Non-Linearity in Corporate Finance Studies: Bank Size Matters When It Comes to Leverage Components

Abstract

We propose a regression-based procedure to account for non-linearity, while maintaining robustness to multicollinearity and endogeneity. To illustrate our method, we focus on capital structure, a fundamental topic in corporate finance, and examine excess, non-deposit and short-term components of leverage. We model those leverage measures as functions of competition, diversification, and liquidity, interacting with bank size. Our analysis begins with fully specified second-order models for each determinant in combination with bank size, revealing significant non-linear effects. To address potential multicollinearity among second-order terms, we apply lasso regression for variable selection and initial coefficient estimation. We then augment the selected models with bank and time fixed effects to control for unobserved heterogeneity and address endogeneity concerns. Our findings indicate that linear specifications often misattribute significance to less relevant variables by failing to account for underlying non-linearities and interactions. This omission leads to biased estimates and distorted interpretations. Our approach provides a practical and reliable method for obtaining unbiased and interpretable estimates in the presence of complex variable relationships.