutionally contingent nature of ownership effects.