Neuro-Symbolic Frameworks for Corporate Leverage and Debt Maturity: Evidence from Econometric and Machine Learning Models

Abstract

Forecasting corporate leverage adjustments remains challenging due to persistent financing behavior, firm heterogeneity, and changing macroeconomic conditions. This study investigates whether increasing model complexity improves the forecasting of corporate leverage adjustment by comparing dynamic econometric models, machine learning algorithms, and a neuro-symbolic artificial intelligence framework. The analysis is based on an unbalanced panel of 39,226 firm-year observations from 3001 publicly listed non-financial firms across 18 countries. The empirical analysis compares Fixed Effects and two-step Difference GMM estimators with regularized regression, gradient boosting, artificial neural networks, and a theory-guided neuro-symbolic framework that incorporates economically meaningful financial constraints through a resampling-based approximation of a differentiable rule-based penalty. Model performance is evaluated using out-of-sample forecasting accuracy measured by the Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), and the coefficient of determination (R2). The results indicate that corporate leverage exhibits substantial persistence, with estimated adjustment speeds of approximately 29–36% annually. Machine learning algorithms do not improve forecasting accuracy relative to benchmark dynamic econometric models when evaluated out of sample, while incorporating symbolic financial constraints provides only limited additional predictive benefits. These findings suggest that leverage persistence dominates model complexity and that parsimonious dynamic econometric models remain highly effective for forecasting corporate leverage adjustment. The study contributes to the growing literature on explainable artificial intelligence in corporate finance by providing a comprehensive comparison of dynamic econometric, machine learning, and neuro-symbolic approaches within a unified forecasting framework for emerging economies in the MENA region.