A Multi-Digit Benford's Law Approach for Detecting Income Smoothing Sub-Variables: An Advanced Quantitative Analysis of Saudi Listed Companies

Abstract

This study develops and empirically validates a comprehensive multi-digit Benford's Law framework for detecting income smoothing sub-variables among companies listed on the Saudi Stock Exchange (Tadawul). Using a sample of 2,580 firm-year observations from 172 companies (2015-2024), the study employs Smart PLS-SEM to analyze relationships between Benford's Law deviations (MAD₁, MAD₂, MAD₃, MAD₄) and five income smoothing dimensions. The findings reveal hierarchical detection capability where MAD₁ exhibits strongest overall detection power (β = 0.456, p < 0.001) for traditional smoothing methods, while MAD₃ and MAD₄ prove essential for detecting sophisticated timing manipulations (β = 0.412, p < 0.001). The model demonstrates substantial explanatory power (R² = 0.512-0.634) and superior predictive performance compared to traditional methods (45-65% improvement in accuracy). The research provides practical tools for the Capital Market Authority (CMA), auditors, and investors to enhance financial reporting quality assessment in Saudi Arabia.